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3 years ago

A hiker at the top of a mountain spots his car back in the parking lot at the

Mathematics

1 answer:

mart [117]3 years ago

3 0

<h2>Answer:</h2><h2>The angle of depression from the hiker to his car, Θ = 56.39 degrees</h2>

Step-by-step explanation:

A hiker at the top of a mountain spots his car back in the parking lot at the

bottom of the trail. If the trail is 632 meters long and the mountain is 420

meters tall,

opposite side = 632 m

adjacent side = 420 m

Angle of depression, Θ = arctan $(\frac{opposite}{adjacent} )$

= arctan $(\frac{632}{420} )$

Θ = 56.39 degrees

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Find m\angle Cm∠Cm, angle, C.<br> Round to the nearest degree.<br><br> Help Course Challenge

astra-53 [7]

Hello,

1. Since Angle C has the longest side for this triangle, it will have the largest degree value.

2. Use the Law of Cosines and inverse properties of “theta” to solve for Angle C. (Ensure that the calculator used is in “degree mode”, not “radian mode”.

c^2 = a^2 + b^2 - 2(a)(b)(cos (C))
15^2 = 11^2 + 14^2 - 2(11)(14)(cos(C))
225 - 317 = -2(11)(14)(cos(C))
-92 / -2(11)(14) = cos(C)
cos(C) becomes ->> cos^-1[92 /-2(11)(14)] = 72.62° ->> to the nearest degree is 73°

The answer for angle C, 73°, is logical because the triangle in the picture represents a 60-60-60 triangle, known as an equilateral triangle.

Good luck to you!

5 0

2 years ago

Read 2 more answers

Which set of numbers best describes the possible values of x in the equation below?[x-1]=[x] all integer values of x all real nu

SCORPION-xisa [38]

[x] represents floor function also called as Greatest integer function.

Floor function is the function that takes as input a real number and gives as output the greatest integer less than or equal to.

like [1.5]=1

[0.7]=0

[-0.3]=-1

Now we have to find set of x-values which satisfies equation [x-1]=[x]

Due to -1 in [x-1], it always produces output value one less than value of [x]

for example when x=0.5 then [x]=[0.5]=0, [x-1]=[0.5-1]=[-0.5]=-1

when x=1.5 then [x]=[1.5]=1, [x-1]=[1.5-1]=[0.5]=0

when x=3 then [x]=[3]=3, [x-1]=[3-1]=[2]=2

From above results we can see that there is no value of x which satisfies the given equation [x-1]=[x]

Hence there is NO solution.

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3 years ago

Read 2 more answers

Solve this quadratic equation. x2 + 5x + 3 = 0

malfutka [58]

Answer:

x=5+132,5−132x=\frac{5+\sqrt{13}}{2},\frac{5-\sqrt{13}}{2}

x= 2 5+√ 13, 2 5−√ 13

Step-by-step explanation: learn yourself

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2 years ago

Find the value of each determinant

Ksenya-84 [330]

Answer:

−4304

Step-by-step explanation:

1. The given determinant is :

$\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}$

We need to find its determinant . It can be solved as follows :

$\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}=7(14)-142(31)\\\\=-4304$

So, the value of determinant is equal to −4304.

6 0

2 years ago

Can someone please help me please

qwelly [4]

Answer:

$1) \dfrac{12+\sqrt{-16}}{4}=\dfrac{12+\sqrt{16i^{2}}}{4}\\\\\\=\dfrac{12+4i}{4}=\dfrac{12}{4}+\dfrac{4i}{4}\\\\\\= 3 + i$

Real part = 3 & imaginary part = 1

2) 4 + 7i - 8 = 4 -8 + 7i

= -4 + 7i

Real part = -4 & imaginary part = 7

$3)\dfrac{\sqrt{9}+\sqrt{-4}}{5}=\dfrac{3+\sqrt{4i^{2}}}{5}\\\\\\=\dfrac{3}{5}+\dfrac{2i}{5}\\\\\\Real \ part = \dfrac{3}{5} \ & \ imaginary \ part = \dfrac{2}{5}$

$4) -2-\sqrt{-25}=-2-\sqrt{25i^{2}}=-2-5i$

Real part = -2 & imaginary part = -5

$5)\dfrac{15-13i}{3}=\dfrac{15}{3}-\dfrac{13i}{3}\\\\\\Real \ part = \dfrac{15}{3} \ & \ imaginary \ part = \dfrac{-13}{3}$

b) 1) 6 + 4i

2) -12+ 5i

3) 5-14i

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2 years ago