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allochka39001 [22]
2 years ago
13

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)
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<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
8 0
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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:

<u>Given</u>

  • 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

<u>Subtract the first equation from the second:</u>

  • 99A + 4B = 1900

<u>We have a restriction in numbers:</u>

  • 0 < A, B, C < 100

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

  • 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.

<u>If A = 16:</u>

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

<u>If A = 18:</u>

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

<u>So we get:</u>

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

<u>Let's proof the numbers:</u>

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

5 0
2 years ago
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