What is the equation of the graph?
1 answer:
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Answer:
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Step-by-step explanation:
Simplifying the numerator :
⇒ (-5m⁷n⁰p⁵)(2m⁴n³p²)³
⇒ (-5m⁷p⁵)(8m¹²n⁹p⁶)
⇒ (-5)(8)(m)⁷⁺¹²n⁹(p)⁵⁺⁶
⇒ <u>-40m¹⁹n⁹p¹¹</u>
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Dividing by the denominator :
⇒
⇒
Answer:
(x, y, z) = (3, -2, 4)
Step-by-step explanation:
The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...
z = 5 -(3 +(-2)) = 4
The solution is (x, y, z) = (3, -2, 4).
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Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:
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If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:
-3x -4y +4(5 -x -y) = 15 ⇒ -7x -8y = -5
(-3x -4y +4z) +(2x -y -4z) = (15) +(-8) ⇒ -x -5y = 7
This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...
-7(-5y -7) -8y = -5 ⇒ 27y = -54 ⇒ y = -2
x = -5(-2) -7 = 3
z = 5 -(3) -(-2) = 4
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<em>Additional comment</em>
If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.
Answer:
Step-by-step explanation:
Area of circle:
By using the area of a circle, we can get the area of a semicircle:
Let's convert the mixed fraction to an improper fraction and then a decimal:
=
=
Now, we solved for the diameter, to get the radius, we need to divide the diameter by 2:
Now we have the radius, so we can plug in our values and find the area: