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2 years ago

If a 25-meter flagpole casts a shadow that is 50 meters long, how long is the shadow cast by a tree that is 40 meters tall

Mathematics

1 answer:

Vedmedyk [2.9K]2 years ago

7 0

Answer:

The shadow cast by the tree is 80 meters long.

Step-by-step explanation:

Flagpole:

object/shadow

25/50 = 1/2

Tree:

object/shadow

40/x

Solve for x:

1/2 = 40/x

x = 80

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Determine the angles made by the vector v = (67)i + (-15)j with the positive x- and y-axes. write the unit vector n in the direc

vivado [14]

Consider the picture attached.

From right triangle trigonometry:

tan(α)=(opposite side)/(adjacent side)=15/67=0.2239

using a scientific calculator we find that arctan(0.2239)=12.62°

thus α=12.62°, is the angle that the vector makes with the positive x-axis.

The angle made with the + y-axis is 12.62°+90°=102.62°.

The length of the vector v can be determined using the Pythagorean theorem:

$|v|= \sqrt{ 67^{2} + 15^{2} }= \sqrt{4489+225}= \sqrt{4714}=68.8$

Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.

This means that the x and y components will also be divided by 68.8, by proportionality.

So, the unit vector in the direction of v is:

(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j


Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j

6 0

3 years ago

Q1. In a fruit cocktail, for every 30 ml

lora16 [44]

Answer:

3/10

Step-by-step explanation:

$\frac{30}{30 + 20 + 50} = \frac{3}{10}$

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2 years ago

Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars)

Natalija [7]

Revenue, R = 130x

Profit, P = Revenue – Cost

P = R – C

P = 130x – 2950 + 6x + 0.1x^2

At P = 0

0 = -2950 + 136x +0.1x^2

X = 21.355, -1381.355

Therefore, manufacture greater than 21.355 items to make profit.

3 0

3 years ago

Read 2 more answers

If you invest $4,500 in an account paying 2% compounded continuously, how much money will be in the account at the end of 4 year

saveliy_v [14]

Total = Principal * e^(rate*years)
Total = 4,500 * 2.718281828459^(.02*4)
Total = 4,500 * 2.718281828459^(.08)
Total = 4,500 * 1.0832870677 
Total = 4,874.79 
calculator for checking the answer:
http://www.1728.org/compint.htm

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2 years ago

It is difficult to override a presidential veto?Why do you think is it difficult? Do you think thisgood thing? Why or why not?

Vanyuwa [196]

It is difficult to overthrow a presidential veto because each house has to have a two-thirds majority vote to overthrow The veto. it is difficult because 2/3 is more than 1/2 and it has to be in each house so it is very difficult. I think this is a good thing because if Congress wanted to pass a bill the president did not like then it is hard for them to pass it and the president is the leader so he should make the big decisions.

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3 years ago