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2 years ago

Please help me, due soon

Mathematics

2 answers:

antiseptic1488 [7]2 years ago

8 0

Answer:

B. 21 and 19/25

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator

21.76=21.761

Multiply to remove 2 decimal places. Here, you multiply top and bottom by 102 = 100

21.761×100100=2176100

Find the Greatest Common Factor (GCF) of 2176 and 100, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 4,

2176÷4100÷4=54425

Simplify the improper fraction,

=211925

In conclusion,

21.76=211925

Strike441 [17]2 years ago

4 0

Answer: B. 21 and 19/25

Step-by-step explanation:

Simplify the improper fraction,

=211925

In conclusion,

21.76=211925

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A lighthouse is located on a small island 5 km away from the nearest point P on a straight shoreline and its light makes seven r

Vaselesa [24]

Answer:

Light is moving at the speed = 77.78 km/min

Step-by-step explanation:

Given:

Distance between island and point P = 5 km

Moving along the the shoreline when it is 1 km from P.

So, x = 1

From the above statement light makes seven revolutions per minute.

Therefore,

$\frac{d\theta}{dt}=\frac{7\times 2\pi\ rad}{1\ min} = 14\pi\ rad/min$

Solution:

From the given figure.

$tan\theta=\frac{x}{5}$

Substitute x = 1

$tan\theta=\frac{1}{5}$ -------------------(1)

Now, first we differentiate both side with respect to t.

$\frac{d(tan\theta)}{dt} = \frac{d}{dt}.(\frac{x}{3})$

Using chain rule.

$\frac{d(tan\theta)}{dt}.\frac{d\theta}{dt} = (\frac{1}{5})\frac{dx}{dt}$

$sec^{2} \theta.\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

$(1+tan^{2} \theta).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

Substitute $tan\theta=\frac{1}{5}$ from equation 1.

$(1+(\frac{1}{3})^{2} ).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

$(1+\frac{1}{9}).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

Substitute $\frac{d\theta}{dt}=14\pi$

$\frac{10}{9}.14\pi = \frac{1}{5}.\frac{dx}{dt}$

Applying cross multiplication rule.

$\frac{dx}{dt}= \frac{700\pi }{9}$

$\frac{dx}{dt}= 77.78\pi$

Therefore, light is moving along the shore at the speed of 77.78 km/min

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3 years ago

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sveta [45]

The formula for finding area of a rectangle is a=lw.

Write what is given
Area is 64.
Length if 16.
Width is unknown.
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