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3 years ago

How to write the ratio 8:30 as a fraction in simplest form

1 answer:

5 0

4/15 because you make it into a fraction: 8/30, you find the GCF which is 2, so then you divide both the numerator and denominator by 2 and get 4/15 at it's simplest term

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Sedaia [141]

Answer: The answer that I think is A

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2 years ago

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6) Solve for x. 2/3 (x + 7) = 10 A)22 B)8 C)- 1 /3 D)41/ 3

Amiraneli [1.4K]

For this case we must find the value of the variable "x" of the following equation:

$\frac {2} {3} (x + 7) = 10$

We multiply by 3 on both sides of the equation:

$2 (x + 7) = 30$

We divide between 2 on both sides of the equation:

$(x + 7) = 15\\x + 7 = 15$

We subtract 7 on both sides of the equation:

$x = 8$

Answer:

Option B

7 0

2 years ago

The ratio of blueberries and strawberries is 1:7. If there are 210 strawberries how many blueberries are there?

Travka [436]

Answer:

There are 30 blue berries

Step-by-step explanation:

1:7

_:210

210/7

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2 years ago

What is the equation?

elena-s [515]

Answer:

cost = 1.35n

$33.75 for 25 songs

Step-by-step explanation:

Based on the numbers given, the cost is proportional to the number of songs downloaded. The constant of proportionality is the cost of one song: 1.35.

cost = 1.35n

For 25 songs, ...

cost = 1.35·25 = 33.75 . . . . dollars

The equation is ...

cost = 1.35n

5 0

3 years ago

Let y(t) be the solution to y˙=3te−y satisfying y(0)=3 . (a) Use Euler's Method with time step h=0.2 to approximate y(0.2),y(0.4

OLEGan [10]

Answer:

$y(0.2)=3$ , $y(0.4)=3.005974448$ , $y(0.6)=3.017852169$ , $y(0.8)=3.035458382$ , and $y(1.0)=3.058523645$

The general solution is $y=\ln \left(\frac{3t^2}{2}+e^3\right)$

The error in the approximations to y(0.2), y(0.6), and y(1):

$|y(0.2)-y_{1}|=0.002982771$

$|y(0.6)-y_{3}|=0.008677796$

$|y(1)-y_{5}|=0.013499859$

Step-by-step explanation:

Point a:

The Euler's method states that:

$y_{n+1}=y_n+h \cdot f \left(t_n, y_n \right)$ where $t_{n+1}=t_n + h$

We have that $h=0.2$ , $t_{0}=0$ , $y_{0} =3$ , $f(t,y)=3te^{-y}$

We need to find $y(0.2)$ for $y'=3te^{-y}$ , when $y(0)=3$ , $h=0.2$ using the Euler's method.

So you need to:

$t_{1}=t_{0}+h=0+0.2=0.2$

$y\left(t_{1}\right)=y\left(0.2)=y_{1}=y_{0}+h \cdot f \left(t_{0}, y_{0} \right)=3+h \cdot f \left(0, 3 \right)=$

$=3 + 0.2 \cdot \left(0 \right)= 3$

$y(0.2)=3$

We need to find $y(0.4)$ for $y'=3te^{-y}$ , when $y(0)=3$ , $h=0.2$ using the Euler's method.

So you need to:

$t_{2}=t_{1}+h=0.2+0.2=0.4$

$y\left(t_{2}\right)=y\left(0.4)=y_{2}=y_{1}+h \cdot f \left(t_{1}, y_{1} \right)=3+h \cdot f \left(0.2, 3 \right)=$

$=3 + 0.2 \cdot \left(0.02987224102)= 3.005974448$

$y(0.4)=3.005974448$

The Euler's Method is detailed in the following table.

Point b:

To find the general solution of $y'=3te^{-y}$ you need to:

Rewrite in the form of a first order separable ODE:

$e^yy'\:=3t\\e^y\cdot \frac{dy}{dt} =3t\\e^y \:dy\:=3t\:dt$

Integrate each side:

$\int \:e^ydy=e^y+C$

$\int \:3t\:dt=\frac{3t^2}{2}+C$

$e^y+C=\frac{3t^2}{2}+C\\e^y=\frac{3t^2}{2}+C_{1}$

We know the initial condition y(0) = 3, we are going to use it to find the value of $C_{1}$

$e^3=\frac{3\left(0\right)^2}{2}+C_1\\C_1=e^3$

So we have:

$e^y=\frac{3t^2}{2}+e^3$

Solving for y we get:

$\ln \left(e^y\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y\ln \left(e\right)=\ln \left(\frac{3t^2}{2}+e^3\right)\\y=\ln \left(\frac{3t^2}{2}+e^3\right)$