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Write a function to represent the point (x, y) rotated 90° counterclockwise about the origin.
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Answers
Here is a Python function to rotate a point (x, y) counterclockwise by 90 degrees about the origin:
import math
import mathdef rotate_90_ccw(x, y):
import mathdef rotate_90_ccw(x, y): # compute the rotated coordinates using the rotation matrix
import mathdef rotate_90_ccw(x, y): # compute the rotated coordinates using the rotation matrix rx = -y
import mathdef rotate_90_ccw(x, y): # compute the rotated coordinates using the rotation matrix rx = -y ry = x
import mathdef rotate_90_ccw(x, y): # compute the rotated coordinates using the rotation matrix rx = -y ry = x # return the rotated coordinates
import mathdef rotate_90_ccw(x, y): # compute the rotated coordinates using the rotation matrix rx = -y ry = x # return the rotated coordinates return rx, ry
The function takes in two parameters, x and y, which represent the coordinates of the point to be rotated. It uses the rotation matrix for counterclockwise rotation by 90 degrees about the origin, which is:
|cos(90) -sin(90)| |0 -1|
|cos(90) -sin(90)| |0 -1||sin(90) cos(90)| = |1 0|
Simplifying this matrix yields:
|0 -1|
|0 -1||1 0|
So, to rotate the point (x, y) counterclockwise by 90 degrees about the origin, we simply need to multiply the point's coordinates by this matrix. This gives us the new coordinates (-y, x), which we return as a tuple.
The function uses the math module to access the cos and sin functions, which are needed to compute the rotation matrix.
Step-by-step explanation:
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The function which represents the point (x, y) rotated 90° counterclockwise about the origin is R(x, y) = (-y, x).
When a point is rotated to a certain angle, then the point changes its position to another point by rotation.
Consider a point (x, y).
When this point is rotated 90° counterclockwise about the origin, then the new point will have the x-coordinate of -y and the y-coordinate of x.
So, the point (x, y) becomes (-y, x).
In the form of function,
R(x, y) = (-y, x)
Hence, the function is R(x, y) = (-y, x).
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The complete question is given below:
Related Questions
Select the correct answer.
A bag contains 5 blue balls, 4 red balls, and 3 orange balls. If a ball is picked from the bag at random, what is the probability that it is a blue ball? Answers have been rounded to the tenths place.
A.
0.5
B.
0.4
C.
0.3
D.
0.2
Answers
Answer:
a
Step-by-step explanation:
Answer:
b. 0.4
Step-by-step explanation:
took text
Find the equation of a straight line which passes through the point (3, 2) and is perpendicular to the line 3x + 5y =10. Hence, determine the gradient and y-intercept of the equation.
Answers
Answer:
Step-by-step explanation:
eq of line perpendicular to 3x+5y=10 is
5x-3y=a
where a is constant.
it passes through (3,2)
5(3)-3(2)=a
a=15-6=9
reqd. eq. is 5x-3y=9
or
3y=5x-9
y=5/3 x-3
gradient=5/3
y-intercept=-3
or
5y=-3x-10
y=-3/5 x-2
slope=-3/5
slope of reqd. line=-1/(-3/5)=5/3
eq. of line through (3,2) is
y-2=5/3(x-3)
3y-6=5x-15
3y=5x-15+6
3y=5x-9
y=5/3 x-3
61.7 is what percent of 64? Round to the nearest thousandth.
Answers
Answer:
96.41
Step-by-step explanation:
it equals 96.40625%
Answer:
96.41
Step-by-step explanation:
big brain and mental math
For each value of w, determine whether it is a solution to -13=
W
9
27
Answers
\( - 13 = \frac{w}{9} - 6 \\ - 13 + 6 = \frac{w}{9} \\ - 7 = \frac{w}{9} \\ w = - 63\)
so only -63 is the solution, the rest three are NOT solution for this equation.
Please help!
What is the area in square units?
Answers
Find the volume of a cone with a radius of 4 ½ m. and a height of 10 m.
Answers
The volume of the cone is approximately 211.06 cubic meters.
Why is that?
Well, the formula for the volume of a cone is:
V = (1/3)πr^2h
where:
Substituting the given values, we get:V = (1/3)π(4.5m)^2(10m)
V = (1/3)π(20.25m^2)(10m)
V = (1/3)π(202.5m^3)
V = 67.5π
Using a calculator, we get:
V ≈ 211.06 cubic meters
Therefore, the volume of the cone is approximately 211.06 cubic meters.
Find the slope of the line passing through the points (3,9) and 12,-5)
Answers
Answer:
9/-24 or ~ -0.38
Step-by-step explanation:
x y
3 9
12 -15
from 9 to -15 it will be subtracting 24
From 3 to 12 it will be adding 9
y/x = 9/-24 or -0.375 ~ -0.38
Negating conditional statement (a V ~ b) => c
Please show your work and give a proper answer
Answers
"p implies q" is equivalent to "(p and q) or not p", which in turn is equivalent to "(p or not p) and (q or not p)". But "p or not p" is always true, so the implication reduces completely to "not p or q". Negating an implication thus gives "not (not p or q)", which is equivalent to "p and not q".
So
not [(a or not b) implies c] <==> (a or not b) and not c
find the maximum value of the function f(x)=-1.8x^2+7x-11 to the nearest hundredth.
Answers
The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is, - 4.19.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The function is,
⇒ f (x) = -1.8x² + 7x - 11
Now, We can differentiate with respect to x as;
⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0
⇒ f ' (x) = - 3.6x + 7
Put f ' (x) = 0
⇒ - 3.6x + 7 = 0
⇒ 3.6x = 7
⇒ x = 1.94
Now, Again differentiate with respect to x as;
⇒ f ' (x) = - 3.6x + 7
⇒ f '' (x) = - 3.6 × 1 + 0
⇒ f '' (x) = - 3.6 < 0
Hence, Substitute x = 1.94 in function to get maximum value,
⇒ f (x) = -1.8x² + 7x - 11
⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11
⇒f (x) = - 6.77 + 13.58 - 11
⇒ f (x) = - 4.19
Thus, The maximum value = - 4.19
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100 POINTS HELP Which account will not appear on a post closing trial balance?
A. accounts payable
B. cash
C. revenue
D. accounts receivable
Answers
Answer:
C revenue
Step-by-step explanation:
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
Answers
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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the triangle ABC is similar to Triangle d e f the measures of the side lengths are in cm which proportional can be used to find the length of EF in cm
Answers
We were told that
traingle ABC is similar to triangle DEF
This means that the ratio of corresponding sides is equal. This means that
AB/DE = BC/EF = AC/DF
10/20 = 6/EF = 7/14
Thus, the proportion that can be used to find the length of EF is
6/EF = 1/2
There are 100 marbles in a jar
There are 9 times as many red marbles
as there are blue marbles. How many
blue marbles are in the jar?
Answers
Answer:
Step-by-step explanation:
take 9 divided by 5 wich = 1.8
I really need help I've answered mainly all the questions but i need some assistance with these few!!! Please show all work, so I can look how you found your answers THANK YOU SM!!!!
Use the function f(x)= - 4^x-1 - 2 to answer the questions below.
1.) State the equation for the asymptote.
2.)What is the range?
3.)What is the domain?
4.) Finally which axis is f(x) reflected over and what caused the reflection?
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
I assume the function you wrote was \(f(x)=-4^{x-1}-2\)
1) The equation for the horizontal asymptote is y=-2 since a function of the form f(x) = a(b^x) + c always has a horizontal asymptote at y = c, so c=-2, therefore the horizontal asymptote equation is y=-2
2) The range is (-∞,-2) since any real value of y that is less than -2 but doesn't equal -2 (since it's not included) will be a solution.
3) The domain is (-∞,∞) since any real value of x will be a solution.
4) The axis that f(x) is reflected over is the x-axis because when you negate a base in an exponential function, that will occur.
Triangles 3 and 4 are identical. They are joined in the poster to form a square. Construct a math argument to show why triangles 3 and 4 are isosceles right angles.
Answers
Triangles 3 and 4 are isosceles right angles because they have same length.
How to explain the triangle?It should be noted be noted that the square has all right angles equal. The largest angle of the triangle is the right angle m.
Here, the triangles are isosceles right angles as both the legs and the acute angles are congruent.
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Find the magnitude of u using the dot product. Write the result in radical form or decimal form, rounded to the nearest hundredth.
Answers
The vector is given as,
\(u\text{ = }\langle\text{ -5, -6 }\rangle\)The magnitude of the vector u is given as,
\(\parallel\text{ u }\parallel\text{ = }\sqrt{\text{ }\langle\text{ -5, -6 }\rangle\text{ . }\langle-5,\text{ -6 }\rangle}\)Calculating the dot product,
\(\begin{gathered} \parallel\text{ u }\parallel\text{ = }\sqrt{(-5)(-6)+(-5)(-6)} \\ \parallel\text{ u }\parallel\text{ = }\sqrt{30\text{ + 30}} \\ \parallel\text{ u }\parallel\text{ =}\sqrt{60} \\ \parallel\text{ u }\parallel\text{ = 7.75} \end{gathered}\)Thus the required answer is,
\(\begin{gathered} Radical\text{ form = }\sqrt{60} \\ Decimal\text{ form = 7.75} \end{gathered}\)the lengths of two sides of a triangle are given. describe the lengths possible for the third side.
6 ft, 12 ft.
Lengths of the third side must be between _____ ft and _____ ft.
Answers
Answer:
7m and 17m
Step-by-step explanation:
The length would be between 7m and 17m. This is because since the sum of two sides of a triangle must be greater than the third side. The sum of the third side and 6 must give us something greater than 12. This means the least the length can be is 7m. Since 6+12=18, the third side also has to be less than 18. This means the greatest the length can be is 17m.
I need help on a problem
Answers
F(t) = 1600 (1.3)^t
Then constant 1.3 = 1+ 0.3 reveals an increment positive of 0.3= 30/100
Increasing rate of 30%
Can you help please on this
Answers
Answer:
5
Step-by-step explanation:
I can’t figure this one out. Someone please help me.
Answers
Answer:
\(d \approx 8.2\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)Step-by-step explanation:
Step 1: Define
Point F (2, 7)
Point G (4, -1)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute [DF]: \(d = \sqrt{(4-2)^2+(-1-7)^2}\)Subtract: \(d = \sqrt{(2)^2+(-8)^2}\)Exponents: \(d = \sqrt{4+64}\)Add: \(d = \sqrt{68}\)Simplify: \(d = 2\sqrt{17}\)Evaluate: \(d = 8.24621\)Round: \(d \approx 8.2\)Identify the next number in the following sequence
25 49 97 ?
Select only one answer
- 124
- 171
- 139
- 193
Answers
Answer:
the correct answer is 193
Step-by-step explanation:
25×1-0=25
25×2-1=49
49×2-1=97
97×2-1=193
Laura started a test at 3:14PM and finished it at 3:32 PM. how long did it take her? give your answer in minutes.
Answers
Answer:
18 minutes
Step-by-step explanation:
This is a simple calculation, all we really need to do is subtract...
Since we started at 3:14 and went to 3:32 pm it is really easy since it is in the same hour.
3:32pm - 3:14pm =
18 minutes
Hope this helps :)
Oh PLEASE HELP ME I'LL GIVE YOU THE Brainliest JUST PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
day 4: 16000
day 5: 32000
day 6: 64000
day 7: 128000
day 8: 256000
day 9: 512000
day 10: 1024000
Step-by-step explanation:
just fill in the day number as x and solve the equation.
I attached a sketch of the graph. My paper isn't big enough to draw in all points, but you should get the idea on how to draw this. On the y axis, you use the number of people infected, on the x axis, the number of days.
Then you draw in each point, just as the exercise is asking for.
Then you also can read on the graph how many people are infected on day 6 and a half and day 11. You read this by checking what y value there is approximately for x = 6.5 and x = 11.
(hint: should be about 90500 for 6.5 days and 2048000 for 11 days)
Express the inequality s > -4 using interval notation
Provide your answer below:
Answers
Answer:
try ( − 4 , ∞ )
Step-by-step explanation:
Use the table that shows the recent population, in millions, of the ten largest U.S. cities.
Find the mean absolute deviation. Round to the nearest hundredth.
The mean absolute deviation =________million.
Answers
The mean absolute deviation for the data-set in the table is given as follows:
1.52 million.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the cardinality of the data-set, which is the number of observations in the data-set.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.The mean for the data-set in this problem is given as follows:
(1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10 = 2.54.
The deviations are given as follows:
|1.5 - 2.54| = 1.04.|3.8 - 2.54| = 1.26.|1.3 - 2.54| = 1.24.|1.6 - 2.54| = 1.06.|2.9 - 2.54| = 0.46.|1.4 - 2.54| = 1.14.|0.9 - 2.54| = 1.64.|2.3 - 2.54| = 0.24.|8.4 - 2.54| = 5.86.|1.3 - 2.54| = 1.24.Hence the mean absolute deviation is given as follows:
(1.04 + 1.26 + 1.24 + 1.06 + 0.46 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24)/10 = 1.52 million.
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In AQRS, QS is extended through point S to point T,
m/QRS = (x+8)°, m/RST = (4x +11)°, and
m/SQR = (x+13)°. Find m/RST.
Answers
The measure of the ∠ RST if, In Δ QRS, QS is extended through point S to point T, a measure of the ∠ QRS = (x + 8)°, m ∠ RST = (4x + 11)°, and m ∠ SQR = (x + 13)°, is 31°.
What is triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices, known as a triangle.
Given:
In Δ QRS, QS is extended through point S to point T, a measure of the ∠ QRS = (x + 8)°, m ∠ RST = (4x + 11)°, and m ∠ SQR = (x + 13)°,
Calculate the value of x as shown below,
∠ RST = ∠ SQR + ∠ QRS (Using exterior angle theorem)
4x + 11 = x + 13 + x + 8
4x - x - x = 13 + 8 - 11
2x = 10
x = 5
Calculate the measure of ∠ RST as shown below,
∠ RST = 4 × 5 + 11
∠ RST = 20 + 11
∠ RST = 31°
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simplify the following expression and write in standard form: 3 x (6y - 4y + 5x) PLEASE HELP
Answers
Answer: 15x^2+6xy
Step-by-step explanation: 3x(6y−4y+5x)
(3x)(6y+−4y+5x)
(3x)(6y)+(3x)(−4y)+(3x)(5x)
18xy−12xy+15x^2
15x^2+6xy
Janet needed 2.7 meters of thread to finish a pillow she was
making. If she has 4 times as much thread as she needs,
what is the length of the thread she has?
Answers
Polygon ABCDE ~ Polygon FGHIJ
What is the scale factor of polygon ABCDE to polygon FGHIJ?
Answers
The scale factor of polygon ABCDE to polygon FGHIJ will be 9/2. Then the correct option is C.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
Polygon ABCDE is similar to the Polygon FGHIJ.
Then the scale factor is given as,
Scale factor = 27 / 6
Simplify the equation, then we have
Scale factor = 27 / 6
Scale factor = 9 / 2
The scale factor of polygon ABCDE to polygon FGHIJ will be 9/2. Then the correct option is C.
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the volume of both of these trapezoid prisms is 24 cubic units. their heights are 6 and 8 units as labeled. What is the area of a trapezoidal base of each prism
Answers
the area of the trapezoidal base of the first prism is 9 square units, and the area of the trapezoidal base of the second prism is 16 square units.
What is Volume of both the trapezoidal prisms?
volume = area of cross section of object* height of object (A)
V = (1/2) * h * (b1 + b2) * H
For the first trapezoid prism, we have:
24 = (1/2) * 6 * (b1 + b2) * 8
Simplifying this equation, we get:
3 = (b1 + b2)
For the second trapezoid prism, we have:
24 = (1/2) * 8 * (b1' + b2') * 6
Simplifying this equation, we get:
4 = (b1' + b2')
A = (1/2) * h * (b1 + b2)
For the first trapezoidal prism:
A = (1/2) * 6 * 3
A = 9 square units
For the second trapezoidal prism:
A = (1/2) * 8 * 4
A = 16 square units
Therefore, the area of the trapezoidal base of the first prism is 9 square units, and the area of the trapezoidal base of the second prism is 16 square units.
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