Which ordered pair is a solution of the equation: Y=-6x+1

Select the correct answer from each drop-down menu.

kompoz [17]

Answer: B has greater spread than A.

Step-by-step explanation:

Since we have given that

Set A: {38, 12, 23, 48, 55, 16, 18}

Range of A = Highest - Lowest

Range of A = 55 - 12

Range of A = 43

Set B:{44, 13, 24, 12, 56}

Range of B = Highest - Lowest

Range of B = 56 - 12

Range of B = 44

Since Range of B is more than range of A.

Hence, B has greater spread than A.

6 0

2 years ago

Which of the following systems of nonlinear inequalities is graphed below?

aivan3 [116]

Answer:

the correct answer is C.

7 0

2 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

2 years ago

Round 3659 to the nearest thousand

Kryger [21]

It is 4,000. :P
The 6 in the hundreds tells you to round up. 4 and under, keep it. 5 and up, raise it by one. :)

5 0

2 years ago

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A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form a

Reika [66]

The correct answer is:

3 inches.

Explanation:

We will use the Rational Roots Theorem to solve this.

First we can divide both sides of the equation by 4 in order to simplify it:

$\frac{4x^3-72x^2+320x}{4}=\frac{420}[4} \\ \\x^3-18x^2+80=105$

In order to solve this, we want the polynomial set equal to 0. To do this, subtract 105 from both sides:

$x^3-18x^2+80x-105=105-105 \\x^3-18x^2+80x-105=0$

The Rational Roots Theorem says that if p/q is a root of the polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is -105. Drawing a factor tree, we find that the factors of this number are 1, -1, 3, -3, 5, -5, 7, -5, 15, -15, 21, -21. The leading coefficient is 1; its only factor is 1. This means p/q must be a whole number, and can be any of the factors of 105.

Using synthetic division, we try 1 in the box:

1 | 1 -18 80 -105

_______ 1__ -17___63__

1 -17 63 -42

Since there is a remainder, this is not a root. Trying -1,

-1 | 1 -18 80 -105

_______-1__ 19 _-99_

1 -19 99 -204

This is not a root; in fact, it shows us that none of the negatives will be a factor, as the absolute values increase as we complete the synthetic division.

Trying 3,

3 | 1 -18 80 -105

________3__-45___105_

1 -15 35 0

Since there is no remainder, 3 is a root, and is the answer we are looking for.

3 0

2 years ago

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