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Nadya [2.5K]
3 years ago
6

When Morgan's dad returned from the store, he went for a jog. He jogged for 1 hour and 15 minutes at a pace of 4.8 miles per hou

r. How far did he jog?
Mathematics
1 answer:
alisha [4.7K]3 years ago
6 0
1 hour and 15 mins
60mins=1hr
15/60=1/4

1hr and 15mins=1 and 1/4hr or 1.25hr

1.25 times 4.8=6

jogged 6 miles
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3 0
3 years ago
Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum
otez555 [7]

<u>Step-by-step explanation:</u>

To prove:

\cos 3x=\cos^3x-3\sin^2 x\cos x

Identities used:

\cos(A+B)=\cos A\cos B+\sin A\sin B      ......(1)

\sin 2A=2\sin A\cos A        ........(2)

\cos 2A=\cos^2A-\sin^2 A     .......(3)

Taking the LHS:

\Rightarrow \cos 3x=\cos (x+2x)

Using identity 1:

\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x

Using identities 2 and 3:

\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x

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Mrs. Benton is making treat bags for her class. She has 245 Chocolate Twisters. If she puts 9 Chocolate Twisters in each treat b
Alex17521 [72]

Answer:

She can make 27 bags

2 pieces of candy is left over

Step-by-step explanation:

She has 245 Chocolate Twisters.

she puts 9 Chocolate Twisters in each treat bag,

1 bag hold 9 chocolates

9 chocolates = 1 bag

So 245 chocolates in how many bags

Divide 245 by 9

use long division

                       2 7 -----------> Quotient

                   ------------------------------------

          9           245

                        18                           (subtract it)

                   -------------------------

                          65

                          63              (subtract it)

                ----------------------------

                            2 -----------> remainder

She can make 27 bags

2 pieces of candy is left over

                       

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Answer:

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