All categories

3 years ago

If y varies directly as the square if x. If y=27 when x=3, find x when y=81?

Mathematics

1 answer:

Dima020 [189]3 years ago

5 0

Answer:

x = 3 $\sqrt{3}$

Step-by-step explanation:

Given y varies directly as x², then the equation relating them is

y = kx² ← k is the constant of variation

To find k use the condition y = 27 when x = 3 , then

27 = k × 3² = 9k ( divide both sides by 9 )

3 = k

y = 3x² ← equation of variation

When y = 81, then

81 = 3x² ( divide both sides by 3 )

27 = x² ( take the square root of both sides )

x = $\sqrt{27}$ = $\sqrt{9(3)}$ = 3 $\sqrt{3}$

You might be interested in

13. Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (u, P, o) for the indica

liraira [26]

Answer:

Null Hypothesis, $H_0$ : P = 4.1%

Alternate Hypothesis, $H_A$ : P > 4.1%

Step-by-step explanation:

We are given that a psychologist claims that more than 4.1% of the population suffers from professional problems due to extreme shyness.

Let p = true percentage of the population that suffers from extreme shyness.

So, Null Hypothesis, $H_0$ : P = 4.1%

Alternate Hypothesis, $H_A$ : P > 4.1%

Here, null hypothesis states that % of the population who suffers from professional problems due to extreme shyness is equal to 4.1%.

On the other hand, alternate hypothesis states that more than 4.1% of the population suffers from professional problems due to extreme shyness.

So, the above hypothesis would be appropriate for conducting the test.

8 0

4 years ago

Question 16 need help thank you

Mariulka [41]

You need to find the surface area of the rectangular prism and the triangular prism and add them up to find the answer.

Rectangular prism:
SA=2(lw+wh+lh)
SA=2(437.5+406.25+1137.5)
SA=2(1981.25)
SA=3962.5 sq cm

Triangular prism:
SA=2(1/2bh)+3(slanted height)*w
SA=2(235.75)+3(293.75)
SA=471.5+881.75
SA=1352.75 sq cm

3962.5+1352.75=5315.25 sq cm

5 0

4 years ago

Find the equation to the line below .

andrew-mc [135]

Answer:

y = 4x + 1

Step-by-step explanation:

y = mx + b

The line goes thru (0, 1) and (1, 5)

The slope = m = (5 - 1)/ 1 - 0) = 4/1 = 4

The y-intercept is (0, 1), so b = 1

y = 4x + 1 is the equation of the line

8 0

3 years ago

Least to greatest 4 1/4, 4 1/8, 5 10/11, 4 2/12

andrezito [222]

Firs you need to convert the mixed numbers to decimals (left to right): 4.25; 4.125; 5.909091; 4.166667.. Then you organize them from least to greatest: the 4 as the whole number comes first, adding from the greater place values later; and then the 5 as it's the biggest number.. which makes the order:: 4.125, 4.166667,4.25, 5.909091.. (sorry if explained the way of how kind of bad.. I'm not very good at explanations, but I know my math..)

6 0

3 years ago

The gcf of 54 and 84 is what

Vaselesa [24]

Greatest Common Factors are the greatest numbers that go into a given group of numbers. The GCF of 54 and 84 is 6.

4 0

3 years ago