using pythagorean theorem
a^2 + b^2 =c^2
a^2 +8^2 =14^2
a^2 +64 = 196
subtract 64 from each side
a^2 = 132
take the square root of each side
a^2 = sqrt (132)
a=11.48912529
a =11.5
Answer:
They are congruent
Step-by-step explanation:
Because they size are same
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.
The sphere with the volume 1436.03 m³ has 7m long radius.
To find out the approximate length of its radius by using the formula to calculate volume of sphere is:
V= 4πr³/3
The value of π is 22/7 or 3.14.
So, V = 4 × 3.14 × r³ / 3
Volume of the sphere is given which is 1436.03 m³.
Thus, r³ = 1436.03×3 / 4×3.14
r = ³√ 4308.09/12.56 = ³√343 = 7 m.
Hence, the radius of the given sphere is 7 m.
The cube root of a number is the factor that we multiply by itself three times to get that number.
For example, the cube root of 27 is 3.
To learn more about the sphere click here brainly.com/question/19868745
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Answer:
s = 6
Step-by-step explanation:
