Answers
Answer:
–11 and 2
Step-by-step explanation:
observe
x² + 9x – 22 = 0
(x + 11)(x – 2) = 0
x = –11 or x = 2
Related Questions
Write the equation of the graph obtained when the graph of y -
is compressed vertically by a factor of 0.25, translated 4 units
right, and then translated 3 units up.
Answers
Answer: y = 0.25*f(x - A) + 3
Step-by-step explanation:
Initially we have the graph of y = f(x)
If we do a vertical compression, this means that we multiply the function by the scale factor, in this case the scale factor is 0.25
So now our graph is y = 0.25*f(x)
A translation to the right by A units means that now we valuate the function in x - A, in this case A = 4, so our graph now is:
y = 0.25*f(x - 4)
A vertical translation means that we add a constant to the function, if the constant is positive the tranlsation is upwards, if the constant is negative the translation is downwards.
Here the translation is of 3 units upwards, so our new graph is:
y = 0.25*f(x - A) + 3
please list
first 5 multiples of:
20
30
first correct answer is the brainliest
Answers
multiples of 30: 60,90,120,150,180
hope this helps!
Answer:
Step-by-step explanation
First five multiples of 2030 are: 2, 5, 7, 10 an 14
Find the Lowest Common Multiple of 2, 3 and 7.
Answers
Answer:
42Step-by-step explanation:
2: 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42
3: 3 6 9 12 15 18 21 24 27 30 33 36 39 42
7: 7 14 21 28 35 42
Write the terms a 1a1, a 2a2, a 3a3, and a 4a4 of the following sequence. If the sequence appears to converge, make a conjecture about its limit. If the sequence diverges, explain why. a Subscript n Baseline equals StartFraction (negative 1 )Superscript n plus 1 Over 5 n minus 4 EndFractionan= (−1)n+1 5n−4 What are the first four terms of the sequence? a 1a1equals= nothing a 2a2equals= nothing a 3a3equals= nothing a 4a4equals= nothing (Type integers or simplifed fractions.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answers
Answer:
Step-by-step explanation:
WE are given that [tex]a_n = \frac{(-1)^{n+1}}{5n-4}[/tex]. Then, to now the first for terms, we must replace n by 1,2,3,4 respectively. Then
[tex]a_1 = \frac{(-1)^2}{5(1)-4} = \frac{1}{1}= 1 [/tex]
[tex]a_2 = \frac{(-1)^3}{5(2)-4} = \frac{-1}{6} [/tex]
[tex]a_3 = \frac{(-1)^4}{5(3)-4} = \frac{1}{11}= 1 [/tex]
[tex]a_4 = \frac{(-1)^5}{5(4)-4} = \frac{-1}{16}= 1 [/tex]
Note that as n increase, [tex]a_n[/tex] gets closer to 0. So, the limit of this sequence is 0.
A family of recurrences has the following form for constants a and c: T(1) = a T(n) = T(n-1) + c for n > 1 Solve this recurrence for T(n) in terms of a and c. Then demonstrate that you have the solution by identifying, from the list below, the correct formula for T(n) in terms of specific values of a and c. a) If a=1 and c=3, then T(n) is 3n - 2. b) If a=1 and c=3, then T(n) is n + 2. c) If a=3 and c=5, then T(n) is 3n + 2. d) If a=3 and c=5, then T(n) is 5n + 3.'
Answers
Answer:
T(n) = cn +(a-c)
Step-by-step explanation:
Note that T(1) = a, then T(2) = a+c, T(3) = (a+c)+c = a+2c, T(4) = (a+2c)+c = a+3c. Thus, our hypotheis is that T(n) = a+(n-1)c. We will prove this by strong induction.
Note that T(1) = a = a+(1-1)c. So the base case is proved. Assume that the result is true for all k<n. Then
T(n) = T(n-1)+c = (a+(n-2)c)+c = a+(n-1)c= cn+ (a-c).
So, by induction, the result holds.
Note that if a=1 and c = 3 then T(n) = 1+(n-1)3 = 3n-3+1 = 3n-2, which invalidates option b)
If a=3 and c=5 then we have that T(n) = 5n+(3-5) = 5n-2, which invalidates c) and d).
Then the formula is correct.
Answer:
(a) is correct
[tex]T(n) = a+(n-1)c[/tex]
Step-by-step explanation:
Notice that according to the information that you are given
[tex]T(1)=a \\T(2)=T(1)+c = a+c\\T(3)=T(2)+c = a+c+c = a+2c[/tex]
If you think about it there is a clear pattern, it would be
[tex]T(n) = a+(n-1)c[/tex]
Now notice that (a) is correct if we set a=1 and c=3 we get
[tex]T(n) = 1+3(n-1) = 3n-2[/tex]
20 times the sum of 4 and 2
Answers
Answer:
120
Step-by-step explanation:
add 4 and 2 then multipy by 2 and add a zero
Round 43.3333 to the nearest hundredth.
A) 43.3
B) 43.33
C) 43.34
D) 43.4
Answers
Answer: B
Step-by-step explanation:
Can't really explain it. A tenth is .1, a hundredth is .01
A __________ determines how far a particular value is from the mean relative to the data set's standard deviation. a. percentile b. coefficient of variation c. z-score d. variance
Answers
Answer:
z-score
Step-by-step explanation:
Z-score gives the relative value of any data population in relation to its mean. It depicts at what distance any data is from the mean. In technical terms it can be termed as the number of times a data is data away from the mean. Positive value of z score means value is more than mean while a negative value signifies data is less than that of mean.
Z – score is primarily used in qualitative analysis of numerical data by the statistician after data is arranged in normal distribution form. Z score of 0 means the value is same as mean while z-score of value 1 means data is one standard deviation away from the mean.
The z-score is the measure that determines the distance of a value from the mean in terms of standard deviations which is option c.
A z-score determines how far a particular value is from the mean relative to the data set's standard deviation. Given an experimental value, X, the mean, μ (mu), and the standard deviation, σ (sigma), the z-score is calculated using the formula Z = (X - μ) / σ. A z-score represents the number of standard deviations an experimental value is above or below the mean. For example, if a data value has a z-score of 2, it is two standard deviations above the mean. Contrarily, a z-score of -1.5 indicates that the value is one and a half standard deviations below the mean. Z-scores are used across various fields to compare different values within a data set or among different data sets with different means and standard deviations.
What is the arc length of a circle that has an 8-inch radius and a
central angle that is 95 degrees? Use 3.14 for I and round your
answer to the nearest hundredth. (5 points)
760.01 inches
95.08 inches
0.53 inches
13.26 inches
Answers
Answer:
The answer is d (13.26)
Step-by-step explanation:
set it up like this: (95/360) times (2 times pi times 8)
after plugging this equation into a calculator you get 13.26450232 and round to 13.26
Final answer:
The arc length of a circle with an 8-inch radius and a central angle of 95 degrees is 13.26 inches when we use 3.14 for π and round to the nearest hundredth.
Explanation:
To find the arc length of a circle, we use the formula arc length (Δs) = rΘ, where 'r' is the radius and Θ is the central angle in radians. Since there are 2π radians in a full 360-degree rotation, we can find the radian measure of 95 degrees by using the conversion ratio π radians/180 degrees. The radian measure is (95/180)π.
Using 3.14 for π and the given radius of 8 inches, the calculation becomes: Δs = 8 * (95/180) * 3.14. Simplifying this equation gives the arc length as 13.26 inches when rounded to the nearest hundredth
The length of the base of an isosceles triangle is x. The length of a leg is 3x-6. The perimeter of the triangle is 51. Find x
Answers
Answer:
x = 9
Step-by-step explanation:
The perimeter is the sum of the lengths of the base and the two equal legs:
51 = x + 2(3x -6)
51 = 7x -12 . . . . . eliminate parentheses
63 = 7x . . . . . . . . add 12
9 = x . . . . . . . . . . divide by 7
HELP ASAP PLEASE!!!
Which of the following lines are parallel?
a. line c and line d
b. line b and line c
c. line a and line b
d. line d and line e
You may pick more than one.
Answers
Answer:
The answer is d: LINE D AND LINE E
The other answer is c LINE A AND LINE B
Step-by-step explanation:
Please please help
Prove that the diagonals of a rectangle bisect each other.
The midpoints are the same point, so the diagonals _____
Answers
Answer: A. have the same slope
Step-by-step explanation:
b. bisect means right in half but not fully intersecting kinda looks like this _l_ *oh and it asked you to prove that they bisect so clicking on it don't really make sense*
c. perpendicular means there is four equal angels and that is 90 degree angels
d. parallel... well it's obviously not parallel because parallel are two lines that are exactly the same but never intersect
*intersect means touch*
Write the equation for the line graphed below.
Answers
Answer:
y = 1/2x -1
Step-by-step explanation:
to find the y-intercept you find where the line crosses the y axis
for the slope you need to use the equation
change of y2 - change of y1
change of x2 - change of x1
y=ax+b
(-2; -2); (0;-1); (2; 0)
-1=a*0+b => b=-1
0=a*2+b
0=a*2-1
a*2=1 => a=1/2
y=x/2 -1
There are four steps in solving one's personal financial challenges:
1. considering opportunity costs
2. assessing risks and returns
3. setting short- and long-term goals
4. assessing needs and wants
Which of these is the correct order of these steps?
O 2,3,1,4
O 1,2,3,4
O4, 1,2,3
3,1.4.2
Answers
Answer:
a
Step-by-step explanation:
The order of four steps are Assessing needs and wants, Considering opportunity costs, Assessing risks and returns and Setting short- and long-term goals, Option C is correct.
What is Finance?Finance is the study and discipline of money, currency and capital assets.
The correct order of the four steps in solving one's personal financial challenges is indeed:
Assessing needs and wants
Considering opportunity costs
Assessing risks and returns
Setting short- and long-term goals
Hence, the order of four steps are Assessing needs and wants, Considering opportunity costs, Assessing risks and returns and Setting short- and long-term goals, Option C is correct.
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You come up with what you think is a great idea for a new advertising campaign for your company. Your boss is worried that the ads will cost a lot of money and she wants to be 99% confident that the ads increase sales before rolling the new ads out nationwide. You run the ads in a typical city and take a random sample to see if people who saw the ad are more likely to buy the product. When you reported the results to your boss, you made a Type II error. 18. Explain in words the statistical meaning of this type of error.
Answers
Answer:
Type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.
Step-by-step explanation:
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.
β = Probability of accepting H₀ when H₀ is false.
In this case we need to test the hypothesis whether the new advertising campaign increases the sales or not.
The hypothesis can be defined as:
H₀: The new advertising campaign does not increases the sales.
Hₐ: The new advertising campaign increases the sales.
The confidence level wanted here is 99%.
The type II error will be made if we conclude that the new advertising campaign does not increases the sales when in fact the sales are increased after the advertising campaign.
The type II error could have been made because of the following reasons:
The sample size selected is too small. The smaller the sample size, greater is the probability of type II error. Significance level of the test must be small. If the significance level is small then the rejection regions decreases. Thus, reducing the chances of correctly rejecting the null hypothesis.Thus, the type II error might have been committed because of small sample size or small significance level.
If p is inversely proportional to the square of q, and p is 28 when q is 7, determine p when q is equal to 2
Answers
Answer: The answer is p = 343
Given that 'p' is inversely proportional to the square of 'q', we first found the constant of proportionality (k) by substituting the given 'p' and 'q' values. With 'k' known, we substituted the new value of 'q' to find the corresponding value of 'p', which turned out to be 343 when q=2.
Explanation:The given question describes an inverse proportionality. Specifically, it states that p is inversely proportional to the square of q. To express this mathematically, we write it as p = k/(q^2), where k is the constant of proportionality. For finding this constant, we use the given values of p and q, so 28 = k/(7^2), which means k = 28*49 = 1372.
Now, we substitute the value of k and the new value of q into the equation to find the corresponding value of p. Hence, when q = 2, p = 1372/(2^2) = 1372/4 = 343. Therefore, when q = 2, p equals 343.
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The coach of an age group swim team needs to assign swimmers to a 200-yard medley relay team to send to the Junior Olympics. Since most of his best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the best times (in seconds) they have achieved in each of the strokes (for 50 yards) are
Answers
Answer:
a) add a dummy stroke to make the problem as an assignment problem of adding 5 strokes to 5 swimmers. see first attachment.
b) applying the Hungarian method.
4.8 0 0.9 4.1 2.5
10.3 0 9.1 1.6 8.7
4.8 0 10.4 1.9 5.1
2.8 0 3.2 2.1 4.7
0 0 0 0 0
Deduct the smallest element in each column from the other elements of the column.
2 0 0 2.5 0
7.5 0 8.2 0 6.2
2 0 9.5 0.3 2.6
0 0 2.3 0.5 2.2
0 0 0 0 0
Which implies:
2 8.2 2.5 6.2
7.5 9.5 0.3 2.6
2 2.3 0.5 2.2
33.8 + 34.7 + 28.5 + 29.2 = 126.2
David = Back Stroke
tony = Breast Stroke
Chris = Butterfly
Carl = Free Style
The question is about assigning swimmers in a team to different strokes to achieve the best total time. It's a combinatorial optimization problem which can be solved by considering all the permutations of swimmers' assignments to each stroke and selecting the one with least total time.
Explanation:The subject of this question is an optimization problem in Mathematics, specifically in the field of Combinatorics. Deciding the arrangement of swimmers to minimize the total time spent can be approached using techniques from this field. Unfortunately, the information provided does not give the exact times of the swimmers, so achieving a detailed solution isn't possible. However, the problem could hypothetically be solved by enumerating all possible assignments of swimmers to strokes and selecting the assignment that has the least total time.
This problem resonates with high school level math, where students begin to tackle optimization problems and permutations.
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Can someone help me please
Answers
Answer:
√37
Step-by-step explanation:
It is helpful to know the squares of small integers. Then you become aware of the approximate magnitudes of square roots.
Point C is between 6 and 7, so the value of C² will be between 6² = 36 and 7² = 49. Since C is closer to 6 than to 7, it represents the root of a number closer to 36 than to 49.
Only one answer choice is in this range: √37, Option 1.
Solve:
3(4 – 2x) = -x+1
Answers
Answer:
11/5 =x
Step-by-step explanation:
3(4 – 2x) = -x+1
Distribute
12 -6x = -x+1
Add 6x to each side
12 -6x+6x = 6x-x +1
12 = 5x +1
Subtract 1 from each side
12-1 = 5x+1-1
11= 5x
Divide each side by 5
11/5 =5x/5
11/5 =x
Steps to solve:
3(4 - 2x) = -x + 1
~Distribute
(3 * 4) + (3 * -2x) = -x + 1
~Simplify
12 - 6x = -x + 1
~Subtract 12 to both sides
12 - 12 - 6x = -x + 1 - 12
~Simplify
-6x = -x - 11
~Add x to both sides
-6x + x = -x + x - 11
~Simplify
-5x = -11
~Divide -5 to both sides
-5x/-5 = -11/-5
~Simplify
x = 11/5
Best of Luck!
If the height of the parallelogram shown is increased by 1 cm and the base is increased by 2 cm, what is the area of the new parallelogram?
28 cm2
39 cm2
55 cm2
60 cm2
Answers
Answer:
55 cm2
Step-by-step explanation:
The area of the new parallelogram is 55 sq.cm, the correct option is C.
What is a Parallelogram?A polygon with four sides such that the opposite sides are parallel and equal is called a Parallelogram.
The height of the parallelogram is 4 cm
The base of the parallelogram is 9cm
The height of the parallelogram is increased by 1 cm
New height = 5cm
The base of the parallelogram is increased by 2 cm
New base = 11 cm
Area of a parallelogram is = Base * Height
Area of parallelogram is = 5 * 11 = 55 sq.cm
Therefore, the area of the new parallelogram is 55 sq.cm.
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1.) The independent variable x is missing in the given differential equation. Proceed as in Example 2 and solve the equation by using the substitution u = y'.(y + 7)y'' = (y' )22.) The independent variable x is missing in the given differential equation. Proceed as in Example 2 and solve the equation by using the substitution u = y'.y'' + 6y(y')3 = 0
Answers
Answer:
The solution to the differential equation y'(y + 7)y'' = (y')²
y = Ae^(Kx) - 7
Step-by-step explanation:
Given the differential equation
y'(y + 7)y'' = (y')² ..................(1)
We want to solve using the substitution u = y'.
Let u = y'
The u' = y''
Using these, (1) becomes
u(y + 7)u' = u²
u' = u²/u(y + 7)
u' = u/(y + 7)
But u' = du/dy
So
du/dy = u/(y + 7)
Separating the variables, we have
du/u = dy/(y + 7)
Integrating both sides, we have
ln|u| = ln|y + 7| + ln|C|
u = e^(ln|y + 7| + ln|C|)
= K(y + 7)
But u = y' = dy/dx
dy/dx = K(y + 7)
Separating the variables, we have
dy/(y + 7) = Kdx
Integrating both sides
ln|y + 7| = Kx + C1
y + 7 = e^(Kx + C1) = Ae^(Kx)
y = Ae^(Kx) - 7
Final answer:
To solve the given differential equations by using the substitution u = y', substitute u for y' and find the values of u. Then, solve the resulting first order ordinary differential equation by separating variables and integrating to determine the solution.
Explanation:
To solve the given differential equations by using the substitution u = y', we need to substitute u for y' and find the values of u. Let's take the first equation as an example:
Start by substituting u for y' in the equation: (y + 7)y'' = (y')^2
Replace y' with u in the equation: (y + 7)u' = u^2
Then, we can solve this first order ordinary differential equation by separating variables and integrating:
Divide both sides by (y + 7): u' = (u^2) / (y + 7)
Separate the variables: (y + 7)dy = (u^2)du
Integrate both sides: (1/2)(y^2 + 14y) = (1/3)u^3 + C (where C is the constant of integration)
Solve for y by rearranging the equation: y^2 + 14y = (2/3)u^3 + 2C
This is the solution to the given differential equation.
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 31 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode? Select the [Alternative Hypothesis, Value of the Test Statistic].
Answers
Answer:
We conclude that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode.
Step-by-step explanation:
We are given that there are 31 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo.
After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.
Let [tex]p_1[/tex] = true percentage of those in the first group who suffer a second episode.
[tex]p_2[/tex] = true percentage of those in the second group who suffer a second episode.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1-p_2\leq[/tex] 0 or [tex]p_1\leq p_2[/tex] {means that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1-p_2[/tex] > 0 or [tex]p_1>p_2[/tex] {means that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode}
The test statistics that will be used here is Two-sample z proportion test statistics;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of people in the first group who suffer a second episode = 11%
[tex]\hat p_2[/tex] = sample proportion of people in the second group who suffer a second episode = 9%
[tex]n_1[/tex] = sample of people in first group = 31
[tex]n_2[/tex] = sample of people in second group = 45
So, the test statistics = [tex]\frac{(0.11-0.09)-(0)}{\sqrt{\frac{0.11(1-0.11)}{31}+ \frac{0.09(1-0.09)}{45}} }[/tex]
= 0.283
Now, at 0.1 significance level, the z table gives critical value of 1.2816 for right-tailed test. Since our test statistics is less than the critical value of z as 0.283 < 1.2816, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.
Therefore, we conclude that the true percentage of those in the first group who suffer a second episode is less than or equal to the true percentage of those in the second group who suffer a second episode.
A hypothesis test can determine whether there is enough evidence to support the claim that the new drug is effective in reducing second episodes of heartburn. It involves defining null and alternative hypotheses, calculating a test statistic, and comparing it to a critical value based on the set significance level.
Explanation:We start by defining our null and alternative hypotheses. In this case, we are testing against the claim that the true percentage of those in the first group who suffer a second episode is more than the true percentage of those in the second group who suffer a second episode.
So, our null hypothesis (H0) is: The percentage of heart attempts in group 1 is equal to or less than that of group 2.
And, our alternative hypothesis (Ha) is: The percentage of heart attempts in group 1 is greater than that of group 2.
We conduct the hypothesis test using a standard test of proportions. Calculating our test statistic can be done using the formula: Z = (p1 - p2)/sqrt(p(1 - p)[(1/n1) + (1/n2)])
Where, p1 and p2 are the proportions of the two groups, n1 and n2 are the sizes of the two groups, and p is the combined proportion.
Based on the information in the problem, the calculated test statistic value and the critical z-value for a one-tailed test at the significance level 0.1, we can make a decision to reject or fail to reject the null hypothesis. If the calculated absolute z-value is greater than the critical z-value, we reject the null hypothesis and conclude that there is enough evidence at the 0.1 level. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.
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what is x= 0.393 as a fraction
Answers
Answer:
393/1000
Step-by-step explanation:
Answer:
Step-by-step explanation:
393/1000
Subract 8 from the quotient of 15
Answers
Answer: These would be my two thoughts.
Step-by-step explanation:
ANSWER #1. 15-8= 7
ANSWER #2. 3-8= -5
Consider the function f(x) = 3x2 + 7x + 2.
Answers
Final answer:
The function in question, f(x) = 3x^2 + 7x + 2, is a quadratic function, and its properties such as graph shape, intercepts, and vertex can be studied. Additionally, the derivative of this function, obtained through power rule differentiation, is f'(x) = 6x + 7.
Explanation:
The question asks about the function f(x) = 3x2 + 7x + 2. This appears to be a quadratic function, which is a fundamental concept in algebra and pre-calculus. Detailing the characteristics of a quadratic function involves finding its graph, which is a parabola, its vertex, axis of symmetry, intercepts, and possibly its extrema (maximum or minimum values).
In mathematics, finding the derivative of a function is a common operation in calculus. Given the information on different functions and their derivatives from the provided reference text, we can deduce that the derivative of f(x) would be found through power rule differentiation: for f(x) = axn, the derivative f'(x) = naxn-1. Applying this to the given function, we find the derivative f'(x) = 6x + 7.
a) What fraction is equal to 50% of 1/3
b) What fraction is equal to 75% of 1/2
Answers
b) 3/8
hope this helps!
Answer:
a) 1/6
b) 3/8
Step-by-step explanation:
Even i struggle with fractions but im sure you will get it one day (✿◡‿◡)
The solid S has a base region B defined by the curves y = 5x − x 2 and y = x. (A) Find the volume of S if the cross-sections through S perpendicular to the x-axis are squares with an edge along the base. (B) Find the volume of S if the cross-sections through S perpendicular to the x-axis are equilateral triangles with an edge along the base. 3 (C) Find the volume of S if the cross-sections through S parallel to the x-axis are semicircles with their diameter along the base. (D) Find the volume of S if the cross-sections through S parallel to the x-axis are isosceles right triangles with a leg along the base.
Answers
Answer:
a) The volume of S is 34.13
b) The volume of S is 14.8
c) The volume of S is 5.17
d) The volume of S is 11.33
Step-by-step explanation:
a) The cross section area is equal to:
[tex]A=a^{2} =((5x-x^{2})-x)^{2} =(4x-x^{2} )^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^4_0 {A(x)} \, dx =\int\limits^4_0 {(4x-x^{2})^{2} } \, dx =34.13[/tex]
b) The cross section area is equal to:
[tex]A=\frac{a^{2}\sqrt{3} }{4} =\frac{\sqrt{3} }{4} ((5x-x^{2} )-x)^{2} =\frac{\sqrt{3} }{4} (4x-x^{2} )^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^4_0 {A(x)} \, dx =\frac{\sqrt{3} }{4} \int\limits^4_0 {(4x-x^{2})^{2} } \, dx =14.8[/tex]
c)
[tex]y=5x-x^{2} \\\frac{dy}{dx} =0\\5x-x^{2} =0\\x=5/2\\y(5/2)=25/4\\y=5x-x^{2} \\x^{2} -5x+y=0\\x=\frac{5+-\sqrt{25-4y} }{2}[/tex]
The cross section area is equal to:
[tex]A_{1} =\frac{1}{2} \pi r_{1}^{2} =\frac{1}{2} \pi (\frac{1}{2} (\frac{5+\sqrt{25-4y} }{2} -\frac{5-\sqrt{25-4y} }{2} ))^{2} =\frac{1}{8} \pi (25-4y)\\A_{2} =\frac{1}{2} \pi r_{2}^{2}=\frac{1}{2}\pi (\frac{1}{2} (y-\frac{5-\sqrt{25-4y} }{2} ))^{2} =\frac{1}{32} \pi (2y-5+\sqrt{25-4y} )^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^a_b {A_{1}(y) } \, dy+\int\limits^4_0 {A_{2}(y) } \, dy ,where-a=25/4,b=4\\Vol_{S} =\int\limits^a_b {\frac{1}{8}\pi (25-4y)} \, dy +\int\limits^a_b {\frac{1}{32}\pi (2y-5+\sqrt{25-4y} )^{2} } \, dy =5.17[/tex]
d) The cross section area is:
[tex]A_{1} =\frac{1}{2}ab=\frac{1}{2} a^{2} =\frac{1}{2} (\frac{5+\sqrt{25-4y} }{2}-\frac{5-\sqrt{25-4y}}{2} )^{2} =\frac{1}{2} (25-4y)\\A_{1}=\frac{1}{2}ab=\frac{1}{2} a^{2} =\frac{1}{2}(y-\frac{5-\sqrt{25-4y}}{2}} )^{2} =\frac{1}{8} (2y-5+\sqrt{25-4y}})^{2}[/tex]
The volume of S is equal to:
[tex]Vol_{S} =\int\limits^a_b {A_{1}(y) } \, dy +\int\limits^4_0 {A_{2}(y) } \, dy ,where-a=25/4,b=4\\Vol_{S}=\int\limits^a_b {\frac{1}{2}(25-4y) } \, dy +\int\limits^4_0 {\frac{1}{8}(2y-5+\sqrt{25-4y})^{2} } \, dy =11.33[/tex]
A limited edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20. 70. Which equation can be used to find the y value after x years
Answers
Answer: The answer is y = 18(1.15)^x
Step-by-step explanation:
Answer:
y = (18) * (1.15)^x
Step-by-step explanation:
A limited edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20. 70. Which equation can be used to find the y value after x years.
To find this equation, this is an exponential equation, meaning that the number increases at a rapid rate. In this case the post increases each year by 15% and started at $18. The equation you would use to find this is: y = a * b^x. We can fill in the a and b values based off the given information. Since the value is increasing by 15% we will add 1 to 15% to get 1.15. This will be the b value. The a value is our initial value which in this case is $18. Now we can plug everything in to get: y = (18) * (1.15)^x.
A can of tomato soup is 4 1/4 inches tall and has a diameter of 3 inches. The company that makes the cans uses sheets of metal that are 1000in^2.
1.How many whole cans can the company make out of each sheet of metal?
2. Will there be any metal left over? If so how much?
Answers
Answer: a) 21 cans
b) 10.83 square inches.
Step-by-step explanation:
The cans are cylinders of 4 and 1/4 inches tall (or 4.25 in)
and the diameter is 3 inches.
The surface of a cylinder is equal to:
S = pi*r^2 + h*2*pi*r
where r is the radius, half of the diameter, so we have that r = 3in/2 = 1.5 in.
h is the height, h = 4.25 in
pi = 3.14
Then the surface needed for a can is:
S = 3.14*1.5^2 + 4.25*2*3.14*1.5 = 47.1 square inches.
if the sheet is 1000 in^2, we can make an amount of:
N = 1000/47.1 = 21.23
but we can not do a 0.23 of a can, so we need to round down.
A) we can make 21 cans out of a sheet of metal.
B) the 0.23 of a can that we removed earlier is the amount of metal leftover. The total is 0.23*47.1 in^2 = 10.83 in^2
Answer:
Step-by-step explanation:
To determine the amount of metal needed to make each can, we would determine the total surface area of each can. Since the cans are cylindrical, the formula for determining the total surface area of a cylinder is used. It is expressed as
Total surface area = πr² + 2πr
r = radius of the can
h = height of the can
π = 3.14
From information given,
Diameter = 4.25 inches
Radius = diameter/2 = 4.25/2 = 2.125 inches
Total surface area = 3.14 × 2.125² + 2 × 3.14 × 2.125 = 27.5 in²
1) since 1000 in² sheet material is available, the number of cans that can be made is
1000/27.5240625 = 36 cans
2) The amount of metal sheet left is
1000 - (36 × 27.5) = 10 in²
The triangle shown below has an area of 121212 units^2
2
squared.
Find xxx.
Answers
Answer:
4
Step-by-step explanation:
Let's set up an equation using the formula for the area of a triangle.
Hint #22 / 3
\begin{aligned} \text{Area of a triangle} &= \dfrac12 \cdot \text{base} \cdot \text{height}\\\\ 12&= \dfrac12 \cdot 6 \cdot x \\\\ 12&= 3x \\\\ \dfrac{12}{\blueD{3}}&= \dfrac{3x}{\blueD{3}} ~~~~~~~\text{divide both sides by } {\blueD{ 3}}\\\\ \dfrac{12}{\blueD{3}}&= \dfrac{\cancel{3}x}{\blueD{\cancel{3}}}\\\\ x &=\dfrac{12}{\blueD{3}}\\\\ x &=4\end{aligned}
Area of a triangle
12
12
3
12
3
12
x
x
=
2
1
⋅base⋅height
=
2
1
⋅6⋅x
=3x
=
3
3x
divide both sides by 3
=
3
3
x
=
3
12
=4