Use the position function ?(?) = −16?^ 2 + ?0? + ?0 for the following vertical motion of objects on earth.

5) An object is launched vertically from a 75ft building with an initial velocity of 240 ft/sec.

a) Find the velocity of the object 2 second after launch. Is it travelling up or down?

b) When will the object reaches its maximum height?

c) How long will the object travel in the air? (Hint: how long does it take to hit the ground?)

d) Determine the velocity when the subject hits the ground.

6) An object is fired downward with a speed of 12ft/sec from the top of a 80ft building.

a) Write the position function ?(?) that represents the height of the object, in feet, from the ground.

b) Determine the time for the object to hit the ground.

c) Determine the velocity at impact

a.)Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y^2=x and x = 2y about the y-axis

b.) Find the volume of the solid that results when the region bounded by x=y^2 and x=2y+15 is revolved about the y-axis

c.) Find the length of the curve y=ln(x) ,1≤x≤sqrt(3)

d.)Consider the curve defined by the equation xy=5. Set up an integral to find the length of curve from x=a to x=b

A chemist needs 10 liters of a 25% acid solution. The solution is to be mixed from three solutions whose concentrations are 10%, 20% and 50%. How many liters of each solution will satisfy each condition?

a) Use 2 liters of the 50% solution.

b) Use as little as possible of the 50% solution.

c) Use as much as possible of the 50% solution.

1] Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and verify the real zeros and the given function value.

n=​3;

2 and 5i are zeros;

f(1) = 52

f(x)= ?

​(Type an expression using x as the variable. Simplify your​ answer.)

2] Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing​ utility, use it to graph the function and verify the real zeros and the given function value.

n= 3;

- 3 and 7+2i are zeros;

f(-1)= 136

f(x)= ?

​(Type an expression using x as the variable. Simplify your​ answer.)

3] Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.

n= 4;

i and 5i are zeros;

f(-1) = 104

f(x) = ?

​(Type an expression using x as the variable. Simplify your​ answer.)

Use Euler's method with each of the following step sizes to estimate the value of y(0.8), where y is the solution of the initial-value problem: y' = y, y(0) = 5.

(i)    h = 0.8

y(0.8) = 9

(ii) h = 0.4

y(0.8) = 9.8

(iii)    

h = 0.2

y(0.8) = ?

The error in Euler's method is the difference between the exact value and the approximate value. Find the errors made in part (a) in using Euler's method to estimate the true value of y(0.8), namely 5e^0.8.

(Round your answers to four decimal places.)

1. solve the initial value problem.

(t^(2)+1)y'+2ty=tant , y(0)=2

2.find the solution to this initial value problem.

yy'=e^x+x , y(0)=y_0

y_0 is a nonzero constant.

The exponent rules are needed in order to perform operations on polynomials. In your own words:
Explain what a polynomial is and identify the different parts of a polynomial
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms- explain how foil helps us to accomplish this, and what category of polynomials foil applies to
There are two special case products where the product takes on special patterns- explain these two cases and when they occur
For each of the two special cases, illustrate your explanation with an appropriate exercise from the text (note the pg. and exercise number in your post), showing how the multiplication is performed using the special pattern formula, then also showing the same result using foil.

Using a scalar surface integral, compute the surface area of the portion of the unit
sphere that is above the cone z = sqrt(x^2+y^2)

Factor the following:

a) f(x)=x^5+5x^4-21x^3-137x^2-88x+240, knowing that f(5)=0 and f(-3)=0.

b) f(x)=x^3+8x^2+5x-50

c)f(x)=-x^4-4x^3+19x^2+46x-120, knowing that (x+5) and (x-2) are factors.

Consider the function and the value of a.

f(x) =

, a = 9. (a) Use m_tan = lim h→0

to find the slope of the tangent line m_tan = f '(a).

m_tan =  

(b)Find the equation of the tangent line to f at x = a.

(Let x be the independent variable and y be the dependent variable.)