Answer:
20ln(3)
Step-by-step explanation:
Put 15 for A and solve for t.
15 = 45e^(-.05t)
15/45 = 1/3 = e^(-.05t) . . . . divide by 45
ln(1/3) = -.05t . . . . . . . . . . . take natural logs
20ln(3) = t . . . . . . . . . . . . . . multiply by 20, simplify
It will take 20·ln(3) years for the area to decrease to 15 km^2.
Answer:
Step-by-step explanation:
roots are (2+3i) and (2-3i)
reqd. eq. is (x-2-3i)(x-2+3i)=0
or (x-2)²-(3i)²=0
or x²-4x+9-9i²=0
or x²-4x+9+9=0
or x²-4x+18=0
Note that x is the hypotenuse of a right triangle. Applying the Pyth. Thm.,
x^2 = 2^2 + 6^2, or x^2 = 4 + 36 = 40.
Thus, the hypotenuse is +sqrt(40), or 2sqrt(10).
The rate of change in temperature is −17°F/min
<h3>Rate of change of a function</h3>
The formula for calculating the rate of change of a function is expressed as:
Rate of change = rise/run
This is also known as the slope of the function
Given the following parameters
Temperature = −25.5°F
Cooling time = 1.5mins
Determine the rate of change
Rate = −25.5°F/1.5min
Rate = −17°F/min
Hence the rate of change in temperature is −17°F/min
Learn more on rate of change here: brainly.com/question/8728504
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If the width of the cardboard = x cm then its length is given by x + 8 cm.
Then the length of the box will be x + 8 - 2(2) = x + 4
and the width = x - 2(2) = x - 4 cm The height is 2 cm
Volume = h*w*l = 2(x - 4)(x + 4) = 256
2(x^2 - 16) = 256
x^2 - 16 = 128
x^2 = 144
x = 12 cm
Dimensions of the box are:-
length = 12 + 4 = 16cm
width = 12 - 4 = 8 cm
height = 2 cm
