Example 1. Let us start with the functionf(x) = x2. We have

So

which means f '(a) = 2a.
What about the derivative of f(x) = xn. Similar calculations, using the binomial expansion for (x+y)n (Pascal's Triangle), yield

Answer:
15% discount was offered with the family ticket option.
Step-by-step explanation:
So adult is 55 so 55 x 2=110
45 x 2=90
110+90=200 so 170 ( Family ticket )
170 divide by 200=0.85 x 100=85% 100% - 85%=15%
Answer:
12/35
Step-by-step explanation:
Multiply both numerators and denominators.
2/5 * 6/7
=12/35
Answer:
History test
Step-by-step explanation:
28 divided by 40 is 0.7 which equals 70 percent.
39 divided by 60 is 65 percent .
Answer:
See below.
Step-by-step explanation:
a.
The first figure has 1 square. The second figure has a column of 2 squares added to the left. The third figure has a column of 3 squares added to the left. Each new figure has a column of squares added to the left containing the same number of squares as the number of the figure.
b.
Figure 10 has 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 squares.
c.
The formula for adding n positive integers starting at 1 is:
1 + 2 + 3 + ... + n = n(n + 1)/2
For figure 55, n = 55.
n(n + 1)/2 = 55(56)/2 = 1540
d.
Let's use the formula set equal to 190 and solve for n. If n is an integer, then we can.
n(n + 1)/2 = 190
n(n + 1) = 380
We know that 380 = 19 * 20, so n = 19.
Answer: yes
e.
Use the formula above,
S = n(n + 1)/2, where S is the sum.
f.
n(n + 1) = 1478
38 * 39 = 1482
37 * 38 = 1406
