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3 years ago

What is the vertical asymptote for the reciprocal of y=8x-4

Mathematics

1 answer:

rjkz [21]3 years ago

6 0

Answer:

The vertical asymptote for the reciprocal of y=8x-4 is $\frac{1}{2}$

Step-by-step explanation:

Given Equation : $y = 8x-4$

Reciprocal of given equation = $\frac{1}{y}=\frac{1}{8x-4}$

Now to find the vertical asymptote

$\frac{1}{y}=\frac{1}{8x-4}$

Equate denominator to 0

8x-4=0

8x=4

$x=\frac{4}{8}$

$x=\frac{1}{2}$

So, The vertical asymptote is $\frac{1}{2}$

Hence the vertical asymptote for the reciprocal of y=8x-4 is $\frac{1}{2}$

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A cylinder has a 12-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed wi

Tems11 [23]

The volume of the cylinder is the space occupied by the cylinder. The volume of the water in the cylinder is 1583.36266 in³.

<h3>What is the volume of a cylinder?</h3>

The volume of the cylinder is the space occupied by the cylinder. It is calculated with the help of the formula,

$\text{Volume of the cyllinder}= \pi r^2h$

As it is given that the diameter of the cylinder is 12 inches while the height of the cylinder is 15 inches, also, it has a ball of the diameter of 6 inches placed inside the cylinder, therefore, the volume of the water that is inside the cylinder is the difference in the volume of the cylinder and the volume of the spherical ball.

$\text{Volume of the cyllinder}= \pi r^2h = \dfrac{\pi}{4}d^2 h$

Substitute the values,

$\begin{aligned}\text{Volume of the cyllinder}&= \dfrac{\pi}{4}d^2 h\\& = \dfrac{\pi}{4} \times (12^2) \times 15\\ &=1696.46\rm\ in^3\end{aligned}$

Now, the volume of the ball is equal to the volume of the sphere therefore, the volume of the ball can be written as,

$\text{Volume of the sphere} = \dfrac{4}{3}\pi r^3$

$= \dfrac{4}{3}\pi r^3\\\\= \dfrac{4}{3}\times \pi \times (3^3)\\\\= 113.097\rm\ in^3$

Further, the volume of the water that is inside the cylinder can be written as,

The volume of water = Volume of the cylinder - Volume of the sphere

= 1696.46 - 113.097

= 1583.36266 in³

Hence, the volume of the water in the cylinder is 1583.36266 in³.

Learn more about Volume of the Cylinder:

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2 years ago

your patient has a 2500 cc bag of irrigation solution hanging, and 750 cc of fluid has been infused. what percentage of irrigati

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Answer: 30%

Step-by-step explanation:

Given : Patient has a 2500 cc bag of irrigation solution hanging.

Irrigation has been infused = 750cc

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Hence, the percentage of irrigation solution has been infused = 30%

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3 years ago

Arthur bought a life insurance policy at $10.98 per month for a 20 year term. What will he pay over 20 years for the premium?

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12(months) x 20 (years) = 240

10.98 x 240 = 2635.20

So Arthur will pay $2635.20 over 20 years for premium.

I hope this helps :)

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3 years ago

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Choose the answer that validates that the rate of change is constant by showing that the ratios of the two quantities are propor

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Given:

The table of values is

Number of Students : 7 14 21 28

Number of Textbooks : 35 70 105 140

To find:

The rate of change and showing that the ratios of the two quantities are proportional and equivalent to the unit rate.

Solution:

The ratio of number of textbooks to number of students are

$\dfrac{35}{7}=5$

$\dfrac{70}{14}=5$

$\dfrac{105}{21}=5$

$\dfrac{140}{28}=5$

All the ratios of the two quantities are proportional and equivalent to the unit rate.

Let y be the number of textbooks and x be the number of students, then

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Hence the rate of change is constant that is 5.

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3 years ago

I hate math but it doesn't mean i'll fail the year :D

natita [175]

Answer:

the answer is c

Step-by-step explanation:

it just is lol

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