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3 years ago

Write the phrase as an algebraic expression: 3 less than 4 times a number

Mathematics

2 answers:

Diano4ka-milaya [45]3 years ago

8 0

Answer:

3 $\leq$ 4x

Step-by-step explanation:

mina [271]3 years ago

6 0

Answer:

4x-3 is the expression to your question

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Which point on the number line represents the product of 4 and –2?

Goshia [24]

Answer:

It's A

Step-by-step explanation:

the one above me is incorrect it's "A"

5 0

3 years ago

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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

PLEASE HELP SOLVE THIS!!!!!!!!!!!

Sphinxa [80]

9514 1404 393

Answer:

a) yes; 12/15/17 ~ 20/25/x; SAS

b) x = 28 1/3

Step-by-step explanation:

The left-side segments are in the ratio ...

top : bottom = 12 : 8 = 3 : 2

The right side segments are in the ratio ...

top : bottom = 15 : 10 = 3 : 2

These are the same ratio, and the angle at the peak is the same in both triangles, so the triangles are similar by the SAS postulate.

Normally, a similarity statement would identify the triangles by the labels on their vertices. Here, there are no such labels, so we choose to write the statement in terms of the side lengths, shortest to longest:

12/15/17 ~ 20/25/x

The sides of similar triangles are proportional, so the ratio of longest to shortest sides will be the same in the two triangles. In the smaller triangle, the longest side is 17/12 times the length of the shortest side. The value of x will be 17/12 times the length of the shortest side in the larger triangle:

x = 17/12 · 20 = 340/12

x = 28 1/3

4 0

3 years ago

Calculate the slope of the line that contains the points (-2, -4) and (2, 4).

liubo4ka [24]

Answer:

Slope is 2

Step-by-step explanation:

(-2, -4) and (2, 4)

Slope:

m=(y2-y1)/(x2-x1)

m=(4+4)/(2+2)

m=8/4

m = 2

6 0

3 years ago

A piece of bad news about your hotel goes viral. If each person, spreads the news to 5 people within 1 minute, how long will it

Lady_Fox [76]

A 20,000,000

Hope my answer helped

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3 years ago

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