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ser-zykov [4K]
3 years ago
12

Integral of of sin x/cosˆ2 x

Mathematics
1 answer:
marin [14]3 years ago
7 0

Answer:

\sec x + c

Step-by-step explanation:

\int \frac{ \sin \: x}{ { \cos}^{2}x }  \: dx \\  \\  =  \int \frac{ \sin \: x}{ { \cos}x } . \frac{ 1}{ { \cos}x } \: dx \\  \\  =  \int  \tan x . \sec  x \: dx \\  \\  =  \sec x + c

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Taylor runs a smoothie shop and is in placing his order for a week.Each week he needs to have 2 gallons of pineapple juice and 4
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Answer:

For pineapple juice

He need 160 more ounces of pineapple juice.

For orange juice

He needs 352 ounces more of orange juice.

Step-by-step explanation:

1 liquid gallon = 4 liquid quarts

1 liquid quart = 32 fluid ounces

Taylor runs a smoothie shop and is in placing his order for a week.

We are told that:

Each week he needs to have

a) For pineapple juice

2 gallons of pineapple juice

We convert these to quarts and ounces

1 gallons = 4 quarts

2 gallons = 2 × 4

= 8 quarts of pineapple juice

If he already has 3 quarts of pineapple juice

She needs: 8 quarts - 3 quarts

= 5 quarts

Converting these to ounces

1 liquid quart = 32 fluid ounces

5 quarts = x

Cross Multiply

=5 × 32 fluid ounces

= 160 fluid ounces

2) For orange juice

She needs to have 4 gallons of orange juice on hand

We convert these to quarts and ounces

1 gallons = 4 quarts

4 gallons = 4 × 4

=Hence she needs to have: 16 quarts of pineapple juice

If he already has 5 quarts of orange juice

She needs: 16 quarts - 5 quarts

= 11 quarts more

Converting these to ounces

1 liquid quart = 32 fluid ounces

11 quarts = x

Cross Multiply

=11 × 32 fluid ounces

= 352 fluid ounces

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