4. a horse is tethered to one corner of a square plot of side 42 m, by a rope 35 m long. find i) what area it can graze ii) what area will be left ungrazed.

Answers:

i) It can graze an area of approximately 961.625 square meters

ii) The ungrazed area is roughly 802.375 square meters

note: I used pi = 3.14 which is approximate; if you want more accuracy, use more decimal digits in pi

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Explanation:

Check out the attached image below for a visual diagram.

The area of a circle is the formula

A = pi*r^2

Use r = 35 as the radius and pi = 3.14 as the approximation for pi, to get,

A = pi*r^2

A = 3.14*35^2

A = 3846.5

Then divide this by 4 to get the area of a quarter circle

A/4 = 3846.5/4 = 961.625

This is the approximate area the horse can graze

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Subtract this from 42^2 = 42*42 = 1764 because this is the area of the entire square. Doing this will get you the ungrazed area

Ungrazed area = (entire plot) - (grazed area)

Ungrazed area = (entire area of square) - (area of quarter circle)

Ungrazed area = 1764 - 961.625

Ungrazed area = 802.375

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1