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3 years ago

Which awnser is an equation in point-slope form for the given point and slope?

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

3 0

The correct answer is B) y + 9 = 2(x - 1)

In order to find this, simply take the point and the slope and plug into the base form of point-slope form.

y - y1 = m(x - x1)

Use the slope for m and the point for (x1, y1)

y + 9 = 2(x - 1)

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What is 233 x 234 ???

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Step-by-step explanation:

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Find the volume of a cone that has radius = 2 1/2 and height = 5.

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Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

$x'=\frac{dx}{dt}$

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in c)

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution m=α±βi where α=0 and β=2

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where A and B are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

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3 years ago

What is 5 2/7 as a decimal

choli [55]

Answer:5.285

Step-by-step explanation:

2/7 is equal is .285 If you add .285 to your whole number which is 5 it would equal to 5.285

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2 years ago

Which equation graphs as a vertical line with an undefined slope? A) y = 3x B) x = 2 3 C) y = 2 3 D) y = − 2 3 x + 1

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Answer:

Step-by-step explanation:

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x = a - vertical line (a - any real number) - undefined slope

y = mx + b - diagonal line (m - any real number except 0, b - any real number) - m - slope

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3 years ago