Answer:
4 lines of reflection can the combined figure reflect onto itself.
Step-by-step explanation:
Given Square ABCD and square EFGH share a common center on a coordinate plane and is parallel to diagonal.
We have to find that how many lines of reflection can the combined figure reflect onto itself.
Line of reflection is the line through which the figure will reflect to give a mirror image i.e the midway line between the pre-image and its image reflection. In the figure drawn in attachment according to given question we see that the line passes through the center of one square which is the diagonals of other square reflect the given figure onto itself.
Hence, there are 4 lines of reflection i.e 4 lines of reflection can the combined figure reflect onto itself.
Answer:
2.67 inches.
Step-by-step explanation:
Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).
The formula for a rectangular box = L × B × W
= (23 -2y)(13-2y) (y)
= (299 - 46y - 26y + 4y²)y
= 299y - 72y² + 4y³
Now for the maximum volume:
dV/dy = 0
This implies that:
299y - 72y² + 4y³ = 299 - 144y + 12y² = 0
By using the quadratic formula; we have :
where;
a = 12; b = -144 and c = 299
Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33
Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.
Answer:
153
Step-by-step explanation:
i = square root of -1
i = √-1
(3+12√-1) (3-12√-1)
√a times √b = √ab
a√b times c√d = (a times c) √ (b times d)
9 - (36√-1) + (36√-1) - (144(√-1)^2) =
9 - 0 - (144 * -1) =
9 - 0 - (-144) =
9 - (-144) =
9 + 144 =
153
*** funny thing is if you put
(3+12i) (3-12i)
in a calculator
it works!
it gives you the answer 153
another way:
Expand the expression using
(a-b) (a+b) =
a²-b² :
3²-(12i)²
Simplify using exponent rule with same exponent
(a*b)^n =
a^n*b^n:
3²-12²* i²
Calculate the power:
9-144* i²
Rewrite by definition
i²=-1:
9–144×(−1)
Calculate the product or quotient: 9+144
Calculate the sum or difference: 153
Answer: 153
gathmath
I don't see the graph sorry i can't help you