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Anit [1.1K]
3 years ago
10

Consider the following functions.G(x) = 4x2; f(x) = 8x(a)

Mathematics
1 answer:
noname [10]3 years ago
8 0

Answer:

(a) B. G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.

(b) Every function of the form 4x^2+C is an antiderivative of 8x

Step-by-step explanation:

A function <em>F </em>is an antiderivative of the function <em>f</em> if

F'(x)=f(x)

for all x in the domain of <em>f.</em>

(a) If f(x) = 8x, then G(x)=4x^2 is an antiderivative of <em>f </em>because

G'(x)=8x=f(x)

Therefore, G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.

Let F be an antiderivative of f. Then, for each constant C, the function F(x) + C is also an antiderivative of <em>f</em>.

(b) Because

\frac{d}{dx}(4x^2)=8x

then G(x)=4x^2 is an antiderivative of f(x) = 8x. Therefore, every antiderivative of 8x is of the form 4x^2+C for some constant C, and every function of the form 4x^2+C is an antiderivative of 8x.

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Pls say the answer to me​
lozanna [386]

Answer:

Sohan has read more pages and Sonali was more faster

7 0
2 years ago
The middle side of a triangle is half of 3 times the length of the shortest side. The longest side is 2 centimeters longer than
USPshnik [31]

<u>Answer:</u>  

The difference between the longest and shortest sides of the triangle is 4 cm.

<u>Explanation:</u>

<em>Step Number One:</em>

Let the shortest side of the triangle have a length of x.

The middle side of the triangle has a length that is half of 3 times the length of the shortest side. This can be written as 1/2*3x, which equals 3/2x.

The longest side of the triangle has a length that is 2 centimeters longer than the length of the middle side. This can be written as 3/2x + 2.

<em>Step Number Two: </em>

The perimeter of the triangle, which can be found by adding the lengths of all of the sides of the triangle, is 18 centimeters. This can be shown by the following equations:

Shortest Side + Middle Side + Longest Side = Perimeter

x + 3/2x + 3/2x + 2 = 18

4x + 2 = 18

4x = 16

x = 16/4

x = 4

<em>Step Number Three: </em>

This means that the shortest side of the triangle has a length of 4 centimeters and the longest side of the triangle has a length of 8 centimeters.

8 cm - 4 cm = 4 cm

--------------------------------------------------------------------------------------------------------------

Are you still confused? Not feeling confident in your ability to solve these types of problems? Some helpful topics to practice are listed below!

<u>Still confused on ...</u>

Step 1 - Practice equation solving!

Step 2 - Practice perimeter!

Step 3 - Practice addition and subtraction!

Remember: Certain problems may be tricky, but practice makes perfect!

--------------------------------------------------------------------------------------------------------------

<em>Answer by Math_Is_Me_123         </em>

7 0
3 years ago
Answer It With Solution!
Leya [2.2K]

The correct answer is 2.8 liters

Explanation:

The volume of the water in the bottle can be calculated by subtracting 3.5 liters from the volume of water the pail can hold (6.3 liters) because the volume in the bottle is 3.5 liters less than the one in the pail. Below, you can find the process.

volume in the pail - 3.5 liters = volume in the bottle

6.3 liters - 3.5 liters = 2.8 liters

This means the volume of water in the bottle is 2.8 liters. Also, you can double-check this answer by adding the volume in the bottle and the 3.5 liters (2.8 + 3.5 = 6.3).

6 0
3 years ago
How many 16-ounce bottles would be needed to hold the same total amount of water 56 bottles that each holds 20 ounces
snow_lady [41]

70 bottles will hold 16 ounces amount same as 56 bottles hold 20 ounces.

Step-by-step explanation:

Given,

56 bottles hold 20 ounces each.

Total amount 56 bottles hold= 56x20

Total amount hold by 56 bottles= 1120 ounces

Let the number of 16 ounces bottles be = x

Total amount hold by x bottles = 16x

According to the given statement both amounts are same;  

16x=1120\\Dividing\ both\ sides\ by\ 16\\\frac{16x}{16} = \frac{1120}{16} \\x=70

70 bottles will hold 16 ounces amount same as 56 bottles hold 20 ounces.

Keywords: Division, Multiplication

Learn more about division at:

  • brainly.com/question/2035523
  • brainly.com/question/2088305

#LearnwithBrainly

6 0
3 years ago
I NEED HELP PLSS ITS LIKE 200 POINTS
zysi [14]

Answer:

y=-3/2x+3

Step-by-step explanation:

(0,3) and (2,0) tell us that the y intercept is 3 because at x = 0, y = 3.

This leaves the first and last choice only.

We can calculate the slope by 0-3 and 2-0, so -3/2 is the slope

3 0
3 years ago
Read 2 more answers
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