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2 years ago

Maths a²(5a - 3b) -3a²

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

4 0

Answer:

$5a^{3} - 3a^{2} b-3a^{2}$

Step-by-step explanation:

$a^{2} (5a-3b)-3a^{2} |$

Expand brackets

$5a^{3} - 3a^{2} b-3a^{2}$

Final Answer is

$5a^{3} - 3a^{2} b-3a^{2}$

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The pair of points is on the graph of an inverse variation. Find the missing value. (1.6,6) and (8,y)

____ [38]

<h3>Answer: y = 1.2</h3>

Work Shown:

Inverse variation equations can be written in the form x*y = k for some fixed number k. Let's plug in the first point (x,y) = (1.6, 6) to compute the value of k

x*y = k

1.6*6 = k

9.6 = k

k = 9.6

Therefore the equation updates to

x*y = 9.6

Plug in x = 8 and solve for y

x*y = 9.6

8*y = 9.6

y = 9.6/8 .... divide both sides by 8

y = 1.2

5 0

3 years ago

Solve the equation <img src="https://tex.z-dn.net/?f=%2835%20x%5E%7B4%7D%20y%2B14%20x%5E%7B5%7D%20y-2%20y%5E%7B3%7D-4x%20y%5E%7B

jeka94

$\underbrace{35x^4y+14x^5y-2y^3-4xy^3}_M\,\mathrm dx+\underbrace{7x^5-6xy^2}_N\,\mathrm dy=0$

$M_y=35x^4+14x^5-6y^2-12xy^2$
$N_x=35x^4-6y^2$

$\dfrac{N_x-M_y}N=\dfrac{-14x^5+12xy^2}{7x^5-6xy^2}=-2$

This suggests an integrating factor depending on $x$ only is possible, and given by

$\mu(x)=\exp\left(-\displaystyle\int\frac{N_x-M_y}N\,\mathrm dx\right)=e^{2x}$

Distributing across the ODE, we end up with

$\underbrace{(35x^4y+14x^5y-2y^3-4xy^3)e^{2x}}_{M^*}\,\mathrm dx+\underbrace{(7x^5-6xy^2)e^{2x}}_{N^*}\,\mathrm dy=0$

The equation is now exact, with

${M^*}_y={N^*}_x=(35x^4+14x^5-6y^2-12xy^2)e^{2x}$

Now we find the solution:

$F_x=M^*$
$F=\displaystyle\int(35x^4+14x^5-2y^3-4xy^3)e^{2x}\,\mathrm dx$
$F=(7x^5y-2xy^3)e^{2x}+f(y)$

$F_y=N^*$
$(7x^5-6xy^2)e^{2x}+f'(y)=(7x^5-6xy^2)e^{2x}$
$f'(y)=0$
$\implies f(y)=C$

The general solution is then

$F(x,y)=(7x^5y-2xy^3)e^{2x}=C$

7 0

3 years ago

What scale factor should be applied to a solid to produce a volume that is four times as large as the original volume? 64 1.12 4

Anton [14]

4

If i want the number 5 to be 4 times as large, i will multiply 5 x 4

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3 years ago

Read 2 more answers

10% of the total time at school out of 360 minutes a day , how much time was spend at lunch ?

Anvisha [2.4K]

Answer:

36 minutes

Step-by-step explanation:

360/10=36 (percent is division of the number)

8 0

3 years ago

Pixel goes shopping with one hundred dollars and ends up buying three different types of items: A, B, and C. The unit price of A

mixas84 [53]

Answer:

A - 16, B - 79, C - 5

Step-by-step explanation:

Given

A costs 5$
B costs $0.25
C costs $0.05
A + B + C = 100
5A + 0.25B + 0.05C = 100 ⇒ 100A + 5B + C = 2000

Subtract the first equation from the second:

99A + 4B = 1900

We have a restriction in numbers:

0 < A, B, C < 100

Since 4B can be max 400, we get 99A > 1500 and 99A < 1900 so:

A > 1500/99 > 15

and

A < 1900/99 < 19

A can be 16 or 18 as it should be even number to get B the whole number.

If A = 16:

99*16 + 4B = 1900
4B = 1900 - 1584
4B = 316
B = 316/4 = 79

If A = 18:

99*18 + 4B = 1900
4B = 1900 - 1782
4B = 118
B = 118/4 = 29.5, discarded as decimal

So we get:

A = 16, B = 79 and C = 100 - (16 + 79) = 5

Let's proof the numbers:

16*5 + 79*0.25 + 5*0.05 = 100, confirmed

5 0

2 years ago

Maths a²(5a - 3b) -3a²​

Maths a²(5a - 3b) -3a²