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Mathematics

1 answer:

makvit [3.9K]2 years ago

4 0

$\sqrt[c]{a^{b}} = a^{\frac{b}{c}}$

$3^{\frac{6}{5} } = \sqrt[5]{3^{6}} \\ \\a = 3, b=6, c=5$

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Which of the following is NOT possible? A = A triangle where one angle measures 20 degrees and another angle measures 45 degrees

ArbitrLikvidat [17]

Answer:

Step-by-step explanation:

the angle measures of triangles must add up to 180 degrees. Since we are only given two angles, we can assume that all of the answers that add up to be below 180 degrees fulfill this requirement with the third angle. However, answer choice C adds up to 190 degrees on the first two angle, which means that no matter how low the third angle is, it will never add up to 180 degrees.

5 0

3 years ago

Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integ

liq [111]

Answer:

1/2

Step-by-step explanation:

The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that

$\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy$

Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.

Mx(x,y) = d/dx 8x²y = 16xy
Ly(x,y) = d/dy 7y²x = 14xy

Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy$

We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2$