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3 years ago

Solve the equation for the indicated variable. Q = 8rs^2, for r

Mathematics

2 answers:

Elis [28]3 years ago

8 0

Answer:

r = Q/(8s^2)

Step-by-step explanation:

Divide by the coefficient of r.

Q/(8s^2) = 8rs^2/(8s^2) = r

Karolina [17]3 years ago

8 0

ANSWER

$\boxed { r = \frac{Q}{8 {s}^{2} } }$

EXPLANATION

The given equation is;

$Q=8rs^2$

We want to solve this equation for r.

This means that we need to isolate r, so that it will be on one side of the equation, while all other variables and constants are also on the other side.

Let us divide both sides of the equation by

$8 {s}^{2}$

to obtain,

$\frac{Q}{8 {s}^{2} } = \frac{8rs^2}{8 {s}^{2} }$

We cancel out the common factors to obtain,

$\frac{Q}{8 {s}^{2} } =r$
Or

$r = \frac{Q}{8 {s}^{2} }$

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What is true of the graph of two lines 3y-8=-5x and 6y=-10x+16

Murljashka [212]

Answer:

Both lines are equal (they are the same)

Step-by-step explanation:

Given

$3y - 8 = -5x$

$6y = -10x + 16$

Required

What is true about graph of both lines

Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check if both lines are either parallel or perpendicular

To do this,

The first thing to do is to calculate the slope of both lines

$3y - 8 = -5x$

Add 8 to both sides

$3y - 8 + 8 = -5x + 8$

$3y = -5x + 8$

Divide both sided by 3

$\frac{3y}{3} = -\frac{5x}{3} + \frac{8}{3}$

$y = -\frac{5x}{3} + \frac{8}{3}$

The slope of the line is the coefficient of x;

$Slope = -\frac{5}{3}$

Solve for the y intercept; Let x = 0

$y = -\frac{5 * 0}{3} + \frac{8}{3}$

$y = 0 + \frac{8}{3}$

$y = \frac{8}{3}$

Solve for the x intercept; Let y = 0

$0 = -\frac{5x}{3} + \frac{8}{3}$

Subtract $\frac{8}{3}$ from both sides

$0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}$

$- \frac{8}{3} = -\frac{5x}{3}$

Subtract both sides by $-\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = x$

$\frac{3}{5} * \frac{8}{3} = x$

$\frac{8}{5} = x$

$x = \frac{8}{5}$

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$6y = -10x + 16$

Divide both sides by 6

$\frac{6y}{6} = -\frac{10x}{6} + \frac{16}{6}$

$y = -\frac{10x}{6} + \frac{16}{6}$

Simplify fractions to lowest term

$y = -\frac{5x}{3} + \frac{8}{3}$

The slope of the line is the coefficient of x;

$Slope = -\frac{5}{3}$

Solve for the y intercept; Let x = 0

$y = -\frac{5 * 0}{3} + \frac{8}{3}$

$y = 0 + \frac{8}{3}$

$y = \frac{8}{3}$

Solve for the x intercept; Let y = 0

$0 = -\frac{5x}{3} + \frac{8}{3}$

Subtract $\frac{8}{3}$ from both sides

$0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}$

$- \frac{8}{3} = -\frac{5x}{3}$

Subtract both sides by $-\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = x$

$\frac{3}{5} * \frac{8}{3} = x$

$\frac{8}{5} = x$

$x = \frac{8}{5}$

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

By comparing the slope, x intercept and y intercept of both lines;

It'll be observed that they have the same slope, x intercept and y intercept

This implies that both lines are equal; in other words, they are the same.

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From these points, we can also see that when the x value is zero, the y value is 14. Therefore the y-intercept is 14.

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Step-by-step explanation:

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