Answer:
Step-by-step explanation:
height = 14tan(24°)
area = 0.5(base)(height)
Find the angle that triples the height.
tanθ = 3×14tan(24°)
θ = arctan(3×14tan(24°)) ≅ 53.2°
Let the numbers be x and y, then
2x + y = 47 . . . (1)
x + 3y = 56 . . . (2)
(2) x 2 => 2x + 6y = 112 . . . (3)
(1) - (3) => -5y = -65 => y = -65/-5 = 13
From (2), x + 3(13) = 56 => x = 56 - 39 = 17
The two numbers are 13 and 17.
X = first integer, y = second integer (right after x)
since y is right after x, we can say
y = x+1
If the product of the two integers (x and y) is 42, then
x*y = 42
x*( y ) = 42
x*( x+1 ) = 42 ... y is replaced with x+1
x*x + x*1 = 42
x^2 + x = 42
x^2 + x - 42 = 0
(x + 7)(x - 6) = 0 ... factor
x + 7 = 0 or x - 6 = 0
x = -7 or x = 6
The result must be positive as the problem states it, so we toss out x = -7
The only answer is x = 6
If x = 6, then
y = x+1
y = 6+1
y = 7
The two consecutive numbers are 6 and 7
The final answer is 6
Sure enough, 6*7 = 42 checks out
Answer:
It will take 55 years for the account value to reach 38200 dollars
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
.
In this problem, we ahve that:
So
First we find how much we have to earn in interest.
.
How much time to earn this interest?
Rounding up
It will take 55 years for the account value to reach 38200 dollars
