Data from an independent research company found that the annual cost per worker for insurance​ (health, life,​ liability, etc.) was increasing according to the function f(x)=64.91e^(0.34 ×), where f(x) is the cost in dollars per year at time​ x, and x is the number of years measured from the beginnning of the year 1997. That is x=0 corresponds to the start of 1997. Find the total increase in costs during the next 4 years, beginning in 1997.

Four marbles are drawn simultaneously and at random from an urn containing 8 black, 7 white, and 5 red marbles.

What is the probability that at least one of them is white?

y2 − y − 6

1. Describe the origin of exponents in 2-3 paragraphs

(please cite)

Let T: R² -> R² be a linear transformation defined by T(x₁ , x₂) = (x₁ + 2x₂ , 2x₁ + 4x₂)

a. Find the standard matrix of T.

b. Find the ker(T) and nullity (T).

c. Is T one-to-one? Explain.

A small plane can fly 350 miles with tailwind in 1 3/4 hour. In the same amount of time, the same plane can travel only 210 miles with a headwind. What is the speed of the plane in still air and the speed of the wind?

1.    You have an annual salary of $62,000 from which they deduct 3% for medical insurance and 18% for taxes. Your rent is $1200 a month. Your water bill comes every 3 months for $123, and your light bill is $138 a month. You have a child that goes to a 30-minute piano class twice a week for $18 per session and you receive child support for that child every month in the amount of $125. Every week you put 130 miles on your car that gives you 20 miles per gallon and gas cost $2.27 per gallon. You pay a premium of $1,019 every six months for car insurance. You spend $120 a week on food. You also have a student loan that you are paying $150 on every month. and you spend $100 every 2 weeks just to treat yourself.

make a monthly budget and find your monthly cash flow. You must show work (Assume, that there are 52 weeks in a year)

Let f(x)= cos³ – 1.25cos²x + 0.225. Determine f ̍ (x_o) at the point x_o  at (π/2, π) where f(x_o)=0

Step by step procedure to understand the exercise please.
The solution of the book is not acceptable, since they do not explain where the result comes from.

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.

How fast is the top of the ladder moving down the wall when the base is 15 feet from the wall?

Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 15 feet from the wall.

Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 15 feet from the wall.

Whats is the proof for the long exact sequence in cohomology?

A projectile is fired at an angle of 28 degrees above the horizontal with an initial velocity of 1800 feet per second from an altitude of 1,000 feet above the level ground.  

A) Formulate the vector valued function (in simplified form) for the position of the projectile at any time,t.

B) When and where (in terms of down range distance) does the projectile strike the ground? Be clear and label your results, including units.

C) When does the projectile reach it's maximum height and what is the maximum height? Be clear and label your results including units.  

Please explain answers.  

la place transform of

1. y´´+4y´+3y=0. y(0)=3, y´(0)=1

2. y´´+2y´+y=0. y(0)=1, y´(0)=1

Given v′(t)=2ti+j, find the arc length of the curve v(t) on the interval [−2,3]. You may use technology to approximate your solution to three decimal places.

a) Find the Taylor series for sinh(x) (centered at x=0), for e^x (centered at x=0) and hyperbolic sine and hyperbolic cosine.

b) same as a but cosh(x) instead