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3 years ago

Which is greater 7/3 or 5/2? How do you know

2 answers:

6 0

In order to understand which one is greater, you need to make the denominator on both fractions equal.

7/3 (2)= 14/6
5/2 (3)= 15/6

Since 15/6 is greater than 14/6:

5/2 is the greater fraction.
Hope this helps!!!

labwork [276]3 years ago

5 0

You need to get the denominator at the same number first. The Lowest common denominator is 6. So multiple 7/3 by 2 and 5/2 by 3 to get 14/6 and 15/6. 15/6 is greater. 15/6 is 5/2, so the answer is 5/2. I hope this helps!

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Dy/dx = 2xy^2 and y(-1) = 2 find y(2)

Anarel [89]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2887301

—————

Solve the initial value problem:

dy
——— = 2xy², y = 2, when x = – 1.
dx

Separate the variables in the equation above:

$\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\
\mathsf{y^{-2}\,dy=2x\,dx}$

Integrate both sides:

$\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\
\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\
\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{y}=x^2+C_1}$

$\mathsf{\dfrac{1}{y}=-(x^2+C_1)}$

Take the reciprocal of both sides, and then you have

$\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}$

In order to find the value of C₁ , just plug in the equation above those known values for x and y, then solve it for C₁:

y = 2, when x = – 1. So,

$\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\
\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\
\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}$

$\mathsf{C_1=-\,\dfrac{3}{2}}$

Substitute that for C₁ into (i), and you have

$\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\
\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}\cdot \dfrac{2}{2}}\\\\\\
\mathsf{y=-\,\dfrac{2}{2x^2-3}}$

So y(– 2) is

$\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{5}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

Tags: <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

7 0

3 years ago

Will ran four miles on his first day of training. The next day he ran one-third that distance. How far did he run the second day

igomit [66]

1.3333333333333333333333333333333333333

4 0

2 years ago

A farmer has a square garden that has an area of 100 feet squared. He needs to

stellarik [79]

Answer:

40ft

Step-by-step explanation:

The shape of the garden (square) tells you that both the length and the width of the garden are the same measure.

If the area is 100sqft, you can determine that side * side = 100. To find this answer, you can take the square root of 100. side=10, because 10 * 10= 100 (the area).

Now, we know that each side measures 10 feet. Try drawing and labeling a picture to help you visualize the garden. Next, label each side of the square garden 10ft. To find the feet of fencing is needed to enclose the garden,

We need to find the perimeter, so we can calculate

10ft * 4 sides = 40 feet of fencing.

5 0

2 years ago

What’s the distance between (8,-5 ) and (6,4)

Ierofanga [76]

Answer:

Step-by-step explanation:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(6-8)^2+(4+5)^2

d^2=4+81

d^2=85

d=(85)^(1/2)

d=9.22 (rounded to nearest hundredth)

6 0

2 years ago

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What is the value of x3 . y4 when x<br> 3 and y = 0?

jonny [76]

Answer:

Step-by-step explanation:

$x^3 \times y^4\\\\x = 3\\y =0 \\\\(3)^3\times 0^4\\\\3^3\times\:0^4\\\\\mathrm{Apply\:rule}\:0^a=0\\0^4=0\\\\=3^3\times\:0\\\\\mathrm{Apply\:rule}\:0\times\:a=0\\=0$

6 0

3 years ago

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