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balu736 [363]
3 years ago
15

A man wants to cut down a tree in his yard. To ensure that the tree doesn't hit anything, he needs to know the height of the tre

e. He measures his distance from the tree at 11 meters and the angle of elevation to the tree at 61 degrees. What is the height of the tree to the nearest tenth of a meter?
Mathematics
1 answer:
Alisiya [41]3 years ago
8 0

Answer:

19.8m

Step-by-step explanation:

In the attached diagram:

  • The man's eye level is at point A,
  • The height of the tree is BC.
  • The angle of elevation at A is 61 degrees.
  • The distance of the man at A to the tree BC is 11 meters.

This forms the right triangle ABC.

We want to determine the height labeled h.

Using Trigonometry:

\tan \theta =\dfrac{BC}{AB}\\ \tan 61^\circ =\dfrac{h}{11}\\h=11 \times  \tan 61^\circ\\h=19.8$ m

The height of the tree is 19.8 meters to the nearest tenth of a meter.

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Let f(x) = x2 − 8x + 5. Find f(−1)
rewona [7]

Answer:

14

Step-by-step explanation:

f(x)=x^2-8x+5

now substitute x for -1

f(-1)=(-1)^2-8(-1)+5

now solve

f(-1)=1+8+5

f(-1)=14

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2x - 11 = -8x + 14<br> Simplify
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Answer:

x = 2.5

Step-by-step explanation:

2x - 11 = -8x + 14

Add 8x to both sides

10x - 11 = 14

Add 11 to both sides

10x = 25

Divide both sides by 10

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A grocery store manager notices that this month her store sold a total of 623 gallons of ice cream, which represents a decrease
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Answer:

- The store sold 733 gallons of ice cream last month.

- The store sold 748 pounds of broccoli last month.

Step-by-step explanation:

Given

Ice\ Cream = 623

\%\ Ice\ Cream = 15\%

Broccoli = 912

\%\ Broccoli = 22\%

Solving (a): Gallons of Ice Cream

<em>Let Gallons sold last month be G1; Gallons sold this month be G2;</em>

The relationship between both is:

G2 =G1 - 15\% * G1

Substitute 623 for G2

623 =G1 - 15\% * G1

623 =G1 - 0.15 * G1

623 =G1 - 0.15 G1

623 =0.85 G1

Divide through by 0.85

G1 = 623/0.85

G1 = 732.941176471

G1 = 733

Solving (b): Pounds of Broccoli

<em>Let Pounds sold last month be P1; Pounds sold this month be P2;</em>

The relationship between both is:

P2 =P1 + 22\% * P1

Substitute 912 for P2

912 =P1 + 22\% * P1

912 =P1 + 0.22 * P1

912 =P1 + 0.22 P1

912 =1.22 P1

Divide through by 1.22

P1 = 912/1.22

P1 = 747.540983607

P1 = 748

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