Answer:
Step-by-step explanation:
5+n+4+7+n+8=360
24+2n=360
2n=360-24
2n=336
n=168
Given:
$600 principal
8% rate = 8/100 = 0.08
3 years time
Solving for A:
A = P⋅e^rt
where:
A is the amount
P is the principal
e is the mathematical constant
r is the rate of interest
t is the time in years
A = P⋅e^rt
= 600⋅e^(0.08⋅3)
= 600(2.718281828459045)^(0.24)
A = $762.70
$600 compounded continuously at a rate of 8% for 3 years will yield a final amount of $762.70
X² <span>+ 11x = -28
to find the solution of this polynomial, it'll be easiest to try and factor it. the first thing you need to do is move everything to one side:
</span>x² + 11x = -28 ... add 28
x² + 11x + 28 = 0 ... factor
(x + 7)(x + 4) = 0 ... now set both of your factors equal to zero and solve for x
x + 7 = 0
x = -7
x + 4 = 0
x = -4
Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
Answer:
162.06
Step-by-step explanation:
sorry i'm not the best an explaining but i'm confident in my answer.
the first thing to do is get rid of the ² in x²+y²=24, we do this by √24 which ≅4.90 (i rounded to the hundreth place)
then we have this
x-y=6
x+y=4.90
I am using the elmination method. To do that you need to get two letters to have the same coefficient (in 4x 4 is the coefficient) with oposite signs (one possitive one negitive)
In our equation here we see that the same coefficient is 0, and there is oposite signs for y. Therefore we can add the two equations and get
2x=10.9 (the y cancels out)
now we have a simple equation and all that is left is to solve it
10.9/2=5.45
x=5.45
Now we need to find y we do that by pluging the x value into one of the equations I choose the first one becasue its easiest.
(5.45)-y=6
y= - .55
now that we have both x and y plug them into the final equation (5.45)³-(-.55)³= 161.89-(-.17) =162.06
Therefore x³-y³≅162.06!
(if you have any questions or would like to debate the answer please let me know!)
