Answer:
Step-by-step explanation:
Part A
xf = xo + vo* t + 1/2 a*t^2 Subtract xo
xf - xo = 0*t + 1/2 a*t^2 multiply by 2
2(xf - xo) = at^2 divide by t^2
2(xf - xo ) / t^2 = a
Part B
Givens
xo =0
vo = 0
a = 10 m/s^2
xf = 120 m
Solution
xf = xo + vo* t + 1/2 a*t^2 Substitute the givens
120 = 0 + 0 + 1/2 * 10 * t^2 Multiply by 2
120*2 = 10* t^2
240 = 10*t^2 Divide by 10
240/10 = t^2
24 = t^2 take the square root of both sides.
√24 = √t^2
t = √24
t = √(2 * 2 * 2 * 3)
t = 2√6
Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
Answer:
1 pink marble
Step-by-step explanation:
If Jamie selected 10 times the pink marble in a total of 420 tries, we can assume that the proportion of pink marble in the total number of marbles is:
10 / 420 = 1/42
So to predict a good number of pink marbles in the total 40 marbles, we just need to multiply the 40 marbles by the proportion found above:
pink marble = 40 * (1/42) = 0.9524
As this number needs to be a whole number, a good assumption is that there is 1 pink marble in the 40 marbles.
Answer:
(-7, 3) i think, not 100% sure
Step-by-step explanation:
The Answer Would Be 64 because if you divide 8/4.5 its equal to 64/36.