Please help me with this Imma on a time limit

the table shows the gallons filled in a pool overtime. complete the table. determine a unit rate for this situation.

Fiesta28 [93]

*assuming the pool is filled at a constant, steady rate*
*we can immediately see that if
$\frac{1}{2} = 500$
then in half the time (divide both by 2)
$\frac{1}{4} = 250$
and again in half of that time (divide by 2 again)
$\frac{1}{8} = 125$
now to find 5/8, we simply multiply 1/8 by 5
$\frac{5}{8} = 625$

8 0

3 years ago

Read 2 more answers

Which relationship describes angles 1 and 2?

blondinia [14]

Answer:

Supplementary Angles

Adjacent Angles

Step-by-step explanation:

Angles 1 and 2 share a vertex and form a straight line. These angles are called supplementary angles. They add to 180 degrees and form a straight line. They are adjacent as well because they share a vertex and side.

5 0

2 years ago

Determine another point on the line given two points on the line. (-2, 9), (2, -1)

Gnom [1K]

Answer:

(4,-6)

Step-by-step explanation:

1) First, let's find the slope of the line between the two points. Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$ , substitute the x and y values of (-2,9) and (2,-1) into it, then solve:

$m = \frac{(-1)-(9)}{(2)-(-2)}\\m = \frac{-1-9}{2+2} \\m =\frac{-10}{4} \\m = -\frac{5}{2}$

So, the slope of the line is $-\frac{5}{2}$ .

2) Now, using that slope, let's find another point on the line. You can do this by drawing the two points on a graph (picture below). Now, remember that the slope is $\frac{rise}{run}$ . So, starting from any of the two points (I chose (2,-1), as seen below) count 5 units down, then 2 units to the right. This gives an answer, (4,-6).

5 0

2 years ago

If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

So

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

6 0

3 years ago

Isabel offers to buy a team photo for 8 of her teammates,

masha68 [24]

Answer:

The expression is 5(8 - 2).

Isabel will spend $30

Step-by-step explanation:

A-P-E-X Learning

(I did the quiz and got it right :))

8 0

3 years ago