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NikAS [45]
3 years ago
7

A 12 pack of diet soda has dimensions 4.75in and 28.5in whats the volume of the 12 pack round to the nearest ten

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
6 0

Answer:

Volume = 643.0\ in^3

Step-by-step explanation:

Given

Dimension: 4.75in, 4.75in and 28.5in

<em>[The complete dimension is missing from the question]</em>

Required

Calculate the volume

The volume is calculated as thus:

Volume = 4.75in * 4.75in * 28.5in

Volume = 643.03125in^3

Volume = 643.0\ in^3 --- approximated

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Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side
maria [59]

Answer:

cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = -\frac{1}{3}

cos(b) = -\frac{1}{4}

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = -\sqrt{1-(-\frac{1}{3})^2} [Since, sin(a) = \sqrt{(1-\text{cos}^2a)}]

         = -\sqrt{\frac{8}{9}}

         = -\frac{2\sqrt{2}}{3}

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be  negative.

sin(b) = -\sqrt{1-(-\frac{1}{4})^2}

         = -\sqrt{\frac{15}{16}}

         = -\frac{\sqrt{15}}{4}

By substituting these values in the identity,

cos(a + b) = (-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})

                = \frac{1}{12}-\frac{\sqrt{120}}{12}

                = \frac{1}{12}(1-\sqrt{120})

                = \frac{1}{12}(1-2\sqrt{30})

Therefore, cos(a + b) = \frac{1}{12}(1-2\sqrt{30})

5 0
3 years ago
The amount in kilograms, a, of a radioactive element that remains after t hours can be modeled by the equation a= 0.65(0.92)to t
elena-14-01-66 [18.8K]

Answer:

The rate of decrease is 8%

Step-by-step explanation:

we know that

The general equation for the radioactive decay can be written as:

a=a_0(1-r)^t

where

a is the amount in kilograms after time t.

a_0 is the original amount of the substance or y-intercept of the function

r is the decay rate, written in decimals.

t is the time

In this problem we have

a=0.65(0.92)^t

so

a_0=0.65\\(1-r)=0.92

solve for r

r=1-0.92=0.08

Convert to percentage

0.08(100)=8\%

6 0
3 years ago
Please answer this correctly
MrMuchimi

Answer:

11 pt

Step-by-step explanation:

There are 2 pints in one quart. This means that there are 10 pints in 5 quarts, plus 1 would be 11.

3 0
2 years ago
Juan spent $7.00 of the $20.00 in his wallet. Which decimal represents the fraction of the $20.00 Juan spend?
swat32

Answer:

Juan still has $13.00 left after spending $7.00 as a percentage that is 35% and as a fraction that is 35/100 or 0.35.

Step-by-step explanation:

I hope I helped in any way.

5 0
3 years ago
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D. asymptote

In the attached graph, the function has two asymptotes, one horizontal (the x-axis) and one vertical (the line x = 2).


7 0
3 years ago
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