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3 years ago

I'll give more points here is what I need.

Mathematics

1 answer:

Serga [27]3 years ago

5 0

Answer:

The answer to your question is x = 3; y = 3

Step-by-step explanation:

Data

angle = 45°

Opposite side = x

Adjacent side = y

hypotenuse = 3√2

To solve this problem, use trigonometric functions.

1) To find x, use the trigonometric function sine.

sin Ф = Opposite side / hypotenuse

-Solve for Opposite side (x)

Opposite side = hypotenuse x sin Ф

-Substitution

Opposite side = 3√2 sin 45

-Simplification

Opposite side = 3√2 (1 / √2)

Opposite side = 3(1)

-Result

x = 3

2) To find y use the trigonometric function cosine

cos Ф = Adjacent side / hypotenuse

-Solve for Adjacent side

Adjacent side = hypotenuse x cos Ф

-Substitution

Adjacent side = 3√2 x cos 45

-Simplification

Adjacent side = 3√2 x (1/√2)

Adjacent side = 3(1)

-Result

y = 3

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3 years ago

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3 years ago

The perimeter of a rectangle is 200 yards. what are the dimensions of the rectangle if the length is 80 yards more than the? wid

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3 years ago

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3 years ago

Which point is in the solution set of the given system of inequalities 3x+y>-3,x+2y<4

Dima020 [189]

Step 1. Solve both inequalities for $y$ :
$3x+y\ \textgreater \ -3$
$y\ \textgreater \ -3x-3$

$x+2y\ \textless \ 4$
$2y\ \textless \ -x+4$
$y\ \textless \ - \frac{1}{2} x+2$

Step 2. To check a point in the solution of the given system of inequalities, look for the intercepts of the lines $-3x-3$ and $- \frac{1}{2} x+2$ :

$y=-3x-3$ (1)
$y=- \frac{1}{2} x+2$ (2)

Replace (1) in (2):
$-3x-3=- \frac{1}{2} x+2$
Solve for $x$ :
$\frac{5}{2} x=-5$
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Replace (3) in (1):
$y=-3x-3$
$y=-3(-2)-3$
$y=6-3$
$y=3$

We can conclude that the point (-2,3) is in the solution of the system if <span>inequalities</span>; also any point inside the dark shaded area of the graph of the system of inequalities is also a solution of the system.

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3 years ago

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