Answers
A) State the chain rule for integration
Ans. The chain rule for integration is also known as " Integration by substitution "
Integration by substitution is taken in order to make integration solve easily in few steps.
For, [tex]I = \int\limits (x+2)^{2} \,dx[/tex]
Instead of expanding term [tex](x+2)^{2}[/tex]
With substitution of [tex]u = (x+2) [/tex] and [tex]du= 1 dx [/tex]
We simplified the integration as
[tex]I = \int\limits (u)^{2} \, du[/tex]
[tex]I = \frac{(u)^{3}}{3}+C[/tex]
By replacaing value of u=x+2
[tex]I = \frac{(x+2)^{3}}{3}+C[/tex]
B) State the rule of differentiation for the sine function.
Ans. We know that [tex]\frac{d}{dx}Sinx dx = Cosx [/tex]
C) Find the indefinite integral using substitution.
Ans.
Given, [tex]I = \int\limits {\frac{Cos14x}{Sin14x} } \, dx[/tex]
Take y = Sin14x
Differentiating both side
[tex]dy=14Cos14x dx [/tex]
[tex]\frac{dy}{14} = Cos14x\, dx[/tex]
Substituting values in integration,
[tex]I = \int\limits {\frac{Cos14x}{Sin14x} } \, dx[/tex]
[tex]I = \int\limits {\frac{1}{y} } \,\frac{dy}{14} [/tex]
[tex]I = \frac{1}{14}\int\limits {\frac{1}{y} } \,dy [/tex]
[tex]I = \frac{1}{14} lny + C [/tex]
Replacing values in the integration
[tex]I = \frac{1}{14} ln(14Sin14x) + C [/tex]
D)Check your work by taking a derivative of your answer from part C.
Ans.
Answer for Part C is [tex]I = \frac{1}{14} ln(14Sin14x) + C [/tex]
Differentiating the answer
we get,
[tex]=\frac{1}{14}\frac{d}{dx}[ ln(Sin14x) + C]\\=\frac{1}{14}\frac{1}{Sin14x} \frac{d}{dx}(Sin14x)+ \frac{d}{dx}C\\=\frac{1}{14}\frac{1}{Cos14x}(14Cos14x)\\=\frac{Cos14x}{Sin14x} \\ =I[/tex]
Related Questions
Franks electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used. Approximately how many kilowatt-hours of electricity did frank use in March?
Answers
Answer:
I got 469.8 kilowatt-hours. I got this by taking the total of Frank's bill, which was $85.78, and subtracting the flat monthly fee of $20.00. I did this because I need to find out the number of kilowatt-hours Frank used. Then, I divided $65.78 by $0.14 since that is the price per kilowatt-hour and got about 469.8 kilowatt-hours used by Frank.
The power utilised by frank in the month of march is 470 kilowatts - per hour.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Franks's electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used.
The equation will be written as,
B = 20 + 0.14K
85.78 = 20 + 0.14k
k = ( 80.78 - 20 ) / 0.14
K = 65.78 / 0.14
K = 470 Kilowatt-hour
Therefore, the power utilised by frank in the month of march is 470 kilowatts - per hour.
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The Quadratic Formula 7:Solving Quadratic Equations
laro
The Quadratic Formula
Text
Guided Practice
Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth.
8x2-3x - 7=0
A. 1.12, -0.74
B. 1.14,-0.77
C. -1.14,0.77
Answers
Answer:
B. 1.14, -0.77
Step-by-step explanation:
As you know the quadratic formula gives you the solution to
ax² + bx + c = 0
as ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, we have a=8, b=-3, c=-7, so the formula tells us the solution is ...
[tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(8)(-7)}}{2(8)}=\dfrac{3\pm\sqrt{233}}{16}\\\\x\approx \{-0.7665,1.1415\} \qquad\text{matches choice B}[/tex]
Answer:
1.14, –0.77
Step-by-step explanation:
I got it right in grandpoint.
You are given a choice of taking the simple interest on $10,000 invested for 2 years at a rate of 3% or the interest on $100,000 invested for 2 years at an interest rate of 3% compounded daily (use the Banker's rule ).
Which investment earns the greater amount of interest?
Give the difference between the amounts of interest earned by the two investments.
Answers
Answer:
Compount interest earns more. Difference between 2 interest is $92 445.39
Step-by-step explanation:
Simple Interest:
[tex]I = \frac{prt}{100} [/tex]
p = $10000
r = 3%
t = 2years
I = (10000×3×2)/100
= $600
Total amount = $10 600
Compound Interest:
[tex]A = p( {1 + \frac{r}{100}) }^{n} [/tex]
p = $100000
r = 3/730 (daily)
t = 730 (2yrs)
A = 100000[1+(3/73000)]^730
= $103 045.39 (2d.p)
Difference = $103045.39 -
$10600
= $92 445.39
(Correct me if i am wrong)
Please Help
What is the solution for x in the equation?
9 − 10x = 2x + 1 − 8x
Answers
Answer:
x=2
Step-by-step explanation:
9-10x=2x+1-8x
9-10x=1-6x
8=4x
x=2
Combine like terms in the equation 9 − 10x = 2x + 1 − 8x to simplify it to 9 − 10x = −6x + 1. Rearranging the equation to -4x = -8 and dividing by -4, we find that x = 2.
Explanation:The solution for x in the equation 9 − 10x = 2x + 1 − 8x can be found by first combining like terms on both sides of the equation.
On both the left and right side, the terms involving x are −10x and 2x − 8x respectively. After combining, the equation simplifies to 9 − 10x = −6x + 1.
Then, we can solve for x by shifting terms around. Getting all x-terms on one side and constant terms on the other side, we get -10x + 6x = 1 - 9. This simplifies to -4x = -8.
Finally, dividing the equation by -4 which is the coefficient of x, we obtain the solution x = 2.
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Tim is looking at two websites that allow customers to print their own designs on T-shirts. One website charges $24 per T-shirt plus $8 shipping. The other website uses the equation C = 22 n + 12 C=22n+12 to find the total cost, C C, of printing on T-shirts. What is the difference in the cost of each website if Tim orders 10 T-shirts?
Answers
Answer: The difference is $16
Step-by-step explanation:
n will equal the amount of t-shirts bought
Website 1's Costs: c = 24n + 8
Website 2's cost: c = 22n + 12
Then, we substitute 10 for n
c = 24(10) + 8
c = 240 + 8
c = 248
c = 22(10) + 12
c = 220 + 12
c = 232
248 - 232 = 16
The difference between the total cost of the first website and that of the second based on the given function will be $16.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given,
On the first website,
Cost to buy 10 T-shirts.
C = 24(10) + 8
C = 240 + 8
C = $248
The second website
The total cost to buy 10 T-shirts
C = 22(10) + 12
C= 220 + 12
C= $232
The differnce $248 - $232 = $16
Hence "The difference between the total cost of the first website and that of the second based on the given function will be $16".
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What property is shown in step 8?
Answers
D??
I think, because its in brackets, you multiply? not too sure though!
A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounce. They want to test whether the standard deviation has changed. What is the null hypothesis?
Answers
Answer:
Null Hypothesis: [tex]\sigma=0.2[/tex]
Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)
Step-by-step explanation:
s represent the sample standard deviation
[tex]\sigma[/tex] represent the population standard deviation (variable of interest)
[tex]\sigma_o =0.2[/tex] represent the value that we want to test
n represent the sample size
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Based on this the system of hypothesis should be:
Null Hypothesis: [tex]\sigma=0.2[/tex]
Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)
In order to test these system of hypothesis we need to select a significance level [tex]\alpha[/tex], then we need to calculate an statistic given by this formula.
[tex]\chi^2 =\frac{(n-1)s^2}{\sigma^2_o}[/tex]
Then we need to calculate the degrees of freedom for the statistic on this case
[tex]df=n-1[/tex]
And after this we need to calculate the pvalue based on the significance, the alternative hypothesis and the statistic calculated.
If the [tex]p_v <\alpha[/tex] we reject the null hypothesis
If the [tex]p_v >\alpha[/tex] we FAIL reject the null hypothesis
Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Write an equation relates the total amount of gasoline in the tank
Answers
Answer: y = x + 4
Step-by-step explanation:
Let "y" be the total number of gallons in the tank, and let "x" be the total number of unfilled gasoline.
Since we already have an initial "4 gallons" in the tank, the total capacity of the tank will be "x + 4".
Answer:
A y=4+x
Step-by-step explanation:
$12,400 is invested, part at 6% and the rest at 5%. If the interest earned from the amount invested at 6% exceeds the interest earned from the amount invested at 5% by $577.00, how much is invested at each rate? (Round to two decimal places if necessary.) Define variables x and y and set up a system of two linear equations that represents the information given in the problem.
Answers
Answer: $10881.81 is invested at 6% and $1518.18 is invested at 5%.
Step-by-step explanation:
Since we have given that
Amount invested = $12400
Rate of interest for first part = 6%
Rate of interest for second part = 5%
Let the amount invested for 6% be 'x'.
Let the amount invested for 5% be 'y'
According to question, we get that
[tex]0.06x-0.05y=577\\\\x+y=12400\\\\\implies x=12400-y[/tex]
So, it becomes,
[tex]0.06(12400-y)-0.05y=577\\\\744-0.06y-0.05y=577\\\\-0.11y=577-744\\\\-0.11y=-167\\\\y=\dfrac{167}{0.11}\\\\y=1518.18[/tex]
x=12400-y=12400-1518.18=$10881.81
Hence, $10881.81 is invested at 6% and $1518.18 is invested at 5%.
The monthly output P of a light bulb factory is given by the formula P = 450LK, where L is the amount invested in labor and K the amount invested in equipment (in thousands of dollars). If the company needs to produce 4,000 units per month, how should the investment be divided among labor and equipment to minimize the cost of production? The cost of production is L + K. (Round your answers to the nearest cent.)investment in labor _______ $investment in equipment ________$
Answers
Answer:
C(p) = 4,96 (in thousands of dollars)
l = 2980 $ invest in labor
k = 2980 $ invest in equipment
Step-by-step explanation:
Information we have:
Monthly output P = 450*l*k ⇒ k = P/450*l
But the production need to be 4000
Then k = 4000/450*l
Cost of production = l * k (in thousands of dollars)
C(l) = l + 4000/450*l
Taking derivatives (both members of the equation)
C´(l) = 1 - 400 /45*l² ⇒ C´(l) = 0 ⇒ 1 - 400/45l² = 0
45*l² - 400 = 0 ⇒ l² = 400/45
l = 2.98 (in thousands of dollars)
l = 2980 $ And
k = 400/45*l ⇒ k 400/45*2.98
k = 2.98 (in thousands of dollars)
C(p) = l + k
C(p) = 2980 + 2980
C(p) = 5960 $
Consider the following problem: A farmer with 850 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?
Answers
Answer:
18,062.5 square feet
Step-by-step explanation:
The largest area will be obtained when half the fence is used in each of the orthogonal directions. That is, the pen will have two parallel sides that total 425 feet, and 5 parallel sides and partitions that total 425 feet.
The long sides are 212.5 feet, and the short sides are 85 feet, so the overall area is ...
(212.5 ft)(85 ft) = 18,062.5 ft²
__
Working Out
Suppose the long side is length x. Then the lengths of the 2 ends and 3 dividers are ...
short side = (850 -2x)/5
Then the overall area is the product of long side and short side:
A = x(850 -2x)/5 = (2/5)(x)(425 -x)
This equation is that of a parabola that opens downward. Its vertex (maximum) is at the value of x halfway between the zeros of 0 and 425. That is, area is a maximum when x=212.5.
That maximum area is ...
A = (2/5)(212.5)(425 -212.5) = 18,062.5 . . . square feet
A hovercraft takes off from a platform. Its height (in meters), xxx seconds after takeoff, is modeled by h(x)=-(x-11)(x+3)h(x)=−(x−11)(x+3)h, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 11, right parenthesis, left parenthesis, x, plus, 3, right parenthesis How many seconds after takeoff will the hovercraft land on the ground?
Answers
Answer:
After 11 seconds the hovercraft will land on ground
Step-by-step explanation:
Given function that shows the height of a hovercraft,
[tex]h(x) = -(x-11)(x+3)[/tex]
Where,
x = number of second.
When the hovercraft land the ground,
[tex]h(x) = 0[/tex]
[tex]-(x-11)(x+3)=0[/tex]
[tex]\implies (x-11)(x+3)=0[/tex]
By zero product property,
x - 11 = 0 or x + 3 = 0
⇒ x = 11 or x = -3 ( not possible ),
Hence, after 11 seconds the hovercraft will land on ground.
at the time I am writing this the other answer only has a 3.2 rating, but I can vouch that the answer is still correct: 11 seconds !
Geoffrey has 30 problems to do for math homework he finished 60 percent of them before play practice how many problems did Geoffrey finish before play practice
Answers
Answer:
18 answers
Step-by-step explanation:
1) 30 of 60%
2)30*.6
3)18
check:
18/30=0.6
0.6=60%
Step-by-step explanation:
30=100%
? =60
=18 problems
A warehouse employs 21 workers on first shift, 15 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly two second shift workers and two third shift workers.
Answers
Answer: Our required probability is 0.11.
Step-by-step explanation:
Since we have given that
Number of workers in first shift = 21
Number of workers in second shift = 15
Number of workers in third shift = 13
We need to find the probability of choosing exactly two second shift workers and two third shift workers.
So, it becomes,
[tex]\dfrac{^{15}C_2\times ^{13}C_2\times ^{21}C_4}{^{49}C_8}\\\\=0.11[/tex]
Hence, our required probability is 0.11.
The probability question asks to determine the chance of choosing two second shift and two third shift workers from a warehouse workforce. Combinations are used to calculate the number of ways to select the workers, and the probability is found by dividing the desired combination by the total number of ways to choose eight workers.
Explanation:The question involves calculating the probability of choosing a specific combination of warehouse workers from different shifts for interviews. There are a total of 49 workers (21 first shift, 15 second shift, and 13 third shift). To find the probability of choosing exactly two second shift workers and two third shift workers, we need to consider the total number of ways to choose eight workers and the number of ways to choose two workers from each of the specified shifts.
The probability of selecting exactly two second shift workers is calculated as the combination of 2 from 15, and the probability of selecting exactly two third shift workers is the combination of 2 from 13. Since we're choosing 8 workers in total, we also have to choose the remaining 4 workers from the first shift, which can be done in combinations of 4 from 21. The probability is then calculated by dividing these combinations by the total number of ways 8 workers can be chosen from all 49 workers.
To calculate the combinations, we use the combination formula C(n, k) = n! / (k!(n-k)!). Then the overall probability is a fraction where the numerator is the product of the combinations for each selection and the denominator is the combination of 8 from 49.
A rectangular parking lot has a perimeter of 384 meters. The length of the parking lot is 36 meters less than the width. Find the length and the width.
Answers
Answer:
The length and width of the parking lot is 78 meters and 114 meters respectively.
Step-by-step explanation:
Given;
Perimeter of the parking lot = [tex]384\ m[/tex]
Solution,
Let the width of the parking lot be x.
Then, according to question length = (x-36).
The perimeter of a rectangle is sum of all the sides of rectangle. Which is given by an expression;
[tex]perimeter=2\times(length+width)[/tex]
Now substituting the values, we get;
[tex]384=2\times(x-36+x)\\\frac{384}{2}=(2x-36)\\192=2x-36\\192+36=2x\\2x=228\\x=\frac{228}{2}= 114[/tex]
Width = [tex]114\ m[/tex]
Length = [tex]x-36=114-36=78\ m[/tex]
Hence the length and width of the parking lot is 78 meters and 114 meters respectively.
The radius of a circle is increased from 8.008.00 to 8.038.03 m. Estimate the resulting change in area, and then express the estimate as a percentage of the circle's original area. The estimated change in area is nothing msquared2.
Answers
Answer:
Step-by-step explanation:
The area of a circle is expressed as
Area = πr^2
Where r = radius of the circle
π = constant = 3.14
The radius of a circle is increased from 8.00800 to 8.03803 m. This means that the original radius of the circle is 8.00800 and the new radius of the circle is 8.03803
Area of original circle =
3.14 × 8.00800^2 = 201.36212096
Area of new circle =
3.14 × 8.03803^2 = 202.87516852203
Increase in area = 202.87516852203 - 201.36212096
= 1.51304756203
Expressing the change as a percentage, it becomes
1.51304756203/201.36212096 ×100
Percentage change = 0.75 %
v11.1% complete This is a Single Choice Question; skip ahead to question content A B C D E Confirm The label on a ceiling lighting fixture warns you to use a lightbulb of 60 watts or less. The voltage to the lightbulb is 120 volts. An intern calculated how much amperage a bulb of the maximum allowed wattage will draw. You are checking her work, shown below. If there is an error, what is the first step that has an error, and why is it an error? Step 1 volts × amps = watts write down formula Step 2 120 × ? = 60 fill in what is known Step 3 It looks like 0.5 will work 120 × 0.5 = 60 check Step 4 amps = 0.5 Step 1, because the formula should be amps = watts ÷ volts. Step 2, because the question mark should be by itself on the right side of the equation. Step 3, because you can’t just guess at a solution. Step 4, because the answer in the previous step was 60. There is no error. Report Content Errors © 2019 by ACT, Inc. All rights reserved. Terms of UsePrivacy PolicyContact Support
Answers
Answer:
There is no error
Step-by-step explanation:
While it is not necessary to guess an answer, because the answer can be calculated using the properties of equality, guessing is a legitimate solution method actually taught in (some) schools these days.*
The equation is properly written, data properly filled in, and the solution properly verified. There is no error.
_____
* What doesn't seem to be taught in US schools are methods of refining an incorrect guess. These are actually well-developed, and are legitimate ways to get to a good answer.
Final answer:
The correct formula to find the current is I = P ÷ V, which gives 0.5 amps for a 60W lightbulb at 120V. The error in the calculation is in Step 1 where the formula was not rearranged to solve for current.
Explanation:
The calculation for determining the current drawn by a 60-watt (W) lightbulb with a voltage supply of 120 volts (V) requires use of the power formula, which relates power (P), voltage (V), and current (I): P = V × I, where P stands for power in watts, V for voltage in volts, and I for current in amperes (amps).
In this scenario, the correct step to find the amperage of the bulb would be to rearrange the power formula to solve for current (I): I = P ÷ V. By inserting the known values, we get I = 60 W ÷ 120 V, which simplifies to I = 0.5 amps.
The error in the intern's calculation is in Step 1, as the formula written should be amps = watts ÷ volts, not volts × amps = watts as it needs to be rearranged to solve for the unknown current.
If 40% of a number is 32, what is 25% of that number?
Answers
Answer:
I think that the answer is 24
Answer:
The number is 80. 25% of that number is = 20.
Step-by-step explanation:
4^1/2 equals 2. Why? Show steps and explain
Answers
raising some base to the power of 1/2 is the same as square root
Answer:
Step-by-step explanation:
4 to the first power is 4
then divide by 2
The bacterial strain Acinetobacter has been tested for its adhesion properties, which is believed to follow a normal distribution. A sample of five measurements gave readings of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm. Assume that the standard deviation is known to be 0.7 dyne-cm_2 and that the scientists are interested in high adhesion (at least 2.66 dyne-cm^2)(a) Should the alternative hypothesis be one-sided or two-sided? Write down the null and alternative hypotheses.(b) Based on your answer to part (a), test the hypothesis to see if the mean adhesion is at least 2.66 dyne-cm_2 (Use the p-value approach) What can be concluded?
Answers
Answer:
a) Alternative hypothesis should be one sided. Because Null and Alternative hypotheses are:
[tex]H_{0}[/tex]: μ=2.66 dyne-cm.
[tex]H_{a}[/tex]: μ<2.66 dyne-cm.
b) the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
Step-by-step explanation:
Let μ be the mean adhesion in dyne-cm.
a)
Null and alternative hypotheses are:
[tex]H_{0}[/tex]: μ=2.66 dyne-cm.
[tex]H_{a}[/tex]: μ<2.66 dyne-cm.
b)
First we need to calculate test statistic and then the p-value of it.
test statistic of sample mean can be calculated as follows:
t=[tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where
X is the sample mean M is the mean adhesion assumed under null hypothesis (2.66 dyne-cm) s is the standard deviation known (0.7 dyne-cm_2)N is the sample size(5)Sample mean is the average of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm, that is [tex]\frac{2.69+5.76+2.67+1.62+4.12}{5}[/tex] ≈ 3.37
using the numbers we get
t=[tex]\frac{3.37-2.66}{\frac{0.7}{\sqrt{5} } }[/tex] ≈ 2.27
The p-value is ≈ 0.043. Taking significance level as 0.05, we can conlude that sample proportion is significantly higher than 2.66 dyne-cm.
Thus, according to the sample the hypothesis that mean adhesion is at least 2.66 dyne-cm is true
Miguel took a taxi to the beach 23 miles from his hotel. After his day at the beach, he took a bus back for 11 miles. Then a friend pick him up and drove another 12 miles towards the hotel. How many more miles does Magill need to go until he is back at his hotel
Answers
Answer:
0 additional miles
Step-by-step explanation:
Miguel travelled from his hotel to the beach by taxi. Total distance travelled by Miguel during the journey is 23 miles.
During the return journey, he travelled by a bus for 11 miles to an intermediate location.
From this point his friend picked him up and drove him towards the hotel for 12 miles.
So the total distance travelled by Miguel during the return journey = 11 + 12 = 23 miles
But this is the same distance as the onward journey. So at the end, Miguel is back at the hotel and there are 0 additional miles that he needs to cover.
Answer: 0 miles
Step-by-step explanation:
Miguel took a taxi to the beach 23 miles from his hotel. After his day at the beach, he took a bus back for 11 miles. This means at this point, his distance from his hotel is 23 - 11 = 12 miles. Then a friend pick him up and drove another 12 miles towards the hotel. This means that they covered the remaining 12 miles from the hotel. Therefore
Miguel needs to go 12 - 12 = 0 miles until he is back at his hotel.
Write a quadratic function in vertex form whose graph has the vertex (-2,-4 ) and passes through the point (-1,-6)
Answers
Answer:
[tex]y = (-2)(x + 2)^2 - 4[/tex].
Step-by-step explanation:
The vertex form of a quadratic function is in the form
[tex]y = a (x - h)^2 + k[/tex],
where
[tex]a[/tex] is a coefficient that needs to be found, and [tex](h, k)[/tex] is the vertex of this function.In this question, the vertex of this quadratic function is at the point [tex](-2, -4)[/tex]. In other words, [tex]h = (-2)[/tex] and [tex]k = (-4)[/tex]. Substitute these value into the general equation:
[tex]y = a (x - (-2))^2 +(- 4)[/tex].
Simplify to obtain:
[tex]y = a (x + 2)^2 - 4[/tex].
The only missing piece here is the coefficient [tex]a[/tex]. That's likely why the problem gave [tex](-1, -6)[/tex], yet another point on this quadratic function. If this function indeed contains the point [tex](-1, -6)[/tex], [tex]y[/tex] should be equal to [tex](-6)[/tex] when [tex]x = (-1)[/tex]. That is:
[tex]-6 = a(-1 + 2)^2 -4[/tex].
Solve this equation for [tex]a[/tex]:
[tex]a = -6 - (-4) = -2[/tex].
Hence the equation of the quadratic function in its vertex form:
[tex]y = (-2)(x + 2)^2 - 4[/tex].
The quadratic function in vertex form that the student is looking for is f(x) = -2(x+2)² - 4. We obtained this by substituting the given vertex (-2, -4) and the point (-1, -6) into the general form of a vertex form quadratic function.
Explanation:The question is asking us to find the equation of a quadratic function, also known as a second-order polynomial, in vertex form. The vertex form of a quadratic function can be written as f(x) = a(x-h)² + k, where (h, k) is the vertex and 'a' is a non-zero number.
The vertex is given as (-2, -4). Therefore, h = -2 and k = -4. The equation becomes f(x) = a(x+2)² - 4. We also know that the graph passes through the point (-1, -6), which we can substitute into the equation to get: -6 = a(-1 + 2)² - 4. We solve this equation for 'a', and find that a = -2. Therefore, the quadratic function in vertex form is f(x) = -2(x+2)² - 4.
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Based on counting the number of galaxies in a small patch of the sky and multiplying by the number of such patches needed to cover the entire sky, the total number of galaxies in the observable universe is estimated to be approximately
A) 100 million.
B) 100 billion.
C) 1 billion.
D) 1 trillion.
E) 10 billion.
Answers
Answer:
100 billion
Step-by-step explanation:
Some astronauts reveals that there are 100 billion galaxies in the universe.
Serious answers only. Do not answer if you dont know please!How does the graph of the circle described by x^2 + (y-7)^2 = 49 change when its equation is changed to (x +5)^2 + (y-4)^2 =64. Select each correct answer. The circles radious increases, The circle moves up, The circle moves left, The circles radious decreases, The circle moves down, The circle movea right.
Answers
Answer:
The circles radious increases The circles moves left The circles moves downStep-by-step explanation:
The equation of a circle can be written as [tex](x-a)^2+(y-b)^2=r^2[/tex], where "r" is the radious, and (a,b) are the coordenates in the axis x and b respectively.Then, in the first circle the coordenates are (0,7), which means that the circle will be center there, and the radious is 7 ([tex]\sqrt{49}[/tex]).The second circle have different coordenates: (-5,4), which means that the circle has moved left (from 0 to -7 in the x axis) and down (from 7 to 4 in the y axis). Additionally, its radious has increased from 7 ([tex]\sqrt{49}[/tex], from 8 ([tex]\sqrt{64}[/tex]).See the attached figure please.Then, the correct answers are:The circles radious increases (from r=7 to r=8)The circles moves left (from x=0 to x=-5)The circles moves down (from y=7 to y=4)Trixie has 3/4 packages on marigold seeds he plants 1/6 of those seeds in this garden and divides the rest equally into 10 fraction packages of seed is planted in each flower pot
Answers
Answer:
[tex]\frac{7}{120}[/tex] of seed planted in each flower pot.
Step-by-step explanation:
Given:
Total number of marigold seeds packages Trixie have= ¾
Number of seeds Trixie planted in the garden= 1/6
Number of fraction into which Trixie dived the remaining seed =10
To Find:
Fraction of seed planted in each flower pot=?
Solution:
Seed left after planting 1/6 of seeds in the garden = [tex]\frac{3}{4}-\frac{1}{6}[/tex]
=>[tex]\frac{18-4}{24}[/tex]
=>[tex]\frac{14}{24}[/tex]
=>[tex]\frac{7}{12}[/tex]
Now Trixie divides these remaining seeds into 10 parts
=>[tex]\frac{\frac{7}{12} }{10}[/tex]
=>[tex]\frac{7}{12}\times\frac{1}{10}[/tex]
=>[tex]\frac{7}{120}[/tex]
24 Attitudes toward alcohol At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed.
Answers
Answer:
From the solution we come to know that every student in a party contain 10% chance of being chosen . And it is not SRS because student have been grouped into over 21 and under 21
Step-by-step explanation:
This question asks about sampling methods in statistics to determine attitudes toward alcohol at a party.
Explanation:This question is about sampling methods in statistics. The goal is to determine the attitudes toward alcohol of students at a party. To achieve this, the party attendees are divided into two groups: those over 21 and those under 21. Then, a random sample of 3 students over 21 and a random sample of 2 students under 21 are chosen to be interviewed. This method ensures that each student at the party has an equal chance of being interviewed and provides a representative sample of the party's attendees.
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Is it possible for two numbers to have a difference of 6
Answers
Answer:
yes
Step-by-step explanation:
For example, 8 and 2.
8 - 2 = 6.
6 is the difference
A high school drama club is selling tickets to their show. There is a maximum of 400 tickets. The tickets cost $10 (if bought before day of show) and $15 (if bought day of show). Let x represent the number of tickets sold before the day of the show and y represents the number of tickets sold the day of the show. To meet the expenses of the show, the club must sell at least $3500 worth of tickets. The club sells 300 tickets before the day of the show. Is it possible to sell enough additional tickets on the day of the show to meet the expenses of the show? Justify your answer.
Answers
Answer:
yes
Step-by-step explanation:
The club can sell 100 more tickets before they reach their maximum. If they sell those at the "day-of" price, they will have additional revenue of ...
100 × $15 = $1500
Then their total revenue would be ...
300 × $10 + $1500 = $4500 . . . . more than enough to meet expenses.
_____
To make up the additional $500 they need, the drama club only needs to sell ...
ceiling($500/$15) = 34 . . . tickets at the "day-of" price.
At a restaurant you order a lunch that costs $6.50 and a beverage that costs $1.50.You leave a 20% tip and the sales tax is 7%.What is the cost of the meal
Answers
Answer:8.45
Step-by-step explanation:
A stockbroker trades shares she does not own with an obligation of later repayment, and in the hope that the price of traded shares will fall. She then repays share debt with shares purchased at a lower price and pockets the spread between initial share price and repayment price. This attempt to profit from a falling stock price is known as ___________.
Answers
Answer:
short selling
Step-by-step explanation:
Short-selling is a process when a shareholder buys shares and sold them instantly and expecting that he or she will be able to have them at cheaper price later on .After then seller transfer them to lender from where he/she borrow the stock and after keep the difference as a income.
Short selling is a simple idea in which a shareholder borrow a stock, sells the stock to other person, then again buys that stock to give it back to a lender. Short sellers believe that the stock they have sell is going to fall in value