Hey there!
The distance across a circle is called the diameter. Half of the diameter is the radius. To find the area of a circle, you take the radius, square it, and then multiply it by pi. Let's do it below.
8²=64
64*3.14=200.96
Therefore, the area of the rug is 200.96 ft².
I hope this helps! Have a great day.
Answer:
6.6
Step-by-step explanation:
Triangles ADE and ABC are similar.
Therefore,
AD/AB=AE/AC
3/8=4/AC
3AC=32
AC=10.6(3 s.f)
CE=10.6-4=6.6
Answer: 
Step-by-step explanation:
The acceleration 
of the satellite can be calculated by the following equation:
Where:
is the final speed of the satellite
is the initial speed of the satellite (it was "stationary" before the release)
is the time
Isolating :
Finally:
The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
brainly.com/question/145452
#SPJ1
Answer:
Mean = 5 feet 2 inches.
Step-by-step explanation:
1 feet = 12 inches
Height of Dad = 6 feet 2 inches = {(6 × 12)+2} = 74 inches
Mom is 3 inches shorter than dad = 74 - 3 = 71 inches (5 ft 11 in)
Since mom is 2 inches taller than Ivan,
Height of Ivan = 71 - 2 = 69 inches (5 ft 9 in)
Marica is 5 inches shorter than Ivan,
Height of Marica = 69 - 5 = 64 inches (5 ft 4 in)
Marica is twice as tall as Sally-Jo.
Height of Sally-Jo = 64 ÷ 2 = 32 inches (2 ft 8 in)
Hence the mean height of the Schuller family
= 
= 62 inches
converting 62 inches to feet = 
= 5 feet 2 inches
Mean height of the Schuller family is 5 feet 2 inches.
