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3 years ago

Solve: |x + 9| User: Evaluate 5|7 - 9| - 2. -12 0 1 8

2 answers:

8 0

Solve:

$[x+9]$ - there is nothing to simplify

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

Evaluate:

$5(7-9)-2$

= $35 -45-2$

= $-10-2$

= $-12$

or

$5(7-9)-2$

= $35 -45-2$

= $35-47$

= $-12$
------------------------------------------
So, -12 is the answer.

AlexFokin [52]3 years ago

8 0

I believe it is 8. Sorry if I´m wrong.

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Steven wishes to save for his retirement by depositing $2,000 at the beginning of each year for thirty years. Exactly one year a

Ad libitum [116K]

Step-by-step explanation:

i = interest 3% for 30 years

This is a simple dynamical system for whom the the solutions are given as

$S=R[\frac{(i+1)^n-1}{i}](i+1)$

putting values we get

S=2000[\frac{(1.03)^{30}-1}{0.03}](1.03)

= $98005.35

withdrawal of money takes place from one year after last payment

To determine the result we use the present value formula of an annuity date

$P = R\frac{1-(1+i)^{-n}}{i}{i+1}$

we need to calculate R so putting the values and solving for R we get

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8 0

3 years ago

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

One eighth of a number is ten less than one third of the number. Find the number.

GarryVolchara [31]

X/8 - 10 = x/3

bring the values with the variable on one side

x/3 - x/8 = 10

find a common denominator and subtract these fractions

8x/24 - 3x/24 = -10

now subtract fractions

8x - 3x = 5x

5x/24 = -10

multiply both sides by 24

5x = -240

divide both sides by 5

x = -48

the number is -48

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3 years ago

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