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Dovator [93]
3 years ago
12

X/5 = 15 (Solving Linear Equations)

Mathematics
1 answer:
tiny-mole [99]3 years ago
3 0
\dfrac{x}{5}=15\\
x=75
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A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the
Zigmanuir [339]

Answer:

Step-by-step explanation:

aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:

tanθ = opp/adj = y/x

y = xtanθ

What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):

dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)

We need to find out values for all of the variables:

The observer is not moving, therefore dx/dt = 0.

The observer is standing 4 miles away from the lift-off point, so x = 4.

The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.

The rate of change for the angle, dθ/dt, is 0.1.

Just plug all the numbers in:

dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)

dy/dt = 0 + 1.6

dy/dt = 1.6 mi/min

5 0
2 years ago
Please show your work. Thank you for taking the time of day to help me!
34kurt

Answer:

30

Step-by-step explanation:

Look at the bottom line of the chart.

He sold 41 sides of French fries and 40 sides of onion rings.

41 + 40 = 81

Since he sold a total of 81 sides with bacon cheeseburgers, that means he sold a total of 81 bacon cheeseburgers.

We have a ratio:

81 bacon cheeseburgers to 40 sides of onion rings

Now he sold 120 bacon cheeseburgers, so we set up a proportion to find the number of sides of onion rings. Let the unknown number be x.

81 burgers is to 40 sides as 120 burgers is to x sides

81/40 = 120/x

We solve for x by cross multiplying.

81x = 40 * 120

81x = 4800

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That means he serves 59 sides of onion rings.

Each serving of onion rings is half pound.

59 * 0.5 = 29.5

For 120 bacon cheeseburgers, he serves approximately 29.5 lb of onion rings.

Answer: 30

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13. 23 boat rides; 22 are full, and the first one has 301 passengers.

12. $11,067.50

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In triangle DEF, side DE is 3 inches, side EF is 4 inches, and sides DF is 5 inches. The largest angle is opposite which side.?
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The longest angle would be across from the one with the longest side. In this case it would be across from DF
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2+2+1 3/4+1 1/4+1+1=9 . Hope this helps :)
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