Answer:
160m/s
Step-by-step explanation:
The object can hit the ground when t = a; meaning that s(a) = s(t) = 0
So, 0 = -16a² + 400
16a² = 400
a² = 25
a = √25
a = 5 (positive 5 only because that's the only physical solution)
The instantaneous velocity is
v(a) = lim(t->a) [s(t) - s(a)]/[t-a)
Where s(t) = -16t² + 400
and s(a) = -16a² + 400
v(a) = Lim(t->a) [-16t² + 400 + 16a² - 400]/(t-a)
v(a) = Lim(t->a) (-16t² + 16a²)/(t-a)
v(a) = lim (t->a) -16(t² - a²)(t-a)
v(a) = -16lim t->a (t²-a²)(t-a)
v(a) = -16lim t->a (t-a)(t+a)/(t-a)
v(a) = -16lim t->a (t+a)
But a = t
So, we have
v(a) = -16lim t->a 2a
v(a) = -32lim t->a (a)
v(a) = -32 * 5
v(a) = -160
Velocity = 160m/s
The answer is a+b+c = d it’s is equivalent to a and d
Answer:
4. 54- 8.5x>20
Step-by-step explanation:
Catherine only has $54, so she cannot spend more than that.
The canvas will cost at least $20, but we don't know how much exactly.
The tubes cost $8.50 each.
So, she starts with a total budget of $54, out of which she will buy paints (8.5x) and she wants to have at least $20 left for canvas.
So, we transpose those facts into the inequity:
54 - 8.5x > 20
Answer: a= 0.0231
Step-by-step explanation:
n=8
p=0.75
q=1 - 0.75 = 0.25
(p=x)
p(5) = 8C5 (0.25)^5 (0.75)^8-5
p(5)= 0.0231
Or 2.31%
Answer:
Mrs. Wright's paycheck is $630
Step-by-step explanation:
Let x = Mrs. Wright's paycheck.
Mrs. Wright spent 2/9 of her paycheck on food. This means that the amount of money spent on food is 2/9 × x = 2x/9
She spent 1/3 on rent. This means that the amount spent on rent is
1/3 ×x x = x/3
Amount she spent on food and rent is x/3 + 2x/9 =3x + 2x /9
= 5x/9
The remainder is her pay check - the amount that she spent on food and rent. It becomes
x - 5x/9 = (9x- 5x)/9 = 4x/9
She spent 1/4 of the remainder on transportation. It means that she spent 1/4 × 4x/9 = x /9 on transportation.
Amount left = 4x /9 - x/9= 3x/9
She had $210 left. Therefore,
210 = 3x/9
3x = 9×210 = 1890
x = 1890/3
x = $630
