Answer:
Step-by-step explanation:
My drawing tool is Desmos. It can be used at no cost.
the graph will not work unless you combine -2x^ and -4x^2 to give - 6x^2.
If you try and graph it as given, you get a straight line going for quadrant 4 to quadrant 2.
But you will note that when you make the addition of the 2 middle terms, it gives you the graph that I have enclosed, which is the one you should expect. I'm wondering why you get a straight line when you try and graph what you were given.
Answer:
27/2
Step-by-step explanation:
Given
Vertices (0, 0), (3, 0), and (0, 3)
Since the base of the equilateral in the plane perpendicular to the x-axis goes from the x-axis to the line y = 3 - x.
So, the length of each side of the triangle is (3-x)
Calculating the area;
Area = ½bh
Where b = base = 3 - x
height is calculated as;
h² = (3-x)² + (½(3-x))² --- from Pythagoras
h² = 9 - 6x + x² + (3/2 - ½x)²
Let h² = 0
0 = 9 - 6x + x² + (9/4 - 6/4x + ¼x²)
0 = 9 + 9/4 - 6x - 6/4 + x² + ¼x²
0 = 45/4 - 30x/4 + 5x²/4
0. = 5x²/4 - 30x/4 + 45/4
0 = 5x² - 15x/4 - 15x/4 + 45/4
0 = 5x(x/4-¾) - 15(x/4 - ¾)
0 = (5x - 15)(x/4 - ¾)
5x = 15 or x/4 = 3/4
x = 3 or x = 3
So, h = 3
Area = ½bh
Area = ½ * (3-x) * 3
Area = ½(9-3x)
Volume= Integral of ½(9-3x) {3,0}
V = 9/2 - 3x/2 {3,0}
V = 9x/2 - 3x²/4 {3,0}
V = 9(3)/2 - 3(3)²/4
V = 27/2 - 27/4
V = 27/2
Add the two known angles together and subtract that number from 180° and that is your answer.
To solve this, first subtract 3kx from both sides so that both the x variables are on the same side. This will result in: 24=9kx-3kx.
Since 9kx and -3kx are like terms, they will combine and you will get 24=6kx
Now, divide 6k from both sides to isolate x and you get x=24/6k.
However, you notice that 24 and 6k both have a common factor which is 6, so you simplify 24/6k to 4/k which gives you your answer of x=4/k
