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3 years ago

Find the area of the shaded region in the simplest form

Mathematics

2 answers:

balandron [24]3 years ago

8 0

Answer:

A = 24t² + 2t

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of outer square - area of rectangle

= (5t)² - t(t - 2)

= 25t² - t² + 2t

= 24t² + 2t

JulijaS [17]3 years ago

8 0

What’s the woman said above ☺️

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2 years ago

An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.8 millimeters per minute At what rate is the

julia-pushkina [17]

Answer:

The rate of decrease is: $43.2mm^3/min$

Step-by-step explanation:

Given

$l = 18mm$

$\frac{dl}{dt} = -0.8mm/min$ ---- We used minus because the rate is decreasing

Required

Rate of decrease when: $l = 18mm$

The volume of the cube is:

$V = l^3$

Differentiate

$\frac{dV}{dl} = 3l^2$

Make dV the subject

$dV = 3l^2 \cdot dl$

Divide both sides by dt

$\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}$

Given that: $l = 18mm$ and $\frac{dl}{dt} = -0.8mm/min$

$\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)$

$\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min$

$\frac{dV}{dt} = -43.2mm^3/min$

<em>Hence, the rate of decrease is: 43.2mm^3/min</em>

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3 years ago