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2 years ago

If a bag contains 10 red,6 yellow,24 blue,and 8 white balloons , what part-to-whole ratio of blue balloons to all balloons

Mathematics

1 answer:

Anna11 [10]2 years ago

5 0

Answer:

A. 1:2.

Step-by-step explanation:

24: 10+6+8+24

24:48

$\frac{24}{24}$ = 1

$\frac{48}{24}$ = 2

1:2

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Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.

fredd [130]

$\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

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$f'(y)=0\implies f(y)=C$

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With $y(1)=2$ , we have

$8+\ln9=C$

$\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}$

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2 years ago

Two equations are given below: a – 3b = 9 a = b – 3 What is the solution to the set of equations in the form (a, b)?

Vilka [71]

A-3b=9
a=b-3

b-3-3b=9
-2b-3=9
-2b=12
2b=-12
b=-6

a=-6-3
a=-9

Solution: (-9,-6)
----
Check:
-9=-6-3
-9=-9
TRUE

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3 years ago

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rewona [7]

Answer:

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Step-by-step explanation:

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y = $\frac{3}{7}$ x + 11 is in this form with m = $\frac{3}{7}$

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subtract 7x from both sides

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y = - $\frac{7}{3}$ x + $\frac{13}{3}$ ← in slope- intercept form

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