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DENIUS [597]
3 years ago
10

A triangle has side lengths 85,84, and 13. Is the triangle a right triangle? Explain

Mathematics
1 answer:
irakobra [83]3 years ago
7 0

Answer:

yes

Step-by-step explanation:

2 of the sides are around equal length (one slightly longer because it is diagonal) and one is straight. the bottom one is a lot shorter.

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A race track is in the form of a ring whose inner circumference is 157 m and outer circumference is 314 m. Find the area of the
ASHA 777 [7]
49,298 is the answer
3 0
3 years ago
Find the mass of the lamina that occupies the region D = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} with the density function ρ(x, y) = xye
Alona [7]

Answer:

The mass of the lamina is 1

Step-by-step explanation:

Let \rho(x,y) be a continuous density function of a lamina in the plane region D,then the mass of the lamina is given by:

m=\int\limits \int\limits_D \rho(x,y) \, dA.

From the question, the given density function is \rho (x,y)=xye^{x+y}.

Again, the lamina occupies a rectangular region: D={(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

The mass of the lamina can be found by evaluating the double integral:

I=\int\limits^1_0\int\limits^1_0xye^{x+y}dydx.

Since D is a rectangular region, we can apply Fubini's Theorem to get:

I=\int\limits^1_0(\int\limits^1_0xye^{x+y}dy)dx.

Let the inner integral be: I_0=\int\limits^1_0xye^{x+y}dy, then

I=\int\limits^1_0(I_0)dx.

The inner integral is evaluated using integration by parts.

Let u=xy, the partial derivative of u wrt y is

\implies du=xdy

and

dv=\int\limits e^{x+y} dy, integrating wrt y, we obtain

v=\int\limits e^{x+y}

Recall the integration by parts formula:\int\limits udv=uv- \int\limits vdu

This implies that:

\int\limits xye^{x+y}dy=xye^{x+y}-\int\limits e^{x+y}\cdot xdy

\int\limits xye^{x+y}dy=xye^{x+y}-xe^{x+y}

I_0=\int\limits^1_0 xye^{x+y}dy

We substitute the limits of integration and evaluate to get:

I_0=xe^x

This implies that:

I=\int\limits^1_0(xe^x)dx.

Or

I=\int\limits^1_0xe^xdx.

We again apply integration by parts formula to get:

\int\limits xe^xdx=e^x(x-1).

I=\int\limits^1_0xe^xdx=e^1(1-1)-e^0(0-1).

I=\int\limits^1_0xe^xdx=0-1(0-1).

I=\int\limits^1_0xe^xdx=0-1(-1)=1.

No unit is given, therefore the mass of the lamina is 1.

3 0
3 years ago
A number consists of two digit whose sum is five
Nataly [62]

Answer:

23

Step-by-step explanation:

5 0
3 years ago
Point D is the centroid of Triangle ABC. Find CD and CE.<br> DE = 9
sukhopar [10]

Given:

Point D is the centroid of Triangle ABC and DE = 9.

To find:

The measures of CD and CE.

Solution:

We know that, centroid is the intersection of medians and it divides each median in 2:1.

In triangle ABC, CE is a meaning and centroid D divided CE in 2:1. So,

Let the measures of CD and DE are 2x and x respectively.

DE = 9                (Given)

x=9

Now,

CD=2x

CD=2(9)

CD=18

And,

CE=CD+DE

CE=18+9

CE=27

Therefore, the measure of CD is 18 units and the measure of CE is 27 units.

6 0
3 years ago
What is the area of a rectangle with a length of 88 inches and width of 56 inches?
Alecsey [184]

Answer:

C. 4928 in2

Step-by-step explanation:

88 X 56 = 4928 in2

4 0
3 years ago
Read 2 more answers
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