Answer: 21 ft³
<u>Step-by-step explanation:</u>
Let x represent the height of the box.
Then the 5 ft width of cardboard is (5 - 2x) when creating the box
and the 9 ft length of cardboard is (9 - 2x) when creating the box.
Volume = length x width x height
= (9 - 2x)(5 - 2x)(x)
= 45x - 28x² + 4x³
Using Calculus to solve for x, set the derivative equal to zero and use the quadratic formula to solve for x:
V' = 45 - 56x + 12x²
0 = 12x² - 56x + 45
x = 3.6, x = 1.0
Use those values to find the width, length, and volume:
height(x) × width (5 - 2x) × length (9 - 2x) = Volume
3.63 × -2.26*
1 × 3 × 7 = 21
*width cannot be negative so the height cannot be 3.63
Answer:
A. f(x) = (x − 3)^2 + 3
Step-by-step explanation:
For vertex (h, k), the equation is ...
y = (x -h)^2 +k
For the given vertex of (3, 3), the equation is ...
y = (x -3)^2 +3 . . . . . matches choice A
Answer: 'Both f(x) and g(x) have the same output value at x = 5' is true statement.
Step-by-step explanation:
Since, for a function f(x), x is the input value and f(x) is the output value,
Here, f(x) and g(x) are two functions,
Such that f(x) = g(x) at x = 5,
⇒ The output value of both function is equal for the input value of x.
⇒ Fourth option is the true statement.
Note : For other options, the adequate information is not given.
That's why we can not say them true.
Expanded form of 3( 6 + 7) is
<h3><u>Solution:</u></h3>
Need to use distributive property to write the expanded form of 3(6 + 7)
Let’s understand what is distributive property.
The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.
According to distributive property, for numbers a , b and c
----- eqn 1
3(6 + 7) can be rewritten as 3 ( 6 + 4 + 3 ) = 3 ( 10 + 3 )
Now in our case a = 3 , b = 10 and c = 3
On substituting the values of a , b and c in equation 1 we get
So expanded form of 3( 6 + 7) is
Answer:
A) X=pi/2 or X=-pi/2
B) X=pi/6 or X=-pi/6
C) X=pi/4 , 3pi/4, 5pi/4 and 7pi/4
D) X= 1-cos^2(x/2)
E) X= pi/3 +2pi N, 5pi/3+2pi N
Step-by-step explanation:
Don't even bother asking. :)