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3 years ago

A cone has a diameter of 12 and an inclination angle of 25. What is the height?

Mathematics

1 answer:

ANEK [815]3 years ago

5 0

Check the picture below.

make sure your calculator is in Degree mode.

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Find a particular solution to the nonhomogeneous differential equation y??+4y?+5y=?10x+e^(?x).

Firdavs [7]

Answer:

A) Particular solution:

$2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

B) Homogeneous solution:

$y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))$

C) The most general solution is

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

Step-by-step explanation:

Given non homogeneous ODE is

$y''+4y'+5y=10x+e^{-x}---(1)$

To find homogeneous solution:

$D^{2}+4D+5=0\\D^{2}+4D+4-4+5=0\\\\(D+2)^{2}=-1\\D+2=\pm iD=-2 \pm i\\y_{h}=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))---(2)$

To find particular solution:

$y_{p}=Ax+B+Ce^{-x}\\\\y'_{p}=A-Ce^{-x}\\y''_{p}=Ce^{-x}\\$

Substituting $y_{p},y'_{p},y''_{p}$ in (1)

$y''_{p}+4y'_{p}+5y_{p}=10x+e^{-x}\\Ce^{-x}+4(A-Ce^{-x})+5(Ax+B+Ce^{-x})=10x+e^{-x}\\$

Equating the coefficients

$5Ax+2Ce^{-x}+4A+5B=10x+e^{-x}\\5A=10\\A=2\\4A+5B=0\\B=-\frac{4A}{5}B=-\frac{8}{5}2C=1\\C=\frac{1}{2}\\So,\\y_{p}=2x+\frac{1}{2}e^{-x}-\frac{8}{5}---(3)\\$

The general solution is

$y=y_{h}+y_{p}$

from (2) ad (3)

$y=e^{-2x}(c_{1}cos(x)+c_{2}sin(x))+2x+\frac{1}{2}e^{-x}-\frac{8}{5}$

6 0

3 years ago

60 pts for the person that answer and brainiest

vodomira [7]

Answer:

the answer is b because it justifies why the theory of evolution is a theory not a law.

6 0

3 years ago

Read 2 more answers

What is the equation of the line that passes through the points (-3,5) (6,8)

Ratling [72]

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-3)}}}\implies \cfrac{3}{6+3}\implies \cfrac{3}{9}\implies \cfrac{1}{3}$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-5=\cfrac{1}{3}(x+3)\implies y-5=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+6$

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2 years ago

define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.

Savatey [412]

The picture is the answer

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3 years ago

Use the position equation given below, where s represents the height of the object (in feet),

mariarad [96]

The answers to the questions are

The mathematical model is given as s = −16t2 + 1054
The height after 4.5 seconds is 730 feet

the time it would take to strike the ground is 8.11 seconds.

<h3>How to solve for the position of the object</h3>

The mathematical model of this problem would be written as

s = −16t2 + v0t + s0

s0 = 1054

then we would have

s = −16t2 + 1054

b. after 4.5 seconds the height is going to be

s = −16t2 + 1054

= −16(4.5)² + 1054

= -16 * 20.25 + 1054

= 730

C. the time that it takes to strike the ground

s = −16t² + 1054

= 16t² = 1054

t² = 1054/16

= 65.88

t = √65.88

t = 8.11

Hence the time it would take to strike the ground is 8.11 seconds.