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4 years ago

Math help, I'm stuck with my homework and I want to get it done.

Mathematics

1 answer:

ivann1987 [24]4 years ago

4 0

Answer:

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

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 7 is in this form with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-4}$ = $\frac{1}{4}$

Hence the value of m = $\frac{1}{4}$

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 7x6, y

IgorC [24]

Answer:

The volume is $\frac{490\pi}{39}$ cubic units.

Step-by-step explanation:

The given curve is

$y=7x^6$

The given line is

$y=7x$

Equate both the functions to find the intersection point of both line and curve.

$7x^6=7x$

$7x^6-7x=0$

$7x(x^5-1)=0$

$7x=0\rightarrow x=0$

$x^5-1=0\rightarrow x=1$

According to washer method:

$V=\pi \int_{a}^{b}[f(x)^2-g(x)^2]dx$

Using washer method, where a=0 and b=1, we get

$V=\pi \int_{0}^{1}[(7x)^2-(7x^6)^2]dx$

$V=\pi \int_{0}^{1}[49x^2-49x^{12}]dx$

$V=49\pi \int_{0}^{1}[x^2-x^{12}]dx$

$V=49\pi [\frac{x^3}{3}-\frac{x^{13}}{13}]_0^1$

$V=49\pi [\frac{1^3}{3}-\frac{1^{13}}{13}-(0-0)]$

$V=49\pi [\frac{1}{3}-\frac{1}{13}]$

$V=49\pi (\frac{13-3}{39})$

$V=49\pi (\frac{10}{39})$

$V=\frac{490\pi}{39}$

Therefore the volume is $\frac{490\pi}{39}$ cubic units.

5 0

3 years ago

Emma, Gabriel, Jorge, and Makayla each drew a different triangle. Find clues to classify each persons triangle as isosceles, equ

Allushta [10]

Emma: Isosceles Gabriel: Scalene Jorge: idk Makayla: Equilateral

6 0

3 years ago

Read 2 more answers

Solve the following system by the elimination method. Check the solution. 5x−5 = −7y, 3x+2y = - 8

torisob [31]

5x-5=-7y
3x+2y=-8

First, you need to rearrange the first equation so it is in the same format as the second one.
5x-5=-7y
Add 5 to both sides
5x-5+5=-7y+5
Add 7y to both sides
5x+7y=-7y+7y+5
So you have 5x+7y=5

Now you need to multiply that equation by 3
3(5x+7y=5)
15x+21y=15

Multiply the second equation by -5
-5(3x+2y=-8)
-15x-10y=40

Now add them together
15x+21y=15
+(-15x-10y=40)
---------------------
11y=55
y=5

Now plug y=5 into one of the original equations and solve for x.
3x+2(5)=-8
3x+10=-8
3x=-8-10
3x=-18
x=-6

To check the solution plug them both into the other equation:
5(-6)-5=-7(5)
-30-5=-35
-35=-35

It checks.

Hope that helps.

4 0

3 years ago

60 km<br> 32 km<br> What is the length of the hypotenuse?

Anni [7]

The length of the hypotenuse is 68 km.

6 0

3 years ago

Which graph represents a function?

Sliva [168]

Answer:

Step-by-step explanation:

A function is where each input (here, the input is x) corresponds to exactly one output (here, the output is y). In other words, if a function is graphed, we should be able to draw a vertical line through every single part of it that will intersect it at only one place.

Let's examine each choice.

(A) Well, if we draw a vertical line through the graph, it will obviously intersect the entire line - which is an infinite number of intersections, so this is not a function.

(B) If we draw a vertical line through the portion of the graph that lies near the positive x-axis, we note that it will intersect twice, so this is not a function.

(C) If we strategically draw a vertical line through the y-axis, we see it will intersect two times, so this is not a function.

(D) We can draw a vertical line through any portion of this graph and know that it will only intersect once.

Therefore, the answer is D.

5 0

3 years ago

Read 2 more answers