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3 years ago

Find equation of a line that is perpendicular to y= -1/2x+9 and passes through (4,12).

Mathematics

1 answer:

Georgia [21]3 years ago

7 0

Answer:

y=2x+4

Step-by-step explanation:

m=2 because it is perpendicular to (-1/2)

y-12=2(x-4)

y=2x+4

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A) Find a particular solution to y" + 2y = e^3 + x^3. b) Find the general solution.

Reptile [31]

Answer:

a.P.I= $\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)$

b.G.S= $C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x}$

Step-by-step explanation:

We are given that a linear differential equation

$y''+2y=e^{3x}+x^3$

We have to find the particular solution

P.I= $\frac{e^{3x}}{D^2+2}+\frac{x^3}{D^2+2}$

P.I= $\frac{e^{3x}}{3^2+2}+\frac{1}{2} x^3(1+\frac{D^2}{2})^{-2}$

P.I= $\frac{e^{3x}}{11}+\frac{1-2\frac{D^2}{4}+3\frac{D^4}{16}+...}{2}x^3$

P.I= $\frac{e^{3x}}{11}+\frac{x^3-2\frac{\cdot3\cdot 2x}{4}}{2}+0}$ (higher order terms can be neglected

P.I= $\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)$

b.Characteristics equation

$D^2+2=0$

$D=\pm\sqrt2 i$

C.F= $C_1cos \sqrt2x+C_2 sin\sqrt2 x$

G.S=C.F+P.I

G.S= $C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x)$

3 0

3 years ago

The height of a stack of 12 pennies is 18.24 millimeters. What is the thickness of each penny.

Helga [31]

I’m not great at math so I could easily be wrong, but

I divided the 18.24 millimeters by 12 pennies and got 1.52

So if the pennies are all the same size, each penny should 1.52 millimeters.

To show work:

18.24/12=1.52

4 0

3 years ago

A class of 30 is divided into 2 groups such that the size of the smaller group is 2/3 the size of the larger group. How large is

pogonyaev

Answer:

I kinda did a lil of this in my head so i might not be 100% correct, but i would say the bigger group is 20 and the smaller group is 10

6 0

3 years ago

Im having trouble figuring out the missing length and solving this, can I have some help?

belka [17]

I think the answer is 17

8 0

2 years ago

Use the graph to fill in the blank with the correct number.<br><br> f(0) = ________

Keith_Richards [23]

Answer:

55 square feet jsjjjis the answer

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3 years ago