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Anna [14]
3 years ago
6

Each month, Stacey places a portion of her earnings in a retirement account. Her savings are invested in two companies. For ever

y $9 invested in company A, $2 is invested in company B. Stacey quizzes her children, Krista and Kevin, about how much money she will invest in company A if she invests $24 in company B. Krista and Kevin used two different methods to arrive at the answer to Stacey’s problem. Let’s see who found the correct answer and how. You’ll answer some questions along the way.
What is the ratio of the amount invested in company A to the amount invested in company B? Write the answer as a fraction using the values given. Do not include any variables.
Mathematics
2 answers:
Levart [38]3 years ago
7 0
It might be about 6 dollars

4vir4ik [10]3 years ago
3 0

The ratio of the amount invested in company A to the amount invested in company B is .


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Show that an implicit solution of 2x sin2(y) dx − (x2 + 12) cos(y) dy = 0 is given by ln(x2 + 12) + csc(y) = C. Differentiating
natima [27]

Answer:

See explanation

Step-by-step explanation:

Given the equation:

2x\sin (2y)dx-(x^2+12)\cos ydy=0

Separate variables x and y:

2x\sin (2y)dx=(x^2+12)\cos y dy\\ \\\dfrac{2x\sin (2y)dx}{x^2+12}=\cos ydy\ [\text{Divided by non-zero expression }x^2+12]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{\cos y}{\sin (2y)}dy\ [\text{Divided by }\sin (2y)]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{\cos y}{2\sin y\cos y}dy\ [\text{Use formula }\sin (2y)=2\sin y\cos y]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{1}{2\sin y}dy\ [\text{Simplify when }\cos y\neq 0]

Now,

\int \dfrac{2x}{x^2+12}dx=\int \dfrac{1}{2\sin y}dy\\ \\\int \dfrac{d(x^2)}{x^2+12}=\dfrac{1}{2}\int \dfrac{\sin y}{\sin^2 y}dy\\ \\\int \dfrac{d(x^2+12)}{x^2+12}=-\dfrac{1}{2}\int \dfrac{d(\cos y)}{1-\cos^2 y}\\ \\\ln (x^2+12)+C=-\dfrac{1}{2}\int \left(\dfrac{1}{2(1-\cos y)}+\dfrac{1}{2(1+\cos y)}\right)d(\cos y)\\ \\\ln (x^2+12)+C=-\dfrac{1}{4}\int \dfrac{d(\cos y)}{1-\cos y}-\dfrac{1}{4}\int \dfrac{d(\cos y)}{1+\cos y}\\ \\\ln (x^2+12)+C=\dfrac{1}{4}\ln (1-\cos y)-\dfrac{1}{4}\ln (1+\cos y)

\ln (x^2+12)+C=\dfrac{1}{4}\ln \dfrac{1-\cos y}{1+\cos y}

Find the constant solutions, if any, that were lost in the solution of the differential equation:

When

\cos y=0,

then

y=\dfrac{\pi }{2}+\pi k,\ k\in Z

5 0
3 years ago
An isosceles triangle has an angle that measures 68°. Which could be the measure of another angle in the triangle? A. 22° B. 56°
Lisa [10]

Answer:

B

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5 0
4 years ago
A triangle has one side of length 29 units and another of length 40 units. Determine the range in which the length of the third
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Answer:

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So sides are given 29 and 40.

Sum is 29 + 40 = 69

Difference is 40 - 29 = 11

Hence, the third side would be BETWEEN 11 and 69

C is the correct choice.

4 0
3 years ago
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