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3 years ago

Divide. Reduce the answer to lowest terms. 2 1/9 ÷ 3 1/3

Mathematics

2 answers:

nevsk [136]3 years ago

6 0

Answer:

7/31 is the answer you are looking

Varvara68 [4.7K]3 years ago

5 0

7/31! Hope it helps!

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Solve the following differential equation: y" + y' = 8x^2

PtichkaEL [24]

Answer:

$y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$

Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

$y'= 3ax^2+2bx+c$ and

$y''= 6ax+2b$

$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

5 0

2 years ago

What is the surface area of this triangular pyramid?

solniwko [45]

Answer:

Step-by-step explanation:

Hence, the surface area of a triangular pyramid is 140 square units.

3 0

2 years ago

One-stray Problem Solving

anygoal [31]

A) 5000 m²
b) A(x) = x(200 -2x)
c) 0 < x < 100
Step-by-step explanation:
b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground:
A(x) = x(200 -2x)
__
a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m²
__
c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.

3 0

1 year ago

6051 m is equal to how many km?

Luba_88 [7]

6,051m = 6,000m + 51m

1km=1,000 metres

--------------------------------

Therefore:

6,051 metres = 6,000/1,000km + 51/1,000km

=6,051/1,000km

=6.051km

8 0

2 years ago

Read 2 more answers

Is 86, 75, 97, 58. 94, and 58, odd or even

alexira [117]

This is even because they all can be divided if it was odd you would not be able to decide them

5 0

2 years ago