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3 years ago

Need the answer/step by step explanation

Mathematics

1 answer:

Brrunno [24]3 years ago

6 0

Answer:

8 weeks

Step-by-step explanation:

m=12+0.5w

Replace the m with the 16 and solve

16=12+0.5w

4=0.5w

8=w

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Find the general solution of the nonhomogeneous differential equation x^2y''-2y=3(x^2) -1, (x>0).

Ira Lisetskai [31]

Answer:

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Step-by-step explanation:

We are given that non-homogeneous differential equation

$x^2y''-2y=3(x^2)-1$

It is Cauchy Euler equation

Substitute x=e^t x>0

Auxillary equation

$D'(D'-1)-2=0$

$D'^2-D'-2=0$

$(D'-2)(D'+1)=0$

$D'-2=0 \implies D'=2$

$D'+1=0\implies D'=-1$

Complementary solution

$y=C_1e^{-t}+C_2e^{2t}$

$y=C_1\frac{1}{x}+C_2x^2$

Particular solution

$y_p=\frac{3e^{2t}}{D'^2-D'-2}-\frac{e^{0t}}{D'^2-D'-2}$

$y_p=te^{2t}+\frac{1}{2}=x^2logx+\frac{1}{2}$

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Hence, general solution G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

6 0

4 years ago

The equation of a circle is given below. Identify the center and radius. Then graph the circle.

Blizzard [7]

Answer:

Center = (3, 0)
Radius = 3
Graph = see below

Concept:

Here, we need to know the idea of the circle equation.

Circle equation: (x - h)² + (y - k)² = r²

(h, k) = center

r = radius

x = variable

y = variable

Solve:

Given expression

(x - 3)² + y² = 9

Find the point of the center

(h, k) = $\boxed{(3,0)}$

Find the length of the radius

r² = 9

$\boxed{r=3}$

Hope this helps!! :)

Please let me know if you have any questions

3 0

3 years ago

Read 2 more answers

Emanuel drove home from college traveling an average speed of 70 mph and drove back to the college the following week at an aver

xz_007 [3.2K]

Answer:

Step-by-step explanation:

Let t represent the time it took Emanuel to drive home from college. If the total round trip took 11 hours, it means that the time it took

Emanuel to drive from home back to college would be (11 - t) hours.

Emanuel drove home from college traveling an average speed of 70 mph.

Distance = speed × time

Distance covered by driving from college to home is

70 × t = 70t

He drove back to the college the following week at an average speed of 62.7 mph.

Distance covered by driving back to college from home is

62.7(11 - t) = 689.7 - 62.7t

Since the distance travelled is the same, then

689.7 - 62.7t = 70t

70t + 62.7 = 689.7

132.7t = 689.7

t = 689.7/132.7

t = 5.19 hours.

Therefore, the time that it took Emanuel to drive from home back to college is

11 - 5.19 = 5.81 hours

3 0

3 years ago

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If g(x) = x2 + 2, find g(3). (2 points) a 9 b 8 c 11 d 6

kap26 [50]

Answer:

c) 11

Step-by-step explanation:

g(x)= x² + 2

x = 3

substitute x for 3

g(3) = (3)² + 2

g(3) = 9 + 2

g(3) = 11

4 0

3 years ago

Which statement about rigid transformations is true?. . A rigid transformation preserves only the side lengths of a polygon.. .

Vladimir [108]

A rigid transformation is a transformation of the plane that preserves length. In a rigid transformation the initial shape and the image shape are congruent.

Main properties:
1. distance (lengths of segments remain the same)
2. angle measures (remain the same)
 3. parallelism (parallel lines remain parallel)
 4. collinearity (points remain on the same lines)
 5. orientation (lettering order remains the same)

Taking these properties into account, the correct choice is C.

8 0

3 years ago

Read 2 more answers