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3 years ago

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Find two consecutive numbers whose cubes differ by 631

1 answer:

yan [13]3 years ago

4 0

Let the two numbers be x and y, in which x is larger than y. From these variables, we can formulate the following equations:

x = y + 1 --> eqn 1
x³ - y³ = 631 --> eqn 2

Since there are two unknowns and two independent equations, this system is solvable. Substitute equation 1 to equation 2, then solve for y.

(y + 1)³ - y³ = 631
Solving for y,
y = 14
x = y + 1 = 14 + 1 = 15

<em>Therefore, the two consecutive numbers are 14 and 15.</em>

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2 years ago

What is the slope of the line that contains the points (-4;2) and (6;-3) ?

tester [92]

Answer:

-1/2

Step-by-step explanation:

First you use to the formula m=y2-y1/x2-x1 and then you get -5/10 or -1/2. (m= slope)

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2 years ago

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Sedaia [141]

Answer:

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Step-by-step explanation:

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2 years ago

Find an equation of the line. Write the equation using function notation.

Gemiola [76]

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Step-by-step explanation:

Given equation of line is:

$4y=x-8$

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

$\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2$

Let m1 be the slope of given line

Then

$m_1 = \frac{1}{4}\\$

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

$m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4$

The slope intercept form of line is given by:

$y = m_2x+b$

Putting the value of slope

$y = -4x+b$

to find the value of b, putting (3,-3) in equation

$-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9$

Putting the value of b in the equation

$y = -4x+9$

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Keywords: Equation of line, slope

Learn more about equation of line at:

#LearnwithBrainly

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2 years ago