Answer:
Step-by-step explanation:
We have the plane 2x-2y+z-8=0 and the paraboloid z=x²+y².
We match the equations:
z=8-2x+2y
z=x²+y²
x²+y²=8-2x+2y
Then, we get the equation of the curve:
x²+2x+y²-2y=8 (adding +2x and -2y in both members of the equation)
(x²+2x+1)+(y²-2y+1)=8+1+1
Trinomials can be reduced as squared binomials
(x+1)²+(y-1)²=10
This is a circle with center in (-1,1) and radius √10
The generic
The parametric expression of the circle is:
#1.
Question: <span><span><span><span>2x^2 </span>− 3x</span> − 35</span> = 0</span>
<span><span><span>Step 1: Factor left side of equation): (<span>2x + 7</span>) </span><span>(x − 5) </span></span>= 0</span>
Step 2: Set factors equal to 0.): <span><span><span>2x + 7 </span>=<span><span> 0 or x </span>− 5</span></span> = 0</span>
ANSWER: <span><span>x =<span><span><span> −7/2</span> or </span>x </span></span>= 5</span>
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#2.
Question: 56z^2 + 2 = 22z
<span>Step 1: Subtract 22z from both sides.):
</span><span><span><span><span>56<span>z^2 </span></span>+ 2</span> −<span>22z</span></span> = <span><span>22z </span>−<span> 22z
</span></span></span><span><span><span><span>56<span>z^2 </span></span>−<span> 22z </span></span>+ 2 </span>= 0</span>
<span>Step 2: Factor left side of equation.):
</span>
<span><span><span>2<span>(<span><span>7z </span>− 1</span>)</span></span><span>(<span><span>4z </span>− 1</span>)</span></span> = 0
</span><span>Step 3: Set factors equal to 0.):
</span>
<span><span><span><span>7z </span>− 1 </span>=<span><span><span> 0 or </span><span>4z</span></span> − 1</span></span> = 0
ANSWER: </span><span><span>z =<span><span><span> 1/7</span> or </span>z </span></span>=<span> 1/4</span></span>
Answer:
Below.
Step-by-step explanation:
You could multiply the first equation by 3 and the second one by -2 so that the 2 y terms would be -6y and 6y:
12x - 6y = 21
-6x + 6y = -30
Adding these will eliminate the y variable.
Answer: 8/9 divided by 4 is 2/9.
Step-by-step explanation: If you want to divide fractions, first you need to find the reciprocal of the second term. The reciprocal is when you swap the numerator and the denominator. The reciprocal of 4 is 1/4. Then, you multiply 8/9 is 1/4. 8 x 1 is 8, and 9 x 4 is 36. The answer is 8/36, which you can simplify into 2/9.