A rectangle has length of 5.25 cm and area of 44.625 cm2. What does the length of the rectangle have to be?
1 answer:
<u>Answer:</u>
The length of the rectangle is 8.5 cm
<u>Solution:</u>
The area of the rectangle is given as 44.625
But we do not know the length of the rectangle, we are only given the width which is 5.25 cm.
We have been asked to find the length of the rectangle from the area and width.
So, let length and width be denoted as l and b respectively.
We know the area of the rectangle is
Now, we can substitute the values of width and area in eq1 and calculate the value of length
Therefore, by calculating we found out that the length of the rectangle is 8.5 cm.
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Answer:
Minimum : -37 at x=2.4 and
Maximum = 37 at x=-2.4.
Step-by-step explanation:
Given:
; [-3,3]
Explanation:
In order to find minimum/maximum of a function, we need to find the first derivative of the function and then set it equal to 0 to get critical points.
Therefore,
Setting derivative equal to 0, we get
On applying quadratic formula, we get
x=2.4, -2.4, -0.7, 0.7.
So, those are critical points of the given function.
Plugging the values x=2.4, -2.4, -0.7, 0.7, -3 and 3 in above function, we get
f(2.4)=(2.4)^5-10(2.4)^3+9(2.4)= -37.01376 : Minimum.
f(-2.4)=(-2.4)^5-10(-2.4)^3+9(-2.4)= 37.01376 : Maximum.
f(0.7)=(0.7)^5-10(0.7)^3+9(0.7) = 3.03807
f(-0.7)=(-0.7)^5-10(-0.7)^3+9(-0.7) = -3.03807
f(-3)=(-3)^5-10(-3)^3+9(-3) =0
f(3)=(3)^5-10(3)^3+9(3) =0
Therefore the approximate values of the minimum and maximum points of f(x) = on [-3,3] are:
Minimum : -37 at x=2.4 and
Maximum = 37 at x=-2.4.