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2 years ago

graph the following functions to find how many points of intersection there are in y=(x+2)^2+3 and (x+2)^2+(y-2)^2=9

Mathematics

1 answer:

Finger [1]2 years ago

7 0

Refer to the image that I attached to my answer.

According to the graphing calculator, the two equations have two points of intersections (the points where the different colored lines cross).

Happy Studying~

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Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago

Help me in this 2 question pleaseee

Dennis_Churaev [7]

For the first one it is a falling line and the second is 0

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3 years ago

Read 2 more answers

How do you find vertical, horizontal and oblique asymptotes for f(x) = (5x-15 )/ (2x 14)?

Andrei [34K]

For vertical asymptotes, find the values which make the function indetermine in this case x=-7,so this is the only vertical asymptote.
For horizontal asymptotes, find the limit when x tends to infinity:
=(5x/x-15/x)/(2x/x+14/x) = 5/2, this is the horizontal asymptote y=5/2
For obliques, you have to meet the degree of the numerator is exactly a greater degree than the denominator, in this case they are the same degree so no oblique asymptote.

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3 years ago

Describe the cross-section of the rectangular prism

ser-zykov [4K]

Answer:

The cross-section of the rectangular prism is a:

rectangle

Step-by-step explanation:

When you take a cross-section of a rectangular prism, regularly you will obtain a rectangle because this was the base or the two-dimension figure that was used to form the three-dimension figure, in this case, the rectangular prism, the form of obtaining other figure is using how reference the square face, in that case, the cross-section would be a square, this happens because the cross-section is bind with the reference face. Possibly you think the cross-section in the figure doesn´t appear a rectangle, this happens by the perspective because we are looking at the rectangular prism with an inclination of 45°, but if the inclination was 90°, you would see a blue rectangle.

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3 years ago

What is the first thing you need to do to add 1/9+5/6? A.add the number. B.add the denominators. C.find the least common denomin

QveST [7]

C.)Find the lest common denominator.

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3 years ago