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Elan Coil [88]
3 years ago
9

A biker notices a mountain directly in front of her and determines that the angle of elevation to the summit is 3.5. After hikin

g 15 miles toward the mountain she records that the angle of elevation is 11. How tall is the mountain? Round the height to the nearest hundredth of a mile

Mathematics
1 answer:
OleMash [197]3 years ago
4 0

Answer:

The mountain is 1.34 miles tall.

Step-by-step explanation:

See the attached diagram.

The height of the mountain is h miles (say).

Now, from the right triangle Δ ABC,

\tan 3.5^{\circ} = \frac{AB}{AC} = \frac{h}{x + 15}

⇒ x + 15 = \frac{h}{\tan 3.5^{\circ}} = 16.35h ........... (1)

Again, from the right triangle Δ ABD,

\tan 11^{\circ} = \frac{AB}{AD} = \frac{h}{x}

⇒ x = \frac{h}{\tan 11^{\circ}} = 5.14h ............. (2)

Now, solving equations (1) and (2) we get,

15 = (16.35 - 5.14)h = 11.2h

⇒ h = 1.34 miles (To the nearest hundredth of a mile)

Therefore, the mountain is 1.34 miles tall. (Answer)

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Tems11 [23]

Answer:

A dependent variable is a factor that changes because of procedures conducted on the independent variable

Step-by-step explanation:

Using a cause and effect analogy, the independent variable is the causal variable. The independent variable or variables are the variables on which what is being measured, has no effect, and it is the variable the investigator manipulates to find the effect on the dependent variable.

The dependent variable are the variables that shows he effect of the changes made and manipulations to the independent variable. The dependent variable is therefore, the effect variable

Therefore, the correct option is ' A dependent variable is a factor that changes because of procedures conducted on the independent variable'

6 0
3 years ago
Question : A square game board is divided into smaller squares, each with sides one-ninth the length of the sides of the board.
bagirrra123 [75]

Answer:

Therefore the game board is divided into 81 smaller squares.

Step-by-step explanation:

Given that, there is a square game.

Consider x be length of one side the square.

The volume of the square is = side ×side

                                               =x² square units

Since the length of side of smaller square is one-ninth of the game board.

Then one side length of the smaller square is \frac19x units.

The area of a smaller square is =(\frac19x)\times (\frac19x)

                                                    =\frac{1}{81}x^2

Let a number of square is formed from the game board.

a ×The area of one smaller square= The area of game board.

According to the problem,

a\times (\frac{1}{81}x^2)=x^2

\Rightarrow a =\frac{x^2\times 81}{x^2}

\Rightarrow a= 81

Therefore the game board is divided into 81 smaller squares.

4 0
3 years ago
Crystal's mud mask costs $23 for a 0.45 oz jar. She found the same mud mask online for $72. What is the size of the jar Crystal
adell [148]
Because .45 divided by 23 is .0195621739
That is how much it is per dollar
That answer times 72 is 1.408695652
So the size of the jar is about 1.41 oz
5 0
2 years ago
Twin brothers,billy and Bobby, can mow their grandparents lawn together in 72 minutes. Billy could mow the lawn by himself in 15
Alla [95]

Answer:

Billy used 28 mins 30 sec to mow the lawn and Bobby used 43 mins 30 sec to now the lawn both within 72 mins

Step-by-step explanation:

let x represent Billy

let x+15 represent Bobby

x + x + 15 = 72

2x = 72 - 15

2x = 57

2x/2 = 57/2

x = 28.5 minutes = 28 minutes 30 seconds

Bobby = x + 15

= 28.5 + 15

= 43.5 minutes= 43 minutes 30 seconds

6 0
2 years ago
SOMEONE PLEASE HELP!
Andrews [41]

Answer:

17.2°

Explanations

To find angle A, use the cosine rule.

a^2 = b^2 + c^2 - 2 × a × c cos A

4^2 = 7^2 + 10^2 - 2 × 7 × 10 cos A

16 = 49+ 100 - 140 × cosA

16 = 149 - 140cosA

16- 149 = - 140cosA

-133 = - 140cosA

cosA = 133/140

cosA = 0.95

A = 17.2°

7 0
1 year ago
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