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defon
3 years ago
9

A 50-foot flagpole near an office building casts a shadow

Mathematics
1 answer:
Alexus [3.1K]3 years ago
8 0

Step-by-step explanation:

Here are some hints: "At the same time,"means you need to set up a proportion (two ratios equal each other).

The shadow is always on the ground.

A person and a flagpole always stands up straight, like a wall (vertical height)

Underline key words and numbers. Draw a picture for sure.

|

|X 5.5 ft. |

|____________ |____

flagpole=50 feet person's shadow=4 feet

shadow

Since it is easier to work with one type of measurement, change the person's height to feet only. The person is 5feet, 6inches Note: 12 inches= 1 foot, so 6 inches= 1/2 a feet and 6 inches= .5 feet

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Write an equation to describe the proportional relationship in this table. Explain your thinking and how you got your answer.
creativ13 [48]

Focus on the values in red outside the table (on the left and right sides). As the output increases by 4, the input increases by 1. This leads to the slope being rise/run = 4/1 = 4. The slope is the number just to the left of the x variable. So that's how they ended up with the equation y = 4x.

You can think of it as y = 4x+0, and note how it's in the form y = mx+b

m = 4 = slope

b = 0 = y intercept

The y intercept is the value of y when x = 0.

--------

Now because x = 0 and y = 0 pair up together, we can find the slope a different way: Pick any row other than the first row. Divide the y value over its paired x value. So let's say we pick on row two and we'd get a slope of y/x = 4/1 = 4.

Or we could pick on row three and get y/x = 8/2 = 4.

Picking on the fourth row gets us the slope to be y/x = 12/3 = 4. We end up with the same slope value each time. Again, this trick only works if (x,y) = (0,0) is on the line. Otherwise, you'll need to use the first method or use the slope formula.

For equations like this, we consider them a direct proportion. As x increases, so does y. As x increases by 1, y increases by 4. This is the same throughout the table.

----------

A real world example of this could be that x represents the number of sodas you buy, and if each soda is $4, then y = 4x represents the total cost of buying x number of sodas.

For instance, if you bought x = 10 sodas, then y = 4*x = 4*10 = 40 dollars is what you spend overall.

7 0
3 years ago
1.) A tower casts a shadow that is 60 feet long when the angle
Fynjy0 [20]

Answer:

128.67 ft

Step-by-step explanation:

Let the height of the tower be x feet.

\tan \: 65 \degree =  \frac{x}{60}  \\  \\ 2.1445069205 =  \frac{x}{60}  \\  \\ x = 2.1445069205 \times 60 \\ \\  x = 128.670415 \\  \\ x = 128.67 \: ft

8 0
2 years ago
I neeeddd helppppppppp
Marina CMI [18]

Answer:

4.

Step-by-step explanation:

A and D are opposite.

A is in the negative side and d is in the positive side.

6 0
3 years ago
What is the total probability of rolling a single die twice, and having it land on 3 the
Shtirlitz [24]

Answer:

0,5*0,5=0,25

Step-by-step explanation:

assuming a die of 6 faces

25

0,5 for < 4; 0,5 for < 3

5 0
2 years ago
If one person runs 8.1 miles per hour in one direction and another with a speed of 6.3 in an other direction how many hours woul
djverab [1.8K]

Answer:

1.4 hours

Step-by-step explanation:

Runner A:

Speed = 8.1 mph

Time, = t

Runner B :

Speed = 6.3 mph

Time, = t

Distance apart = 20.16 miles

Distance = speed * time

Distance of Runner A + Distance of runner B = distance apart

8.1t + 6.3t = 20.16

14.4t = 20.16

t = 20.16 / 14.4

t = 1.4 hours

Number of hours, t = 1.4 hours

7 0
2 years ago
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