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3 years ago

Without adding, find the sum of :d) 1+3+5+7+9+11+13+15+17+19

Mathematics

1 answer:

erik [133]3 years ago

6 0

Answer: 99 or 100 because you can tell.

Have a great day

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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

TAKE ANY UNMARKED BOWL OR GLASS AND FILL IT EXACTLY 3/5 FULL WITH WATER.

Wittaler [7]

Answer:

Take a glass, and fill it completely with water.

Now, pour that water in a marked bowl and measure how much water is in the bowl, that amount of water will be 100% of the total water that the glass can have.

Now you need to pour 3/5 of the water back in the glass, it is easier for water until the water in the bowl is exactly 2/5 of the initial amount.

You can do this as follows.

2/5 = 0.4 or 40% in percentage form.

Then if the amount of water in the marked bowl is A, the amount of water that must remain in the marked bowl is A*0.4

Then drop the water in the glass until the water in the marked bowl is the quantity that you found previously.

In this way, you can be sure that the glass is 3/5 full of water.

8 0

3 years ago

6.7 divided by 643.2 find the quotient

katrin2010 [14]

Answer:

1/96 or 0.01041666667

Step-by-step explanation:

5 0

3 years ago

Pls help me it's due today

Dimas [21]

Answer:

r³ + 15r² - 10r - 4

Step-by-step explanation:

First, note you can remove the brackets, in this case they contribute nothing at all.

Then, group the like terms and add them, e.g., we have 3r³ and -2r², they add up to r³.

Finally, order them from greatest power of r to smallest power of r.

That's all!

8 0

3 years ago

What is the expression for "the sum of 8 times a number and two"?

LiRa [457]

Answer:

8 N + 2

Step-by-step explanation:

==> 8 N + 2

-----------_________-------------

8 0

2 years ago

Without adding, find the sum of :d) 1+3+5+7+9+11+13+15+17+19​

Without adding, find the sum of :d) 1+3+5+7+9+11+13+15+17+19