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3 years ago

Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x^2-21=0

Mathematics

1 answer:

zavuch27 [327]3 years ago

7 0

Answer:

x = 1.53, -1.53.

Step-by-step explanation:

9x^2 - 21 = 0

9x^2 = 21

x^2 = 21/9

x = +/- √21 / 3

x = 1.53, -1.53.

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3. A person standing 3 feet away from the base of a lamp post casts a shadow 4 feet long. If the person is 6 feet tall and walks

german

Answer:

533.33 ft/min

Step-by-step explanation:

We are given that

x=3 feet

y=4 feet

Height of person,h=6 feet

$\frac{dx}{dt}=400 ft/min$

Triangle ABC and A'B'C are similar because all right triangles are similar

By using similarity property

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$h'=10.5 feet$

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$\frac{h'}{6}=\frac{x+y}{y}$

$\frac{10.5}{6}=\frac{x+y}{y}$

$10.5y=6x+6y$

$10.5y-6y=6x$

$4.5y=6x$

Differentiate w.r.t t

$4.5\frac{dy}{dt}=6\frac{dx}{dt}$

$\frac{dy}{dt}=\frac{6\times 400}{4.5}ft/min$

$\frac{dy}{dt}=533.33ft/min$

Hence, If the person is 6 feet tall and walks away from the lamp post at a speed of 400 feet per minute then his shadow moving at the rate 533.33 ft/min

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2 years ago