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kari74 [83]
3 years ago
5

A falcon flying at a height of 200 yards spots a sparrow flying at a height of 150 yards. The location of the sparrow makes an a

ngle of 40° from the horizontal line through the falcon's location. What is the distance x between the falcon and the sparrow? Assume that the ground beneath the birds is level.
Mathematics
1 answer:
Sonja [21]3 years ago
4 0
The difference of the heights of the falcon and the sparrow:
200 - 150 = 50 yards
sin 40° = 50 / x
x = 50 / sin 40°
x = 50 / 0.6428
x = 77.8 ≈ 78 yd
Answer:
The distance between the falcon and the sparrow is D ) 78 yards.
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mixas84 [53]

So x + y = 45, and 4x + 5y = 195. Get y by itself. Subtract x from both sides in the first equation to get y = 45 -x, and subtract 4x from the second equation to get 5y = 195 - 4x. Divide by 5 to both sides to get y = 39 - 4/5x. 39 - 4/5x = 45 - x. Add x to both sides to get 39 - 1/5x = 45. Subtract 39 from both sides to get -1/5x = 6. Divide by -1/5 to get x = -30, or 30. In the first equation, do 30 + y = 45. Subtract 30 from both sides to get y = 15. Check. 4(30) + 15(5) = 195, or 120 + 75 = 195.


5 0
4 years ago
Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation h = ?16t + 160t + 12
insens350 [35]

Answer:

The time taken for the flare to hit the ground is approximately 10.7 seconds.

Step-by-step explanation:

Given : Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation h =- 16t^2+ 160t + 120 models the h height at t seconds of the flare.

To find : How long will it take for the flare to hit the ground?

Solution :

The equation  h =- 16t^2+ 160t + 120 models the h height at t seconds of the flare.

The flare to hit the ground when h=0.

Substitute in the equation,

-16t^2+ 160t + 120=0

Applying quadratic formula, x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Where, a=-16, b=160 and c=120

x=\frac{-160\pm\sqrt{160^2-4(-16)(120)}}{2(-16)}

x=\frac{-160\pm\sqrt{33280}}{-32}

x=\frac{-160\pm 182.42}{-32}

x=\frac{-160+182.42}{-32},\frac{-160-182.42}{-32}

x=−0.70,10.70

Reject the negative value.

Therefore, the time taken for the flare to hit the ground is approximately 10.7 seconds.

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Step-by-step explanation:

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I think the answer is c sorry if I’m wrong
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