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Yuri [45]
2 years ago
15

a man casts a 3 feet long shadow. if the suns rays strike the ground 62°, what is the height of the man?

Mathematics
1 answer:
Romashka [77]2 years ago
7 0

Answer:

h = 3*tan(62) where h is the height

Step-by-step explanation:

You basically have a right triangle.  the standing man is the vertical line, the shadow is the horizontal line and the 62 degrees is the angle betweenthe horizontal line and the hypotenuse.

So, relative to the angle we have the adjacent angle and opposite.  What uses those?  Tangent.  tan(x) = opp / adj

tan(62) = h/3

h = 3*tan(62) where h is the height

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If the second number is subtracted from the sum of the first number and 2 times the third number, the result is 1. The thrid num
weeeeeb [17]

Answer:

<h2>x = 0, y = 5, z = 3</h2>

Step-by-step explanation:

x,\ y,\ z-\text{three numbers}\\\\\left\{\begin{array}{ccc}(x+2z)-y=1&(1)\\z+2x=3&(2)\\x+3y+z=18&(3)\end{array}\right\\\\(2)\\z+2x=3\qquad\text{subtract}\ 2x\ \text{from both sides}\\z=3-2x\qquad(*)\\\\\text{Substitute}\ (*)\ \text{to (1) and (3)}\\\\\left\{\begin{array}{ccc}x+2(3-2x)-y=1&\text{use the distributive property}\\x+3y+(3-2x)=18\end{array}\right

\left\{\begin{array}{ccc}x+(2)(3)+(2)(-2x)-y=1\\x+3y+3-2x=18&\text{subtract 3 from both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+6-4x-y=1&\text{subtract 6 from both sides}\\(x-2x)+3y=15\end{array}\right\\\left\{\begin{array}{ccc}(x-4x)-y=-5\\-x+3y=15\end{array}\right\\\left\{\begin{array}{ccc}-3x-y=-5&\text{multiply both sides by 3}\\-x+3y=15\end{array}\right

\underline{+\left\{\begin{array}{ccc}-9x-3y=-15\\-x+3y=15\end{array}\right}\qquad\text{add all sides of the equations}\\.\qquad-10x=0\qquad\text{divide both sides by (-10)}\\.\qquad\boxed{x=0}\\\\\text{Put it to the second equation:}\\-0+3y=15\\3y=15\qquad\text{divide both sides by 3}\\\boxed{y=5}\\\\\text{Put the value of}\ x\ \text{to}\ (*):\\\\z=3-2(0)\\\boxed{z=3}

7 0
3 years ago
Which of the following of x and y would make up the following expression represent a real number? (4+5i)(x+yi)
salantis [7]

Answer:

x = 4 and y = - 5

Step-by-step explanation:

note that the product of a complex number and it's conjugate is real

That is

(a + bi)(a - bi) where a, b are real

= a² - abi + abi - b²i²

= a² + b² ← a real number

For (4 + 5i)(x + yi) to be real

we require (x + yi) to be the conjugate of 4 + 5i , that is 4 - 5i

(4 + 5i)(4 - 5i) ⇒ x = 4 and y = - 5



8 0
2 years ago
Which angle measures create a triangle with three different side lengths?
kenny6666 [7]

13°, 66°, and 101° ......

8 0
3 years ago
Which value is a solution of the equation 85= 120-w?
Ronch [10]
85=120-w\\85-120=120-w-120\\-35=-w\\\frac{-35}{-1}=\frac{-w}{-1}\\35=w

w = 35
8 0
3 years ago
Read 2 more answers
Which of the following is equivalent to cos x?
Otrada [13]

ANSWER

D) sin Y

EXPLANATION

The given triangle is a right triangle.

This implies that that:

x + y = 90 \degree

Then we have

y= 90 - x

Recall that

\cos(x)  =  \sin(90 - x)

But

90 - x = y

When we do the substitution, we get,

\cos(x)  =  \sin(y)

Therefore cos(x) is a equivalent to sin(y).

The correct answer is D.

3 0
3 years ago
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