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Lunna [17]
2 years ago
6

An element with mass 310 grams decays by 5.7% per minute. How much of the element is remaining after 9 minutes, to the nearest 1

0th of a gram?
Mathematics
1 answer:
katen-ka-za [31]2 years ago
8 0
1st
I need to find out what percentage is left after 1 minute
100 - 5.7 = 94.3% (0.943)

2nd plug into the formula A =  A_{0}  r^{t}

A0 = 310
r = 0.943
t = 9

A = 310(0.943)^{9} \\ A = 310(0.58966) \\ A = 182.8 g
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Answer: Sara multiplied by 3 when she should have multiplied by 8.

Step-by-step explanation:

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3 years ago
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

= (-720/sin²(67.38))*0.0042

= (-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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