Answer:
4
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Step-by-step explanation:
<u>Step 1: Define</u>
a = 3, b = 5, c = 1
b - c
<u>Step 2: Evaluate</u>
- Substitute: 5 - 1
- Subtract: 4
Answer:
Part 1)
Part 2)
Step-by-step explanation:
we know that
In a parallelogram opposite sides and opposite angles are congruent, and consecutive angles are supplementary
Part 1)
<u>Find the value of x</u>
----> opposite sides are congruent
solve for x
<u>Find the value of m</u>
----> consecutive angles are supplementary
solve for m
Part 2)
<u>Find the value of x</u>
---> opposite sides are congruent
using a graphing tool
see the attached figure N 1
The solutions are
<u>Find the value of m</u>
---> opposite sides are congruent
solve for m
using a graphing tool
see the attached figure N 2
The solutions are
Answer:
Number 4, the last one
Step-by-step explanation:
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
