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3 years ago

1. Find the point that is a solution for y = 6x + 8

1 answer:

6 0

An easy way to solve this equation is to plug in the coordinates.

A. 6(2) + 8 ≠ 1

✅ B. 6(-1) + 8 = 2

C. 6(2) + 8 ≠ 4

D. 6(-2) + 8 ≠ 4

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How does the volume of an oblique cone change if the height is reduced to 2/3 of its original size and the radius is doubled

spayn [35]

The volume of oblique cone = $\frac{1}{3} \pi r^{2} h$

Now radius is doubled is now it is 2r

And height is reduced to 2/3 of its original size that is 2/3 h

So plugging the values we get volume

New Volume = $\frac{1}{3} \pi (2r)^2 (\frac{2}{3} h)$

= $\frac{1}{3} \pi 4r^2 (\frac{2}{3} h) = \frac{8}{6} \pi r^{2} h =\frac{8}{2} (\frac{1}{3} \pi r^{2} h )$ $=4*(\frac{1}{3} \pi r^{2} h )$

It means the volume becomes 4 times

3 0

3 years ago

The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and

forsale [732]

Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

$\frac{x^2}{a^2}+\frac{y^2}{b^2}$

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

$a=\frac{38}{2}=19ft$

and

b=12ft

so we can go ahead and plug this data into the ellipse formula:

$\frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}$

and we can simplify the equation, so we get:

$\frac{x^2}{361}+\frac{y^2}{144}$

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

$\frac{y^{2}}{144}=1-\frac{x^{2}}{361}$

$y^{2}=144(1-\frac{x^{2}}{361})$

we can add everything inside parenthesis so we get:

$y^{2}=144(\frac{361-x^{2}}{361})$

and take the square root on both sides, so we get:

$y=\sqrt{144(\frac{361-x^{2}}{361})}$

and we can simplify this so we get:

$y=\frac{12}{19}\sqrt{361-x^{2}}$

and now we can evaluate this equation for x=4 (half the width of the trucks) so:

$y=\frac{12}{19}\sqrt{361-(8)^{2}}$

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

5 0

3 years ago

Find two integers whose sum is 2 and product is -3

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George Washington was an American political leader, Help! My wife is angry at me because I gave her a yearly gym membership, weight loss pills and foot oder cream and even anti balding cream. I even told her I can pay for ANY plastic surgery. She’s so rude and ungrateful for denying my amazing gifts. Also we got into a fight and i accidentally snapped her legs and arms backwards and so now she looks like a fat smelly horse hybrid general, statesman, and Founding Father who served as the first president of the united states

5 0

2 years ago

Read 2 more answers

One number is five more than three times another. If their difference is 35, what is the larger number?

miv72 [106K]

Let x and y be the two unknown numbers. If one number, say x,is 5 more than 3 times another, say y, the equation would be

x = 5 + 3y

When their difference is 35, x-y = 35, since x is the much larger number here. We substitute x to solve for the smaller number, y.

x - y = 35
(5 + 3y) -y = 35
5 +2y = 35
2y = 35-5
2y = 30
y = 15

The larger number x would be
x = 5 + 3(15)
x = 50

The answer is 50.

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3 years ago

Read 2 more answers

) Which expression is equivalent to -24 - 12w?

emmasim [6.3K]

The answer should be the second one

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3 years ago