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2 years ago

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

Mathematics

1 answer:

erastova [34]2 years ago

8 0

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 = $\frac{1}{6}$

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What type of exponential function is f(x)=0.6(2.4)^x ?

Vsevolod [243]

Answer:

The function is of an exponential growth type

Rate of change is 240%

Step-by-step explanation:

Exponential Function

The expression of an exponential function is

$f(x)=c.a^{bx}$

For a,b,c constants.

The function will be of an exponential growth type if, when x increases, f increases. That behavior comes from the combination of the three constants a,b,c. The best approach to find that out is by taking the first derivative

$f'(x)=b.c.lna.a^{bx}$

Since $a^{bx}$ is always positive, the product of b.c.lna must be positive to make f increasing. For example, if a>1 and both b and c are of the same sign, f increases for all x. If 0<a<1, then, since lna<0, the product b.c must be negative, i.e. both should have different signs

The function is expressed as

$f(x)=0.6\ 2.4^x$

we can see a>1, b and c are positive, so the function is of an exponential growth type.

Talking about rates change of real functions takes us to the derivative function. We have already seen the derivative is dependent on all three constants and also of the value of x, so it cannot be predicted as a fixed percentage.

Now, if we picture the function as the general term of a sequence, where x can only take natural values, we can say

$\displaystyle \frac{0.6(2.4)^{x+1}}{0.6(2.4)^{x}}=2.4$

Each term is obtained as the previous term by 2.4. It's accurate to say the rate of change is 240%

3 0

2 years ago

Read 2 more answers

Of the girls on the Alden Middle School soccer team, % also play on a travel team. How many of the girls on the middle school te

Wewaii [24]

Answer:

The question is incomplete, so I looked for similar ones and found:

Of the 25 girls on the Alden Middle School soccer team, 40% also play on a travel team. How many of the girls on the middle school team also play on a travel team?

we can solve this the following way:

25 girls on the soccer team x 40% that play on a travel team = 10 girls form the soccer team that play on a travel team

we can also multiply (25 girls x 40) / 100 = 10 girls

we can check our work by:

10 girls / 40% = 25 girls in total

8 0

3 years ago

Lines x and y are parallel and are cut by the transversal b. If the measure of angle 1 is 57°, what is the measure of angle 6? E

lana [24]

Answer:

$\angle6=123$