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bekas [8.4K]
2 years ago
11

If the area (in square units) of the region under the curve of the function f(x) = 3x − 1 on the interval [a, 4], where a < 4

, is 12 square units, identify all the possible values of a.
-3
0
-16/5
8/3
-2
7/2

Mathematics
1 answer:
Goryan [66]2 years ago
8 0

Answer:

  • 8/3
  • -2

Step-by-step explanation:

The integral from a to 4 is ...

\int\limits^4_a {(3x-1)} \, dx =\dfrac{3}{2} (4^2-a^2)-(4-a) = 20+a-\dfrac{3}{2}a^2

We want the value of this to be 12, so we can write ...

  -3/2a^2 +a +20 = 12

  3a^2 -2a -16 = 0 . . . . . subtract the left side and multiply by 2

  (3a -8)(a +2) = 0 . . . . . factor

  a = 8/3 or -2  . . . . . . . .values of a that make the factors zero

The only possible values of a are 8/3 and -2.

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Analyze the diagram below and complete the instructions that
Novosadov [1.4K]

9514 1404 393

Answer:

  D.  x = 15; y = 5√3

Step-by-step explanation:

You don't need to know any trig to select the correct answer. You only need to know that the lengths of both sides must be less than the length of the hypotenuse. It is also helpful to know that √3 is about 1.732, so 10√3 ≈ 17.32.

Since x < 10√3, only answer choices A and D are viable.

Since y < 10√3, only answer choice D is viable.

_____

If you want to solve this using trig relations, you can recall that the sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. This means short side y is half the length of the hypotenuse 10√3, so y = 5√3. It also means longer side x is √3 times y, so is x = (5√3)√3 = 5·3 = 15.

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3 years ago
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