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Zolol [24]
3 years ago
6

Write a function describing the relationship of the given variables.

Mathematics
2 answers:
zhuklara [117]3 years ago
8 0

Answer:

The function is A = 10√r

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

  variables that can be expressed by an equation in which one

  variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

 constant of variation

* Now lets solve the problem

# A is varies directly with the square root of r

- Change the statement above to a mathematical relation

∴ A ∝ √r

- Chang the relation to a function by using a constant k

∴ A = k√r

- To find the value of the constant of variation k substitute A and r

 by the given values

∵ r = 16 when A = 40

∵ A = k√r

∴ 40 = k√16 ⇒ simplify the square root

∴ 40 = 4k ⇒ divide both sides by 4 to find the value of k

∴ 10 = k

- The value of the constant of variation is 10

∴ The function describing the relationship of A and r is A = 10√r

Anni [7]3 years ago
5 0

Answer:

A = 10\sqrt{r}

Step-by-step explanation:

Given A varies directly with the square root of r then the equation relating them is

A = k\sqrt{r} ← k is the constant of variation

To find k use the condition r = 16 , A = 40

k = \frac{A}{\sqrt{r} } = \frac{40}{\sqrt{16} } = \frac{40}{4} = 10

A = 10\sqrt{r} ← equation of variation

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Below the function h (x) ang g (x) are graphes. At which values of x is true that h (x) > g (x)? Select all that apply.
rodikova [14]

Answer:

25

Step-by-step explanation:

5 0
2 years ago
Find values a and b that satisfy a∙〈5,-4,0〉+b∙〈2,2,-3〉=〈11,-16,-6〉.
WARRIOR [948]

The right hand side of the equation is 〈11 , -16 , 6〉

The values of a and b are a = 3 , b = -2

Step-by-step explanation:

If n . <a , b> + m . <c , d> = < x , y>, then

  • na + mc = x
  • nb + md = y

∵ a  ∙〈5 , -4 , 0〉 + b ∙ 〈2 , 2 , -3〉 = 〈11 , -16 , 6〉

- By using the rule above

∴ a(5) + b(2) = 11 ⇒ (1)

∴ a(-4) + b(2) = -16 ⇒ (2)

∴ a(0) + b(-3) = 6 ⇒ (3)

Use equation (3) to find the value of b

∵ a(0) + b(-3) = 6

∴ 0 - 3b = 6

∴ -3b = 6

- Divide both sides by -3

∴ b = -2

Substitute b in equation (1) or equation (2) to find a

∵ a(5) + b(-2) = 11

∴ 5a - 2b = 11

∵ b = 2

∴ 5a - 2(2) = 11

∴ 5a - 4 = 11

- Add 4 to both sides

∴ 5a = 15

- Divide both sides by 5

∴ a = 3

To check your answer substitute a and b in equation (2)

∵ a(-4) + b(2) = -16

∴ -4a + 2b = -16

∵ a = 3 , b = -2

∵ The left hand side is -4a + 2b = -4(3) + 2(-2) = -12 - 4 = -16

∵ The right hand side is -16

∴ L.H.S = R.H.S

∴ The values of a and b are 3 , -2

The values of a and b are a = 3 , b = -2

Learn more:

You can learn more about the equations in brainly.com/question/11306893

#LearnwithBrainly

8 0
3 years ago
Determine the constant of variation for the direct variation given.
ohaa [14]

Answer:

B. 5

Step-by-step explanation:

We have been given that R varies directly with S. When S is 16, R is 80. We are asked to find constant of variation.

We know that two directly proportional quantities are in form y=kx, where,

k = Constant of variation.

Upon substituting our given values, we will get:

R=k*S

80=k*16

\frac{80}{16}=\frac{k*16}{16}

5=k

Therefore, the constant of variation is 5 and option B is the correct choice.

6 0
3 years ago
Select each equation which is equivalent to 60% of 25.
loris [4]

Answer:

0.6 x 25 = x

Step-by-step explanation:

60% of 25

= 60/100 x 25

= 0.6 x 25

= 15

Though the question states as in a "select-all question," Only answer 0.6 x 25 = x will be correct.

8 0
3 years ago
Read 2 more answers
72 students are out sick There are 600 students total what percent of the student population is ill?
g100num [7]

Answer:

12 percent of the students are ill

Step-by-step explanation:

To find the percent, you want to find the fraction 72/600. If you get your calculator adn divide the fraction, you get 0.12 which is 12 percent. Hope this helps!

5 0
3 years ago
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