Area of square = 24cm²
⇒ Length = √24
Find the diagonal of half the square:
a² + b² = c²
c² = (0.5√24)² + (√24)²
c² = 6 + 24
c² = 30
c = √30
The diagonal of half of the square is the radius of the circle.
⇒ radius = √30
Area of the semicircle = 1/2πr² = 1/2π(√30)² =15π
Answer: 15π²
These are all the possible answers i know from experience.
2x + 2y = 7
x^2 - 4y^2 = 8
2x = -2y + 7
x = -y + 7/2
(-y + 7/2)^2 - 4y^2 = 8
y^2 - 7y + 49/4 - 4y^2 = 8
0 = 3y^2 + 7y + 8 - 49/4
0 = 12y^2 + 28y + 32 - 49
0 = 12y^2 + 28y - 17
y = (-b ± √(b^2 - 4ac))/(2a)
y = (-28 ± √(28^2 - 4(12)(-17)))/(2(12))
Dividing by 2 is like dividing by √(4):
y = (-14 ± √(7*28 + (12)(17)))/(2*6)
y = (-7 ± √(7*7 + (3)(17)))/6
y = (-7 ± 10)/6 = 1/2 or -17/6
x = -y + 7/2 = 3 or 19/3
<span>Solutions are (3,1/2) and (19/3,-17/6)</span>
Answer:
144 seconds
Step-by-step explanation:
To do solve this question, we must find the LCM (least common multiple) of 12, 16, and 18.
Let's start by prime factorizing (finding the prime factors) all the numbers.
Now, we must find the greatest quantity of each [prime] number and multiply them together to obtain the least common multiple.
Upon further evaluation of the [prime] factors, we can see that we need four 2s and two 3s. Therefore...
They will be fired together again after 144 seconds.
Factoring this expression using the identity of a²-b² = (a+b)(a-b)
Given :-
25 - x²
<em>This can be broken down into:- </em>
... ( 5 )² - ( x )²
<em>In this case, a is 5 and b is x </em>
... ( 5 + x ) ( 5 - x ) Is the answer.
Hope it helps!!
The two numbers are 3 and 18, if the sum of two number is 21 and the second number is six times the first number.
Step-by-step explanation:
The given is,
The sum of two numbers is 21
The second number is six times the first number
Step:1
Let, m - First number
n - Second number
Step:2
From given,
n - 6m ( The second number is six times the first number )
Equation becomes,
Sum = m + n
Where,
21 = m + ( 6m )
21 = 7m
m = 3
Substitute m value n becomes,
n = 6m
= (6 × 3)
n = 18
Result:
The two numbers are 3 and 18, if the sum of two number is 21 and the second number is six times the first number.
