Answer:
28
Step-by-step explanation:
<em> -10 -10 -10 -10</em>
<em>68 </em>→ <em>58 </em>→ <em>48 </em>→ <em>38 </em>→ <em>28</em>
<em>Here is another example I can provide;</em>
<em>https://prnt.sc/lcgrt3</em>
<em>Apologies about the terrible handwriting. </em>
<em></em>
Answer:
x = - 1
Step-by-step explanation:
Given
(x - 4) = 2x ( multiply both sides by 5 to clear the fraction )
2(x - 4) = 10x
2x - 8 = 10x ( subtract 2x from both sides )
- 8 = 8x ( divide both sides by 8 )
- 1 = x
First all, the decay formula is
where:
is the remaining quantity after
years
is the initial sample
is the time in years
is the decay constant
From the problem we know that
and
, but we don't have the time
; to find it we will take advantage of the half-life of the Carbon-14. If you have a sample of 100 mg and Carbon-14 has a half-life of 5730, after 5730 years you will have half of your original sample i.e. 50 mg. We also know that after
years we have a remaining sample of 33mg, so the amount of the sample that decayed is
. Knowing all of this we can set up a rule 3 and solve it to find
:
Now that we know our time
lets replace all the values into our decay formula:
Notice that the constant
we need to find is the exponent; we must use logarithms to bring it down, but first lets isolate the exponential expression:
We can conclude that the decay constant
is approximately -0.000144
<em>Look</em><em> </em><em>at</em><em> </em><em>the</em><em> </em><em>attached</em><em> </em><em>picture</em><em>⤴</em>
<em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>:</em><em>)</em>
The parametric equations for x and y describe a circle of radius 10 m, so the length of the base of the fence is the length of the circumference of a circle of radius 10 m. The formula for that circumference (C) is ...
... C = 2πr
... C = 2π·(10 m) = 20π m
The height as a function of angle (t) is found by substituting for x and y.
... h(t) = h(x(t), y(t)) = 4 + 0.01·((10cos(t))²-)10sin(t))²) = 4+cos(2t)
The average value of this over the range 0 ≤ t ≤ 2π is 4, since the cosine function has two full cycles in that range, and its average value over a cycle is zero.
Thus, the area of one side of the fence is that of a rectangle 20π m long and 4 m wide. That will be
... (20π m)·(4 m) = 80π m²
The amount of paint required to cover both sides of the fence is
... 2×(80π m²)×(1 L)/(10 m²) = 16π L ≈ 50.3 L
_____
You can work out the integral for area as a function of t. When you do, you will find it gives this same result.