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Lubov Fominskaja [6]
3 years ago
8

A lawn is in the shape of a trapezoid with a height of 7070 feet and bases of 4040 feet and 160160 feet. how many full bags of f

ertilizer must be purchased to cover the lawn if each full bag covers 40004000 square feet and only full bags of fertilizer can be​ bought?
Mathematics
1 answer:
Leni [432]3 years ago
7 0
Area of the trapezium = 1/2 (40 + 160) x 70
Area of the trapezium = 7000 ft²

One bag of fertilizer = 4000 ft²

Number of bags of fertilizer needed  = 7000 ÷ 4000 = 1.75 bags.

Since only full bags of fertilizer can be bought, 2 bags of fertilizer are needed.

------------------------------------
Answer: 2 bags of fertilizer
------------------------------------

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The gear is one of the oldest mechanical devices. It has been used since ancient times for its ability to increase or decrease r
eduard

The large gear attached to the pedals connected to the smaller gear

attached to the wheel allows the bicycle to travel further per rotation.

Correct responses:

Part A: Approximately 10.47 inches

Part B: 300°The d

Part C: Approximately 125.66 inches

Part D: The distance traveled increases by approximately 62.83 inches

<h3 /><h3>Methods used to calculate the above values</h3>

Given:

The radius of the large central gear, <em>r</em> = 4 inches

Radius of the small gear = 2 inches

Part A:

The distance travelled by the larger gear when the angle of rotation is 150° is given as follows;

\displaystyle Distance \ travelled \ by \ larger \ gear = \mathbf{\frac{150^{\circ}}{360^{\circ}} \times 2 \times \pi \times  4 \, inches} = \frac{10}{3} \cdot \pi \ inches

  • \displaystyle Distance \ traveled \ by \ the \ outer \ edge = \frac{10}{3} \cdot \pi \ inches  \approx \underline{ 10.47 \ inches}

Part B:

When the small gear travels the same linear distance as the large gear in part A, we have;

\displaystyle Degree \ of \ rotation = \frac{\frac{10}{3} \cdot \pi }{2 \times \pi \times  2 } \times 360^{\circ}= 300^{\circ}

  • The degree of rotation of the small gear = <u>300°</u>

Part C:

The distance travelled, <em>C</em>, by a single rotation of the large gear is given as follows;

C = 2 × π × 4 inches = 8·π inches

The degree of rotation of the smaller gear following one rotation of the large gear is therefore;

Degree  \ of \ rotation = \displaystyle \frac{8\cdot \pi \ inches}{4 \cdot \pi \ inches } \times 360^{\circ} = \mathbf{ 720^{\circ}}

720° = 2 × 360°

1 complete rotation is equivalent to 360°.

Therefore'

720° is equivalent to two complete rotation.

Therefore, the smaller gear and the wheel rotates twice for each rotation of the large gear

The distance the bicycle travels = 2 × The circumference of the wheel

Therefore;

Distance traveled by the bicycle = 2 × 2 × π × 10 inches = 40·π inches

  • Distance traveled by the bicycle = 40·π inches ≈ <u>125.66 inches</u>

Part D:

If the radius of the small gear is 1.5 inches and the radius of the large gear is 4.5 inches, we have;

Number of rotation of the small gear for each rotation of the large gear = 3 rotations

Therefore, number of rotation of the wheel = 3

Distance the bicycle travels = 3 × 2 × π × 10 inches = 60·π inches

The difference in distance traveled = 60·π inches - 40·π inches = 20·π inches

  • The distance traveled by the bicycle increases by 20·π inches ≈ <u>62.83 inches</u>

Learn more about gear transmission here:

brainly.com/question/14646065

brainly.com/question/3926797

8 0
2 years ago
1.404 divided by 0.45
Ipatiy [6.2K]
The answer to your questions is 3.12
7 0
3 years ago
A rectangular prism is 12 inches long, 9 inches wide, and 6 inches high. What is the volume of the prism?
zmey [24]

Answer:

Volume = 12×9×6 = 648 inches^3

Step-by-step explanation:

Hope this helps! Have a nice day!

5 0
3 years ago
Can someone please help me
nadya68 [22]

Answer:

<u>Right</u><u> </u><u>option</u><u> </u><u>is</u><u> </u><u>B</u><u>.</u><u> </u>

Step-by-step explanation:

\sf  \longrightarrow \frac{ \sec x \sin( - x)  +  \tan( - x) }{1 +  \sec( - x) }  \\  \\  \sf \longrightarrow  \frac{ \sec x( -  \sin x) -  \tan x}{1 +  \sec x}  \\  \\  \sf  \longrightarrow   \frac{  - \frac{1}{ \cos x } \times  \sin x -  \tan x }{1 +  \sec x}  \\  \\  \sf  \longrightarrow \frac{ -  \tan x -  \tan x}{1 +  \sec x}   \\  \\  \sf  \longrightarrow  \frac{ - 2 \tan x}{1 +  \sec x}  \\  \\  \sf \longrightarrow   \frac{  \frac{ - 2 \sin x}{ \cos x} }{1 +  \frac{1}{ \cos x} }  \\  \\  \sf  \longrightarrow  \frac{  \frac{ - 2 \sin x}{ \cos x} }{ \frac{ \cos x + 1}{ \cos x} }  \\  \\     \boxed{  \sf{\longrightarrow \frac{ - 2 \sin x}{ \cos x + 1}  }}

4 0
1 year ago
The school buses at a middle school each hold 38 students. The school has, b, buses.
mel-nik [20]

Answer:

38bs

Step-by-step explanation:

multiply the number of students that each bus can hold by the no of buses 38s×b=38bs

8 0
3 years ago
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