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musickatia [10]
4 years ago
14

2+3(5c-17) I do not know how to simplify the expression

Mathematics
2 answers:
nalin [4]4 years ago
7 0

Answer:

15c - 49

Step-by-step explanation:

2+3(5c-17)

2+15c - 51

15c - 49

katrin2010 [14]4 years ago
3 0

2 + 3(5c - 17)

First you must distribute the 3 to the numbers inside the parentheses, which would be 5c and -17...

2 + (3 * 5c) + (3 *(-17))

2 + 15c + (-51)

2 + 15c - 51

Now you must combine like terms. Like terms are numbers that have matching variables OR are numbers with out variables. In this case the like terms are 2 and -51, since they both don't have variables

(2 + (-51)) + 15c

-49 + 15c

OR

15c - 49

Hope this helped!

~ Just a girl in love with Shawn Mendes

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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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