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valentinak56 [21]

2 years ago

8

The volume of a prism is 230 mm3.

1 answer:

Lorico [155]2 years ago

7 0

The answer would be E because as you may know, 10 mm is equal to 1 cm. So, 230 mm³ is equal to 23 cm³.

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Solve the given initial-value problem. the de is of the form dy dx = f(ax + by + c), which is given in (5) of section 2.5. dy dx

shutvik [7]

$\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)$

Let $v=x+y$ , so that $\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}$ :

$\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1$

Now the ODE is separable, and we have

$\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx$

Integrating both sides gives

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx$

For the integral on the left, rewrite the integrand as

$\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v$

Then

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C$

and so

$\csc v-\cot v=x+C$

$\csc(x+y)-\cot(x+y)=x+C$

Given that $y(0)=\dfrac\pi2$ , we find

$\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1$

so that the particular solution to this IVP is

$\csc(x+y)-\cot(x+y)=x+1$

5 0

2 years ago

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White raven [17]

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2 years ago

BRAINLIESTTT ASAP! PLEASE HELP ME :)<br><br> Find the inverse of :

muminat

Answer:

$h^{-1}(x) = \dfrac{5x - 6}{2}$

Step-by-step explanation:

$h(x)= \dfrac{2x + 6}{5}$

(a) Rename h(x) as y

$y = \dfrac{ 2x+ 6}{5}$

(b) Solve for x :

$\begin{array}{rcl}y& = &\dfrac{2x + 6}{5}\\\\5y & = & 2x + 6\\5y - 6 & = & 2x\\x & = & \mathbf{\dfrac{5y - 6}{2}}\end{array}$

(d) Switch x and y

$y = \dfrac{5x -6}{2}$

(e) Rename y as the inverse function

$h^{-1}(x) = \mathbf{\dfrac{5x - 6}{2}}$

The graphs of inverse functions are reflections of each other across the line y = x.

In the diagram, the graph of h⁻¹(x) is the reflection of h(x) about the line y = x.

5 0

2 years ago

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How does the reflection of a square over the x-axis affect the interior angles of the square?

nignag [31]

Interior angles of a square always sum to 360°. A reflection in the x-axis would not change this.

6 0

2 years ago

Which is bigger 2.0 or 2

alekssr [168]

Answer:

both are the same

Step-by-step explanation:

2.0 = 2

hope this helps ^-^

4 0

2 years ago

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