Answer:
the first one is 150
the second one is 2205
(and no one is stupid on here some people understand stuff and some don't, so yeah I don't think your stupid:-))
Answer:
See explanation
Step-by-step explanation:
Statement: P(n) = "a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps".
A. P(18) = a postage of 18 cents can be formed using two 7-cent stamps and one 4-cent stamp.
P(19) = a postage of 19 cents can be formed using one 7-cent stamp and three 4-cent stamps.
P(20) = a postage of 20 cents can be formed using five 4-cent stamps.
P(21) = a postage of 21 cents can be formed using three 7-cent stamps.
B. Inductive hypothesis is to assume that P(n) is true for all n < 18
C. In the inductive step we need to prove that P(n+1) is true.
D. Let k ≥ 21, then
- if k = 4l, we get the case of P(20);
- if k = 4l + 1, we get the case of P(21);
- if k = 4l + 2, we get the case of P(18);
- if k = 4l + 3, we get the case of P(19).
E. Since all natural numbers are of the form 4l, 4l + 1, 4l + 2, 4l + 3, we can state that P(n) is true for all n ≥ 18.
A graphing calculator shows the x-intercepts of the expression on the left to be -1, 4, 7.
The real solutions to the cubic equation are x ∈ {-1, 4, 7}.
h = -4.9t^2 + vt
In our problem,
v = 12
t = 2
Let's plug our numbers into the equation.
h = -4.9(2)^2 + (12)(2)
h = -19.6 + 24
h = 4.4 m