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Sauron [17]
2 years ago
10

A rope is tied to the bottom of a hot air balloon ad shown below The rope makes an angle of 35 with the ground and is 75 ft long

. How far is the bottom of the balloon from the ground to the nearest foot .
Mathematics
1 answer:
damaskus [11]2 years ago
6 0

Answer:

The answer to your question is 43 ft

Step-by-step explanation:

Data

angle = Ф = 35°

length = 75 ft

height = ?

Process

To solve this problem, use trigonometric functions. The trigonometric function that relates the Opposite side (height) and the hypotenuse (length) is sine.

               sin Ф = Height / length

-Solve for height

                height = length x sin Ф

-Substitution

                height = 75 x sin 35

-Simplification

                height = 75 x 0.574

-Result

                 height = 43 ft

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IrinaVladis [17]

Answer:

  • 3/5 kg

Step-by-step explanation:

The weight of an object on Moon is 6 times smaller than same on Earth.

<u>If it weights 18/5 kg on Earth then its weight  on Moon is:</u>

  • 18/5 * 1/6 = 3/5 kg
4 0
2 years ago
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Find the equation of the circle with center at the origin and x-intercepts 12 and -12
Troyanec [42]
Since the radius is 12, the equation is
.. x^2 +y^2 = 144
5 0
3 years ago
Lizzie has 30 coins that total $4.80. All of her coins are dimes, D, and quarters, Q. Algebraically determine how many of each t
Gnom [1K]

Lizzie has 18 dimes and 12 quarters

<em><u>Solution:</u></em>

Let "d" be the number of dimes

Let "q" be the number of quarters

We know that,

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

Given that LIzzie has 30 coins

number of dimes + number of quarters = 30

d + q = 30 ---- eqn 1

Also given that the coins total $ 4.80

number of dimes x  value of 1 dime + number of quarters x  value of 1 quarter = 4.80

d \times 0.10 + q \times 0.25 = 4.80

0.1d + 0.25q = 4.8 ------ eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

d = 30 - q ---- eqn 3

Substitute eqn 3 in eqn 2

0.1(30 - q) + 0.25q = 4.8

3 - 0.1q + 0.25q = 4.8

0.15q = 1.8

<h3>q = 12</h3>

From eqn 3,

d = 30 - 12

<h3>d = 18</h3>

Thus she has 18 dimes and 12 quarters

6 0
3 years ago
If x varies directly with y and x = 2.5 when y = 10, funny x when y = 16.
amid [387]

Answer:

Should be 4.0(Not sure tho. my thought process is complicated but to me it makes sense)

Step-by-step explanation:

If y=10 and x =2.5, if y were to = 20, then x would equal 5. so you take that ratio, and say 6 is 3/5's the way to 10, so you also divide 2.5 by 3/5

you get 1.5, you add that to x already and you get 4.0

so if y=16, x should =4.0

3 0
3 years ago
Divide 3xsquared - 11x - 4 by x - 4<br><br>a. x+1<br>b. x-23<br>c. 3x+1<br>d. 3x-23​
Dmitriy789 [7]

Answer:

c. 3x+1

Step-by-step explanation:

Since the divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, <em>-c</em> gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

4| 3 −11 −4

↓ 12 4

_______________

3 1 0 → 3x + 1

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [3x² - 11x - 4]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 3 in your quotient can be a 3x, and the 1 follows right behind it, giving you the quotient of 3x + 1.

I am joyous to assist you anytime.

5 0
3 years ago
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