Answer:
Step-by-step explanation:
(a+ b)² = a² + b² + 2ab
(2x + y)² = (2x)² + y² + 2*2x *y
= 4x² + y² + 4xy
(a- b)² = a² + b² - 2ab
(3x - 2y)² = (3x)² + (2y)² - 2*3x *2y
= 9x² + 4y² - 12xy
(a - b)(a +b) = a² - b²
(x - 4y(x + 4y) = x² - (4y)²
= x² - 16y²
(2x + y)² - (3x - 2y)² + (x - 4y)(x +4y)
= 4x² + y² + 4xy - (9x² + 4y² - 12xy) + x² - 16y²
= 4x² + y² + 4xy - 9x² - 4y² + 12xy + x² - 16y²
= 4x² - 9x² + x² + y² - 4y² - 16y²+ 4xy + 12xy
= -4x² - 19y² + 16xy
In this question, you're solving for x.
Solve for x:
2(x - 8) + 4x = 6(x - 2) - 4
Distribute the 2 to the variables inside the parenthesis.
2x - 16 + 4x = 6(x - 2) - 4
Distribute the 6 to the variables inside the parenthesis.
2x - 16 + 4x = 6x - 12 - 4
6x - 16 = 6x - 12 - 4
6x - 16 = 6x - 16
Subtract 6x from both sides
-16 = -16
Add 16 to both sides
0 = 0
Answer:
All real numbers and solutions
1. To find the vertex of a parabolla whose equation is written in the standard form, you must apply the following proccedure:
2. You have:
y=-0.18x²+4.4x-12
a=-0.18
b=4.4
3. You must apply the following formula:
<span>
x=-b/2a
x=-4.4/2(-0.18)
x=-4.4/-0.36
x=12.22
4. When you susbtitute x=12.22 into the equation </span>y=-0.18x²+4.4x-12, you obtain:
y=-0.18x²+4.4x-12
y=-0.18(12.22)²<span>+4.4(12.22)-12
</span> y=14.88 feet
5. The answer is: The maximum height of the tunnel is <span>14.88 feet</span>
Time required for the pendulum to swing from its position furthest to the right to its position furthest to the left: 1.25 seconds
Step-by-step explanation:
A pendulum is a system consisting of a rod/string connected to a mass which is left free to oscillate back and forth around its equilibrium position, straight vertical.
The period of a pendulum is the time the pendulum takes to complete one full oscillation, that means it is the time the pendulum takes to go from its furthest position on the left to the same position again. It is calculated as
where L is the length of the pendulum and g the acceleration of gravity.
The figure in this problem represents the position of the pendulum. We observe that the time it takes for the pendulum to do one complete oscillation is 2.5 seconds.
The time it takes for the pendulum to swing from its position furthest to the right to its position furthest to the left is half the period: therefore, it is
Learn more about period:
brainly.com/question/5438962
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