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Margaret [11]
3 years ago
9

Find the specific solution of the differential equation dy/dx equals the quotient of 2 times y and x squared with condition y(-2

) = e. (4 points)
A. y equals negative 1 minus 2 divided by x

B. y equals e raised to the negative 2 over x power

C. y equals negative 1 times e raised to the 1 over x power

D. None of these
Mathematics
1 answer:
love history [14]3 years ago
6 0

Answer:

B.   y = e^(-2/x).

Step-by-step explanation:

dy/dx = 2y / x^2

Separate the variables:

x^2 dy = 2y dx

1/2 * dy/y =  dx/x^2

1/2  ln y = = -1/x  + C

ln y = -2/x +  C

y = Ae^(-2/x)  is the general solution ( where A is a constant).

Plug in the given conditions:

e = A e^(-2/-2)

e = A * e

A = 1

So the specific solution is y = e^(-2/x).

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What are the roots of the polynomial equation x3 - 10x=-3x2+ 24? Please help
snow_tiger [21]

Answer:

x = -2, 3, -4.

Step-by-step explanation:

x^3 - 10x = -3x2 + 24 = 0

x^3 + 3x^2 - 10x - 24 = 0

The last term is 24 and the coefficient of x^3 is 1 so +/- 1,  +-2, +/- 3 and +/- 4 could be among the roots ( by The Rational Root Theorem).

Let x = 1

f(x) = 1^3 +3(1)^2 - 10 - 24 = -30 so it's no t .

f(-1) = -1 + 3 + 10 - 24 = -12  so it's not -1.

Let  x = 2:

f(2) =  2^3 +3*4 - 20 - 24 = -32  so its not 2

f(-2) = -8 + 12 + 20 - 24 = 0  so x = -2 is a root

and therefore x+ 2 is a factor and we divide:

x + 2 ) x^3 + 3x^2 - 10x - 24   (  x^2 + x - 12   <------ The quotient

          x^3 + 2x^2

                      x^2 - 10x

                       x^2 + 2x

                              -12x - 24

                              -12x - 24

                                ..............

Now x^2 + x - 12 = (x - 3)(x + 4)

So (x + 2)(x - 3)(x + 4) = 0

This gives

x = -2, 3, -4.

7 0
3 years ago
Read 2 more answers
What is 87.319 to the nearest tenth?
EleoNora [17]

Answer:

87.3

The answer to get 87.3 is to see if the number in the hundredths  place (this case 1) is bigger or the same as the value of 5. If it is round the tenth up but if not then cut the rest of the numbers off.      

4 0
2 years ago
The lower supports are and the area of the two supports is square meters. The upper arch can be decomposed as one semicircle wit
Galina-37 [17]

Answer:

 The lower supports are <u>Congruent Rectangles</u> and the area of the two supports is<u> 24 square meters.</u>

The upper arch can be decomposed as one semicircle with radius<u> 6 </u>meters minus a semicircle with radius 3 meters.

The area of the archway is <u>(13.5 π</u> + 24) square meters.

Step-by-step explanation:

See attachment for the firgure,

In order to determine the area of archway = The area of upper support + area of lower support.

As given, the lower support are two congruent rectangles consists of dimension 3 m × 4 m

Therefore, the area of lower support can be written as,

The area of lower support = 3 × 4 + 3 × 4 = 12 + 12 = 24 square m.

Now, the upper support arch can be decomposed as the two concentric semi circles having radius 3 m and 6 m,

Hence, the area of the upper support = Area of semi circle having radius i.e 6 m - Area of semi circle having radius i.e 3 m

=> π6²/2 - π3²/2= 27π/2= 13.5π square m

Therefore, the area of the archway =  (13.5 π + 24) square meters

4 0
3 years ago
I don’t understand!!!!!!
HACTEHA [7]
The solution is greater than one but less than or equal to 8.
7 0
3 years ago
Pleaseeeeeeeeeeeeeeeeee help
olganol [36]

Answer:

Jumping Jacks:7,<u>21,28</u>,42

Push-ups:2,6,8,<u>12</u>

8 0
3 years ago
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