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seropon [69]
3 years ago
10

PLEASE HELP!!! solve the right triangle​

Mathematics
1 answer:
DIA [1.3K]3 years ago
7 0

Answer:

UV = 4.5 (not rounded)

TV = 3√3

m∠U = 60˚

Step-by-step explanation:

UV = Use sin function since you’re finding the hypotenuse with a given angle and opposite side.

sin(30) = 9/UV

9sin(30) = UV

4.5 = UV

TV = Use Tangent function (opp. over adj.) since you’re finding the adjacent side with a given angle and opposite side.

tan(30) = 9/TV

9tan(30) = TV

3√3 = TV

m∠U = Sum of all interior angles of a triangle is 180˚:

90˚ + 30˚ = 120˚

180˚ - 120˚ = 60˚

Hope this helps :)

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Find the absolute maximum and minimum values of the function, subject to the given constraints. k(x,y)=−x2−y2 4x 4y; 0≤x≤3, y≥0,
grigory [225]

For function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

For given question,

We have been given a function k(x, y) = -x² - y² + 4x + 4y

We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

First we find the partial derivative of function k(x, y) with respect to x.

⇒ k_x=-2x+4

Now, we find the partial derivative of function k(x, y) with respect to y.

\Rightarrow k_y=-2y+4

To find the critical point:

consider    k_x=0     and      k_y=0

⇒       -2x + 4 = 0     and    -2y + 4 = 0

⇒          x = 2            and       y = 2

This means, the critical point of function is (2, 2)

We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

Consider k(0, 0)

⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)

⇒ k(0, 0) = 0

Consider k(3, 3)

⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)

⇒ k(3, 3) = -9 - 9 + 12 + 12

⇒ k(3, 3) = -18 + 24

⇒ k(3, 3) = 6

Therefore, for function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

Learn more about the absolute maximum and absolute minimum values of the function here:

brainly.com/question/16270755

#SPJ4

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1 year ago
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rewona [7]

We will need to shade the region above f(x) and the region below the function g(x).

<h3>How to transform the graph into the solution set?</h3>

We have:

f(x) = x² - 2

g(x) = -x² + 5

Both of these are already graphed, and we want to transform it into:

y > f(x)

y ≤ g(x)

The first inequality means that we need to graph f(x) with a dashed line, because f(x) is not part of the solution, and then we shade all the region above f(x).

For the other inequality, we use a solid line (because the points on the line are solutions) and then we shade the part below the curve.

Learn more about inequalities on:

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8 0
2 years ago
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