Consider the following. x = t2 − 2t, y = t5, 1 ≤ t ≤ 4 Set up an integral that represents the length of the curve. 4 1 dt Use your calculator to find the length correct to four decimal places.

Answers

Answer 1

Answer:

L ≈ 1023.0562

Step-by-step explanation:

We are given;

x = t² - 2t

dx/dt = 2t - 2

Also, y = t^(5)

dy/dt = 5t⁴

The arc length formula is;

L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt

Where α and β are the boundary points. Thus, applying this to our question, we have;

L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt

L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt

L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt

Using online integral calculator, we have;

L ≈ 1023.0562

Answer 2

The length of the curve is 1023.0562 and this can be determined by doing the integration using the calculator.

Given :

[tex]\rm x = t^2-2t[/tex][tex]\rm y=t^5[/tex][tex]\rm 1\leq t\leq 4[/tex]

First, differentiate x and y with respect to 't'.

[tex]\rm \dfrac{dx}{dt}=2t-2[/tex]

[tex]\rm \dfrac{dy}{dt}=5t^4[/tex]

Now, determine the length of the curve using the below formula:

[tex]\rm L = \int^b_a\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2} dt[/tex]

Now, substitute the value of the known terms in the above formula and then integrate it.

[tex]\rm L = \int^4_1\sqrt{(2t-2)^2+(5t^4)^2} dt[/tex]

[tex]\rm L = \int^4_1\sqrt{25t^8+4t^2-8t+4} \;dt[/tex]

Now, simplify the above integration using the calculator.

L = 1023.0562

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Related Questions

Enclosing the Largest Area The owner of the Rancho Grande has 3,052 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose

Answers

Answer:

the shorter side = 1526

the longer side = 763

area = 1164338

Step-by-step explanation:

lets say

a=length

b = width

a + 2b = 3052

this is the perimeter

such that

a = 3052 - 2b

the area of a rectangle is a*b

= (3052 - 2b)b

= 3052b - 2b²

we differentiate this to get:

= 3052 - 4b

such that

3052 = 4b

divide through by 4, to get b, the width

3052/4 = 763

b = 763

put the value of b into a

a = 3052 - 2b

a = 3052 - 2(763)

a = 3052 - 1526

a = 1526

therefore

the shorter side = 1526

the longer side = 763

area = a x b

area = 1526 x 763

area = 1526 x 763

= 1164338

Which phrase describes the algebraic expression 8f+7?
the product of 8 and 7 more than a number
the quotient of 8 and 7
8 times the sum of a number and 7
8 times a number plus 7​

Answers

Answer:

8 times a number plus 7

Step-by-step explanation:

Let the number be f.

Simply, 8 f+7 is the expression.

Thank you!


Which of the following is the correct notation of the complex number?

Answers

Answer:

-84 + 10i

Step-by-step explanation:

Standard Complex Form: a + bi

Step 1: Evaluate

√-100 = √-1 x √100 = i x 10 = 10i

-84 = -84

Step 2: Combine

10i - 84

Step 3: Rearrange

-84 + 10i

Answer:

Last Option

Step-by-step explanation:

√-100 - 84

(√(100×-1)) - 84

(√100)(√-1)-84

√-1 = i

10i - 84 or -84 + 10i

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? –15 –9 3 9

Answers

Answer:

b = -9.

Step-by-step explanation:

The line passes through (4, 3) and (7, 12). First, we need to find the slope: the rise over the run.

(12 - 3) / (7 - 4) = 9 / 3 = 3.

Now that we have the slope, we can say that m = 3. So, we have an equation of y = 3x + b. To find b, we can use M(4, 3) and say that y = 3 and x = 4.

3 = 3 * 4 + b

b + 12 = 3

b = -9.

Hope this helps!

The value of b in the equation is -9

How to determine the value of b?

The points are given as:

M(4, 3) and N(7, 12)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1[/tex]

This gives

[tex]y = \frac{12 -3}{7 -4} * (x - 4) + 3[/tex]

Evaluate the quotient

y = 3 * (x - 4) + 3

Open the bracket

y = 3x - 12 + 3

Evaluate the difference

y = 3x - 9

Hence, the value of b is -9

Read more about linear equations at:

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2/5(10c -35) (the 35 is negative)

Answers

Answer:

The simplified form is 2 (c - 7).

Step-by-step explanation:

The expression to be solved is:

[tex]f (c)=\frac{2}{5} (10c -35)[/tex]

Simplify the expression as follows:

[tex]f (c)=\frac{2}{5} (10c -35)[/tex]

       [tex]=[\frac{2}{5}\times 10c]-[\frac{2}{5}\times 35]\\\\=[2\times 2c]-[2\times 7]\\\\=4c-14\\\\=2(c-7)[/tex]

Thus, the simplified form is 2 (c - 7).

The population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches. A sample of 50 men and 40 women is selected. What is the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights

Answers

Answer:

The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.

Step-by-step explanation:

We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.

A sample of 50 men and 40 women is selected.

The z-score probability distribution for the two-sample normal distribution is given by;

                          Z  =  [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex]  ~ N(0,1)

where, [tex]\mu_M[/tex] = population mean height of men at UMBC = 69 inches

           [tex]\mu_W[/tex] = population mean height of women at UMBC = 65 inches

           [tex]\sigma_M[/tex] = standard deviation of men at UMBC = 4 inches

           [tex]\sigma_M[/tex] = standard deviation of women at UMBC = 3 inches

           [tex]n_M[/tex] = sample of men = 50

           [tex]n_W[/tex] = sample of women = 40

Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P([tex]\bar X_M-\bar X_W[/tex] > 5 inches)

 P([tex]\bar X_M-\bar X_W[/tex] > 5 inches) = P( [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex] > [tex]\frac{(5)-(69-65)}{\sqrt{\frac{4^{2} }{50}+\frac{3^{2} }{40} } }[/tex] ) = P(Z > 1.35)

                                         = 1 - P(Z [tex]\leq[/tex] 1.35) = 1 - 0.9115 = 0.0885

The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.      

Let f (x)
sinx cosx, then f'(x) =
A. Cos2x
B. sin2x
C. tan 2x
D. cos2x - sin2x

Answers

Answer:

A. Cos2x

Step-by-step explanation:

f(x) = sin(x)cos(x) = (1/2) sin(2x)   using double angle formula.

f'(x) = ( (1/2)sin(2x) )' = 2(1/2)cos(2x) = cos(2x)

Identify the recursive formula for the sequence given by the explicit formula f(n) = 20 – 4(n − 1).

Answers

Answer:

[tex]\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]

Step-by-step explanation:

[tex]f(n)=20-4(n-1)=20+(n-1)(-4)\\\\\text{It's an explicit formula of an arithmetic sequence:}\\\\f(n)=a_1+(n-1)(d)\\\\a_1-\text{first term}\\d-\text{common difference}\\\\\text{Conclusion:}\\\text{Next term}=\text{previous one}\ -4\\\\\text{The recursive formula:}\\\\\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]

Answer:

Step-by-step explanation:

someone answered already

Ava placed the point of her pencil on the origin of a regular coordinate plane. She marked a point after moving her pencil 4 units to the left and 7 units up. Which ordered pair identifies where Ava marked her point?

Answers

[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]

So, Let's solve this question by using cartesian plane.

Here, Origin is shown by (0, 0)Ava moves 4 units left from origin. On the left side of origin, negative x axis begins. So, she reached (-4, 0) now.Then, from that point she moved 7 units upwards. On the upper side, there is positive y axis. So, Finally she will reach point (-4, 7).(-4, 7) is the coordinate of point which is 4 units left from y axis and 7 units up from x axis.It lies on the second quadrant.

Well, What is cartesian plane?

A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. 

━━━━━━━━━━━━━━━━━━━━

The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.

Answers

Answer:

36

Step-by-step explanation:

formula of area for square:

A=s^2

s=6

A=6^2

A=36

Answer:

36

Step-by-step explanation:

I got it right

HELP PLZ A circle inscribed in a triangle:

Answers

Answer:

The answer is the second photo.

Step-by-step explanation:

It's literally a circle in a triangle. So, it's the second one.

If there are 80 students in a class and 20 are seniors, what proportion of students are not seniors?

Answers

Answer:

3/4

Step-by-step explanation:

First find the number that are not seniors

80 -20 = 60

60 are not seniors

The ratio of not seniors to total

60/80

Divide top and bottom by 20

3/4

Answer:

60 students

Step-by-step explanation:

80 -20 = 60

the bold answer is incorrect. what is the right answer?

Answers

Answer: first choice

Explanation:

A complementary angle are two angles add up to 90 degree

A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?

Answers

Answer:

Total expected amount = $0.04375

Step-by-step explanation:

We need to calculate probability of getting heads on every combination of coin tosses

HHH = 1/8 = 3 heads

HHT = 1/8 = 2 heads

HTH = 1/8 = 2 heads

HTT = 1/8 = 1 head

THH = 1/8 = 2 heads

THT = 1/8 = 1 head

TTH = 1/8 = 1 head

TTT = 1/8 = 0 head

So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175

Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225

Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375

Total expected amount = 0.00375 + 0.0225 + 0.0175

Total expected amount = $0.04375

A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you decide to collect data from a random sample of students to assess whether the publisher's claim is reasonable, and you find that in a random sample of 22 college students, the mean price of textbooks for the fall 2019 semester was $433.50 with a standard deviation of $86.92. At the 0.01 significance level, is there sufficient evidence to conclude that the mean price of college textbooks for a single semester is different from the value claimed by the publisher?

Answers

Answer:

We accept H₀ . We don´t have enough evidence to express the publisher claim is not true

Step by Step explanation:

We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher

n < 30 then we must use t - distrbution

degree of freedom   n  - 1     df = 22 - 1     df = 21

As the question mentions " different " that means,  a two-tail test

At 0,01 significance level     α  = 0,01       α/2  =  0,005

and t(c)  = 2,831

Test Hypothesis

Null Hypothesis                      H₀          μ  =  μ₀

Alternative hypothesis           Hₐ          μ  ≠  μ₀

To calculate t(s)

t(s)  =  (  μ  -  μ₀ ) /σ/√n

t(s)  =  (  433,50 - 385 ) / 86,92 / √22

t(s)  =  2,6171

Comparing   t(c)   and t(s)

t(s) < t(c)

Then  t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim

Use the frequency distribution, which shows the number of American voters (in millions) according to age, to

find the probability that a voter chosen at random is in the 18 to 20 years old age range

Ages

18 to 20

21 to 24

25 to 34

35 to 44

45 to 64

65 and over

Frequency

4.2

7.8

20.8

23.7

50.1

28 2

Date

07/2

3:29

The probability that a voter chosen at random is in the 18 to 20 years old age range is 0.0311

(Round to three decimal places as needed.)

07/2

8:52

Question Viewer

07/1

8:03

07/1

5:46

>

07/1

12:2

07/1

5:39

07/1

2:42

Question is complete. Tap on the red indicators to see incorrect answers.

07/1

12:00

Answers

Answer:

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

Step-by-step explanation:

We can find the probability by simply dividing the frequency of the ages range of 18-20 by the total frequency.

Ages                Frequency

18 to 20             4.2

21 to 24             7.8

25 to 34           20.8

35 to 44           23.7

45 to 64           50.1

65 and over       28.2

∑                        134.8

The probability of an event is given by the occurrence of an event by the total occurrences .

So

Here the occurrence of ages 18-20 is given by 4.2

and the total frequency is 134.8

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g?

Answers

Answer:

The probability that the box will contain less than the advertised weight of 453 g is 0.00034.

Step-by-step explanation:

Let X represent the weight (in grams) of cereal in a box of Lucky Charms.

It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.

Compute the probability that the box will contain less than the advertised weight of 453 g as follows:

[tex]P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})[/tex]

                  [tex]=P(Z<-3.4)\\=0.00034[/tex]

*Use the z-table.

Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.

The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm.
A. Use differentials to estimate the maximum error in the calculated volume.
What is the relative error?
B. Use differentials to estimate the maximum error in the calculated volume.
What is the relative error?

Answers

Answer:

A) Maximum error = 170.32 cm³

B)Relative error = 0.0575

Step-by-step explanation:

A) Formula for circumference is: C = 2πr

Differentiating with respect to r, we have;

dC/dr = 2π

r is small, so we can write;

ΔC/Δr = 2π

So, Δr = ΔC/2π

We are told that ΔC = 0.5.

Thus; Δr = 0.5/2π = 0.25/π

Now, formula for Volume of a sphere is;

V(r) = (4/3)πr³

Differentiating with respect to r, we have;

dV/dr = 4πr²

Again, r is small, so we can write;

ΔS/Δr = 4πr²

ΔV = 4πr² × Δr

Rewriting, we have;

ΔV = ((2πr)²/π) × Δr

Since C = 2πr, we now have;

ΔV = (C²/π)Δr

ΔV will be maximum when Δr is maximum

Thus, ΔV = (C²/π) × 0.25/π

C = 82 cm

Thus;

ΔV = (82²/π) × 0.25/π

ΔV = 170.32 cm³

B) Formula for relative error = ΔV/V

Relative error = 170.32/((4/3)πr³)

Relative error = 170.32/((4/3)C³/8π³)

Relative errror = 170.32/((4/3)82³/8π³)

Relative error = 170.32/2963.744

Relative error = 0.0575

For a moving object, the force acting on the object varies directly with the objects acceleration. When a force of 60 N acts on a certain object, the acceleration of the object is 10 m/s^2 . If the force is changed to 54 N, what will be the acceleration of the object

Answers

Step-by-step explanation:

Hey, there!!!

According to your question,

case i

force (f) = 60 n

acceleration due to gravity (a)= 10m/s^2

now,

force = mass × acceleration due to gravity

or, 60 = m × 10

or, 10m= 60

or, m= 60/10

Therefore, the mass is 6 kg.

now,

In case ii

mass= 6kg {Because there was no change in mass only change in force}

force= 54 n

now, acceleration due to gravity = ?

we have,

f=m×a

or, 54= 9×a

or, 9a= 54

or, a= 54/9

Therefore, the acceleration due to gravity is 6m/ s^2.

Hope it helps....

Can I have somebody answer a few more of the questions that I need please and this one too?

Answers

Answer:

x > 22

Step-by-step explanation:

Hey there!

Well to solve,

52 - 3x < -14

we need to single out  x

52 - 3x < -14

-52 to both sides

-3x < -66

Divide both sides by -3

x > 22

The < changes to > because the variable number is a - being divided.

Hope this helps :)

Answer:

x > 22

Step-by-step explanation:

First, rearrange the equation

52 - 3 × x - (-14) < 0

Then, pull out the like terms:

66 - 3x

Next, apply algebra to the equation by dividing each side by -3. It should now look like this: x > 22.

Therefore, the solution set of the inequality would be x > 22.

What is 32 divided by the opposite of 4

Answers

Answer: -8

Since we are dividing the OPPOSITE of 4 then we are dividing 32÷-4

When multiplying or dividing a POSITIVE to a NEGATIVE you get a NEGATIVE

P/N=N

N/N=P

P*P=P

P=Positive

N=Negative

Divide

32/-4=-8

So your answer is -8

When 32 is divided by opposite of 4 the obtained result is - 8.

What is additive inverse ?

Additive inverse of a number is such a number when the original number and it's additive inverse is added we get zero.

4 + ( - 4 ) = 0.So the additive inverse of 4 is - 4.

According to the given question we have to obtain the result when 32 is divided by opposite of 4.

Here opposite of 4 means additive inverse of 4 which is -4.

∴ 32/-4

= - 8.

learn more about additive inverse here :

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How long will it take $3800 to grow into $5700 if it’s invested at 6% interest compounded continuously?

Answers

Answer: 25 years

Step-by-step explanation:

t = I / Pr

t = 5700 / ( 3800 × 0.06 ) = 25

t = 25 years

2. Write the equation of the circle in general form. Show your work.

Answers

Answer:

[tex] {(x + 1)}^{2} + {(y - 1)}^{2} = 9[/tex]

[tex] {x} ^{2} + {y} ^{2} + 2x - 2y - 7 = 0 [/tex]

I need help ? which linear function is represented by the graph?​

Answers

Answer: f(x) = (-1/2)x+1, choice B

=================================================

Explanation:

The diagonal line passes through 1 on the vertical y axis. So the y intercept is b = 1. This means the location of the y intercept is (0,1).

Start at (0,1) and move down 1 and to the right 2 to arrive at (2,0). This is another point on the diagonal line. The motion of "down 1 and right 2" is effectively the slope

slope = rise/run = -1/2

rise = -1, run = 2

The rise being negative means we have gone downhill as we move to the right.

With m = -1/2 as the slope and b = 1 as the y intercept, we go from y = mx+b to y = (-1/2)x+1

The last thing to do is replace y with f(x) to get f(x) = (-1/2)x+1 as the final answer.

Answer:

it's b

Step-by-step explanation:

b

Rational equation of 3/x+1=2/x-3

Answers

Answer:

x = 11

Step-by-step explanation:

3/x+1=2/x-3

Solve by using cross products

2 (x+1) = 3 (x-3)

Distribute

2x+2 = 3x-9

Subtract 2x

2x+2-2x = 3x-2x-9

2 = x-9

Add 9 to each side

2+9 =x-9+9

11 =c

What is the equation of the parabola that has its vertex at (8,-1) and a y-intercept of (0,-17)?

Answers

y = a(x  + 1.5)^2 - 12.5

y intercept is (0,-8) so:-

-8 = a(0+1.5)^2 - 12.5

-8 = 2.25a - 12.5

a =  4.5/ 2.25 = 2

so we have  

y  = 2 ( x +1.5)^2 - 12.5

solving for x  when y = 0:-

(x + 1.5)^2 = 12.5/2 = 6.25

taking sqrt's  x + 1.5  = +/- 2.5

x =  -4,   1

so the x intercepts are (-4,0) and (1,0)

Answer:

y = –1∕4(x – 8)^2 – 1

Step-by-step explanation:

I took the exam and  got  it  right.

PLEASE HELP QUICK!!!!!!! Find the length of a rectangle that has one side of length 8 and area 32

Answers

Answer:

4

Step-by-step explanation:

Length of one side=8

Area=32

Length of another side=x

8 into x = 32

X=32/8

=4

Joey’s pizza sells large cheese pizzas for $12.00. Each additional topping costs $0.50. Basketball Boosters bought 12 large pizzas, each with 3 toppings. There are 8 slices per pizza. How much does it cost per slice? Round to the nearest cent.

Answers

Answer:

So first you do $0.50 x 3 = 1.5

then you add that to $12.00

$12.00 + 1.5 = 13.5

13.5 is the cost of one pizza.

Since they bought 12:

The total cost of the 12 pizza is $162 <== not important

13.5 divided by 8 is 1.687

round 1.56875 to the nearest cent 1.7 = $2

so each slice costs $2

a company should stop making a part internally and buy externally when

Answers

Answer:

Make-or-Buy Decision

Step-by-step explanation:

What is the volume of a square pyramid whose length of one side of its base is 9cm and whose height is 15cm. Show your work

Answers

Answer:

The answer is 405cm³

Step-by-step explanation:

Volume of a pyramid is given by

[tex]V = \frac{1}{3} \times area \: of \: base \: \: \times height[/tex]

height = 15cm

From the question the pyramid is a square pyramid which means it's base is a square

Area of a square = l²

where l is the length of one side

l = 9cm

Area of square = 9² = 81cm²

So the volume of the pyramid is

[tex]V = \frac{1}{3} \times 81 \times 15[/tex]

[tex]V = 27 \times 15[/tex]

We have the final answer as

V = 405 cm³

Therefore the volume of the pyramid is

405cm³

Hope this helps you

Other Questions
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