For the answer to the question above,
1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4
2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57
3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65
4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.
5. V = (q -2x) (p - 2x) (x)
Answer:
Triangle #2
Step-by-step explanation:
Translation involves the movement of a triangle without changing its direction or shape. It basically involves the sliding of a triangle, so Triangle 2 satisfies the definition of translation.
Answer:
D and E
Step-by-step explanation:
because the rule to make triangle is
a<b+c with a, b and c is the side of the triangle
Answer:
Yes they can all be written in y = mx + b. You just have to move the terms around.
Step-by-step explanation:
y = 2x -3, this is already in slope-intercept form
Now, y - 2 = x + 2: We can add 2 on both sides to cancel out the one on the left side:
y - 2 = x + 2
y - 2 + 2 = x + + 2
y = x + 4 <-- This is in y = mx + b form
Now the last one, 3x = 9 + 3y
We can first divide all terms by 3,
3x = 9 + 3y
/3 /3 /3
x = 3 + y: Then we can subtract 3 from both sides:
x - 3 = 3 + y - 3
x - 3 = y
These are all linear equations because none of the x's have bigger powers than 1. x^2 is a quadratic equation and x^3 is cubic equation.
