MATHEMATICS MIDDLE SCHOOL

The expression below shows the population of butterflies in a forest after 4x years. f(x) = 40(1.04)4x

Which of the following is an equivalent function?
a. f(x) = 40(4.1600)x
b. f(x) = 480(1.04)x
c. f(x) = 40(1.1699)x
d. f(x) = 480(4.1600)x

Answers

Answer 1
Answer: For this case we have the following exponential function:
 
 By power properties we can rewrite this function.
 We have then that the equivalent expression is:
 
 Rewriting we have:
 
 Answer:
 the following is an equivalent function
 c. f (x) = 40 (1.1699) x
Answer 2
Answer: The answer is C

Because: (1.04)^4 = 1.1699

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COLLEGE

2. A damped spring–mass system is given an initial velocity of 50 m/s from the equilibrium position. Find y(t) if M = 4 kg, K = 64 N/m, and C = 40 kg/s.

Answers

Answer:

Step-by-step explanation:

We are given that

Initial velocity

M=40 kg

K=64 N/m

C=40 Kg/s

We have to find the y(t)

Displacement equation for damped motion

Substitute the values

Auxillary equation

When roots are distinct and real

Then,

Substitute the values

Substitute t=0

Then,

Substitute y(0)=0 because when motion does not start then displacement y(t)=0

Differentiate w.r.t t

Substitute the values v(0)=50 and t=0

Substitute the value

Substitute the values

HIGH SCHOOL

lee needed to make drapes the length from the top of the floor to the top of the window.the wall beneath the window head height of 2 2/3 feet in the height of just the window measured 2 3/4 feet. how long do the drapes have to be?

Answers

If I am reading this correctly, you are saying that the window is 2 3/4 feet and the distance between the bottom of the window to the floor is 2 2/3 feet. In this case, you simply add both numbers. The answer is 5 5/12 feet
MIDDLE SCHOOL

Consider the sequence -101, -91, -81, -71, ... Determine an explicit formula for the nth term of the sequence.

Answers

Answer: a n = 10 n − 111

Step-by-step explanation:

Use the formula  a n = a 1 +d ( n − 1 )  to identify the arithmetic sequence.

a n = 10 n − 111

HIGH SCHOOL

Gina wants to ride the waves at flagship pier in Galveston, so she rents a surfboard for $5 per hour plus an initial, or beginning, payment of $20. For how many hours can gina rent a surfboard if she has $90?

Answers

Gina can rent a surfboard for 14 hours if she has $90 if Gina wants to ride the waves at the flagship pier in Galveston, so she rents a surfboard for $5 per hour plus an initial.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Gina wants to ride the waves at the flagship pier in Galveston, so she rents a surfboard for $5 per hour plus an initial, or beginning, payment of $20.

The amount GIna has = $90

Let x be the number of hours GIna can rent a surfboard.

The linear equation can be framed in one variable:

5x = 90 - 20

5x = 70

Divide by 5 on both side:

5x/5 = 70/5

x = 14

Thus, Gina can rent a surfboard for 14 hours if she has $90 if Gina wants to ride the waves at the flagship pier in Galveston, so she rents a surfboard for $5 per hour plus an initial.

Learn more about the linear equation here:

brainly.com/question/11897796

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We know that Gina has $90 to begin with.  But she has to pay $20 just to start surfing, and then $5 an hour.  So the equation would be: ($90-$20)/$5=14.  Therefore, Gina can rent a surfboard for 14 hours.
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