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3 years ago

What is 5.989 in scientific notation

Mathematics

1 answer:

Vika [28.1K]3 years ago

6 0

Answer:

5.989x10 with the power of 0

Step-by-step explanation:

Can I have crown?

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Joan puts $400 into a bank account. Each year the account earns 7% simple interest. How much interest will be earned in four yea

Sladkaya [172]

$60

400 ÷ 7 = 57. 1428571429

Since that's not an option we estimate it. The closest number is $60 so, there's your answer!

I hope this helps! sorry if it's wrong :(

~ Kana ^^

3 0

3 years ago

A 51 foot piece of wire is cut into 3 sections so that the first section is three times as long as the second section and the se

kirill [66]

Answer:

The length of the longest section x = 36 ft

Step-by-step explanation:

Total length of the wire = 51 ft

Let first section of wire = x

Second section of wire = y

Third section of wire = z

According to given data

x = 3 y & y = 4 z

Total length of the wire = x + y + z = 51

$y + 3 y + \frac{y}{4} = 51$

$\frac{17}{4} y = 51$

y = 12

x = 3 × 12 = 36

$z = \frac{y}{4} = \frac{12}{4} = 3$

Therefore the length of the longest section x = 36 ft

8 0

3 years ago

Read 2 more answers

Victor bought a new soccer ball. The original price was $29.99, but the ball was on sale for 15%

enot [183]

Step-by-step explanation:

100-15=85%

85% × 29.99

=$25.49

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3 years ago

Problem 4: Let F = (2z + 2)k be the flow field. Answer the following to verify the divergence theorem: a) Use definition to find

Viktor [21]

Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk $x^2+y^2\le3$ , I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere $x^2+y^2+z^2=3$ .

a. Let $C$ denote the hemispherical <u>c</u>ap $z=\sqrt{3-x^2-y^2}$ , parameterized by

$\vec r(u,v)=\sqrt3\cos u\sin v\,\vec\imath+\sqrt3\sin u\sin v\,\vec\jmath+\sqrt3\cos v\,\vec k$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to $C$ to be

$\vec r_v\times\vec r_u=3\cos u\sin^2v\,\vec\imath+3\sin u\sin^2v\,\vec\jmath+3\sin v\cos v\,\vec k$

Then the upward flux of $\vec F=(2z+2)\,\vec k$ through $C$ is

$\displaystyle\iint_C\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^{\pi/2}((2\sqrt3\cos v+2)\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm dv\,\mathrm du$

$\displaystyle=3\int_0^{2\pi}\int_0^{\pi/2}\sin2v(\sqrt3\cos v+1)\,\mathrm dv\,\mathrm du$

$=\boxed{2(3+2\sqrt3)\pi}$

b. Let $D$ be the disk that closes off the hemisphere $C$ , parameterized by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le\sqrt3$ and $0\le v\le2\pi$ . Take the normal to $D$ to be

$\vec s_v\times\vec s_u=-u\,\vec k$

Then the downward flux of $\vec F$ through $D$ is

$\displaystyle\int_0^{2\pi}\int_0^{\sqrt3}(2\,\vec k)\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv=-2\int_0^{2\pi}\int_0^{\sqrt3}u\,\mathrm du\,\mathrm dv$

$=\boxed{-6\pi}$

c. The net flux is then $\boxed{4\sqrt3\pi}$ .

d. By the divergence theorem, the flux of $\vec F$ across the closed hemisphere $H$ with boundary $C\cup D$ is equal to the integral of $\mathrm{div}\vec F$ over its interior:

$\displaystyle\iint_{C\cup D}\vec F\cdot\mathrm d\vec S=\iiint_H\mathrm{div}\vec F\,\mathrm dV$

We have

$\mathrm{div}\vec F=\dfrac{\partial(2z+2)}{\partial z}=2$

so the volume integral is

$2\displaystyle\iiint_H\mathrm dV$

which is 2 times the volume of the hemisphere $H$ , so that the net flux is $\boxed{4\sqrt3\pi}$ . Just to confirm, we could compute the integral in spherical coordinates:

$\displaystyle2\int_0^{\pi/2}\int_0^{2\pi}\int_0^{\sqrt3}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=4\sqrt3\pi$

4 0

3 years ago

Kim wrote the number 11. Use mental math to tell what number has ??

Eduardwww [97]

2 more 10s then 11 is 31

1 more 10s then 11 is 21

3 more 10s then 11 is 41.

basic math :)

3 0

3 years ago

Read 2 more answers