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morpeh [17]
3 years ago
6

(50 points)There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If t

he total number of swans and ducks in the pond is 12, find the number of ducks.
Mathematics
2 answers:
RoseWind [281]3 years ago
6 0

there are nine ducks and 3 swans

sqrt of 9 equals 3

3 + 9 = 12

kirza4 [7]3 years ago
4 0

Answer:

The number of ducks are 9.

Step-by-step explanation:

There are x ducks in a pond.

The number of swans in the pond is equal to the square root of the number of ducks.

Means swans = \sqrt{x}

If the total number of swans and ducks in the pond is 12.

x+ \sqrt{x} =12

=> \sqrt{x} =12-x

Squaring both sides, we get

x=x^{2} +144-24x

=> Taking everything on one side and equating to 0

x^{2} -x-24x+144=0

=> x^{2}-25x+144=0

=> Solving this we get, x = 9 and x = -16

So, we have number of ducks as 9.

And number of swans = \sqrt{9} =3

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On a morning of a day when the sun will pass directly​ overhead, the shadow of a 60​-ft building on level ground is 25 ft long.
AysviL [449]

Answer:

The shadow is decreasing at the rate of 3.55 inch/min

Step-by-step explanation:

The height of the building = 60ft

The shadow of the building on the level ground is 25ft long

Ѳ is increasing at the rate of 0.24°/min

Using SOHCAHTOA,

Tan Ѳ = opposite/ adjacent

= height of the building / length of the shadow

Tan Ѳ = h/x

X= h/tan Ѳ

Recall that tan Ѳ = sin Ѳ/cos Ѳ

X= h/x (sin Ѳ/cos Ѳ)

Differentiate with respect to t

dx/dt = (-h/sin²Ѳ)dѲ/dt

When x= 25ft

tanѲ = h/x

= 60/25

Ѳ= tan^-1(60/25)

= 67.38°

dѲ/dt= 0.24°/min

Convert the height in ft to inches

1 ft = 12 inches

Therefore, 60ft = 60*12

= 720 inches

Convert degree/min to radian/min

1°= 0.0175radian

Therefore, 0.24° = 0.24 * 0.0175

= 0.0042 radian/min

Recall that

dx/dt = (-h/sin²Ѳ)dѲ/dt

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= (-720/0.8521)*0.0042

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Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min

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3 years ago
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