3 years ago

Write an inequality.

Mathematics

1 answer:

lukranit [14]3 years ago

5 0

Answer:

C ≥ 35/100c

Step-by-step explanation:

c ≥ 35%/100c

Sorry I don't know if this is right but it's my guess.

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Answer:

a) 70

b) 10π ft²/ft

c) 0.24 ft/sec

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1) y = x³ + 2x

$\frac{dy}{dt}=\frac{d(x^3+2x)}{dt}$

$\frac{dy}{dt}$ = $3x^2\frac{dx}{dt}+2\frac{dx}{dt}$

at $\frac{dx}{dt}=5$ and x = 2

$\frac{dy}{dt}$ = $3(2)^2\times(5)+2\times(5)$

$\frac{dy}{dt}$ = 60 + 10 = 70

2) A = πr² ft²

$\frac{dA}{dr}=\frac{d(\pi r^2)}{dr}$

$\frac{dA}{dr}$ = 2(πr)

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$\frac{dA}{dr}$ = 2(π × 5) ft²/ft

$\frac{dA}{dr}$ = 10π ft²/ft

3) From Pythagoras theorem

Base² + Perpendicular² = Hypotenuse²

Thus,

B² + P² = H² .............(1)

here, H = length of the ladder

P is the height of the wall

B is the distance from the wall at bottom

B² + P² = 25² ...........(1)

at B = 20 ft

20² + P² = 25²

P² = 625 - 400

P = √225

P = 15 ft

differentiating (1) with respect to time, we get

$2B\frac{dB}{dt}+2P\frac{dP}{dt}=0$

at B = 20 ft, $\frac{dB}{dt} = 0.18$ and P = 15 ft

⇒ 2(20)(0.18) + $2(15)\frac{dP}{dt}$ = 0

$30\frac{dP}{dt}$ = - 7.2

$\frac{dP}{dt}$ = - 0.24 ft/sec (Here negative sign depicts the ladder slides down)

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