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Crazy boy [7]
3 years ago
8

Mabel has a total of 54 beads. Some beads are black and some are white. The ratio of the number of black beads to the number of

white beads is 7:2. How many more black beads than white beads?
Mathematics
1 answer:
seraphim [82]3 years ago
3 0
7x+2x= 54
9x= 54
X=6

Black 7(6)=42
White 2(6)=12
=54
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Eric invested 5000 dollars in the stock market. The value of his stock increased by 13%. a) what is the amount earned from this
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Answer:

Earnings = 650

New\ Value = 5650

Step-by-step explanation:

Given

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Consider the implicit differential equation <img src="https://tex.z-dn.net/?f=%2849%20y%5E%7B3%7D%20%2B%2045%20xy%29%20dx%20%2B%
BaLLatris [955]
We're looking for an integrating factor \mu(x,y)=x^py^q such that

\mu\underbrace{(49y^3+45xy)}_M\,\mathrm dx+\mu\underbrace{(98xy^2+50x^2)}_N\,\mathrm dy=0

is exact, which would require that

(\mu M)_y=(\mu N)_x
(49x^py^{q+3}+45x^{p+1}y^{q+1})_y=(98x^{p+1}y^{q+2}+50x^{p+2}y^q)_x
49(q+3)x^py^{q+2}+45(q+1)x^{p+1}y^q=98(p+1)x^py^{q+2}+50(p+2)x^{p+1}y^q
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You can verify that (\mu M)_y=(\mu N)_x if you'd like. With the ODE now exact, we have a solution F(x,y)=C such that

F_x=\mu M
F=\displaystyle\int(49y^3+45xy)x^{5/2}y^4\,\mathrm dx
F=10x^{9/2}y^5+14x^{7/2}y^7+f(y)

F_y=\mu N
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