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3 years ago

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Mathematics

2 answers:

Lena [83]3 years ago

7 0

The answer is 30 I believe

andrezito [222]3 years ago

5 0

Answer:

30 calories.

Step-by-step explanation:

First we need to know how many is one gram so do 180/30 to get 6. Then, since we are looking for the amount in 5 grams, multiply 6 by 5 to get 30.

Therefore, there are 30 calories in 5 grams.

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Find the volume of the region between the planes x plus y plus 2 z equals 2 and 4 x plus 4 y plus z equals 8 in the first octant

Alex787 [66]

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

$y=z=0\implies x=2\implies (2,0,0)$

$x=z=0\implies y=2\implies(0,2,0)$

$x=y=0\implies 2z=2\implies z=1\implies(0,0,1)$

Plane 2, 4x + 4y + z = 8:

$y=z=0\implies4x=8\implies x=2\implies(2,0,0)$

$x=z=0\implies4y=8\impliesy=2\implies(0,2,0)$

$x=y=0\implies z=8\implies(0,0,8)$

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

$\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx$

$=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx$

$=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}$

3 0

3 years ago

A flight instructor charges $50 per lesson, plus an

Cerrena [4.2K]

Well, it's 40/4 for one minute, or 10 for one minute. You want 36 mins, so you multiply by the square root (6), to get $60, to which you also add the $90 for the lesson (result is $150)

6 0

3 years ago

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Find the area of a square with the sides 24feet ,27ft.18feet and 30feet

34kurt

Well, this question isn't really fair, considering that those sides aren't possible to make a square since a square has 4 congruent sides.

5 0

3 years ago

Write an equation of a line perpendicular to the line y = -1/5x -3 and goes through the point (6,2), then use Point- Slope form

agasfer [191]

Answer:

The equation of the line would be y = 5x - 28

Step-by-step explanation:

First, we need to know that perpendicular lines have opposite and reciprocal slopes. Give that information, we know that the new line will be the reciprocal and opposite of -1/5. This would be 5. Now that we have that information, we can use it along with a point to fill in the point-slope form of the equation.

y - y1 = m(x - x1)

y - 2 = 5(x - 6)

Then we must solve for y.

y - 2 = 5(x - 6)

y - 2 = 5x - 30

y = 5x - 28

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3 years ago

2 − 10n = 2 + 4n What does n equal?

tiny-mole [99]

Answer:

0 =n

Step-by-step explanation:

2 − 10n = 2 + 4n

Add 10n to each side

2 − 10n+10n = 2 + 4n+ 10n

2 = 2 + 16n

Subtract 2 from each side

2-2 = 2+16n-2

0 = 16n

Divide each side by 16

0/16 = 16n/16

0 =n

8 0

4 years ago

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