Answer:
Step-by-step explanation:
Apply natural log property
ln mn=ln m + ln(n), ln(m/n)=ln(m)-ln(n)
All natural log has base 'e'
cross multiply
add 6e^3 on both sides and -x on both sides
Divide e^3-1 on both sides
a skydiver jumps out from the plane at 10,000 feet above the ground. the skydiver decends at a rate of 175 feet per seconds. how
2 answers:
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Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>
By the Product Rule:
Since we know that dl/dt = 6 and that dw/dt = 5:
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.