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Answer:
The intersection of the horizontal plane with the prism would have a square shape.
Step-by-step explanation:
A right rectangular prism is one in which each side makes an angle of with its base, which is a square. It is a three dimensional figure with six faces.
The point where the horizontal plane and the prism coincides would take the shape of the base of the prism. This is because the prism rests with its base on the horizontal plane. Thus, the shape required is in the form of a square since its base is a square. The length and width of its base are equal.
Answer:
Step-by-step explanation:
We are given the following function in the question:
We have to derivate the given function.
Formula:
The derivation takes place in the following manner
Answer to 1:
First thing you want to do is combine like terms on the bottom. Since it's multiplication, all you have to do is add the exponents. So for x you'd get x raised to the -9 power and for y you'd get 2y raised to the power of 7
Second thing is the numerator of the fraction. Since this is raising what is inside the paranthesis to a power, you must multiply this power by the powers of x and y, respectively. You should get x raised to the power of -6 and y raised to the power of -18
Here's where it gets complicated. to rationalize the problem, you must add parts from the numerator and denominator or vice versa. You cannot have any negative exponents anywhere in the fraction. So that means for x you have to add 9 to the x on the top to cancel out the -6 and rationalize the remaining x's. You should end up with x^3.
For y, you work the opposite way. Since the negatives are only on the top, you simply add 18 to the bottom y's and it remains rationalized.
If done correctly this should come out to x^3/2y^25
Answer to 2:
(x^20y^12)/256
First thing you can do on this one is to cancel out the x^0s. Anything to the power of 0 equals one so only the coefficients will remain. Multiply those together and you'll get 4.
Next you will rationalize the ys. Add the bottom 3 to the top to cancel out the denominator and you're left with y^-3. Leave it like this for now.
Now is the difficult part. You must take everything that is inside the parenthesis to the power of -4. That includes the coefficients and the exponents. 4^-4 = 1/256. This means that you now must move the coefficients to the bottom. You should currently have y^-3/(256x^5).
Now take the exponents to the power using the same rules as question 1. -3*-4 = 12 and 5*-4 = -20. You should now have y^12/(256x^-20)
Lastly, we must rationalize the denominator. To do so, move the x^-20 to the numerator and make the exponent positive. After doing this, you have the answer: (x^20y^12)/256