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2 years ago

Which expressions have a value equal to 22?

Mathematics

1 answer:

BabaBlast [244]2 years ago

3 0

Where are the expressions

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Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A?

mamaluj [8]

Answer:

Step-by-step explanation:

7 0

2 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:

<em>Point a:</em>

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.

<em>Point b:</em>

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 <em>y</em> we get:

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

<em>Point c:</em>

To compute the error in the approximations y(0.2), y(0.6), and y(1) you need to:

Find the values y(0.2), y(0.6), and y(1) using $y=\ln \left(\frac{3t^2}{2}+e^3\right)$

$y(0.2)=\ln \left(\frac{3(0.2)^2}{2}+e^3\right)=3.002982771$

$y(0.6)=\ln \left(\frac{3(0.6)^2}{2}+e^3\right)=3.026529965$

$y(1)=\ln \left(\frac{3(1)^2}{2}+e^3\right)=3.072023504$

Next, where $y_{1}, y_{3}, \:and \:y_{5}$ are from the table.

$|y(0.2)-y_{1}|=|3.002982771-3|=0.002982771$

$|y(0.6)-y_{3}|=|3.026529965-3.017852169|=0.008677796$

$|y(1)-y_{5}|=|3.072023504-3.058523645|=0.013499859$

3 0

3 years ago

Carmen simplifies the expression (4 y 8 x 6) 25 (4 x 6 y 7). The coefficient of the variable y in her simplified answer is 4. 6.

Sever21 [200]

Carmen simplifies the expression and gets the coefficient of y is 10. Thus, the correct option is C.

<h3>What is simplification?</h3>

Simplification is to make something easier to do or understand and to make something less complicated.

Given

Carmen simplifies the expression $\rm (4 y + 8 x + 6) + 25 + (4 x +6 y +7)$ .

We can add x term with x, y term with y, and constant with constant.

On simplifying, we have

$\rm (4 y + 8 x + 6) + 25 + (4 x +6 y +7)\\\\12x + 10y + 38$

Thus, the coefficeint of y is 10.

More about the simplification link is given below.

brainly.com/question/12616840

5 0

1 year ago

Find the volume of each figure

pshichka [43]

Answer:

See explanation

Step-by-step explanation:

1. The first figure shows triangular prism. The volume of the triangular prism is

$V=\text{Base area}\times \text{Height}$

The base of this triangular prism is the triangle with the base of 7 cm and height of $h$ cm (it is not seen).

The base area is

$\text{Base area}=\dfrac{1}{2}\times \text{Base}\times \text{Height}=\dfrac{1}{2}\times 7\times h=\dfrac{7h}{2}\ cm^2$

and the volume of the prism is

$V=\dfrac{7h}{2}\times 13=\dfrac{91h}{2}\ cm^3$

Just substitute the length of the height and calculate the volume.

2. The second figure shows square pyramid. The volume of the square pyramid is

$V=\dfrac{1}{3}\times \text{Base area}\times \text{Height}$

The base of this square pyramid is the square with the side length of 4 yd.

The base area is

$\text{Base area}= \text{Side Lenght}^2=4^2 =16\ yd^2$

and the volume of the pyramid is

$V=\dfrac{1}{3}\times 16\times 12=64\ yd^3$

7 0

2 years ago

Find the inverse of (x) = 1/x-5

monitta

$f(x)=\dfrac{1}{x-5}\\
y=\dfrac{1}{x-5}\\
x-5=\dfrac{1}{y}\\
x=\dfrac{1}{y}+5\\\\
\boxed{f^{-1}(x)=\dfrac{1}{x}+5}$

5 0

3 years ago