Answer:
The answer is ⇒ x = 0.73244
Step-by-step explanation:
∵ 90^x = 27 ⇒ insert log in both sides
∴ 
∵ 90 = 9 × 10 , 27 = 3³
∵ log(a)^<em>b</em> = <em>b</em><em> </em>log(a)
∴ log(9 × 10)^x = x log(9 × 10)
∴ 
∵ log(a × b) = log(a) + log(b)⇒log(9 × 10) = log(9) + log(10)
∴ ![x[log(9)+log(10)]=3log(3)](https://tex.z-dn.net/?f=x%5Blog%289%29%2Blog%2810%29%5D%3D3log%283%29)
∵ log(10) = 1 , 9 = 3²
∴ ![x[log(3)^{2}+1]=3log(3)](https://tex.z-dn.net/?f=x%5Blog%283%29%5E%7B2%7D%2B1%5D%3D3log%283%29)
∴
∴ x = (3log3)/[2log(3)+1]
∴ x = 0.73244
Answer:
a = l²
v = s³
Step-by-step explanation:
The area of a rectangle is the product of its length and width. When that rectangle is a square, the length and width are the same. Here, they are given as "l". Then the area of the square is ...
a = l·l = l²
__
The volume of a cuboid is the product of its height and the area of its base. A cube of edge length s has a square base of side length s and a height of s. Then its volume will be ...
v = s·(s²) = s³
The two equations you want are ...
• a = l²
• v = s³
Answer:
B) A = 52.3°, b = 1.7 m, c = 2.8 m
Step-by-step explanation:
We know that it is a right angle triangle because C = 90°
because of that we can do 180 - 90 + 37.7
which is a=52.3
Because it is a right angle triangle, we can use sin, cos,tan
I will use sin to find the side of c
2.2 is a
sin 52.3 = 2.2/x
x= 2.2/ sin 52.3
x=2.78
You could do cos or tan but the pythagorean theorem for me is much faster
so it looks like this, a^2+b^2 =c^2
in this case we have both a and c we want b
so we rearrange
c^2-a^2=b^2
2.78^2-2.2^2= b^2
=b
1.7=b
therefore it would be this option B) A = 52.3°, b = 1.7 m, c = 2.8 m
Answer:
The answer to your question is:
Hank = 44
John = 32
David = 38
Step-by-step explanation:
Data
John = J
David = D
Hank = H
J + D + H = 114
J = H/2 + 10
H = D + 6
Process
Write the three equations in terms of H
Substitution
H/2 + 10 + H - 6 + H = 114
Times 2 H + 20 + 2H - 12 + 2H = 228
5H + 8 = 228
5H = 228 - 8
5H = 220
H = 220 / 5
H = 44 Hank = 44 years
J = 44/2 + 10
J = 22 + 10
J = 32 John = 32 years
D = 44 - 6
D = 38 David = 38 years