Question
Asked Nov 13, 2019
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The fixed sides of an isosceles triangle are of length L = 8 cm. (See the figure.)
L cm
L cm
If the sides slide outward at a speed of 7 cm/min, at what rate is the area enclosed by the triangle changing when 0 = 30°?
(Use symbolic notation and fractions where needed.)
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The fixed sides of an isosceles triangle are of length L = 8 cm. (See the figure.) L cm L cm If the sides slide outward at a speed of 7 cm/min, at what rate is the area enclosed by the triangle changing when 0 = 30°? (Use symbolic notation and fractions where needed.)

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Expert Answer

Step 1

Given that, the length of the triangle is L = 8 cm and the sliding rate of the side is 7 centimeter per second.

dL
cm
That is, the value of sliding rate
7
min
dt
1
L sin 0
2
Note that, the area of the triangle formula is Area
Differentiate the function Area ( A)=-sin 0 with respect to t.
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dL cm That is, the value of sliding rate 7 min dt 1 L sin 0 2 Note that, the area of the triangle formula is Area Differentiate the function Area ( A)=-sin 0 with respect to t.

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Step 2
Differentiate the function Area (A)=-L'sin6
sin e with respect to t
d1
Lsin e
dA
dt 2
dt
d
sine
dt
ainE)
dL
dt
2
dL
= Lsin 0
dt
=8 xsin(300)x 7
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Differentiate the function Area (A)=-L'sin6 sin e with respect to t d1 Lsin e dA dt 2 dt d sine dt ainE) dL dt 2 dL = Lsin 0 dt =8 xsin(300)x 7

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