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4 years ago

7

y varies inversely with x. If y = 2.4 and k (the constant of variation) = 8.88, what is x? Round to the nearest tenth, if necess

ary.

1 answer:

Archy [21]4 years ago

8 0

Answer:

3.7

Step-by-step explanation:

Inversely means we are taking the constant and dividing it.

So y varies inversely with x means "y=k/x".

k is a constant. We can find the constant if they give us a point on this curve.

The constant is a number that doesn't change no matter your input and output.

$y=\frac{k}{x}$

So they actually give us k=8.88 and y=2.4 so let's input this:

$2.4=\frac{8.88}{x}$

We need to solve this equation for x. You can do your favorite thing in cross-multiply. But how, Freckles? Well just slap a 1 underneath that 2.4. You can do that because 2.4/1 is still 2.4.

$\frac{2.4}{1}=\frac{8.88}{x}$

Cross-multiply:

$2.4x=8.88(1)$

$2.4x=8.88$

Divide both sides by 2.4:

$x=\frac{8.88}{2.4}$

$x=3.7$ when $y=2.4$ .

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Use the given transformation to evaluate the integral. (15x + 15y) dA R , where R is the parallelogram with vertices (−1, 4), (1

MA_775_DIABLO [31]

Answer:

$\int_R 15x+15y dA = \frac{8}{16875}$

Step-by-step explanation:

Recall the following: x = 15u+15v, y = -60u+15v. So, x-y = 75u. Then u = (x-y)/75. 4x+y = 75v. Then v = (4x+y)/75.

We will see how this transformation maps the region R to a new region in the u-v domain. To do so, we will see where the transformation maps the vertices of the region.

(-1,4) -> ((-1-4)/75,(4(-1)+4)/75) = (-1/15, 0)

(1,-4)->(1/15,0)

(3,-2)->(1/15,2/15)

(1,6)->(-1/15,2/15)

That is, the new region in the u-v domain is a rectangle where $\frac{-1}{15}\leq u \leq \frac{1}{15}, 0\leq v \leq \frac{2}{15}$ .

We will calculate the jacobian of the change variables. That is

$\left |\begin{matrix} \frac{du}{dx}& \frac{du}{dy}\\ \frac{dv}{dx}& \frac{dv}{dy}\end{matrix}\right|$ (we are calculating the determinant of this matrix). The matrix is

$\left |\begin{matrix} \frac{1}{75}& \frac{-1}{75}\\ \frac{4}{75}& \frac{1}{75}\end{matrix}\right|=(\frac{1}{75^2})(1+4) = \frac{1}{15\cdot 75}$ (the in-between calculations are omitted).

We will, finally, do the calculations.

Recall that

$15x+15y = 15(15u+15v) + 15(-60u+15v) = (15^2-15\cdot 60 )u+2\cdot 15^2v = 15^2(-3)u+2\cdot 15^2 v$

We will use the change of variables theorem. So,

$\int_R 15x+15y dA = \int_{\frac{-1}{15}}^{\frac{1}{15}}\int_{0}^{\frac{2}{15}} 15^2(-3)u+2\cdot 15^2 v \cdot (\frac{1}{15^2\cdot 5}) dv du = \int_{\frac{-1}{15}}^{\frac{1}{15}}\int_{0}^{\frac{2}{15}}\frac{-3}{5}u+\frac{2}{5}v dvdu$

This si because we are expressing the original integral in the new variables. We must multiply by the jacobian to guarantee that the change of variables doesn't affect the value of the integral. Then,

$\int_{\frac{-1}{15}}^{\frac{1}{15}}\int_{0}^{\frac{2}{15}}\frac{-3}{5}u+\frac{2}{5}v dvdu = \int_{\frac{-1}{15}}^{\frac{1}{15}}\frac{-3}{5}u\cdot \frac{2}{15} + \frac{2}{5}\cdot \left.\frac{v^2}{2}\right|_{0}^{\frac{2}{15}}du = \frac{-3}{5}\left.\frac{u^2}{2}\right|_{\frac{-1}{15}}^{\frac{1}{15}}\cdot \frac{2}{15} + \frac{2}{5}\cdot \left.\frac{v^2}{2}\right|_{0}^{\frac{2}{15}} = \frac{8}{16875}$

5 0

4 years ago

What are the coordinates of the point LaTeX: \frac{3}{4}\:3 4of the way from A to B? coordinate plane with line segment AB. Poin

egoroff_w [7]

Answer: $\left(\dfrac{-7}{2},\dfrac{5}{4}\right)$ .

Step-by-step explanation:

It is given that Point A is at (-5, -4) and point B at (-3, 3).

We need to find the coordinates of the point which is 3/4 of the way from A to B.

Let the required point be P.

$AP:AB=3:4$

$AP:PB=AP:(AB-AP)=3:(4-1)=3:1$

It means, point P divides segment AB in 3:1.

Section formula: If a point divides a line segment in m:n, then

$\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Using section formula, we get

$P=\left(\dfrac{3(-3)+1(-5)}{3+1},\dfrac{3(3)+1(-4)}{3+1}\right)$

$P=\left(\dfrac{-9-5}{4},\dfrac{9-4}{4}\right)$

$P=\left(\dfrac{-14}{4},\dfrac{5}{4}\right)$

$P=\left(\dfrac{-7}{2},\dfrac{5}{4}\right)$

Therefore, the required point is $\left(\dfrac{-7}{2},\dfrac{5}{4}\right)$ .

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4 years ago

April has $3.65 in quarters and nickels in her car. The number of nickels is thirteen more than the numbers of quarters. How man

DiKsa [7]

Answer:

hi

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Eric’s average income for the first 4 months of the year is $1,450.25, what must be his

drek231 [11]

Answer:

Average income of Eric for the remaining 8 months = $\$1946$

Step-by-step explanation:

Given: Average income of Eric for the first 4 months of the year is equal to $1,450.25

To find: average income for the remaining 8 months so that his average income for the year is $1,780.75

Solution:

Average income = Total income for the year/Total number of months

Average income of Eric for the first 4 months = $1,450.25

So,

Total income of Eric for the first 4 months = 1,450.25 × 4 = 5801

Let x denotes total income of Eric for the remaining 8 months

Total income for the year = 5801 + x

Therefore,

Average income for the year = $\frac{5801+x}{12}$

Also, average income for the year is $1,780.75

$1780.75=\frac{5801+x}{12}\\1780.75\times 12=5801+x\\21369=5801+x\\21369-5801=x\\15568=x$

Total income of Eric for the remaining 8 months = $15568

Average income of Eric for the remaining 8 months = $\frac{15568}{8}=\$1946$

7 0

3 years ago

After a baseball is hit, the height h (in feet) of the ball above the ground t seconds after it is hit can be approximated by th

lubasha [3.4K]

Answer:

The ball will take 4.05 seconds to hit the ground.

Step-by-step explanation:

we have

$h=-16t^{2}+64t+3$

This is a quadratic equation (vertical parabola) open down

The vertex is a maximum

we know that

The ball hit the ground when h=0

Solve the quadratic equation

For h=0

$-16t^{2}+64t+3=0$

The formula to solve a quadratic equation of the form

$at^{2} +bt+c=0$ is equal to

$t=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2}+64t+3=0$

so

$a=-16\\b=64\\c=3$

substitute in the formula

$t=\frac{-64(+/-)\sqrt{64^{2}-4(-16)(3)}} {2(-16)}$

$t=\frac{-64(+/-)\sqrt{4,288}} {-32}$

$t=\frac{64(-)\sqrt{4,288}} {32}=-0.05\ sec$ ---> the time cannot be a negative number

$t=\frac{64(+)\sqrt{4,288}} {32}=4.05\ sec$

therefore

The ball will take 4.05 seconds to hit the ground.

4 0

3 years ago