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2 years ago

If a = 8, b = 4, and c = 10, what is a(b + c)?

Mathematics

2 answers:

ladessa [460]2 years ago

7 0

Answer:

112

Step-by-step explanation:

PEMDAS order of operations. Parenthesis go first, Exponents next, Multplication or Division 3rd, Addition and Subtraction last. In this case, you have a(b+c), so you would plug in your numbers to get 8(4+10). You do the things in the parenthesis first, and get 8(14). 8*14=112

Mnenie [13.5K]2 years ago

3 0

A(b+c) with the variables replaced is 8(4+10). Parentheses first so it is simplified to 8(14). A number with no symbol in front of a number inside of parentheses you have to multiply by the number inside the parentheses so it is 8x14 which equals 112.

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The volume of fuel in a tank changes at a rate given by the equation V'\left(t\right)=\frac{4t}{\sqrt[3]{t^2+3}},\:t\ge0 V ′ ( t

Ksju [112]

$V'(t)=\dfrac{4t}{\sqrt[3]{t^2+3}}$

The volume of fuel in the tank after 9 hours is given by

$\displaystyle\int_0^9V'(t)\,\mathrm dt=\int_0^9\dfrac{4t}{(t^2+3)^{1/3}}\,\mathrm dt$

To compute the integral, substitute $u=t^2+3$ , so that $\mathrm du=2t\,\mathrm dt$ . Then when $t=0$ , $u=0^2+3=3$ ; when $t=9$ , $u=9^2+3=84$ .

$\displaystyle\int_0^9V'(t)\,\mathrm dt=2\int_{t=0}^{t=9}\frac{2t}{(t^2+3)^{1/3}}\,\mathrm dt=2\int_{u=3}^{u=84}u^{-1/3}\,\mathrm du$
$=2\cdot\dfrac32u^{2/3}\bigg|_{u=3}^{u=84}=3(84^{2/3}-3^{2/3})\approx51.3$

So the volume of fuel after 9 hours is about 51.3 gallons.

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4 years ago

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3 years ago

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EleoNora [17]

Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

every ninth person in line at a movie theater gets free popcorn. Every sixth person gets free apple juice. Which customer will e

lys-0071 [83]

We are told that every 9th person gets free popcorn and every 6th person gets free apple juice at the movie theater. We want to show if the 36th person is the first to get both free popcorn and apple juice.
Since every 9th gets free popcorn, then the 9th and 18th and 27th and 36th people get it. We can use numbers and show this as multiples of 9.
9, 18, 27, 36, 45, 54, ...
And we repeat it for every 6th and the free juice.
6, 12, 18, 24, 30, 36,....
Shani thinks 36 comes first, and she's wrong. 18 appears on the list before 36 as something that's common. What are we finding is the lowest common muliple of 6 and 9.
6 = 2 x 3
9 = 3 x 3
The lowest common multiple will have a 2, a 3, and a second 3 (because we don't double count). 2 x 3 x 3 = 18. This matches up to the list of multiples.

Thus, Shani is wrong that the 36th person gets both free items, as she did not account for the 18th person gettting both free items

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3 years ago