Mathematics, 26.11.2020 01:20 katelynalivia

A goat is tired to a pole at the center of a square of length of side 20m. If the rope is 10m long. Calculate the (I) area of the square that can't be grazed by the goat (ii) fraction of grazed portion to the whole area

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Answer from: NutMeg6544

percentage = 78.54%

Step-by-step explanation:

The area of a square of side length x is:

A_s=x^2

The area of a circle of radius r is:

$A_c=\pi r^2$

The goat is tied to a pole at the center of a square of a side length of x=20 cm.

The area of the square is:

A_s=20^2

A_s=400~m^2

The rope is 10 m long. The goat is able to graze an area of:

$A_c=\pi 10^2$

$A_c=100\pi~m^2$

(i)

Since the diameter of the circle (20 m) is equal to the length of the square, the area of the circle is contained in the square and the area of the square not grazed by the goat is:

$A = A_s-A_c=400~m^2-100\pi~m^2$

$A=100(4-\pi)~m^2$

Calculating:

A = 85.84~m^2

(ii)

The percentage can be calculated as:

$\displaystyle \frac{A_c}{A_s}*100=\frac{100\pi}{400}*100=25\pi$

Calculating:

percentage = 78.54%

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

Answer from: Quest

b. 18

step-by-step explanation:

so the equation for this is:

ab^2=ac⋅ad

ab being the top length of 6 and ac being the length of 2 and ad being the length of x. let's plug into the equation:

6^2 = 2x

now lets just solve for x:

36 = 2x

18 = x

i hope that !

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