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3 years ago

Evaluate the piecewise function below for f(1):

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

3 0

We need to find f(1)

f(1) means x=1

Now we look at the three inequalities and choose the one where x=1 satisfies

x<=-1 , -1<x<1 and x>=1

x=1 satisfies the inequality x>=1

so we use the third function to find f(1)

$f(x) = 2x^2 + 3$

We plug in 1 for x and find f(1)

$f(1) = 2(1)^2 + 3$ = 2 + 3 = 5

f(1) = 5

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The area of a rectangle varies jointly as its length and width. Find the equation of joint variation if A = 60ft², l = 15ft, and

MaRussiya [10]

Answer: The length is 6 feet and the width is 10 feet.

Step-by-step explanation: The question has specified the area as 60 (square feet) and the length and width are yet unknown. However we know that the length is 4 feet less than the width. What this means is that, if the width is W, then the length is W - 4.

We can now write an equation for the area of the rectangle as follows;

Area = L x W

60 = (W - 4) x W

60 = W^2 - 4W

If we rearrange all terms on one side of the equation, we now have

W^2 - 4W - 60 = 0

This is a quadratic equation and by factorizing, we now have

(W + 6) (W - 10) = 0

Hence,

Either W + 6 = 0 and then W = -6

Or W - 10 = 0 and then W = 10

We know that the side of the rectangle cannot be a negative value, so we go with W = 10.

Having calculated W as 10, the length now becomes

L = W - 4

L = 10 - 4

L = 6

Therefore, length = 6 feet and width = 10 feet

5 0

2 years ago

Read 2 more answers

Let f(x)=e^x and G(x)=x+6. What are the domain and range of g(f(x))?

Lena [83]

Answer:

Domain and Range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively

Step-by-step explanation:

We have the functions, f(x) = eˣ and g(x) = x+6

So, their composition will be g(f(x)).

Then, g(f(x)) = g(eˣ) = eˣ+6

Thus, g(f(x)) = eˣ+6.

Since the domain and range of f(x) = eˣ are all real numbers and positive real numbers respectively.

Moreover, the function g(f(x)) = eˣ+6 is the function f(x) translated up by 6 units.

Hence, the domain and range of g(f(x)) are 'All real numbers' and {y | y>6 } respectively.

3 0

2 years ago

A certain chain of ice cream stores sells 28 different flavors, and a customer can order a single-, double- , or triple-scoop co

astra-53 [7]

Think about the cones with only 1 scoop of ice cream. Isn't it clear that there are 28 of those?
Now think about the two scoop cones. You have 28 choices for the first scoop and 28 choices for the second scoop.
So the number of possibilities is 28(28).
Now think of the 3 scoop cones.
You have 28 choices for the first scoop, 28 choices for the second scoop, and 28 choices for the third scoop or 28(28)(28) possibilities.
Add them all together and you have the total.

So it will be like this:
28^3+28^2+28

I hope my answer helped you.

6 0

3 years ago

You are standing 6 feet away from the stage and your friend is standing 7 feet away from the stage. You are standing on a platfo

coldgirl [10]

Answer:

The distance from your eyes to the stage is 8.85 ft

Step-by-step explanation:

Your distance to the stage is 6 feet

Your eyes are 6.5 feet tall

You need to find the distance of your eyes towards the stage.

This situation can be modeled using a rectangle triangle, where the adjacent side x is the horizontal distance to the stage and the opposite side h is the vertical distance of your eyes to the stage.

Observe the attached image.

Then, we look for the distance z from your eyes to the stage. This distance is the hypotenuse of the right triangle.

So, using the Pythagorean theorem we have:

$z ^ 2 = h ^ 2 + x ^ 2\\\\z = \sqrt{h^2 +x^2}$