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Neporo4naja [7]
3 years ago
14

An oval track is made by erecting semicircles on each end of a 60m by 120m rectangle. Find the length of the track and the area

enclosed by the track

Mathematics
1 answer:
vodomira [7]3 years ago
3 0
Refer to the figure shown below.

Because the question states that the semi circles are at the ends of the rectangle, each semicircle has a radius of 30 m.

The circumference of the oval is
2π(30) + 2*120 = 60π + 240 m = 428.5 m

The area of the oval is 
π(30²) + 60*120 = 900π + 7200 m² = 1.0027 x 10⁴ m²

Note:
If the semi circles are placed on the 120-m sides of the rectangle, then similar calculations yield:
Circumference = 120π + 120 m = 497 m
Area = 3600π + 7200 m² = 1.851 x 10⁴ m²

Answer:
If the semi circles are placed on the 60-m sides of the rectangle, then
Circumference = 60π + 240 m, or 428.5 m
Area = 900π + 7200 m², or 1.0027 x 10⁴ m²

if the semi circles are placed on the 120-m sides of the rectangle, then
Circumference = 120π + 120 m, or 497 m
Area = 3600π + 7500 m², or 1.851 x 10⁴ m²


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A 12-meter ladder leans against a building forming a 30° angle with the building.
KatRina [158]

Answer:

will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

The wall is on the right. The ladder leans against the wall

with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).

The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

The ladder, ground and wall form a right triangle.

 

The hypotenuse (ladder) is 14 feet.

 

 The bottom of the ladder is 6 feet from the wall,

  so the base of this right triangle is 6 feet.

 

The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

 6^2 + h^2 = 14^2   where h is the height

                                 of the top of the ladder to the ground

 

36 + h^2 = 196

 

 h^2 = 196 - 36

 

h^2  = 160

 

h = sqrt(160)

 

   = sqrt(16 * 10)

 

    = sqrt(16)* sqrt(10)

 

    = 4*sqrt(10) <--- exact answer

 

    = 4 * 3.16227766016838....

 

     = 12.64911....

 

    12.65 <--- rounded to 2 digits as directed

 

----------------------------------------------

Option #2: using trig

 

With respect to the angle formed by the bottom of the

ladder with the ground

  cos T = 6/14 = 3/7  

 T = inverse-cosine(3/7) = 64.623006647 degrees

 

 sin(64.623006647) = h/14

 

 h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        

hope this helps

Step-by-step explanation:

5 0
2 years ago
What is 55x690-20+438x129=? <br> I will give brainliest.
frosja888 [35]

Answer:

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7 0
3 years ago
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If there are 16oz in a pound how many oz are in 10 pounds
liq [111]
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4 0
3 years ago
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If c(x)=x-2 what is the value of x if c(x)=3.5
dsp73

Answer:

5.5 = x

Step-by-step explanation:

c(x)=x-2

3.5 = x-2

Add 2 to each side

3.5+2=x-2+2

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3 0
3 years ago
Tan 1.1 – tan 4.6/
VladimirAG [237]

The value of the given equation is –0.37458.

Solution:

Given equation is:

$\frac{\tan 1.1-\tan 4.6}{1+\tan 1.1 \tan 4.6}

Let us first find the values.

The value of tan 1.1 = 1.96475

The value of tan 4.6 = 8.86017

Substitute these values in the given equation.

$\frac{\tan 1.1-\tan 4.6}{1+\tan 1.1 \tan 4.6}

            $=\frac{1.96475-8.86017}{1+1.96475 \times 8.86017}

            $=\frac{-6.89542}{1+17.4080}

            $=\frac{-6.89542}{18.4080}

            = –0.37458

$\frac{\tan 1.1-\tan 4.6}{1+\tan 1.1 \tan 4.6}=-0.37458

Hence the value of the given equation is –0.37458.

7 0
3 years ago
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