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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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Casey spent $2.50 on a snack,$1.24 on gum,$3.76 on a comic book, and $5.50 on lunch. Use mental math to find the total amount he
stellarik [79]

Answer:

$13

Step-by-step explanation:

Given data

$2.50 on a snack,

$1.24 on gum,

$3.76 on a comic book, and

$5.50 on lunch

Total expenses will be

=2.5+1.24+3.76+5.50

=$13

5 0
3 years ago
HELPPPPPPPPPPPPPPPPPP ASAP!!!!!!!!!!!!!!!!
azamat

Answer:

254.5 m^2

Step-by-step explanation:

Area of a Circle: A=\pi r^2

The r is the length of the radius of the circle

The radius of the shown circle is 9 m

A=\pi 9^2

A=81\pi=254.469004941

7 0
2 years ago
Read 2 more answers
brenda and her bestfriend went on a vacation together. They both paid for a flight, and brenda had a fancy room for $150 per nig
AURORKA [14]

Answer:

What is the question?

Step-by-step explanation:

1. Write all of the question to receive a correct answer.

7 0
2 years ago
Mariela recolecto 625 mililitros de agua que gotea de su caño en 10 minutos, ella desea saber ¿cuanta agua gastara en una semana
mario62 [17]

Answer:

En una semana gastará 705,6 litros.

Step-by-step explanation:

Con la información proporcionada, puedes calcular cuánta agua gastará por día usando una regla de tres teniendo en cuenta que un día tiene 24 horas y estas equivalen a 1440 minutos. Además, puedes convertir los 700 ml a litros, considerando que 1 litro son 1000 mL, lo que significa que los 700 mL equivalen a 700/1000=0,7 Litros.

 10 min    →  0,7 L

1440 min →       x

x=(1440*0,7)/10

x=100,8 L

Ahora que conoces la cantidad de agua que gastará por día, puedes multiplicar esta cantidad por 7 que es el número de días en una semana:

100,8*7=705,6 L

De acuerdo a esto, la respuesta es que en una semana gastará 705,6 litros.

4 0
2 years ago
What is the surface area of the figure? Use 3.14 for π.
fredd [130]

Answer:

Option 3

Step-by-step explanation:

We want to work out the surface-area

This is a cylinder and the formula for the surface area of a cylinder is :

2πrh+2πr^2

^ means to the power of

The radius is 15

The length is 18

2(3.14)(15)(18) + 2(3.14){15}^2

Part 1:

(6.28)(15)(18)

(6.28)(270)

1695.6

Part 2:

First, we do the exponents,

15^2 = 225

(6.28)(225)

1413

Part 3:

1695.6 + 1413 = 3108.6

Answer: 3108.6

Hope this helps :)

6 0
2 years ago
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