95% of the students at Veronica's school ride the bus. There are 500 students at her school. How many students ride the bus?

Complete parts a through c for the given function.

victus00 [196]

Answer:

a. The critcal points are at

$x=0,-5,3$

b. Then, $x = -5$ is a maximum and $x=3$ is a minimum

c. The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

Step-by-step explanation:

(a)

Remember that you need to find the points where

$f'(x)=0$

Therefore you have to solve this equation.

$20x^4 + 40x^3 - 300x^2 = 0$

From that equation you can factor out $20x^2$ and you would get

$20x^2 ( x^2 +2x - 15) = 0$

And from that you would have $20x^2 = 0$ , so $x = 0$ .

And you would also have $x^2 +2x-15 = 0$ .

You can factor that equation as $x^2 +2x -15 = (x+5)(x-3) = 0$

Therefore $x=-5 , x=3$ .

So the critcal points are at

$x=0,-5,3$

b.

Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since

$f''(x) = 80x^3 + 120x^2 -600x\\f''(-5) = 80(-5)^3 + 120(-5)^2 -600(-5) = -4000 < 0\\\\f''(3) = 80(3)^3 + 120(3)^2 -600(3) = 1440 > 0 \\$

Then, $x = -5$ is a maximum and $x=3$ is a minimum

c.

The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

6 0

2 years ago

Read 2 more answers

Sequences:

joja [24]

Answer:

<u>The sequence is</u>

1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, ...

Each term is the sum of the consecutive numbers from 1 to that number.

<u>The nth term is the sum of the first n numbers:</u>

aₙ = 1 + 2 + 3 + ... + n
aₙ = 1/2n(1 + n) (formula for sum of the n terms of arithmetic progression with the first term of 1 and common difference of 1)
aₙ = n(n + 1)/2

1) The number of circles in the nth pile is n(n + 1)/2

2) When n tends to infinity the number of circles tends to infinity

4 0

2 years ago

5. Priya mixes 2..5 cups of water with 1/3 cup or orange juice concentrate. Diego mixes 1 2/3 cups of water with 1/4 cup or oran

Snowcat [4.5K]

Priya needs 13⅓ cups of orange juice

Diego 15 cups

Step-by-step explanation:

......................................................................................................................

Priya

......................................................................................................................

Cup of water = 2½

Cup of orange = ⅓

If 2½ cups of water requires ½ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

2½ : ⅓ = 100 : x

5/2 : 1/3 = 100 : x ------------------Convert ratio sign to division

5/2 ÷⅓ = 100/x

5/2 * 3 = 100/x

15/2 = 100/x ---------------Multiply both sides by x

15/2 * x = 100/x * x

15x/2 = 100 ------------------ Multiply both sides by 2

2 * 15x/2 = 2 * 100

15x = 200 --------------- Divide both sides by 15

x = 200/15

x = 13⅓

So, 13⅓ cups of orange is needed by Priya

......................................................................................................................

Diego

......................................................................................................................

Cup of water = 1⅔

Cup of orange = ¼

If 1⅔ cups of water requires ¼ cup of orange juice concentrate

Then 100 cups of water would require x cup of orange

Representing the above statement mathematically

1⅔:¼ = 100:x

5/3 : ¼ = 100:x

5/3 ÷¼ = 100 ÷ x

5/3 * 4/1 = 100 ÷ x

20/3 =100/x----------------------- Multiply x to both sides

20/3 * x = 100/x * x

20x/3 = 100 ------------------------ Multiply 3 to sides by 3

3 * 20x/3 = 100 * 3

20x = 300 ------------- Divide both sides by 2

20x/20 = 300/20

x = 15

So, 15 cups of orange is needed by Diego

6 0

3 years ago

Question 5

krek1111 [17]

Answer: 3/4 or 75%

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

The first number is 4. A rule is multiply by 2 and then subtract 3. What are the fist 6 numbers in the pattern?

Komok [63]

I believe the answer would be: 4.7.9.11.13.15.17

3 0

3 years ago