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3 years ago

Is 16/36 the same value of 4/9?

Mathematics

1 answer:

julia-pushkina [17]3 years ago

8 0

Answer:

Yes, 16/36 and 4/9 are equivalent fractions; the latter is the simplified form of the original fraction: 16/36.

Step-by-step explanation:

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G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

3 years ago

In parallelogram ABCD , BE=7x−2 and ED=x2−10 .

Stells [14]

I'm assuming that the diagonals intersect at E. Since diagonals of a parallelogram bisect each other, BE=ED.

7x-2=x²-10
x²-7x-8=0
(x-8)(x+1)=0
x = -1, 8

As distance must be positive, we reject the negative case, so x=8.

Thus, BE=ED=54.

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2 years ago

A worker uses 900 inches of steel wire to make 600 springs of the same size. At this rate how

a_sh-v [17]

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3 years ago

Omar is born weighing 8 pounds,3 ounces.The doctor says he should gain a about 5 ounces each week for the next 4 weeks.How much

hoa [83]

Start weight- 8.03
week 1 - 8.8
week 2 - 8.13
week 3 - 9.03
week 4 - 9.08

So, the Omar should weigh 9 pounds 8 ounces by the end of 4 weeks.

I hope this helped!

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3 years ago

Read 2 more answers

6x - 2y = 5

laiz [17]

Answer:

The given system has NO SOLUTION.

Step-by-step explanation:

Here, the given system of equation is:

6 x - 2 y = 5 .......... (1)

3 x - y = 10 .... (2)

Multiply equation 2 with (-2), we get:

3 x - y = 10 ( x -2)

⇒ - 6 x + 2 y = - 20

Now, ADD this to equation (1) , we get:

6 x - 2 y - 6 x + 2 y = 5 - 20

or, 0 = - 15

WHICH IS NOT POSSIBLE as 0 ≠ -15

Hence, the given system has NO SOLUTION.

7 0

3 years ago

Is 16/36 the same value of 4/9?​

Is 16/36 the same value of 4/9?