Answer:
after 6 half lives: 210(1/2)^6= 3.28125
Step-by-step explanation:
isotope to be reduced to half its initial mass at first:
210(1/2)=105 half it is original weight
after second life: 210(1/2)^2=105(1/2)=52.5
after third : 210(1/2)^3=52.5/2=26.25
after fourth : 26.25/2=12.125
after fifth : 13.125/2
after 6 half lives: 210(1/2)^6= 3.28125
<span>Best corral has a width and length of 50 feet, enclosing an area of 2500 square feet.
Let's calculate the width (W) of the rectangle as a function of it's length (L). So we have
W = (200 - 2*L)/2
W = 100 - L
Now the area of the rectangle is
A = WL
Substitute the equation for W.
A = (100 - L)L
A = 100L -L^2
Let's make an initial guess of 40 ft and add an error component of e. So we'll use the length of (40+e) and see what we get.
A = 100L -L^2
A = 100(40+e) - (40+e)^2
A = 4000 + 100e - (1600 + 80e + e^2)
A = 4000 + 100e - 1600 - 80e - e^2
A = 2400 + 20e - e^2
Now looking at those 2 "e" terms is interesting. It's pretty obvious that any negative value of e will cause those term to result in a value less than 0, and decrease the available area. Also any value of e greater than 20 will also cause those 2 values to sum to a negative value and decrease the area. But a value of e in the range of 0 to 20 will result in a positive value and cause the area enclosed to be larger. So it's obvious that 40 feet isn't optimal. Let's pick the middle of the e values that result in something positive (0+20)/2 = 10 and add that to our initial guess, getting a length of 50 and replace length by (50+e) and see what happens.
A = 100L -L^2
A = 100(50+e) -(50+e)^2
A = 5000+100e -(2500+100e + e^2)
A = 5000+100e - 2500 - 100e - e^2
A = 2500 - e^2
This looks quite promising. Any non-zero value of e will result in the area enclosed being smaller. So the idea value of e is 0. That means that the idea length of the rectangle is 50 feet. And that makes the width 50 feet as well.
Mind, this problem could have been also solved using the first derivative of the equation A = 100L -L^2, which would have been A' = 100 - 2L, and then solving for 0. But I did this problem to demonstrate that you don't need to resort to calculus for every maximum type of problem.</span>
Step by Step answer
Yes I believe that is correct
Answer:
See attachment. Also, I got 2.36 as the answer with my calculator despite that not being on the multiple choice list
Answer:
y = -2x + 3
Step-by-step explanation:
The given equation is:
First we need to find the slope of the tangent line. This can be done by finding the derivative of the given function.
Slope of the tangent will be the value of the derivative at the given point. So the slope of tangent is:
Now we have slope of the tangent line and a point (0, 3) on the tangent. The point (0,3) is the y-intercept of the tangent line. So we can use slope-intercept form to directly write the equation of the line.
The slope intercept form of an equation is:
y = mx + c
where m is the slope and c is the y-intercept.
Using the values: m = -2 and c = 3, we get:
y = -2x + 3
This equation represents the tangent line