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sashaice [31]
1 year ago
12

Evaluate the following​ integral, where R is bounded by ​, ​, and . Question content area bottom Part 1 enter your response here

​(Simplify your​ answer.)
Mathematics
1 answer:
Volgvan1 year ago
7 0

\iint_{R} y^{2} d A=\int_{x=-2}^{3} \int_{y=-x-2}^{3 x+6} y^{2} d x d y d x

\text { (taking Strip as shown). }

=\int_{-2}^{3}\left(\frac{y^{3}}{3}\right)_{-x-2}^{3 x+6} d x

=\frac{1}{3} \int_{-2}^{3}(3 x+6)^{3}-(-x-2)^{3} d x

\begin{gathered}=\frac{1}{3}[4375]=\frac{4375}{3} \\=1458.33\end{gathered}

What is integral ?

  • Calculating an integral is called integration.
  • Mathematicians utilize integrals to determine a variety of useful quantities, including areas, volumes, displacement, etc.
  • When we discuss integrals, we often refer to definite integrals.
  • For antiderivatives, indefinite integrals are utilized.
  • Apart with differentiation, integration is one of the two main calculus subjects in mathematics (which measure the rate of change of any function with respect to its variables).
  • It's a broad subject that is covered in courses at the higher grade levels, such classes 11 and 12.
  • Broadly speaking, integration by parts and via substitution is explained.
  • You will discover the definition of integrals in mathematics, the integration formulae, and examples here.

So the more about integral visit.

brainly.com/question/2289273

#SPJ4

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The points(0,2) and (4,-10) lie on the same line and the points (-5,-3) and (2,11) lie on another line. Determine by graphing wh
joja [24]
You are asked to do this problem by graphing, which would be hard to do over the Internet unless you can do your drawing on paper and share the resulting image by uploading it to Brainly.

If this were homework or a test, you'd get full credit only if you follow the directions given.

If <span>The points(0,2) and (4,-10) lie on the same line, their slope is m = (2+10)/(-4), or   m =-3.  Thus, the equation of this line is y-2 = -3x, or y = -3x + 2.

If </span><span>points (-5,-3) and (2,11) lie on another line, the slope of this line is:

m = 14/7 = 2.  Thus, the equation of the line is y-11 = 2(x-2), or y = 11+2x -4, or y = 2x + 7.

Where do the 2 lines intersect?  Set the 2 equations equal to one another and solve for x:

</span>y = -3x + 2 = y = 2x + 7.  Then 5x = 5, and x=1.

Subst. 1 for x in y = 2x + 7, we get y = 2(1) + 7 = 9.

That results in the point of intersection (2,9).

Doing this problem by graphing, on a calculator, produces a different result:  (-1,5), which matches D.

I'd suggest you find and graph both lines yourself to verify this.  If you want, see whether you can find the mistake in my calculations.

3 0
3 years ago
Human visual inspection of solder joints on printed circuit boards can be very subjective. Part of the problem stems from the nu
olga_2 [115]

Answer:

a

The probability that the selected joint was judged to be defective by neither of the two inspectors is   P(A' n B' ) = 0.8855

b

The probability that the selected joint was judged to be defective by inspector B but not by inspector A  is  P(A' n B) =0.0403

Step-by-step explanation:

From the question we are told that

   The sample size is n_s =  10000

    The number of outcome for inspector A is  n__{A}} = 742

    The number of outcome for inspector B is  n__{B}} = 745

     The number of joints judged defective by both inspector is n(A u B) =  1145

The the probability that the selected joint was judged to be defective by neither of the two inspectors is mathematically represented as

      P(A' n B' ) =  1 - P(A u B)

Now

       P(A\ u \ B) = \frac{n(Au B)}{n_s }

substituting values

        P(A\ u \ B) = \frac{1145}{ 10 000 }

So  

      P(A' n B' ) =  1 - \frac{1145}{10 000}

     P(A' n B' ) = 0.8855

the probability that the selected joint was judged to be defective by inspector B but not by inspector A  is mathematically represented as

     P(A' n B) =  P(A \ u \ B) -P(A)

Now

        P(A) =  \frac{n__{A}}{n_s}

substituting values

       P(A) =  \frac{742}{10 000}

So

     P(A' n B) =   \frac{1145}{10 000}  - \frac{742}{10 000}

    P(A' n B) =0.0403

7 0
3 years ago
Factor 16xy^2-24y^2z+40y^2
qaws [65]

Answer:

8y^2(2x_3z+5)

.......

3 0
3 years ago
What is the value of the underlined digit in 16,403
Ilia_Sergeevich [38]
If the 1 were underlined it would be 10,000
If the 6 were underlined it would be 6,000
If the 4 were underlined it would be 400
If the 0 were underlined it would be 0
If the 3 were underlined it would be 3

8 0
3 years ago
PLEASE HELP ASAP WILL GIVE BRAINLIEST
Digiron [165]

Answer:

6 mm  slope 3

Step-by-step explanation:

4 0
2 years ago
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