NEED HELP ASAP PLZZZZS????

Mathematics

1 answer:

e-lub [12.9K]3 years ago

4 0

Answer: m∠F = 31°

Solution: The triangle's rotation is irrelevant to the measure of its angles. In other words, angles D, E, and F will all stay the same if the triangle is turned ("rotated"). That being said, we know by definition that the interior angles of a triangle add up to 180°. We are given two of the angles, and we are asked to find the third:

m∠D + m∠E + m∠F = 180°
48° + 101° + m∠F = 180°
149° + m∠F = 180°
m∠F = 31°

You might be interested in

Use green's theorem to evaluate the line integral along the given positively oriented curve. c yex dx 2ex dy, c is the rectangle

Phoenix [80]

The line integral along the given positively oriented curve is mathematically given as

$=3\left[e^{4}-1\right]$

This is further explained below.

<h3>What is the line integral along the given positively oriented curve.?</h3>

Generally,

$\int M d x+N d y=\iint\left(\frac{\partial N}{\partial x}-\frac{\partial M}{2 y}\right) d y d x$

M=y e^{x}

Therefore

x -->0 to 4

y --> 0 to 3

$\end{aligned}\\&=\int_{0}^{4} \int_{0}^{3}\left(2 e^{x}-e^{x}\right) d y d x\\&=\int_{0}^{4} \int_{0}^{3} e^{x} d y d x\\&=3 \int_{0}^{4} e^{x} d x\\&=3\left[e^{x}\right]_{0}^{4}\\&=3\left[e^{4}-e^{0}\right]\\&=3\left[e^{4}-1\right]\end{aligned}$