Answer:
a² + 2ab + b²
Explanation:
⇒ (a + b)²
⇒ (a + b)(a + b)
[apply distributive method: (a + b) (c + d) = ac + ad + bc + bd]
⇒ a² + ab + ab + b²
⇒ a² + 2ab + b²
The function will be
where y is the balance, and x is the number of month.
The raph will be a line on the xy-plain which starts at the point (0, 360), and end in the point (72, 0).
Hope it helps.
Answer:
The midpoint is (3, 3).
Step-by-step explanation:
We are given the two points A(9, 11) and B(-3, -5).
The midpoint is given by:
So:
The midpoint is (3, 3).
We want to show that AM = MB.
We can use the distance formula:
The distance between A(9, 11) and M(3, 3) will then be:
And the distance between B(-3, -5) and M(3, 3) will be:
So, AM = MB = 10.
Since AM = MB = 10, AM + MB = 10 + 10 = 20.
So, we want to prove that AB = 20.
By the distance formula:
This is the missing equation that models the hieght and is misssing in the question:
<span>h= 7cos(π/3 t)
</span>
Answers:
<span>a. Solve the equation for t.
</span>
<span>1) Start: h= 7cos(π/3 t)
</span>
2) Divide by 7: (h/7) = <span>cos(π/3 t)
</span>
3) Inverse function: arc cos (h/7) = π/3 t
4) t = 3 arccos(h/7) / π ← answer of part (a)
b. Find the times at which the weight is first at a height of 1 cm, of 3
cm, and of 5 cm above the rest position. Round your answers to the
nearest hundredth.
<span>1) h = 1 cm ⇒ t = 3 arccos(1/7) / π</span>
t = 1.36 s← answer
2) h = 3 cm ⇒ t = 3arccos (3/7) / π = 1.08s← answer
3) h = 5 cm ⇒ 3arccos (5/7) / π = 0.74 s← answer
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time.
Use the periodicity property of the function.
The periodicity of <span>cos(π/3 t) is 6.
</span><span>
</span><span>
</span><span>So, the second times are:
</span><span>
</span><span>
</span><span>1) h = 1 cm, t = 6 + 0.45 s = 6.45 s ← answer
</span>
2) h = 3 cm ⇒ 6 + 1.08 s = 7.08 s← answer
3) h = 5 cm ⇒ t = 6 + 0.74 s = 6.74 s ← answer
