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3 years ago

If a cross-country runner runs a 55 kilometer (km) race, how many miles is that? Round your answer to one decimal place.

Mathematics

1 answer:

prohojiy [21]3 years ago

5 0

Answer: 34.2

For everyone 1 kilometer=.621371 so if you times that by 55 you get 34.1754 which rounds to 34.2

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A student has a savings account earning 3% simple interest. She must pay $1900 for first-semester tuition by September 1 and $19

Anastaziya [24]

Answer:

$3781.19

Step-by-step explanation:

Let us assume that the student has to earn $(1900 + x) by September 1 so that he can pay the $1900 tuition fee by September 1 and the remaining $x will grow at 3% simple interest to make him able to pay another tuition fee of $1900 by January 1.

So, we can write $x( 1 + \frac{4 \times 3}{12 \times 100}) = 1900$

{Because September 1 to January 1 is 4 months and the monthly simple interest rate is $\frac{3}{12}$ %}

⇒ 1.01x = 1900

⇒ x = $1881.19 (Rounded to the nearest cents)

Therefore, the student has to earn $(1900 + 1881.19) = $3781.19 (Answer)

8 0

3 years ago

What is the reciprocal of x^2/6x?

Rzqust [24]

6x / x²

the reciprocal of a number n is $\frac{1}{n}$

the reciprocal of $\frac{x}{y}$ is $\frac{y}{x}$

The product of a number and it's reciprocal = 1

4 0

3 years ago

What is the quoteint of 2/3 in 2/9

andre [41]

Answer: 3

Explanation:

2/3 divided by 2/9

2/3 times 9/2

= 3

6 0

3 years ago

What is the value of x?<br><br> Please include steps on how to get to the answer. <3

AlekseyPX

We have that
<span>Bisector theorem--------------- >(LM)/(LN)=(OM)/(ON)
therefore
</span>(18)/(10)=(x)/(4)------------------ > x=7.2

the answer is x=7.2

6 0

3 years ago

Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

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

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

6 0

3 years ago