1. A 30-ft ladder makes an angle of 60° with the horizontal when it reaches a given spot on a wall. What angle wil 35-ft ladder makes with the horizontal if it reaches the same spot?

Q: The monthly profit from the sale of a product is given by P = 32x - 0.2x² - 150 dollars. (a) What…

A: We have given monthly profit  P=32x-0.2x2-150 Differentiating profit function with respect to x  P'…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 6x + 30, y = 0, x = 0…

A:

Q: 18. f(x) = 8x³ - x² 7+11x 4x4 -

A:

Q: Sketch the graph of a function f that satisfies all of the given conditions. lim f(x) = 4, lim_f(x)…

A:

Q: Find a formula for f-¹(x) if f(x) = 1, ≥ 0. 5 x²+1,x

A: To find a formula for f-1x if fx=5x2+1, x≥0.

Q: 1.001 -1.01 101 -1.1 41.51 3 steuleve, ils 101 $+$-2 (s) 2 limit and justify each step by indicating…

A:

Q: For each slope below, enter the value correct to four decimal places. f(x+h)-f(x) h Let f(x) = 3.7x²…

A:

Q: Sketch a graph of J(x) where J(X, 10 -9 -8 -7 -6 -5 -4 -3 1 -2 -1 10+ 9 8 7 6 5 4 3 2 + -1 -3 -4 -5…

A:

Q: 2. Find the dy/dx by implicit differentiation. a. (sin(x) + cos (лy))² = 2 b. cscx = x(1 + tany)

A:

Q: -iangle RST, side r measures 88 mm; angle S is 37° and angle T is 107°; find side T. Draw the…

A: Given query is to find the Indicated side.

Q: An object is thrown upward at a speed of 128 feet per second by a machine from a height of 11 feet…

A: given  h(t)=-16t2+128t+111) put  h(t)=168

Q: X 4+x -√4-x

A:

Q: Find f(x) if f(x) = 7 +8 and f(1) = 4.

A: Given that f'(x)=7x4 -(i) and f(1)=4.Our Aim is to find the value of f(x)=?

Q: Evaluate the integral. | 6² ( ₁ 7 2²³ + 5+1 k) dt 5t4 j+ + t². π -j + ln (2) k X

A:

Q: World population¹ is about P = 7.68(1.0103)', with P in billions and t in years since 2020. (a) What…

A: Let's solve given population problem.

Q: Let f(x) = 2 + √√x − 6. Find ƒ−¹(x). ƒ−¹(x) Now for fun, verify that (ƒ o ƒ−¹)(x) = (ƒ−¹ ○ ƒ)(x) O =…

A: The given function fx=2+x-6. We have to find the inverse function f-1x.

Q: Find the distance from the point P to the given line L. P(0, -1, 2) and L: x=2 + 3t, y=-3-2t, z = -3…

A:

Q: The equation r(t) = (4t+9) i+ (5t² − 1) j + (3t) k is the position of a particle in space at time t.…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 3. Find the length of segment JK. Round to the nearest hundredth. J 23 H K 31 29°

A: by using cos law we know  C2=a2+b2-2abcosC

Q: Find the solution of the following differential equations. Show your solutions. 1. (3x + 4y)dy + (y…

A: A detailed solution is given below.

Q: Consider the function Evaluate the definite integral 5₁ f(x) dx = Evaluate the average value of f on…

A: Given that f(x)=x   if x<1 1x if x≥1We have to evaluate definite integral ∫-15f(x)dxand average…

Q: -3 S T -1 5 3- 2- 1. 0 -1- -2- -3- 2 3 5 Limits A function f(x) is continuous at an x value of aif…

A: Given graph of a function f(x)

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A:

Q: Average vs. instantaneous rates of change. Frank was monitoring the population of fruit flies as…

A: Note :- Since you have posted multiple questions with multiple subparts, we will provide the…

Q: Evaluate the limit t³ - 1 1 lim t 1 ²

A:

Q: Given that f(x) = x² - 10x and g(x) = x + 6, find (a) f + g= (b) f-g= (c) fg= f (d) 9 =

A:

Q: x²sin+y²cos + xy In X X X+Y x-y

A:

Q: (a) Let f(x) = (x + 3)¹, x ≥ 0. Find a formula for f-¹(x). 4 √x-3 Answer: 4 √x-3 x ≥ 81 9 (b) For…

A: Given f( x ) = ( x + 3 )4 let f( x ) = y y = ( x + 3 )4

Q: Part C Ajar of crunchy peanut butter contains 1.69 kg of peanut butter. If you use 8.9 % of the…

A:

Q: (siny-2ye¯*sinx) dx + (cosy + 2e-*cosx) dy = = 0

A:

Q: Consider the position function s(t) = 16t+112t representing the position of an object moving…

A:

Q: Change from rectangular to spherical coordinates. (a) (9, 3√3, 6) (P₁0, 9) = (12 (p, 0, ) = (5√2 T 6…

A: Given coordinates:- a) 9,33,6 b) 0,-5,-5

Q: 26 19 cb [²º f(x)dx – [¹³° f(x)dx = ["* f(x)dx - 9 a where a = and b =

A: Given query is to find the value of a and b.

Q: Determine an equation for the plane passing through the line of intersection of the two planes,…

A: Given planes equations:- P1: x-2y=5 P2: y+3z=6P3: 7x+5y-z=-3

Q: 4. A cup of coffee has a temperature of 80°C when it is placed outside where the temperature is…

A: The given data is: A cup of coffee has a temperature of 80 degrees celsius when it is placed outside…

Q: A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides…

A: A detailed solution is given below.

Q: Find the volume of the solid generated by revolving the region about the given line. The region in…

A: Figure:-

Q: If ƒ is an increasing function and ä2 > x1, then ƒ (x₂) < ƒ (x1) True False

A: Given: f is an increasing function and x2&gt;x1

Q: Prove the following identity by working only on the left side of the equation. (1-sinx)(1+cscb)…

A: This is question of trigonometry here equation is given we have to prove it further calculation is…

Q: Consider the position function s(t) = -4.9t+28t+17. Complete the following table with the…

A: Find velocity

Q: Use continuity to evaluate the limit. lim 4 sin(x + sin(x)) X→T

A:

Q: The amount in grams of a drug in the body t hours after taking a pill is given by A(t) = 30(0.85).…

A:

Q: F(x)=x²-5 (F-f)(x)=

A:

Q: A hole in the ground in the shape of an inverted cone is 16 meters deep and has radius at the top of…

A: Firstly we need to find the total density by integrating it with in the limits of depth. Then the…

Q: -3x - 8 if x 2 (a) Compute g(-5), g(-3), g(0) and g(3). (b) Sketch the graph of the function g(x).…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find the volume of the solid obtained by rotating the region bounded by y=sqrt(x-1), y=0, x=5…

A:

Q: Let f(x): This function has: 1) A y intercept at y= A = 2) Roots at A and B, where A < B B = =…

A: We can solve the following problem as follows

Q: n x + 3xn-kyk +yn 2 x² - y²

A: Given: fx,y=xn+3xn-kyk+ynx2-y2 To find: whether the function is homogeneous or not, if yes find the…

Q: In Exercises 7-16, evaluate the limit. X x → ∞ x + 9 7. lim 8. lim x →∞ 3x² + 20x x →∞ 2x² + 3x³ -…

A:

Q: The following table gives the millions of metric tons of carbon dioxide emissions in a certain…

A: