Answer:
144 units²
Step-by-step explanation:
The net of the right triangular prism consists of 3 rectangles and 2 equal triangles
Let's solve for the area of each:
✔️Area of rectangle 1 = L*W
L = 11
W = 3
Area of rectangle 1 = 11*3 = 33 units²
✔️Area of rectangle 2 = L*W
L = 11
W = 4
Area of rectangle 2 = 11*4 = 44 units²
✔️Area of rectangle 3 = L*W
L = 11
W = 5
Area of rectangle 3 = 11*5 = 55 units²
✔️Area of the two triangles = 2(½*base*height)
base = 4
height = 3
Area of the two traingles = 2(½*4*3)
= 12 units²
✔️Surface area of the right triangle = area of rectangle 1 + area of rectangle 2 + area of rectangle 3 + area of the two triangles
= 33 + 44 + 55 + 12
= 144 units²
If you already know that you have . . .
1$ after week 1
2$ after week 2
4$ after week 3
8$ after week 4
. . . You can then tell that every week the money you save doubles (times 2)
So to continue . . . .
16$ after week 5
32$ after week 6
64$ after week 7
128$ after week 8
256$ after week 9
512$ after week 10
You will then know that after ten weeks u will have 512$ which is answer choice D.
Hope this helps! :)
Implicit differentiation
chain rule is important here
I'll show the steps partially
now evaluate for (-2,2)
x=-2 and y=2
that's it, simplest form
Answer:
-4
Step-by-step explanation:
This looks like point-slope form, which I find personally hideous. Let's change it to slope-intercept form to ease my conscience. (remember that slope-intercept form is y=mx+b, where m=slope and b=y-intercept!)
y - 5 = -4(x-8)
y - 5 = -4x + 32
y = -4x + 37
It's in slope-intercept form now! And -4 looks to be our m.
<u>So the slope is -4.</u>
Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft.
Area of rectangle will be:
A=length*width
A=x(50-x)
A=50x-x^2
at maximum area, dA/dx=0
thus
dA/dx=50-2x=0
solving for x we get
2x=50
x=25
thus for maximum area length=25 ft
the size of the width will be
50-x=50-25=25 ft
thus the maximum area will be:
25*25=625 sq. feet
