Can you help me figure out this problem???? Pleaseeeeeeeeeee!!!!!!!!!!!

What is the area of the region bounded between the curves y=x and y=sqrt(x)?

erastova [34]

Answer:

$\frac{1}{6}$

Step-by-step explanation:

y = x .....(1)

$y=\sqrt{x}$ .... (2)

By solving equation (1) and equation (2)

$x = \sqrt{x}$

$\sqrt{x}\left ( \sqrt{x}-1 \right )=0$

$\sqrt{x}=0$ or $\left ( \sqrt{x}-1 \right )=0$

x = 0, x = 1

y = 0, y = 1

A = $\int_{0}^{1}ydx(curve)-\int_{0}^{1}ydx(line)$

A = $\int_{0}^{1}\sqrt{x}dx-\int_{0}^{1}xdx$

A = $\frac{2}{3}[x^\frac{3}{2}]_{0}^{1}-\frac{1}{2}[x^2]_{0}^{1}$

A = $\frac{2}{3}-\frac{1}{2}$

A = $\frac{1}{6}$

8 0

2 years ago

University degree requirements typically are different for Bachelor of Science degrees and Bachelor of Arts degrees. Some studen

ira [324]

Answer:

A. 0.1

B. 0.8

C. 0.5

Step-by-step explanation:

Given:

P(Science) = 0.3

P(Arts) = 0.6

P(none) = 0.2

From the above, it is understood that the events are independently events; meaning that the probability that a students gets a Bachelor of Science degree does not affect the probability of the same student getting a Bachelor of Arts degree.

A. The probability that a student gets a Bachelor of Science and Bachelor of Arts degree

Let P(Arts and Science) = the probability that a student gets a Bachelor of Arts degree and Bachelor of Science degree

For independent events,

P(A) + P(B) - P(A and B) + P(none)= 1

If we translate the above formula to suit our needs, we have something like this

P(Science) + P(Arts) - P(Arts and Science) + P(none) = 1

Or

P(Arts) + P(Science) - P(Arts and Science) + P(none) = 1

From this, we have

0.3 + 0.6 - P(Arts and Science) + 0.2 = 1

1.1 - P(Arts and Science) = 1

-P(Arts and Science) = 1 - 1.1

-P(Arts and Science) = -0.1

P(Arts and Science) = 0.1

B. The probability that a student gets a Bachelor of Science or Bachelor of Arts degree

For independent events

P(A or B) = P(A) + P(B) - P(A and B)

So, P(Arts or Science) = P(Arts) + P(Science) - P(Arts and Science)

P(Arts or Science) = 0.3 + 0.6 - 0.1

P(Arts or Science) = 0.8

C. The probability that a student gets only Bachelor of Arts

P(A only) = P(A) - P(A and B)

P(Arts) = P(Arts) - P(Arts and Science)

P(Arts) = 0.6 - 0.1

P(Arts) = 0.5

6 0

2 years ago

What is the least common multiple of 12 and 10?

attashe74 [19]

The Least Common Multiple is 60

4 0

2 years ago

Find the area ratio of a regular octahedron and a tetrahedron regular, knowing that the diagonal of the octahedron is equal to h

Anton [14]

Answer:

$\frac{4}{3}$

Step-by-step explanation:

The area of a regular octahedron is given by:

area = $2\sqrt{3}\ *edge^2$ . Let a is the length of the edge (diagonal).

area = $2\sqrt{3}\ *a^2$

Given that the diagonal of the octahedron is equal to height (h) of the tetrahedron i.e.

a = h, where h is the height of the tetrahedron and a is the diagonal of the octahedron. Let the edge of the tetrrahedron be e. To find the edge of the tetrahedron, we use:

$h=\sqrt{\frac{2}{3} } e\\but\ h=a\\a=\sqrt{\frac{2}{3} } e\\e=\sqrt{\frac{3}{2} }a$

The area of a tetrahedron is given by:

area = $\sqrt{3}\ *edge^2$ = $\sqrt{3} *(\sqrt{\frac{3}{2} }a)^2=\frac{3}{2}\sqrt{3} *a^2$

The ratio of area of regular octahedron to area tetrahedron regular is given as:

Ratio = $\frac{2\sqrt{3}\ *a^2}{\frac{3}{2} \sqrt{3}*a^2} =\frac{4}{3}$

7 0

2 years ago

Which represents the inverse of the function f(x) = 4x?

Helga [31]

<span>Which represents the inverse of the function f(x) = 4x?
</span>
f-1(x) = x/4

3 0

2 years ago

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