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3 years ago

Sum of n natural numbers is 5n^2 + 4n , find the 8th term

Mathematics

2 answers:

zalisa [80]3 years ago

5 0

Answer:

The 8th term is 79

Step-by-step explanation:

HOPE THIS HELPS UWU ✨

scZoUnD [109]3 years ago

5 0

Answer:

....

Step-by-step explanation:

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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

Okay last one of these, 15 points xox

Vanyuwa [196]

Answer:

<u>13.2 centimeters</u>

Step-by-step explanation:

<u>Finding the missing side</u>

(?)² + (9)² = (16)²
?² + 81 = 256
?² = 175
? = √175
? = <u>13.2 centimeters</u>

7 0

1 year ago

Read 2 more answers

PLEASE HELP! all u have to do is determine whether it is positive or negative!!!

Sever21 [200]

Answer:

positive

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Please help, this chapter was on derivatives...

Usimov [2.4K]

<h3>Answer: ds/dt = 11</h3>

================================================

Work Shown:

Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)

s^2 = x^2+y^2

s^2 = 15^2+20^2

s^2 = 225+400

s^2 = 625

s = sqrt(625)

s = 25

-----------

Now we can apply the derivative to both sides to get the following. Don't forget to use the chain rule.

s^2 = x^2 + y^2

d/dt[s^2] = d/dt[x^2 + y^2]

d/dt[s^2] = d/dt[x^2] + d/dt[y^2]

2s*ds/dt = 2x*dx/dt + 2y*dy/dt

2(25)*ds/dt = 2(15)*5 + 2(20)*(10)

50*ds/dt = 150 + 400

50*ds/dt = 550

ds/dt = 550/50

ds/dt = 11

-----------

Side note: The information t = 40 is never used. It's just extra info.

8 0

2 years ago

Which of the follwing is correxr

agasfer [191]

Answer:

the equation has infinitely amny solutions

3 0

2 years ago

Sum of n natural numbers is 5n^2 + 4n , find the 8th term​

Sum of n natural numbers is 5n^2 + 4n , find the 8th term