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3 years ago

Which rule represents R0, 180°? (x, y) → (–y, x) (x, y) → (–x, –y) (x, y) → (y, –x) (x, y) → (y, x)

Mathematics

2 answers:

muminat3 years ago

7 0

Answer:

(x, y) → (–x, –y)

Step-by-step explanation:

The rule for 180° rotation about the origin is

$(x,y)\to (-x,-y)$

The coordinates of the image are obtained by negating both the x and y coordinates of the preimage.

Whether the rotation is clockwise or counterclockwise, the rule remains the same.

The correct option is (x, y) → (–x, –y)

VLD [36.1K]3 years ago

5 0

Answer:

(x, y) → (–x, –y) option B

Step-by-step explanation:

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The parent volunteers made 120 snow cones in 5 hours. The student council made 100 snow cones in 4 hours. Who made more snow con

marysya [2.9K]

The parent volunteers:
120 snow cones ... 5 hours
x snow cones = ? ... 1 hour

120 * 1 = 5 * x
120 = 5 * x /5
x = 120 / 5 = 24 snow cones

The student council:
100 snow cones ... 4 hours
y snow cones = ? ... 1 hour

100 * 1 = 4 * y
100 = 4 * y /4
y = 100 / 4 = 25 snow cones

Result: The student council made more snow cones per hour (25 > 24).

8 0

3 years ago

• karger's min cut algorithm in the class has probability at least 2/n2 of returning a min-cut. how many times do you have to re

MrRissso [65]

The Karger's algorithm relates to graph theory where G=(V,E) is an undirected graph with |E| edges and |V| vertices. The objective is to find the minimum number of cuts in edges in order to separate G into two disjoint graphs. The algorithm is randomized and will, in some cases, give the minimum number of cuts. The more number of trials, the higher probability that the minimum number of cuts will be obtained.

The Karger's algorithm will succeed in finding the minimum cut if every edge contraction does not involve any of the edge set C of the minimum cut.

The probability of success, i.e. obtaining the minimum cut, can be shown to be ≥ 2/(n(n-1))=1/C(n,2), which roughly equals 2/n^2 given in the question.Given: EACH randomized trial using the Karger's algorithm has a success rate of P(success,1) ≥ 2/n^2.

This means that the probability of failure is P(F,1) ≤ (1-2/n^2) for each single trial.

We need to estimate the number of trials, t, such that the probability that all t trials fail is less than 1/n.

Using the multiplication rule in probability theory, this can be expressed as
P(F,t)= (1-2/n^2)^t < 1/n

We will use a tool derived from calculus that
Lim (1-1/x)^x as x->infinity = 1/e, and
(1-1/x)^x < 1/e for x finite.

Setting t=(1/2)n^2 trials, we have
P(F,n^2) = (1-2/n^2)^((1/2)n^2) < 1/e

Finally, if we set t=(1/2)n^2*log(n), [log(n) is log_e(n)]

P(F,(1/2)n^2*log(n))
= (P(F,(1/2)n^2))^log(n)
< (1/e)^log(n)
= 1/(e^log(n))
= 1/n

Therefore, the minimum number of trials, t, such that P(F,t)< 1/n is t=(1/2)(n^2)*log(n) [note: log(n) is natural log]

4 0

4 years ago

X/3-15=-2 solve for x

Otrada [13]

Answer:

x = 45

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x/3-(15)=0

Step 1 : Simplify

$\frac{x}{3}$

Equation at the end of step 1 :

$\frac{x}{3}$ - 15 = 0

Step 2 :

Rewriting the whole as an Equivalent Fraction :

Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

$15=\frac{15}{1} =\frac{15*3}{3}$

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

$\frac{x-(15*3)}{3} =\frac{x-45}{3}$

Equation at the end of step 2 :

$\frac{x-45}{3} =0$

Step 3 :

When a fraction equals zero :

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

$\frac{x-45}{3}*3=0*3$

Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

x-45 = 0

Solving a Single Variable Equation :

Solve : x-45 = 0

Add 45 to both sides of the equation :

x = 45

One solution was found :

x = 45

3 0

3 years ago

A tank containing 1140.8 gallons can be emptied in 92 minutes. How many gallons is that per minute?

Ivan

Answer:

Divide the volume of the tank (10,000 gallons) by the filling rate of 250 gallons/minute and you will Hours = hr x min x 3785 ml x 55 gal = 208175 = 115.6 hrs.

Step-by-step explanation:

hope it helps

7 0

3 years ago

Which inequality defines the problem below ?

Likurg_2 [28]

Answer:

Step-by-step explanation:

so total travel by x bikers = 50 multiplied by x = 50x

According to the question

50x = 560

dividing 560 miles by 50 miles per biker give ya 11.2 or approximately 12 bikers.

7 0

3 years ago