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1 year ago

8

UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each

additional pound.
How many pounds, p, will it take for UPS and FedEx to cost the same? What is the cost? Write and solve an equation to show your work.

1 answer:

Mamont248 [21]1 year ago

5 0

Answer:19.5

Step-by-step explanation:

7+7=14

14+0.20=14.2

14.2+5=19.2

19.2+0.30=19.5

Your answer is:19.5

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Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

Each vertical cross-section of the triangular prism shown below is an isosceles triangle.

vova2212 [387]

Answer:

Height is 3

Step-by-step explanation:

4.24 x 4.24 x 6

Right triangle base = a + b + c

a^2 + 3^2 = 4.24^2

= a^2 + 9 = 17.98

We cross out b to subtract.

a^2 = 17.98 - 9

a^2 = 8.98

We then square √a^2 = √8.98

a = 2.996

We round up a = 3

We have found the height is 3

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2 years ago

Mark and Sofia walk together down a long, straight road. They walk without stopping for 4 miles. At this point Sofia says their

Marina CMI [18]

Answer:

Sofia is correct.

Step-by-step explanation:

Mark's statement depends on the starting point. He can be correct if they started at the 0 mile, but in this case we don't know where they started. They could had started at the 12 mile and their current position after the walking would be 16 miles.

On the other hand, Sofia's statement doesn't depend on where they started. She refers to how much they walked, not to where they are after the walking. Since they stopped after 4 non-stopping miles, their displacement was exactly 4 miles. So Sofia is correct.

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1 year ago

The value in dollars,v(x),of a certain truck after x years is represented by the equation v(x)=32,500(0.92)^x.To the nearest dol

Vika [28.1K]

Answer: $2193

Step-by-step explanation:

v(x) = 32,500 $(.92)^{x}$

Plug two and three in for x

v(2) = 32,500 $(.92)^{2}$

v(2) = 32,500(.8464)

v(2) = 27,500

v(3) = 32,500 $(.92)^{3}$

v(3) = 32,500(.778688)

v(3) = 25,307.36

Subtract v(3) from v(2)

27,500 - 25,307.36 = 2192.64

Round to the nearest dollar to get $2193

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2 years ago

What is the factored form of the polynomial 27x2y – 43xy2?

snow_tiger [21]

The answer is xy(27x-43y) have a great day :)

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1 year ago

Read 2 more answers