Answer: width = 5 units
Step-by-step explanation:
Let L represent the length of the rectangle.
The width of a rectangle is the length minus 2 units. It means that the width of the rectangle is (L - 2) units.
The formula for determining the area of a rectangle is expressed as
Area = length × width
The area of the rectangle is 35 units. It means that
L(L - 2) = 35
L² - 2L = 35
L² - 2L - 35 = 0
L² + 5L - 7L - 35 = 0
L(L + 5) - 7(L + 5) = 0
L - 7 = 0 or L + 5 = 0
L = 7 or L = - 5
Since the length cannot be negative, then
L = 7 units
Width = 7 - 2 = 5 units
We use the trinomial theorem to answer this question. Suppose we have a trinomial (a + b + c)ⁿ, we can determine any term to be:
[n!/(n-m)!(m-k)!k!] a^(n-m) b^(m-k) c^k
In this problem, the variables are: x=a, y=b and z=c. We already know the exponents of the variables. So, we equate this with the form of the trinomial theorem.
n - m = 2
m - k = 5
k = 10
Since we know k, we can determine m. Once we know m, we can determine n. Then, we can finally solve for the coefficient.
m - 10 = 5
m = 15
n - 15 = 2
n = 17
Therefore, the coefficient is equal to:
Coefficient = n!/(n-m)!(m-k)!k! = 17!/(17-5)!(15-10)!10! = 408,408
Answer: 1232
Step-by-step explanation: ( 8x10 -3) x(2x10 -4)
( 8x10 -3) = 77
(2x10 -4) = 16
77 x 16 = 1232
Answer = 1232
Answer:
13 children and 9 adults if the total cost is $152.5
Step-by-step explanation:
Let x children and y adults
x + y = 22 (1)
5.5x + 9y = 125.5 (2)
y = 22 - x
5.5x + 9(22 - x) = 125.5
5.5x + 198 - 9x = 125.5
-3.5x = 125.5 - 198
-3.5x = -72.5
x = 20.7
y = 22 - x = 1.3
Which is not possible
If the total cost is $152.5
x + y = 22 (1)
5.5x + 9y = 152.5 (2)
y = 22 - x
5.5x + 9(22 - x) = 152.5
5.5x + 198 - 9x = 152.5
-3.5x = 152.5 - 198
-3.5x = -45.5
x = 13
y = 22 - 13 = 9
Answer:
For First Solution: 
is the solution of equation y''-y=0.
For 2nd Solution:
is the solution of equation y''-y=0.
Step-by-step explanation:
For First Solution:
In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.
First order derivative:
2nd order Derivative:
Put Them in equation y''-y=0
e^t-e^t=0
0=0
Hence is the solution of equation y''-y=0.
For 2nd Solution:
In order to prove whether it is a solution or not we have to put it into the equation and check. For this we have to take derivatives.
First order derivative:
2nd order Derivative:
Put Them in equation y''-y=0
cosht-cosht=0
0=0
Hence is the solution of equation y''-y=0.
