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3 years ago

Fill in the blank in the sentence below with the correct term.

1 answer:

4 0

Hopes this can help
Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign =. An inverse operation are two operations that undo each other e.g. addition and subtraction or multiplication and division. You can perform the same inverse operation on each side of an equivalent equation without changing the equality.

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Need help with 2 and 3 and express I’m radical form

kondaur [170]

This is just simple Pythagorean’s theorem. a^2 + b^2 = c^2

Number 2:
5^2 + x^2 = 10^2
25 + x^2 = 100
x^2 = 75
x = sqrt 75 = 5*sqrt(3)

Number 3:
4^2 + x^2 = 7^2
16 + x^2 = 49
x^2 = 33
x = sqrt 33

4 0

3 years ago

Calculus 3 help please.

Reptile [31]

I assume each path $C$ is oriented positively/counterclockwise.

(a) Parameterize $C$ by

$\begin{cases} x(t) = 4\cos(t) \\ y(t) = 4\sin(t)\end{cases} \implies \begin{cases} x'(t) = -4\sin(t) \\ y'(t) = 4\cos(t) \end{cases}$

with $-\frac\pi2\le t\le\frac\pi2$ . Then the line element is

$ds = \sqrt{x'(t)^2 + y'(t)^2} \, dt = \sqrt{16(\sin^2(t)+\cos^2(t))} \, dt = 4\,dt$

and the integral reduces to

$\displaystyle \int_C xy^4 \, ds = \int_{-\pi/2}^{\pi/2} (4\cos(t)) (4\sin(t))^4 (4\,dt) = 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt$

The integrand is symmetric about $t=0$ , so

$\displaystyle 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \,dt$

Substitute $u=\sin(t)$ and $du=\cos(t)\,dt$ . Then we get

$\displaystyle 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^1 u^4 \, du = \frac{2^{13}}5 (1^5 - 0^5) = \boxed{\frac{8192}5}$

(b) Parameterize $C$ by

$\begin{cases} x(t) = 2(1-t) + 5t = 3t - 2 \\ y(t) = 0(1-t) + 4t = 4t \end{cases} \implies \begin{cases} x'(t) = 3 \\ y'(t) = 4 \end{cases}$

with $0\le t\le1$ . Then

$ds = \sqrt{3^2+4^2} \, dt = 5\,dt$

and

$\displaystyle \int_C x e^y \, ds = \int_0^1 (3t-2) e^{4t} (5\,dt) = 5 \int_0^1 (3t - 2) e^{4t} \, dt$

Integrate by parts with

$u = 3t-2 \implies du = 3\,dt \\\\ dv = e^{4t} \, dt \implies v = \frac14 e^{4t}$

$\displaystyle \int u\,dv = uv - \int v\,du$

$\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}$

$\begin{cases} x(t) = 3(1-t)+t = -2t+3 \\ y(t) = (1-t)+2t = t+1 \\ z(t) = 2(1-t)+5t = 3t+2 \end{cases} \implies \begin{cases} x'(t) = -2 \\ y'(t) = 1 \\ z'(t) = 3 \end{cases}$

with $0\le t\le1$ . Then

$ds = \sqrt{(-2)^2 + 1^2 + 3^2} \, dt = \sqrt{14} \, dt$

and

$\displaystyle \int_C y^2 z \, ds = \int_0^1 (t+1)^2 (3t+2) \left(\sqrt{14}\,ds\right) \\\\ ~~~~~~~~ = \sqrt{14} \int_0^1 \left(3t^3 + 8t^2 + 7t + 2\right) \, dt \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 t^4 + \frac83 t^3 + \frac72 t^2 + 2t\right) \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 + \frac83 + \frac72 + 2\right) = \boxed{\frac{107\sqrt{14}}{12}}$

8 0

1 year ago

The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

natita [175]

Answer:

68% of jazz CDs play between 45 and 59 minutes.

Step-by-step explanation:

The correct question is: The playing time X of jazz CDs has the normal distribution with mean 52 and standard deviation 7; N(52, 7).

According to the 68-95-99.7 rule, what percentage of jazz CDs play between 45 and 59 minutes?

Let X = playing time of jazz CDs

SO, X ~ Normal( $\mu=52, \sigma^{2} =7$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, according to the 68-95-99.7 rule, it is stated that;

68% of the data values lie within one standard deviation points from the mean.

95% of the data values lie within two standard deviation points from the mean.

99.7% of the data values lie within three standard deviation points from the mean.

Here, we have to find the percentage of jazz CDs play between 45 and 59 minutes;

For 45 minutes, z-score is = $\frac{45-52}{7}$ = -1

For 59 minutes, z-score is = $\frac{59-52}{7}$ = 1

This means that our data values lie within 1 standard deviation points, so it is stated that 68% of jazz CDs play between 45 and 59 minutes.

6 0

3 years ago

Susie has 4 gallons of juice.How many cups of juice does she have? ANSWER QUICKLY

IgorLugansk [536]

Answer: 64 cups

Step-by-step explanation:

Each gallon has 16 cups so you multiply 16 by 4 because there are 4 gallons and you get 64. Hope that helped. :)

5 0

3 years ago

Read 2 more answers

Sidney takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. The cut she makes is

tatiyna

Answer: The length is 3 or 9 hope this helps.

Step-by-step explanation:

7 0

3 years ago