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2 years ago

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Y varies directly as x. Y=42 when x=6. Find the value of y when x =15.

1 answer:

pentagon [3]2 years ago

4 0

Answer:

y=120

Step-by-step explanation:

Y varies directly as x is written as

$y \alpha x$

introducing a constant

y=kx

<em>from</em><em> </em><em>the</em><em> </em><em>ques</em><em>tion</em><em>,</em><em> </em><em>whe</em><em>n</em><em> </em><em>y</em><em>=</em><em>4</em><em>8</em><em>,</em><em> </em><em> </em><em>x</em><em>=</em><em>6</em>

<em>sub</em><em>stitute</em><em> </em><em>it</em><em> </em><em>in</em><em> </em><em>the</em><em> </em><em>form</em><em>ula</em>

<em>4</em><em>8</em><em>=</em><em>6</em><em>k</em>

<em>making</em><em> </em><em>k</em><em> </em><em>the</em><em> subject</em><em> </em><em>by </em><em>divi</em><em>ding</em><em> </em><em>thr</em><em>ough</em><em> </em><em>by</em><em> </em><em>6</em>

<em> $\frac{48}{6} = \frac{6k}{6}$ </em>

k=48/6

k=8

<em>put</em><em> </em><em>the</em><em> </em><em>va</em><em>lue</em><em> </em><em>of</em><em> </em><em>k</em><em> </em><em>in</em><em> </em><em>the </em><em>expression</em><em> </em><em>y</em><em>=</em><em>kx</em>

<em>y</em><em>=</em><em>8</em><em>x</em>

from the question,the value of y when x=15 is given by

y=8×15

y=120.

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The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use

k0ka [10]

Answer:

$2489ft^{2}$

Step-by-step explanation:

The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.

<h3>Area of each triangle:</h3>

From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:

$A_{t}=\frac{b.h}{2}=\frac{(20ft)(25ft)}{2}=250ft^{2}$

<h3>Area of each circular section:</h3>

From the figure, we know that $\alpha =2.21 radians$ and the radius is $R=30ft$ . So, the are would be calculated with this formula:

$A_{cs}=\frac{\pi R^{2}\alpha}{360\°}$

Replacing all values:

$A_{cs}=\frac{(3.14)(30ft)^{2}(2.21radians)}{6.28radians}$

Remember that $360\°=6.28radians$

Therefore, $A_{cs}=994.5ft^{2}$

Now, the total are of the figure is:

$A_{total}=2A_{t}+2A{cs}=2(250ft^{2} )+2(994.5ft^{2})\\A_{total}=500ft^{2} + 1989ft^{2}=2489ft^{2}$

Therefore the area of the symmetrical pool is $2489ft^{2}$

3 0

2 years ago

Rearrange the steps to solve for the following equation: 2(x-5)=8

OlgaM077 [116]

Answer:

$x=9$

Step-by-step explanation:

$2(x-5)=8$ | Given

$(2x-10)=8$ | Distribute the 2 inside the parentheses

$2x=8+10$ | Add 10 to both sides

$2x=18$ | Add. <em>Optional; not included in your question.</em>

<em /> $x=9$ <em> </em>| Divide by 2 on both sides.

<em />

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2 years ago

A can holds 4 golf balls. The diameter of each golf ball is 5 cm. What is the volume of the empty space inside the can?

forsale [732]

Answer:

Volume of the empty space in the can is 327.05 $cm^3$

Step-by-step explanation:

Given:

Number of golf ball the can holds = 4

Diameter of the golf ball = 5 cm

To Find:

Volume of the empty space in the can = ?

Solution:

Step 1: Finding the volume of one golf ball

Ball is shape of the sphere

So lets use the volume of the sphere formula

Volume of the golf ball = $\frac{4}{3}\pi r^3$

Radius = $\frac{5}{2}$ = 2.5 cm

Substituting the values

Volume of the golf ball

= $\frac{4}{3} \pi \times(2.5)^3$

= $\frac{4}{3} \pi \times (15.625)$

= $\frac{4}{3} \times 49.06$

= $\frac{196.24}{3}$

= 65.41

Step 2: Finding the volume of empty space of the can

volume of empty space of the can = volume of 5 golf ball

= 5 X 65.41

= 327.05

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3 years ago

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FinnZ [79.3K]

Answer:

All three sides of the triangle are different lengths.

Step-by-step explanation:

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3 years ago

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Nat2105 [25]

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3 years ago