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Svetlanka [38]
3 years ago
12

Evaluate the integral (3 - 2x)dx for x = -1 to x = 3 byinterpreting it in terms of areas.

Mathematics
1 answer:
suter [353]3 years ago
5 0

Answer:

4 unit^2

explanation is given at the end.

Step-by-step explanation:

What this integral represents is the net area between the function f(x) = 3 - 2x

and the x-axis, between the range of x between -1 and 3.

\int^{3}_{-1} {3-2x} \, dx \\\left|3x - 2\dfrac{x^2}{2}\right|^{3}_{-1}\\\left|3x - x^2\right|^{3}_{-1}

we have integrated the equation, and now we're going to put the limits find the area under the function f(x)

\left|3x - x^2\right|^{3}_{-1}\\(3(3)-(3)^2)-(3(-1)-(-1)^2)

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

if these seems like a big jump, try to understand it through this:

\left|3x - x^2\right|^{b}_a\\(3(b)-(b)^2)-(3(a)-(a)^2)\\

we've only distributed the limits each time to the same integrated expression.

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

coming back to our solution:

(3(3)-(3)^2)-(3(-1)-(-1)^2)

(0)-(-4)

4

so our area is 4

the area above the x-axis is positive, and the area below the x-axis is negative. Since, our answer is +4. <u>We now know that if within this range [-1,3] the area above and below the x-axis exist, there is more area above the x-axis than below the x-axis</u><u>. In other words, the net area is above the x-axis and that is equal to 4 unit^2 </u>

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lisov135 [29]

Answer: <FGI = 54

Step-by-step explanation:

180-126=54

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6 0
2 years ago
In 4 games, Larry averaged 23 PPG (points per game). How many points does he need to score in the last game to have an average o
ivann1987 [24]
Larry needs to score 33 points in the last game to have an average of 25 PPG.

To find the answer, we can solve the equation:

\frac{(4)23+p}{5}=25

<em />(where <em>p</em> is how many points he needs to score in the last game)

To find the mean of a group of numbers, you add them all up and divide the total by the number of numbers there are. Since Larry averaged 23 PPG in 4 games, we can multiply 23 by 4 to get the total of the first 4 games from the data. Then, we find <em>p</em>, which we will add to get our final total. Then, you divide by the 5 games.

\frac{(4)23+p}{5}=25
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First, I simplified 4 x 23 to get 92. Then, I multiplied each side by 5 to get rid of the denominator. Finally, I subtracted 92 from each side to isolate <em>p</em>, and found that <em>p</em> = 33.


8 0
3 years ago
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stiv31 [10]

Answer:

i think it is the 2nd one and the 5th one.

Step-by-step explanation:

hope this helped!

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3 years ago
Would 1/5 be greater than 1/3 but less than 2/3
makvit [3.9K]
1/5 = 3/15
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So no :)

Reason why:
You want to find the common denominator between all three fractions, so all fractions are the same proportions. So in this case, if you multiply 5*3 you get 15, making it the common denominator. Then since you multiplied the 5 in 1/5 by 3 to get 15, and you have to multiply the 3 in 1/3 and 2/3 by 5 to get 15, then you multiply the numerator by the same number.

Sorry I am terrible at explaining things. Hope this helped though!
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3 years ago
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irga5000 [103]
4:3 for the ratio and for the word ratio you can say that there is 4 squares and 3 triangles
6 0
3 years ago
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