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mash [69]
3 years ago
8

For every 5 balloons in the sky, 2 of them will be rainbow. If there was 150 of them in the sky, how many would be rainbow?

Mathematics
2 answers:
MArishka [77]3 years ago
7 0
Set up the proportion: 2/5=x/150
Cross multiply: 5x=300
Answer= 60 rainbow balloons
Vilka [71]3 years ago
5 0
60 -> 2 times 150 then you divide it by 5.
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5/8 teaspoon baking soda with 1/3 teaspoon of salt equals how many teaspoons together
Korolek [52]
23/24 teaspoons together

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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}}

(c) Parameterize C by

\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
I don’t really understand could you help
givi [52]

Answer:

M: (-7, -3)

A: (0, -3)

T: (0, -8)

Step-by-step explanation:

each of the points are associated with a letter. you can find the points by looking at the points it matches up with in the formatting of (x,y)

for example, for M, you can see that the dot on the x axis seems to be hovering below -7, on the y axis, it seems to be hovering next to -3. therefore, its (-7,-3)

7 0
2 years ago
A bank says you can double your money in 10 years if you put $1,000 in a simple interest account. What annual interest rate does
katrin2010 [14]

The simple interest formula allows us to calculate I, which is the interest earned or charged on a loan. According to this formula, the amount of interest is given by I = Prt, where P is the principal, r is the annual interest rate in decimal form, and t is the loan period expressed in years. The rate r must be converted from a percentage into decimal form.

Then, 2,000 = 1,000 * r * 10 ;

 Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.2

hope this helps you

8 0
3 years ago
An item is regularly priced at $80. It is now priced at a discount of 20% off the regular price. What is the price now?
bekas [8.4K]

Answer:

64

Step-by-step explanation:

80*(1-0.2)

8 0
2 years ago
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