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Solnce55 [7]
3 years ago
8

Please help me with this question!

Mathematics
1 answer:
Alina [70]3 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°, thus

∠1 = 180° - (72 + 57)° = 180° - 129° = 51°

The right angle at the left vertex is composed of 72° and ∠2, thus

∠2 = 90° - 72° = 18°

57° and ∠3 form a straight angle and are supplementary, thus

∠3 = 180° - 57° = 123°

∠4 = 180° - (∠2 + ∠3 ) ← sum of angles in a triangle

∠4 = 180° - (18 + 123)° = 180° - 141° = 39°

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Use integration by parts to find the integrals in Exercise.<br> ∫^3_0 3-x/3e^x dx.
Viefleur [7K]

Answer:

8.733046.

Step-by-step explanation:

We have been given a definite integral \int _0^3\:3-\frac{x}{3e^x}dx. We are asked to find the value of the given integral using integration by parts.

Using sum rule of integrals, we will get:

\int _0^3\:3dx-\int _0^3\frac{x}{3e^x}dx

We will use Integration by parts formula to solve our given problem.

\int\ vdv=uv-\int\ vdu

Let u=x and v'=\frac{1}{e^x}.

Now, we need to find du and v using these values as shown below:

\frac{du}{dx}=\frac{d}{dx}(x)

\frac{du}{dx}=1

du=1dx

du=dx

v'=\frac{1}{e^x}

v=-\frac{1}{e^x}

Substituting our given values in integration by parts formula, we will get:

\frac{1}{3}\int _0^3\frac{x}{e^x}dx=\frac{1}{3}(x*(-\frac{1}{e^x})-\int _0^3(-\frac{1}{e^x})dx)

\frac{1}{3}\int _0^3\frac{x}{e^x}dx=\frac{1}{3}(-\frac{x}{e^x}- (\frac{1}{e^x}))

\int _0^3\:3dx-\int _0^3\frac{x}{3e^x}dx=3x-\frac{1}{3}(-\frac{x}{e^x}- (\frac{1}{e^x}))

Compute the boundaries:

3(3)-\frac{1}{3}(-\frac{3}{e^3}- (\frac{1}{e^3}))=9+\frac{4}{3e^3}=9.06638

3(0)-\frac{1}{3}(-\frac{0}{e^0}- (\frac{1}{e^0}))=0-(-\frac{1}{3})=\frac{1}{3}

9.06638-\frac{1}{3}=8.733046

Therefore, the value of the given integral would be 8.733046.

6 0
3 years ago
Tell whether the number is prime or composite 68?
Blababa [14]
Composite.
Because the definition of them is, <span>A prime number has only two factors: 1 and itself. A composite number has more than two factors. The number 1 is neither prime nor composite. The prime numbers between 2 and 31 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31 since each of these numbers has only two factors, itself and 1.

Hope this helped!!! :)
-Ginger
</span>
3 0
3 years ago
Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.
Rus_ich [418]

Answer:

b must equal 7 and a second solution to the system must be located at (2, 5).

Step-by-step explanation:

Rearranging the first equation:

y = (x - 3)^2 + 4

From this we see that the vertex is at the point (3,4).

So one solution of equation 2 is (3 ,4).

Substituting in equation 2:

4 = -3 + b

b = 7.

So equation 2 is y = - x + 7.

Now we check if  (2, 5) is on this line:

5 = -2 + 7 = 5 , therefore  (2, 5) is on this line.

Verifying if (2, 5)  is also on y = (x - 3)^2 + 4:

5 = (2 - 3)^2 + 4 =  1 + 4 = 5

- so it is. and a second solution to the system is (2, 5).

5 0
3 years ago
PLEASE HELP ME I NEED IT<br> X=<br> Y=
vampirchik [111]
X=33 and Y= 57



Step by step explanation if you see the right angle at 57 degrees it part of x so x plus 57 is 90 and 90 minus 57 is 33 so x is 33 and x and y also form a right angle so x plus y should equal 90 and 90 minus 33 is 7 so that’s Y
7 0
3 years ago
Read 2 more answers
TRUE or FALSE: In the quarter circle, the radius is 4 cm and the diameter is 8 cm.
viktelen [127]

Answer: False.

Step-by-step explanation:

There does not exist a "quarter circle" as a circle with a radius of 4 units, the only notable circle that does exist is the unit circle, that is the circle where the radius is equal to 1, represented by the equatin x^2 + y^2 = 1

The term "quarter circle" actually does refer to a fourth part of a circle, not to a circle of radius 4.

So the statement is false

6 0
3 years ago
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