16) y varies directly as x is the same thing as y=mx where m is the constant
for the first equation where the length is 7 and weight is 49 there fore
7=m49 in which m=1/7 so to find the length of the 2nd equation
y=m63
y=1/7 x63
y=9 inches
17)The raiser with the $6.25 would raise more money because if 25 ticket is sold and money received is $125 then each ticket is sold for $5 which means if the ticket is sold for $6.25 then 25 would bring in $156.25
Answer:
B is our answer 12.56
When finding area for circles we do
radius x radius x pi
Since we don't have the radius in the problem we have to figure it out but it wont be so hard knowing that the radius is half of the diameter so 4 ÷ 2 = 2 so 2 is our radius now we need tp square it in easier words multiply by itself so
2 x 2 = 4 then we just do 4 x pi!
So 4 x 3.14 = 12.56 So our answer is 12.56
Hope this helps!
Difference of two squares is of the form (a + b)(a - b) or vice-versa. Here, a = -5x and b = 3.
(-5x - 3)(-5x + 3)
Answer: 3
Answer:
Sean's rocket lands 3 seconds after Kiara's rocket.
Step-by-step explanation:
Kiara: f(t)= -16t² + 80t
Sean: h(t) = -16t² + 120t + 64
Assume that both rockets launch at the same time. We need to be suspicious of Sean's rocket launch. His equation for height has "+64" at the end, whereas Kiara's has no such term. The +64 is the starting height iof Sean's rocket. So Kiara has a 64 foot disadvantage from the start. But if it is a race to the ground, then the 64 feet may be a disadvantage. [Turn the rocket upside down, in that case. :) ]
We want the time, t, at which f(t) and h(t) are both equal to 0 (ground). So we can set both equation to 0 and calculate t:
Kiara: f(t)= -16t² + 80t
0 = -16t² + 80t
Use the quadratic equation or solve by factoring. I'll factor:
0 = -16t(t - 5)
T can either be 0 or 5
We'll choose 5. Kiara's rocket lands in 5 seconds.
Sean: h(t) = -16t² + 120t + 64
0= -16t² + 120t + 64
We can also factor this equation (or solve with the quadratic equation):
0 = -8(t-8)(2t+1)
T can be 8 or -(1/2) seconds. We'll use 8 seconds. Sean's rocket lands in 8 seconds.
Sean's rocket lands 3 seconds after Kiara's rocket.
Kinetic engery = -1/2mv^2
Work = Fd
Combine:
-1/2mv^2 - Fd = 0
-1/2mv^2 = (0.30*15000*9.81*cos(6))d = 0
Multiply both sides by 2:
v^2 = 2d(0.30*9.81*cos(6))
Solve for d:
d=v^2 / 2(0.30*9.81*cos96))
v = speed:
d = 35^2 / 2*0.30 * 9.81 * cos(6)
d = 1225 / 5.85376
d = 209.27 meters. Round answer as needed.
