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3 years ago

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Mack is repackaging 6/8 pound bags of birdseed into 1 pound bags of birdseed. What is the least number of 6/8 pound bags of bird

seed he heeds in order to fill 1 pound bags without leftover?

1 answer:

Luba_88 [7]3 years ago

3 0

Four 6/8 pound bags would fill three 1 pound bags, so the answer is 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

I need the exponential equation for this.

icang [17]

Answer:

Step-by-step explanation:

3 0

3 years ago

Geometry test please help. <br> 3). Find x <br> 4). find m 5). Find m < y <br> 6.) Find m

Mrac [35]

Answer:

x = 30

m<Y = 60

m<Z = 60

m<X = 60

Step-by-step explanation:

All of this should add up to 180 so...

2x + 2x + 3x - 30 = 180 (collect like terms)

7x - 30 = 180 (add 30 on both sides)

7x = 210 (divide by 7 on both sides)

x = 30

PLUG IN

2(30) = 60

3(30) - 30

90 - 30 = 60

m<Y = 60

m<Z = 60

m<X = 60

equilateral triangle

Hope this helps ya! Keep smiling!

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3 years ago

A number and its absolutely value are equal. If you subtract 2 from the number and its absolute value are not equal. What do you

Naily [24]

$n-the\ number\\\\|n|=n\ then\ n\geq0\\\\|n-2|\neq n-2\ what's\ a\ number\\\\I\ think,\ it's\ n=1\\\\because\ |1|=1\ and\ |n-2|=|-1|=1\ \ \ :correct\ \ :)\\\\3\ is\ not,\ because:\ |3|=3\ and\ |3-2|=|1|=1\to3\neq1$

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3 years ago

There are 65 campers at fun camp. only 53 campers brought sleeping bags. how many campers did not bring sleeping bags?

elena-s [515]

So you have to just subtract, 65-53=12 that didn't bring sleeping bags

8 0

3 years ago