A ball is thrown downward with a speed of 14 ft/s from the top of a 196-foot-tall building. After t seconds, its height above the ground is given by s(t) = -28t- 14t + 196. (a) Determine how long it takes for the ball to hit the ground. sec (b) Determine the velocity of the ball when it hits the ground. ft/sec

Q: 1. Given the function f(x, y) = x² /ÿ. (a) Find the local linear approximation of f at the point (3,...

A:

Q: 9. dx 1+ e* A - In le-* |+ C - In le * + 11 + C B In le*|+ C B D In le-* + 1|+ C

A:

Q: 1. S(Vz5 + Vx ) de с 6 x2/7 +- 2. x5/6 +x³ +C 1 x3 + C 1 7/2 x3 + C х6/5 + - х3 + C + - O A О в O c ...

A:

Q: If the given function is f(x) = x + 1, then which of the following is the solution in finding the an...

A:

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A:

Q: The height (in meters) of a projectile shot vertically upward from a point 4 m above ground level wi...

A: We need to find velocity and height.

Q: A function f has a removable discontinuity at x = c if limf(x) exists by f is not continuous at x = ...

A: Here, the given function is: f(x)=x-2|x|-2 So, function is not defined at x=2,-2

Q: Consider the following sequence: +00 9" {a,} = An+1 - to show that the given sequence {a,} is strict...

A: The given sequence is  an=9n4n2n=1+∞

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)4 f(x) = E Σ ...

A:

Q: Find the exact length of the curve. X = 3 3D 글Vy (y-3), 9sys 25

A:

Q: S tan-3 (x) sec² x dx

A:

Q: 9. Find the bounds of integration a, b, c, d such that T (a, u) dydar. f(x, y) dædy =

A: x≤y≤4x=y →y=xy=40≤x≤4x=0 to x=4  

Q: Solve for B in the given partial fraction: a4-15a-32a2-12z-14 (z+1)(-2)(x+3)(+2) + + + (CE November ...

A:

Q: Find the first derivative of the following functions. Simplify results. Use differentiaion formula.

A: Formula: Derivative of u/v = (u'v-uv') /v2  

Q: 1 6. S dx (x+1)(x2+1) 2x+1 -dx 1. Jx+1)(x²+2) 8. S² х*+3х-1 dx x3-1 (x+1)dx 9. S x(x2+1) 6x2-17x+25 ...

A: Given

Q: a) Consider the surface z = Find the tangent plane to the 3. surface at the point (4, 3, 5). (4.04)3...

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (x2 + 2x) cos(x) dx

A:

Q: (х? + 2х + 3)(5—х) 10. g(x)= Зх + 2

A:

Q: Let X be a continuous random variable whose probability density function is given by the formula if ...

A: P(4≤x≤7) =∫4 7 p(x) dx                  =∫46x27 dx  +∫6723-2x27 dx

Q: The position of the particle at time t is given by s(t) = t- 18t + 80. The particle is moving from r...

A: The given problem is solved below in detail.

Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of th...

A: The circle formed has the area  A=πr2...(1) Differentiating it with respect to t: dAdt=π2rdrdt...(2)

Q: S x²e2** dx

A:

Q: Graphs of the velocity functions of two particles are shown, where t is measured in seconds. (a) Whe...

A:

Q: 7. e*-4e * dx A 2 C. + C 2 + C ex x + - - x +2 e * + C x - 2 e * +C C O E None

A: Here,               We have given an indefinite                             integral now we have to ...

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A:

Q: lim 2tan (2.x) 3n 4

A: This is a basic limit problem

Q: 7. Evaluate the integral r8-2x (x + y + 1)-2 dydr.

A:

Q: PROBLEM 1. Solve for the general solution term by term of the ordinary differential equation given b...

A:

Q: sin x 1+ cosx 1+ cosx + sin x 2cscx 2secx 01

A:

Q: Find the derivative of the following functions using the increment method. *b. f(x) = 6- Зх 1 *а. f(...

A: Topic:- derivatives

Q: dx

A:

Q: cos* (cos x) COS. dx CSc x

A: Given  ∫cos4cosxcscx dx

Q: Penny can see the clock on the top of her town’s courthouse from her front yard. The clock is at a h...

A: Angle of elevation

Q: If f(x) is a differentiable function, and n is a rational number, then Sf(x)" f'(x)dx = L4)"+1 +c n+...

A:

Q: If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then ...

A:  Given:         V=45001-150t2 0≤t≤50     the rate at which water is draining is given by      dVdt=d...

Q: S(cos 3x + sin 7x)² dx

A: Here, when we solve this integration it becomes separate integration of trigonometric term and vario...

Q: (b) Express the following using predicates notations with the least number of words: (i) Each intege...

A:

Q: A 20 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and ...

A: A 20 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and ...

Q: Use the ALEKS calculator to evaluate each expressic Round your answers to the nearest thousandth. Do...

A: As we know that; The logarithmic properties; 1). logaxb=b·logax 2). logcab=logca-logcb   Given: (a)....

Q: du What is the value of u, given the equation equal to? A. x² В. 4 С. 6 D. none of the above

A:

Q: 8. Find a definite integral for the area of the region that lies inside the polar curve r2 = 8cos(20...

A: Here, given that the region is bounded by the curves: r2=8cos(2θ) & r=2 which is

Q: Evaluate: (2x + 1)3 dx by two methods: 11) let u = 2x + 1 %3D 12) Expand (2x + 1)³ Compare the resul...

A: Integration

Q: y = c1x? + c2x + C3 + C2x + C3

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Let's find. 

Q: Evaluate the Integral 2. S V5 + 12x – 9x²dx - ANSWER: 2. (3x-2)v5+12x-9x²+9Sin¬13*- 2]+C (3х-2)

A:

Q: Consider the set of 21 consonants and 5 vowels.  How many distinct arrangement of 8 letters are ther...

A:

Q: The position of the particle at time t is given by s(t) = t² – 16t + 63. The particle is moving from...

A:

Q: Find the derivative of the following functions using the increment method. *b. f(x) = 6 - Зх 1 *а. f...

A:

Q: Given a function g(x, y) defined implicitly by the equation z*y* + sin (x² – y²) = tan-'(xz). (1) dz...

A:

Q: Find the derivative using the formula f'(x)= g'h + gh' 1. cos x cot x

A: Differentiation