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Oksi-84 [34.3K]
3 years ago
11

Why is it important to be able to solve for variables in equations?

Mathematics
2 answers:
GuDViN [60]3 years ago
6 0
Because that way you can find the answer when you are given a large amount of information and you don't have to guess until you get the answer right.
Bad White [126]3 years ago
5 0
SO YOU GET A GOOD GRADE ON YOUR TESTS FOR HIGH SCHOOL AND COLLEGE. 
You might be interested in
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
10. rhombus abcd has vertices at a(-2, 7), b(8, 7), c(2, -1), and d (-8, -1).
horrorfan [7]

Answer: 80

Step-by-step explanation:

We can use the formula A=\frac{d_{1}d_{2}}{2}, where d_{1}, d_{2} are the lengths of the diagonals.

By the distance formula,

AC=\sqrt{(-2-2)^{2}+(-1-7)^{2}}=\sqrt{16+64}=4\sqrt{5}\\BD=\sqrt{(-8-8)^{2}+(-1-7)^{2}}=\sqrt{256+64}=8\sqrt{5}

So, the area is \frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}

6 0
2 years ago
2<br> Find the slope from the 2 points.<br> (-12,-9) and ( 18, 6)<br> -2<br> -1/2<br> 2<br> 1/2
lawyer [7]

Step-by-step explanation:

the slope of a line is the ratio y/x.

that means when going from one point to the other, how many units is y changing, when x changes a certain number of units.

so, going from one point to the other here, x changes by 30 units (from -12 to +18). and y changes 15 units (from -9 to 6).

therefore, the slope is

15/30 = 1/2

8 0
2 years ago
Evaluate log base 12 of y^2, given log base 12=16
Ostrovityanka [42]

Answer:

y = 12^8

Step-by-step explanation:

Log base 12, y^2 = 16

y2 = 12^16

y = sqrt ( 12^16) = (12^16)^1/2

y = 12^8

5 0
3 years ago
24 cooking takes for 384 sprinkles, how many sprinkles would 60 cookies need
alukav5142 [94]

Answer:

960 i think

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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