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3 years ago

Nine less than six times a number is -15

Mathematics

1 answer:

Jlenok [28]3 years ago

8 0

Hello!

6 - 9 × y = -15

When "less than" is used you switch the number before it the number after it. While it seems like it would be 9 -6, its actually 6-9

6 - 9 is -3, you can multiply 3 by 5, to get 15. So your answer would be 5

Hope this helps!

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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 y is a function of x :

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

(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 ≤ x ≤ 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

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

7 0

3 years ago

Text

Mariana [72]

Thislink has the answer: brainly.com/question/19701013?answering=true&answeringSource=greatJob%2FquestionPage%2F3

5 0

3 years ago

5-7 Please explain how to do step by step. 85 points ;) max

AleksandrR [38]

5a: To find the slope, you would divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. So coordinates (15,1.5) and (5,0.5). You would subtract 1.5 form 0.5 which gives you neagtive one. (-1) Then subtract 15 from 5 which is -10. (negative ten) -1 divided by -10 is one tenths. 1/10 is your answer to part a.

5b. To find the slope, you would divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. (Not sure what you meant by "interpret".

5c. The phone bill will increase by $0.50 if you talk for 5 extra minutes.

5d. You talked for 30 minutes if the phone bill costs $3.

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6a. I can't really graph it but I'll interpret the slope. Y would basically be 7.5 times as much as x.

6b. I'm kinda stuck on how to get from 7.5 to 1. Sorry. OnO

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7a. Hamburgers sell faster because there are 60 minutes in a hour. If 2.5 wraps are sold in one minute. Then there would be 150 wraps sold in 60 minutes which is also one hour. Hamburgers sell ten more than wraps per hour.

7b. The equation for wraps is: y=2.5x

The equation for hamburgers is y=2.6667x

Goodnight and hope it helps.~ RIP my sleep...

8 0

3 years ago

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The monthly payment on a $71,000 loan at 12% annual interest is $785.26. What is the balance of principal after the first monthl

fgiga [73]

Answer:

After your payment

A = 71,000 - 785.26 = 70,214.74

You also have an interest payment of

71000 * .12 / 12 = 710

The total owed is

70,214.74 + 710 = 70,924.74

6 0

3 years ago

Read 2 more answers

Please answer, its a test question and i need a good grade on it, giving brainliest

V125BC [204]

Answer:

the answer Is D yiur welcome :

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3 years ago