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Nezavi [6.7K]
3 years ago
15

1. A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2+ 450.

Mathematics
1 answer:
bezimeni [28]3 years ago
7 0
1) The ball's position is described by:
s(t) = 4.9t² + 450
We want to find the velocity, which is the 1st-order derivative of the displacement function (I assume this is an introductory calculus class)
s'(t) = v(t) = 9.8t           
We get this by multiplying 4.9 x 2 and reducing the exponent by 1. Now we simply plug 5 in for t.
v(5) = 9.8* 5
v(5) = 49m/s

2) Our cost function is C(x) = x² - 10,000
To find the average rate of change between these units, we use this formula:
( C(101) - C(100) ) ÷1 .
We find the change in C, and divide by the change in x, which is just one. 
C(101) = 101² - 10,000
C(101) = 201

C(100) = 100² - 10,000
C(100= 0

C(101) - C(100) = 201 
Average rate of change in cost is 201 dollars/ unit between the two points. 
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Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y
tatiyna
If you would like to find the value of a in the polynomial, you can do this using the following steps:

(y - 4)(y^2 + 4y + 16) = y^3 + 4y^2 + 16y - 4y^2 - 16y - 64 = y^3 + 4y^2 + ay - 4y^2 - ay - 64

a = 16

The correct result would be 16.
7 0
3 years ago
Read 2 more answers
HELP ME!!!PLEASE ITS DUE TODAY!!
Radda [10]

Answer:

25quarts of grape juice, 50 quarts of water

Step-by-step explanation:

Do the math

6 0
3 years ago
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I am not sure if this is right can someone check it ASAP please
NikAS [45]

Answer:

x=10

Step-by-step explanation:

3(4x-12) = 84

Divide each side by 3

3/3(4x-12) = 84/3

4x-12 =28

Add 12 to each side

4x-12+12 = 28+12

4x= 40

Divide each side by 4

4x/4 = 40/4

x = 10

6 0
3 years ago
Write 2^8 * 8^2 * 4^-4 in the form 2^n
Eva8 [605]

The given expression 2^8 * 8^2 * 4^-4 can be written in the exponential form 2^n as 2^6.

<h3>What are exponential forms?</h3>

The exponential form is a more convenient way to write repetitive multiplication of the same integer by using the base and its exponents.

<u>For example:</u>

If we have a*a*a*a, it can be written in exponential form as:

=a^4

where

  • a is the base, and
  • 4 is the power.

The power in this format reflects the number of times we multiply the base by itself. The exponent is also known as the index or power. 

From the information given:

We can write 2^8 * 8^2 * 4^-4 in form of 2^n as follows:

\mathbf{= 2^8\times (2^3)^2 \times (2^2)^{-4} }

\mathbf{= 2^8\times (2^6) \times (2^{-8}) }

\mathbf{= 2^{8+6+(-8)}}

\mathbf{= 2^{6}}

Therefore, we can conclude that by using the exponential form, the given expression 2^8 * 8^2 * 4^-4 in the form 2^n is 2^6.

Learn more about exponential forms here:

brainly.com/question/8844911

#SPJ1

4 0
2 years ago
L is between M and N. If NL = 5x, LM = 3x, and NL = 15, find x.
Leona [35]

Answer:

x = 5

Step-by-step explanation:

Given that,

NL = 5x, LM = 3x, and NL = 15

L is between M and N.

To find,

The value of x.

Solution,

It is mentioned that, L is between M and N. So,

LM = LN

Put all the values,

3x = 15

⇒ x = 5

So, the value of x is equal to 5.

Reference,

brainly.com/question/19871240

6 0
2 years ago
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