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4 years ago

7

An electric motor pumps water into a pool at a rate of 500 liters per hour. After a tune up, its rate increases by x liters per

hour. If the motor now takes 3 hours to pump 1800 liters, in which equation does x represent the increase in speed after the tune up?

1 answer:

Alex73 [517]4 years ago

4 0

Answer: 3(500+x)=1800

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keisha drove 380 miles using 14 gallond of gas. At this rate, how many gallons of gas would she need to drive 418 miles?

pychu [463]

14gallons=380miles

14/380=<span>0.03684210526gallons/mile
</span>
418*<span>0.03684210526=15.4gallons
</span>
or you could cross multiply

14gallons=380miles
x gallons=418miles

$\frac{14}{380} = \frac{x}{418}$

380x=5852
divide both sides by 380
x=15.4 gallons

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3 years ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that <em>y</em> is a function of <em>x</em> :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ <em>x</em> ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$

We can simplify this further to

$\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}$

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3 years ago

The circumference of a circular tabletop is 226. 08 inches. What is the area, in square inches, of the tabletop? *

Delicious77 [7]

Answer:

40,143.4 square inches

Step-by-step explanation:

c= 226.08

r= 113.04

area = Pi *r^2

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2 years ago

In ΔNOP, OP = 7, PN = 13, and NO = 19. Which statement about the angles of ΔNOP must be true?

zmey [24]

The angles must be acute and all the measured angles must be different.

<h3>What is a triangle?</h3>

This a shape with 3 sides and angke

If in ΔNOP, OP = 7, PN = 13, and NO = 19, then the measure of the angles must be different as well;

Hence the statement that must be true about the angles is that the angles must be acute and all the measured angles must be different. The given triangle must also be a scalene triangle

Learn more on triangles here: brainly.com/question/2938476

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3 years ago

In 14b, is 14 the variable, coefficient, term, or product?

Kobotan [32]

Answer:

Pretty sure its coefficient

Step-by-step explanation:

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3 years ago