What is the range of the data?

5. Write an equation for the line representing each of the following situations.

gregori [183]

1. Y = 10x
2. Y = 100 + 30x
3. Y = 50 + 1x
5. Y = 15 + .12x

5 0

3 years ago

Read 2 more answers

Find the function of which is the solution of 36y"-48y'-48y=0 with initial conditions y1(0)=1. y1'(0)=0

lilavasa [31]

Answer:

$y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }$

Step-by-step explanation:

Let, $D=\frac{d}{dx}$

Now, us simplify the given differential equation and write it in terms of D,

$36y''-48y'-48y=0$

or, $3y''-4y'-4y=0$

or, $(3D^2-4D-4)y=0$

We have our auxiliary equation:

$3D^2-4D-4=0$

or, $(3D+2)(D-2)=0$

or, $D=2, - \frac{2}{3}$

Therefore our solution is,

$y=Ae^{2x}+Be^{- \frac{2}{3}x}$

and, $y'=2Ae^{2x}-\frac{2}{3}Be^{\frac{2}{3}x }$

Applying the boundary conditions, we get,

$A+B=1$

$2A-\frac{2}{3}B=0$

Solving them gives us,

$A=\frac{1}{4} ,B=\frac{3}{4}$

Hence,

$y=\frac{1}{4} e^{2x}+\frac{3}{4} e^{-\frac{2}{3}x }$

4 0

3 years ago

Given the function f(x) = 2x, find the value of f−1(32). (1 point) f−1(32) = 0 f−1(32) = 1 f−1(32) = 5 f−1(32) = 16

lara31 [8.8K]

The value of the inverse function at x = 32 will be 16. Then the correct option is D.

<h3>What is a function?</h3>

A statement, principle, or policy that creates the link between two variables is known as a function.

The function is given below.

f(x) = 2x

Then the inverse function of the f(x) will be

2f⁻¹(x) = x

f⁻¹(x) = x / 2

Then the value of the inverse function at x = 32 will be

f⁻¹(32) = 32 / 2

f⁻¹(x) = 16

Then the correct option is D.

More about the function link is given below.

brainly.com/question/5245372

#SPJ1

3 0

2 years ago

In a classroom of students 3 out of 5 students are boys. If the total amount of students is 35 how many students are boys. Pleas

Bumek [7]

Answer:

there is 21 boys

Step-by-step explanation:

hope that helps

6 0

2 years ago

Please help with question 2, I’m too tired to think right now, and it’s for my little sister and it’s due tomorrow! Ignore the n

marishachu [46]

Answer:

2000 L

Step-by-step explanation:

There are 1250 L of water in a tank at present. If the tank is 0.625 full, what is the capacity of the tank?

The simple solution is:

1250 L ÷ 0.625 = 2000 L

The algebraic solution is:

Let c equal the capacity of the tank.

Therefore, c × 0.625 = 1250.

Divide both sides by 0.625:

c × 0.625 ÷ 0.625 = 1250 ÷ 0.625

And simplify:

c = 1250 ÷ 0.625

c = 2000

5 0

3 years ago