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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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If sin(t) = 3/5 and t is in the 2nd quadrant, find cos(t).
NemiM [27]

Cosine is \frac{hypotenuse}{adjacent}.

Apply the equation:

sin(t) = \frac{3}{5} \\3^2 + b^2 = 5^2\\b^2 = 5^2 - 3^2\\\\\sqrt{b^2}  = \sqrt{5^2}- \sqrt{3^2}\\\\\\b = 5 - 3 \\\\b = 2

B is the adjacent side so

cosine is:

Cos(t) = 5/2

Have a great day,

And I hope this helps you!

5 0
2 years ago
If f(x)=x2+1, then (f∘f)(x)=
PSYCHO15rus [73]

The resulting composite function (f∘f)(x) is x⁴+2x²+2

When a function is written inside another function, it is known as a composite function

Given the function f(x)=x²+1,

(f∘f)(x) = f(f(x))

f(f(x)) = f(x²+1)

This means we will need to replace x with x²+1 in f(x) as shown:

f(x²+1) = (x²+1)²+1

Expand

f(x²+1) = x⁴+2x²+1+1

f(x²+1) =  x⁴+2x²+2

Hence the resulting composite function (f∘f)(x) is x⁴+2x²+2

Learn more here: brainly.com/question/3256461

3 0
2 years ago
A cell phone provider offers a plan that costs ​$30 per month plus ​$0.10 per text message sent or received. A comparable plan c
mariarad [96]

300 messages would have to be sent or received in order for the plan to cost same each month.

Step-by-step explanation:

Given,

Cost per month = $30

Per text sent or received charges = $0.10

Let,

x be the number of texts sent or received.

A(x) = 0.10x+30    

A comparable plan costs = $60 per month

Text messages are unlimited.

B(x) = 60

For the two plans to cost equal;

A(x) = B(x)

0.10x+30=60\\0.10x=60-30\\0.10x=30

Dividing both sides by 0.10

\frac{0.10x}{0.10}=\frac{30}{0.10}\\x=300

300 messages would have to be sent or received in order for the plan to cost same each month.

Keywords: function, addition

Learn more about functions at:

  • brainly.com/question/2860697
  • brainly.com/question/2977815

#LearnwithBrainly

3 0
3 years ago
the sum of three numbers is 81. the second number is twice the first, and the third number is six more than the second. find the
ElenaW [278]

Answer:

have you tried using math-way just with no -

Step-by-step explanation:

3 0
2 years ago
Number of Bars
Montano1993 [528]

Answer: Disagree. 1 in 8 bars are cinnamon.

Step-by-step explanation:

There are a total of 8 bars in the pack. Cinnamon is 1 of the 8. Therefore, for every 8 bars, one is cinnamon.

7 0
2 years ago
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