When a shape is rotated, it must be rotated around a point.
<em>See attachment for the image of each rotation.</em>
To do this, the top coordinates of the X shape will be transformed using the appropriate rotation rule; the same rule will then be applied to the other parts of the X shape.
The top coordinates of the X shape are:
For 90 degrees counterclockwise rotation, the rule is:
So, we have:
For 180 degrees rotation, the rule is:
So, we have:
For 270 degrees counter rotation, the rule is:
So, we have:
See attachment for the image of each rotation
Read more about rotations at:
brainly.com/question/1571997
You bought a magazine for $5 and four erasers. you spent a total of $25.
Magazine cost: 5$ each
Eraser cost: X$ each
Total cost is the number of items (1 magazine) times the cost of each item (5$). We don't know the cost of each eraser, so we represent that using a variable, X.
1(5) + 4(X) = 25
5 + 4X = 25
subtract 5 from both sides
4X = 25 - 5
4X = 20
divide both sides by 4
X = 20/4
X = 5
Each eraser cost 5$
Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²
This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)
Latus rectum: y-value = 15/2
Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then
Latus rectum = 5
Answer:
the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.
Step-by-step explanation:
if there is no mistake in the problem description, I read the following function :
C(x) = y = 0.3x² - 1.2x + 2
I don't know if you learned this already, but to find the extreme values of a function you need to build the first derivative of the function y' and find its solutions for y'=0.
the first derivative of C(x) is
0.6x - 1.2 = y'
0.6x - 1.2 = 0
0.6x = 1.2
x = 2
C(2) = 0.3×2² - 1.2×2 + 2 = 0.3×4 - 2.4 + 2 = 1.2-2.4+2 = 0.8
so, the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.
