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Scrat [10]
2 years ago
6

R is the 4th quadrant region enclosed by the x-axis and the curve y = x^2 - 2kx, where k>0. find the value of k so that the a

rea of the region r is 36 square units.
a. 2
b. 3
c. 4
d. 6
will vote brainliest, like, and rate!
Mathematics
1 answer:
Ahat [919]2 years ago
4 0

Observe that

y = x² - 2kx = x (x - 2k)

has roots at x = 0 and x = 2k. Since the leading coefficient is 1 > 0, the parabola opens upward, and in particular this means the x-axis lies above the curve.

We can compute the area of R by integrating:

\displaystyle \int_0^{2k} |x^2-2kx| \, dx = - \int_0^{2k} (x^2-2kx) \, dx \\\\ = kx^2 -\frac{x^3}3 \bigg|_{0}^{2k} \\\\ = \frac{4k^3}3

Solve for k :

\dfrac{4k^3}3 = 36 \implies k^3 = 27 \implies \boxed{k=3} ~~~~ (B)

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(2(n+1)-1)^2-(2n-1)^2 simplified
Westkost [7]

Answer: 8n

Let's simplify step-by-step.

(2(n+1)−1)2−(2n−1)2

Distribute:

=4n2+4n+1+−4n2+4n+−1

Combine Like Terms:

=4n2+4n+1+−4n2+4n+−1

=(4n2+−4n2)+(4n+4n)+(1+−1)

=8n

7 0
3 years ago
6x - 9 = 15 linear equations
finlep [7]

Answer:

x = 4

Step-by-step explanation:

6x - 9 = 15

6x - 9 + 9 = 15 + 9

6x = 24

6x / 6 = 24 / 6

x = 4

4 0
3 years ago
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What is √7 rounded to the nearest hundredth?
Rama09 [41]

Answer:

2.64

Step-by-step explanation:

The sqhate root of 7 is 2.64575131106. Usually this would be 2.64 when rounded to nearest hundredth.

4 0
3 years ago
The sum of three consecutive even numbers is one hundred sixty-two. What is the smallest of the three numbers?
zepelin [54]
Since the numbers are consecutive, they must be near each other in size, and therefore near one-third of 168. And since the lower number is -2 off the middle, and the upper number is +2 from the middle, the middle number must be exactly one-third of 168—otherwise the sum of the three could never be 168. Labelling the three consecutive numbers as x, y, and z:

x + y + z = 168

(y-2) + y + (y+2) = 168.

3y = 168

y = 56

therefore the smallest number (x) = 54.
436 viewsView upvotes

1




Related Questions (More Answers Below)
3 0
2 years ago
Read 2 more answers
Events A1, A2 and A3 form a partiton of the sample space S with probabilities P(A1) = 0.3, P(A2) = 0.5, P(A3) = 0.2.
timurjin [86]

Answer:

Step-by-step explanation:

Given that events A1, A2 and A3 form a partiton of the sample space S with probabilities P(A1) = 0.3, P(A2) = 0.5, P(A3) = 0.2.

i.e. A1, A2, and A3 are mutually exclusive and exhaustive

E is an event such that

P(E|A1) = 0.1, P(E|A2) = 0.6, P(E|A3) = 0.8,

P(E) = P(A_1E)+P(A_2E)+P(A_3E)\\= \Sigma P(E/A_1) P(A_1) \\= 0.1(0.3)+0.5(0.6)+0.8(0.2)\\= 0.03+0.3+0.16\\= 0.49

P(A_1/E) = P(A_1E)/P(E) = \frac{0.3(0.1)}{0.49} \\=0.061224

P(A_2/E) = P(A_2E)/P(E) = \frac{0.5)(0.6)}{0.49} \\=0.61224

P(A_3/E) = P(A_3E)/P(E) = \frac{0.2)(0.8)}{0.49} \\=0.3265

4 0
3 years ago
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