First of all, when I do all the math on this, I get the coordinates for the max point to be (1/3, 14/27). But anyway, we need to find the derivative to see where those values fall in a table of intervals where the function is increasing or decreasing. The first derivative of the function is
. Set the derivative equal to 0 and factor to find the critical numbers.
, so x = -3 and x = 1/3. We set up a table of intervals using those critical numbers, test a value within each interval, and the resulting sign, positive or negative, tells us where the function is increasing or decreasing. From there we will look at our points to determine which fall into the "decreasing" category. Our intervals will be -∞<x<-3, -3<x<1/3, 1/3<x<∞. In the first interval test -4. f'(-4)=-13; therefore, the function is decreasing on this interval. In the second interval test 0. f'(0)=3; therefore, the function is increasing on this interval. In the third interval test 1. f'(1)=-8; therefore, the function is decreasing on this interval. In order to determine where our points in question fall, look to the x value. The ones that fall into the "decreasing" category are (2, -18), (1, -2), and (-4, -12). The point (-3, -18) is already a min value.
We get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
An expression is a way in which numbers are written.
It can be variables, constants or a combination of both.
We are given an expression:
64 √2
We know that:
64 = 2 × 2 × 2 × 2 × 2 × 2
64 = 2⁶
Also, we can write √2 as
√2 = 2⁰°⁵
We get that:
2⁶ × 2⁰°⁵
simplifying the expression, we get that:
= 2⁶⁺⁰°⁵
= 2⁶°⁵
Therefore, we get the expression 64√2 in the form 2ⁿ as 2⁶°⁵.
Learn more about expression here:
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Answer:
Step-by-step explanation:
since you are given two points use the point- slope formula and the slope formula
y-y1 = m( x -x1) and m = y2 -y1 / x2 - x1
find the slope m, 1st
p1 = (x1,y1) given (-8,-2)
p2 = (x2,y2) given (-4,-6)
m = -6-(-2) / -4-(-8)
m = -6+2 / -4+8
m = -4 / 4
m = -1 :)
now use the slope you just found and the point-slope with either given point.. pick one.. which ever seems easier... they seem about the same to me
y - (-8) = -1(x-(-2))
y+8 = -1(x+2)
y+8 = -x-2
y = -x-2-8
y= -x-10
and your done :)
Area of Parallelogram ABCD is equivalent to the area of rectangle AXBY.
Area of rectangle AXBY= Length AX * Length AB= 3 ft * 4√2 ft = 12√2 sq.ft.
Thus Area of Parallelogram is 12√2 sq.ft.
Answer: 952 ft squared
Step-by-step explanation:
Surface area, is just the area of all the faces added together.
So, the sides we need to find are measuring:
Triangle side: 10 x 8
Triangle Face; 10 x 8
Square Face: 10 x 10
Square Face: 10 x 10
Rectangular Face: 14 x 10
Rectangular Face: 14 x 10
Bottom Rectangular face: 14 x 10
Side of the Triangular prism: 9 x 14
Side of the Triangular prism: 9 x 14
Because the triangle face has two of them, we only have to do one as opposed to dividing the same face twice.
So, we have a side of 80.
From here, it is just multiplication.
80 + 100 + 100 + 140 + 140 + 140 + 126 + 126 = 952 ft
