Answer Number 16 ONLY. 15. Yogurt containers can be shaped like frustums. Rotate the line y = x around the y-axis to find the volume between y = a and y = b. The variable m is any positive integer.mm² (b³-a³) units³TMa.C. (b³ - a³) units³33b.m² (b³ + a³) units³d.πης(-b³ + a³) units³3316. The arc length is defined as if y=f(x) is a smooth curve on the interval [a,b] then thearc length L of this curve is defined as22a. L=1+dxC. L = 1 +dxdy.b. L = fo 1 +-(2x)² dyd. L = √√√1-dx_17. Find the arc length of the curve y = (x - 1)2 on the interval [a,b].dx.2

We have to find the arc length of the curve y=f(x). According to guide line we solve only one…

b. ·(b³ + a³) units³ 3 d. -b³ + a³) units³ 16. The arc length is defined as if y=f(x) is a smooth curve on the interval [a,b] then the arc length L of this curve is defined as cb (98) ² cb (dy)²

b. ·(b³ + a³) units³ 3 d. -b³ + a³) units³ 16. The arc length is defined as if y=f(x) is a smooth curve on the interval [a,b] then the arc length L of this curve is defined as cb (98) ² cb (dy)²

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter63: Volumes Of Pyramids And Cones

Section: Chapter Questions

Problem 25A

See similar textbooks

Related questions

Q: 10s²+17s+12₁ S³+27 L-¹1²

Q: If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f'(5). f(5)…

A: Topic = Derivative f5=2f'5=15

Q: 7) Find the area of the region enclosed by the cardioid r² = 4 cos 20.

A: To find the area of the region enclosed by the cardioid r2=4 cos 2θ.

Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

Q: Given a function, Based on the function, F(s) = 3s-6 s² +8s+7 a) Determine f(t). b) Based on…

A: Given a function, Fs=3s-6s2+8s+7Based on the function, a To determine ft.b Based on solution ft…

Q: The derivative of sec22x(cos2x−sin2x) with respect to x is?

A: I have appended the formula used in the solution part of the question

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 - 8x² + 2 (a) Find…

Q: 8 hp zh6 S

Q: 29. Given dx where a>0, at what value of p will the integral become convergent? c. p = 1 a. p> 1 b.…

Q: 3 4) Sain ³x cus³x dx 3 a) - + cos²³x (vin³x + ²) + C 2 b) = cos²x (Ain²³x + ²/2 ) + Cc c) - — cos…

A: To evaluate the integral.

Q: dx √x²=2x+17 a) sinh xe ta 4 bì ninh XH + C 4 c) minh? X-1 2 d) none of the above

Q: Find the average of two numbers (x1, x2) and print" pass "if the average is more than 50 and "not…

A: Given numbers : x1,x2 Average of number = (x1+x2)/n where n=2

Q: Which of the following represents the derivative of fat x? f′ (x) = f(x1¬Ax)+f(x1) Ax f′ (x) =…

A: We have to choose the expression that represents the derivative of f at x.

Q: A 1 lb sponge initially contains 5 lb of water. As it is lifted up from the ground, the sponge loses…

A: Answer is option d here decrement in water is linearly (as constant rate)

Q: Q3/ Answer one from the following :- 1- Determine the general solution y(x) for the equation 2y" -…

A: Explanation of the answer is as follows

Q: The normal line to a curve h(x) = -x² + 1 at point Z, is defined as a line that passes through point…

Q: B. 2x³ +2y-3y² = 13x Steps 1. Take the derivative of both sides with respect to x. 2. Since the left…

Q: xdx+sin y ४ (vdx-xdy}=0

Q: ¹.) f(x) = (x³ - 7x² - 6x + (4 +17) f(x) = x-6 7x - 6 2) f(x) 4 - 17x²

A: Explanation of the answer is as follows

Q: Question 2b. Consider the differential equation dy dx ex yee with initial condition y(0) = −1. b)…

A: We use the variable separable method to solve the given differential equation.

Q: Identify and sketch the graph of y = r²+1 in R³.

Q: 4.z=(y'-2) 3/4-2y ;z= dz dy

A: See the details solution in below

Q: E S™ SX 5x5x²x² coscyl dyd z d x "X d 2 +

Q: What is the limo+x².In(x) For answers that are fractions infinity negative infinity write... in…

A: L' Hospital Rule : If limx→a f(x)g(x) = 00 and ±∞±∞ form , then limx→a f(x)g(x) =…

Q: 3- 1 له وال * IT X I sintLy, y Ha

Q: ect the best technique to integrate each function. ® Na'da 5 dx 16 V √ √₂²³-11 ·@fe²√5 + ode x + 7…

A: The objective of the question is matching the given indefinite integral.

Q: The dimensions of Roy and Roger's sandbox are t² meters by t5 meters. One cubic meter of the sandbox…

A: dimensions of the Roy and Roger's sandbox : length = t2 width = t5 height = v2…

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

Q: To say that x + 5| ≤ 3 is the same as saying is in the closed interval [A, B] where A is: and where…

A: The objective is to find A and B.

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Concept: Wronskian method: W(x1(t), x2(t), . . . , xn(t)) =x1(t) x2(t) · · · xn(t) xx1'(t) x2'(t) ·…

Q: Solve the following initial value problem using Laplace transforms. y"-9y=3e¹; y(0) = 0, y'(0)=1

A: Explanation of the answer is as follows

Q: 5|2 X 1 If f(x) = X A. f(x) is continuous at x = 2 B. f(x) is discontinuous at x = 2 C. lim f(x) = 1…

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: According to company's rules, I need to solve first question when multiple questions are posted.. So…

Q: Given f(x)=√ and g(x) = x. Which of the following integrals describes the area between the curves…

Q: Consider the initial-value problem y' + exy = f(x), y(0) = 1. Express the solution of the IVP for…

A: Given:- y'+ex y =f(x) , y(0) =1 Find:- Express the solution of the IVF for x>0 as a non…

Q: Instruction: Evaluate the following Integrals. Write your COMPLETE solutions neatly and organized.…

Q: Determine the area of the region enclosed by the curves y - 3x = 2 and 2x² - 4-2y = 0. Do not…

Q: x" -2x +x= 15; x (0) = 7, x (0) = -16

A: We have solve the given differentiable equation…

Q: f(x) = 2²3 on (0, ∞) x+3

Q: aw C. If w=f(x,y) and x=r. cose, y=1. sing. Prove that ar 1 (dw r² 20 = fix² + fy²

A: Let's prove.

Q: Solve the given initial-value problem. Give the largest interval I over which the solution is…

Q: Find the derivative of each of the following functions using any method. 1.) f(x)= 6x^5 + 7x^4 - 6x³…

Q: 3t 2t - 1 1-t 1+t [][] 3 and B(t) = 51² 51³ t Verify the product law for differentiation, (AB)' =…

A: See the details solution in below

Q: 2. Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1. 2

Q: • How. Find the lengths for the following curver.. 1= r = 1 + cosa

A: Explanation of the answer is as follows

Q: 3) The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the…

A: To find the coordinates of P and find the equation for the line .

Q: What is the derivative of y = sin (x³ sin (x³ – 3x)?

Q: Let A = 4 -8 -2 and B= 2 -3 6 0 and let x = 6-4 and y= sint. Find Ay and Bx. Are the products Ax and…

A: Given A = 40-26-83 B = 26-306-4 x = 3te-t y = t4sin tcos t

Q: Using the definition of derivative that incorporates the idea of limit, prove that if f and g are…

Q: State the order of the given ordinary differential equation. (sin e)y"" - (cos e)y' = 3 Determine…

A: The order of a differential equation is the order of the highest derivative present in the given…

Question

Answer Number 16 ONLY.

15. Yogurt containers can be shaped like frustums. Rotate the line y = x around the y-
axis to find the volume between y = a and y = b. The variable m is any positive integer.
m
m² (b³-a³) units³
TM
a.
C. (b³ - a³) units³
3
3
b.
m² (b³ + a³) units³
d.
πης
(-b³ + a³) units³
3
3
16. The arc length is defined as if y=f(x) is a smooth curve on the interval [a,b] then the
arc length L of this curve is defined as
2
2
a. L=1+
dx
C. L = 1 +
dx
dy.
b. L = fo 1 +
-(2x)² dy
d. L = √√√1-
dx
_17. Find the arc length of the curve y = (x - 1)2 on the interval [a,b].
dx.
2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A vessel is in the shape of a right circular cone. This vessel contains liquid to a depth of 12.8 centimeters, as shown. How many liters of liquid must be added in order to fill the vessel? One liter contains 1000 cubic centimeters.

Recommended textbooks for you

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,