i don't understand the question a and b. so question a, it have to be add all?
When he was young, Captain Conundrum mowed lawns on weekends to help pay his college tuition bills. He charged
his customers according to the size of their lawns at a rate of 5¢ per square foot and meticulously kept a record of
the areas of their lawns in an ordered list:
A=(200,300,50,50,100,100,200, 500,1000,100)
He also listed the number of times he mowed each lawn in a given year, for the year 1988 that ordered list was
f =(20,1,2,4,1,5,2,1,10,6)
-How much did Captain Conundrum earn from mowing lawns in 1988? Write an expression for this amount in
terms of the vectors A and f.
-Suppose Captain Conundrum charged di�erent customers di�erent rates. How could you modify the expression
in part 1c to compute the Captain's earnings?
Well, it looks like Captain Conundrum had quite the lawn mowing business in 1988! Let's break this down with some humor:
- To calculate how much Captain Conundrum earned in 1988, we need to multiply the size of each lawn (in square feet) by the corresponding number of times it was mowed. We can use the dot product to do this.
So in terms of the vectors A and f, the expression for Captain Conundrum's earnings would be: "The sum of the dot product of vector A and vector f, multiplied by 5¢." Or, mathematically: (A . f) * 0.05.
Now, onto the second part of the question:
- If Captain Conundrum charged different rates, we would need another vector to represent the different rates for each lawn. Let's call it r.
To modify the expression from part 1c for computing the Captain's earnings with different rates, we can simply multiply the dot product of vectors A and f by the new vector r.
So the expression would be: "The sum of the dot product of vector A, vector f, and vector r." Or, mathematically: (A . f) * r.
Hope that brings a smile to your face while solving the problem!
To answer question a, you need to calculate the total earnings of Captain Conundrum from mowing lawns in 1988.
To do this, you can multiply each element of vector A (which represents the size of the lawns) by the corresponding element of vector f (which represents the number of times each lawn was mowed). Then, sum up all the resulting products.
Let's break down the steps:
1. Multiply each element of vector A by the corresponding element of vector f:
200 * 20 = 4000
300 * 1 = 300
50 * 2 = 100
50 * 4 = 200
100 * 1 = 100
100 * 5 = 500
200 * 2 = 400
500 * 1 = 500
1000 * 10 = 10000
100 * 6 = 600
2. Sum up all the resulting products:
4000 + 300 + 100 + 200 + 100 + 500 + 400 + 500 + 10000 + 600 = 12400
Therefore, Captain Conundrum earned $12400 from mowing lawns in 1988.
Moving on to question b, if Captain Conundrum charged different customers different rates, you would modify the expression by introducing a new vector R, which represents the individual rates for each lawn.
Assuming vector R is defined as R = (r1, r2, r3, r4, r5, r6, r7, r8, r9, r10), where ri represents the rate for the corresponding lawn in vector A, the modified expression would be:
Total earnings = (A1 * f1 * r1) + (A2 * f2 * r2) + ... + (An * fn * rn),
where A1, A2, ..., An are the elements of vector A, f1, f2, ..., fn are the elements of vector f, and r1, r2, ..., rn are the elements of vector R.
To find out how much Captain Conundrum earned from mowing lawns in 1988, we need to calculate the sum of the products of the areas of the lawns and the number of times each lawn was mowed. Here's how you can get the answer:
1. Multiply each element of vector A (the ordered list of the lawn areas) with the corresponding element in vector f (the list of the number of times each lawn was mowed). This can be done by multiplying the elements at the same index in both vectors. For example, multiply the first element of A (200) with the first element of f (20), then multiply the second element of A (300) with the second element of f (1), and so on. This will give you a new vector, let's call it g.
g = (A[1]*f[1], A[2]*f[2], A[3]*f[3], ..., A[n]*f[n])
In this case, g = (200*20, 300*1, 50*2, 50*4, 100*1, 100*5, 200*2, 500*1, 1000*10, 100*6) = (4000, 300, 100, 200, 100, 500, 400, 500, 10000, 600)
2. Finally, calculate the sum of all elements in vector g. In this case, add up all the numbers in g to get the total earnings:
Total earnings = g[1] + g[2] + g[3] + ... + g[n]
In this case, Total earnings = 4000 + 300 + 100 + 200 + 100 + 500 + 400 + 500 + 10000 + 600 = 12800 cents.
So, Captain Conundrum earned 12800 cents from mowing lawns in 1988.
Now, let's move on to the second question.
If Captain Conundrum charged different customers different rates, we can modify the expression to calculate his earnings by introducing another vector, let's call it r, which represents the rates for each lawn. The length of vector r should be the same as vectors A and f.
3. Multiply each element of vector A with the corresponding element in vector f, and then multiply the result by the corresponding element in vector r. This can be done by multiplying the elements at the same index in all three vectors. Let's call the resulting vector h.
h = (A[1]*f[1]*r[1], A[2]*f[2]*r[2], A[3]*f[3]*r[3], ..., A[n]*f[n]*r[n])
In this case, h = (200*20*r[1], 300*1*r[2], 50*2*r[3], 50*4*r[4], 100*1*r[5], 100*5*r[6], 200*2*r[7], 500*1*r[8], 1000*10*r[9], 100*6*r[10])
4. Finally, calculate the sum of all elements in vector h. Add up all the numbers in h to get the total earnings.
Total earnings = h[1] + h[2] + h[3] + ... + h[n]
The expression to compute Captain Conundrum's earnings when charging different customers different rates would be similar to the expression in part 1c, but you would need to include the vector r.
Note: In both cases, make sure that the vectors A, f, and r are ordered consistently so that the elements at the same index correspond to the same lawn.