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2 years ago

In the figure shown, which pair of angles must be complementary?

Mathematics

1 answer:

Helen [10]2 years ago

8 0

Answer:

mxthwxy or txgermxth

Step-by-step explanation:

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What is the slope of the line through (-4,2) and (3, 3)? "/ yo Choose 1 answer: 19 21 42 142 A А 7 5 B 7 5 5 7 5 7 e slope an

NNADVOKAT [17]

Answer:

1/7

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3-2)/(3-(-4))

m=1/(3+4)

m=1/7

5 0

2 years ago

Nancy has nine books and she has read 8 total books Sally has two times more books the Nancy how many books does Sally have

ankoles [38]

Sally has eight-teen books.

7 0

3 years ago

Solution for dy/dx+xsin 2 y=x^3 cos^2y

vichka [17]

Rearrange the ODE as

$\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y$
$\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3$

Take $u=\tan y$ , so that $\dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}$ .

Supposing that $|y|$ , we have $\tan^{-1}u=y$ , from which it follows that

$\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}$
$\sec^2y=1+\tan^2y=1+u^2$

So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

which is linear in $u$ . Multiplying both sides by $e^{x^2}$ , we have

$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
$\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
$e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx$

Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

$\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt$

Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
$\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)$

You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$

5 0

3 years ago

Find the equation for a polynomial f(x) that satisfies the following:

denis-greek [22]

Answer:

f(x) = 1/2(4 - x)(x - 1)(x - 2)

Step-by-step explanation:

Considering zero's and a coefficient, the function is:

f(x) = a(x - 4)(x - 1)(x - 2)

Considering y-intercept:

f(0) = a(0 - 4)(0 - 1)(0 - 2)

4 = a(-4)(-1)(-2)

4 = -8a

a = -1/2

So the function is:

f(x) = -1/2(x - 4)(x - 1)(x - 2) = 1/2(4 - x)(x - 1)(x - 2)

3 0

2 years ago

Solve this equation 2x - 3=2x - 5

Alex

When you calculate 2x-3=2x-5 it’s going to lead as -3=-5, therefore this statement is inaccurate and doesn’t have a value of x, it doesn’t even have a solution.

5 0

2 years ago