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CaHeK987 [17]
2 years ago
13

If mpho is the 50th fastest and slowest runner in her school,how many students are there in her school

Mathematics
1 answer:
romanna [79]2 years ago
4 0

Answer:

Step-by-step explanation:

i need points lol

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Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =
sashaice [31]
Let R be the solid. Then the volume is

\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta

which follows from the facts that

\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta
(by computing the Jacobian)

and

z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8
(we take the positive solution, since it's clear that R lies above the x-y plane)
r^2+z^2=72\implies z=\pm\sqrt{72-r^2}
(again, taking the positive root for the same reason)
z=r^2\implies 8=r^2\implies r=\sqrt8

\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta
=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr
=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr
=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr
=\dfrac{32(27\sqrt2-35)\pi}3
7 0
3 years ago
What is the remainder when x 3 − 7x + 5 is divided by x + 3 ?
klemol [59]

Step-by-step explanation:

check the image that is your answer

5 0
3 years ago
Hello, I'm new! I need help
melamori03 [73]

The interest in the first month is given as $ 97.1. The principal balance in the second question is $15,030.02

<h3>How to solve for the interest in the first month</h3>

1. We have to solve for the cost of the car

This would be = 19,725*(1.0475)

= 20,661.9375

There is a Down payment = 2,175

balance would be 20661.9375-2,175 = 18,486.94

average rating interest of new car = 6.30%

So the interest accrued in first month = 18,486.94x0.063/12 = $ 97.1

2. cost = 15867

sales tax = 5.25%

10 percent down payment

5.25/100 = 0.0525

cost of car = 15867 + (15867 * 0.0525)

= 16700 dollars

10% of 16700 dollars

= 1670 dollars

principal balance = 16700 - 1670

= $15,030.02

Read more on interest rate here

brainly.com/question/25793394

7 0
1 year ago
Help and explain explain !!!!!!!!!!
tigry1 [53]

Answer:

x=-1\text{ or }x=11

Step-by-step explanation:

For a=|b|, we have two cases:

\begin{cases}a=b,\\a=-b\end{cases}

Therefore, for 18=|15-3x|, we have the following cases:

\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}

Solving, we have:

\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}.

Therefore,

\implies \boxed{x=-1\text{ or }x=11}

3 0
2 years ago
Can u pls help and put them by the answer ​
tiny-mole [99]

Answer:

Step-by-step explanation:

to find range find the lower number and subtract from the biggest number..

so the the bigger number is 54 and the lower number is 3 so you would have to do is 54-3=51

6 0
3 years ago
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