Answer:
8.06 feet
Step-by-step explanation:
use the Pythagorean theorem
9^2 = 4^2 + x^2
81 =16 +x^2
x^2 = 65
x = 8.06 feet
Answer:
HA = 16.2 m
DE = 17 m
Step-by-step explanation:
From the base of the cuboid, HDA will form a right angle triangle, where;
DA = 15 m
HA = 6 m
HA is the hypotenuse
Using pythagoras theorem;
HA = √(15² + 6²)
HA = √(225 + 36)
HA = √261
HA = 16.155 m
Approximating to 1 decimal place gives;
HA = 16.2 m
Similarly, HDE will also form a right angle triangle.
Thus;
DE = √((HD)² + (HE)²)
HD = 16.2 m
HE = 5 m
Thus;
DE = √(16.2² + 5²)
DE = 16.95 m
Approximating to 1 decimal place gives
DE = 17 m
Answer:
3
Step-by-step explanation:
Factorial means multiply that number and all numbers below it
3! = 3*2*1 = 6
0! =1
2! = 2*1 = 2
1! =1
6*1
------
2*1
6/2 =3
Answer:
S₁₅ = 645
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
= 
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Using the nth term formula 
= 5n + 3 , then
a₁ = 5(1) + 3 = 5 + 3 = 8
a₂ = 5(2) + 3 = 10 + 3 = 13 , then
d = a₂ - a₁ = 13 - 8 = 5
Thus
S₁₅ = 
[ (2 × 8) + (14 × 5) ]
= 7.5( 16 + 70)
= 7.5 × 86
= 645
A question such as this one is a little tricky since the people seated are not in a straight line.
For a circular table seating question, (n-1)! formula is used. Without restrictions 5! people can be seated.
You might be wondering why it is not 6!, this is because the first person will the the 6 person so you are accounting for the same person twice.
Hope I helped :)
