Answer:
d
Step-by-step explanation:
what is x= 0.393 as a fraction
Answer:
393/1000
Step-by-step explanation:
Answer:
Step-by-step explanation:
393/1000
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.
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) What fraction is equal to 50% of 1/3
b) What fraction is equal to 75% of 1/2
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 (✿◡‿◡)
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.'
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]
Can someone help me please! Look at the picture
Answer:
12
Step-by-step explanation:
please list
first 5 multiples of:
20
30
first correct answer is the brainliest
Answer:
Step-by-step explanation
First five multiples of 2030 are: 2, 5, 7, 10 an 14
20 times the sum of 4 and 2
Answer:
120
Step-by-step explanation:
add 4 and 2 then multipy by 2 and add a zero
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
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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Round 43.3333 to the nearest hundredth.
A) 43.3
B) 43.33
C) 43.34
D) 43.4
Answer: B
Step-by-step explanation:
Can't really explain it. A tenth is .1, a hundredth is .01
Please please help
Prove that the diagonals of a rectangle bisect each other.
The midpoints are the same point, so the diagonals _____
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*
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
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
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
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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Write the equation for the line graphed below.
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
Verify that the vector X is a solution of the given system. X' = 1 0 1 1 1 0 −2 0 −1 X; X = sin(t) − 1 2 sin(t) − 1 2 cos(t) −sin(t) + cos(t) For X = sin(t) − 1 2 sin(t) − 1 2 cos(t) −sin(t) + cos(t) , one has X' = 1 0 1 1 1 0 −2 0 −1 X = .
Answer:
The solution is shown in the picture attached
Step-by-step explanation:
To verify X as a solution to the system, substitute X into the system and check for equality. X is a vector and X' a matrix. Careful calculations with matrices and trigonometric identities are necessary for the verification.
Explanation:To verify that the vector X is indeed a solution to the given system, we can substitute X into the system and check if both sides are equal. If they are, then X is a solution to the system.
X in this case is a vector whose elements are trigonometric functions of time t. Likewise, X' represents a matrix multiplying the vector X. After applying the multiplication, we can compare the resulting vector with the original vector.
As this involves calculation with matrices and trigonometric identities, careful execution of these steps is necessary to ensure the accuracy of the result.
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Find the Lowest Common Multiple of 2, 3 and 7.
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
A newsletter publisher believes that above 78 % of their readers own a personal computer. Is there sufficient evidence at the 0.01 level to
substantiate the publisher's claim?
State the null and alternative hypotheses for the above scenario.
This problem involves conducting a hypothesis test, stating the null hypothesis as 78% or fewer readers own a personal computer, and the alternative hypothesis as more than 78% own one. A statistical test (like a z-test) is needed to compare the p-value to the 0.01 significance level. The publisher's claim is supported if the p-value is less than 0.01.
Explanation:In this context, we are conducting a hypothesis test to examine a newsletter publisher's claim about their audience's computer ownership. The null and alternative hypotheses would therefore be set up as follows:
Null Hypothesis (H0): p <= 0.78, meaning 78% or fewer readers own a personal computer.
Alternative Hypothesis (Ha): p > 0.78, meaning more than 78% of readers own a personal computer.
We can conduct a hypothesis test to prove or disprove this using statistical methods such as a z-test and by comparing the p-value to the significance level (0.01 in this case). If the p-value obtained from the test is less than 0.01, we can reject the null hypothesis providing sufficient evidence to support the publisher's claim. If not, we fail to reject the null hypothesis which means the evidence is insufficient.
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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].
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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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?
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
Subract 8 from the quotient of 15
Answer: These would be my two thoughts.
Step-by-step explanation:
ANSWER #1. 15-8= 7
ANSWER #2. 3-8= -5
Can someone help me please
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.
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
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.
Solve:
3(4 – 2x) = -x+1
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!
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
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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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.
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
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.
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.
Consider the function f(x) = 3x2 + 7x + 2.
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.
How do I find the area of a circle with the circumference of 18.84 units
A circle with radius r has a circumference of 2πr.
2πr = 18.84 ==> r = 18.84/(2π) ≈ 2.998 units
The same circle has area πr ² sq. units. So the area is
π (2.998)² ≈ 28.246 sq. units
To find the area of a circle with a given circumference, divide the circumference by 2π to find the radius. Then, plug the radius into the formula A = πr^2 to calculate the area.
Explanation:To find the area of a circle when given the circumference, you can use the formula A = πr^2.
First, determine the radius of the circle by dividing the circumference by 2π.
In this case, the circumference is 18.84, so the radius would be 18.84 / (2π) = 3.0.
Then, plug the radius into the formula A = πr^2 to find the area:
A = π(3.0)^2 = 9.0π = 28.27 (rounded to two decimal places)
Therefore, the area of the circle with a circumference of 18.84 units is approximately 28.27 square units.
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
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.
Learn more about inverse proportionality here:https://brainly.com/question/14437120
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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
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.
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
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.