ANSWER
[tex]W''(2, - 3)[/tex]
EXPLANATION
The given point bas coordinates
W(-2,3).
The mapping for reflection over the x-axis is
[tex](x,y)\to(x, - y)[/tex]
[tex]W(-2,3)\to \: W'(-2, - 3)[/tex]
This point W'(-2,-3) is then reflected over the y-axis.
The mapping for reflection over the y-axis is
[tex](x,y)\to (-x, y)[/tex]
[tex]W'(-2,-3)\to \: W''(2, - 3)[/tex]
Point W is initially transformed by reflecting it over the x-axis, which inverses the sign of the y-coordinate, followed by a reflection over the y-axis, which inverses the sign of the x-coordinate. The final position of point W" on the coordinate plane is therefore (2, -3).
Explanation:To answer this mathematics question involving coordinate geometry and reflections, one must understand how reflections in the x-axis and y-axis affect the coordinates of a point.
A reflection of a point across the x-axis changes the sign of the y-coordinate, and a reflection across the y-axis changes the sign of the x-coordinate. Thus, if we start with point W at (-2,3), a reflection over the x-axis to create point W' changes the y-coordinate's sign, yielding point W' at (-2,-3). Then, reflecting W' over the y-axis changes the x-coordinate's sign, yielding our final point W" at (2,-3).
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A person invests $1,450 in an account that earns 6% annual interest compounded continuously. Find when the value of the investment reaches $2,500. If necessary round to the nearest tenth. The Investment will reach a value of $2.500 in approximately ____ years.
Answer:
20.7 years
Step-by-step explanation:
Use the "compound amount, compounding continuously" formula:
A = Pe^(r · t)
Here,
A = $2,500 = $1,450e^(0.06 · t)
Divide both sides by $1,450: 1.724 = e^(0.06 · t)
Taking the natural log of both sides, we obtain:
ln 1.724 = (0.06 · t).
Finally, we divide both sides by 0.06, obtaining:
ln 1.724
------------ = t = 20.7
0.06
The Investment will reach a value of $2.500 in approximately 20.7 years.
Answer:
Years = natural log (total / principal) / rate
Years = natural log (2,500 / 1,450) / .06
Years = natural log (1.724137931) / .06
Years = 0.54472717542 / .06
Years = 9.078786257
Years = 9.1 (rounded)
Step-by-step explanation:
Please help, I don't know what I'm doing wrong!
Answer:
x = 10.1
Step-by-step explanation:
The function SINE stands for Opp. / Hyp. the function that should be used is COSINE. We now know that cos(39) = x/13 and using a calculator we can substitute for cos(39).
Make sure your calculator is in degrees when plugging into your calculator so you don't use radians.
We get 0.777145961457 = x/13 now since we have substituted we can multiply both sides of the equation to get 10.1028974989 = x. When rounded, it is 10.1 units.
20. The surface areas of two similar solids are 216 m² and 1014 m². The volume of the larger one is 2197 m³. What is the volume of the smaller one?
Answer:
216 m³
Step-by-step explanation:
The ratio of linear dimensions is the square root of the ratio of area dimensions.
s = √(216/1014) = √(36/169) = 6/13
Then the ratio of volume dimensions is the cube of that. The smaller volume is ...
v = (6/13)³·2197 m³ = 216/2197·2197 m³ = 216 m³
The volume of the smaller solid is 216 m³.
write an equation for each translation of y=|x| .
7 units up
a.y +7 = | x |
b.y =| 7x |
c.y= | x | - 7
d.y= | x | + 7
Answer:
y = |x| + 7
Step-by-step explanation:
Use desmos.com to see it in action
The answer is Y=|x| +7
The length of a phone conversation is normally distributed with a mean of 4 minutes and a standard deviation of .6 minutes. What is the probability that a conversation lasts longer than 5 minutes? 0.04746 0.45254 0.54746 0.95254
Answer:
0.04746
Step-by-step explanation:
To answer this one needs to find the area under the standard normal curve to the left of 5 minutes when the mean is 4 minutes and the std. dev. is 0.6 minutes. Either use a table of z-scores or a calculator with probability distribution functions.
In this case I will use my old Texas Instruments TI-83 calculator. I select the normalcdf( function and type in the following arguments: :
normalcdf(-100, 5, 4, 0.6). The result is 0.952. This is the area under the curve to the left of x = 5. But we are interested in finding the probability that a conversation lasts longer than 5 minutes. To find this, subtract 0.952 from 1.000: 0.048. This is the area under the curve to the RIGHT of x = 5.
This 0.048 is closest to the first answer choice: 0.04746.
Kahn Academy Question, Please help!
[tex]g\circ f(-9)=g(f(-9))[/tex]
By definition of [tex]f[/tex],
[tex]f(-9)=3\cdot9-8=19[/tex]
and by definition of [tex]g[/tex],
[tex]g\circ f(-9)=g(f(-9))=g(19)=\sqrt{14-19}-10=\sqrt{-5}-10[/tex]
which is undefined if [tex]f,g[/tex] are supposed to be real-valued functions. If they're complex-valued, then [tex]\sqrt{-5}=i\sqrt 5[/tex] and [tex]g\circ f(-9)=-10+i\sqrt 5[/tex].
Which number line represents the solution set for the inequality –x ≥ 4?
Answer:
It is the second choice.
Step-by-step explanation:
-1/2 x ≥ 4
x ≤ 4 * -2
x ≤ -8.
The number line with solid circle at -8 and shaded region extending to the left, serves as the appropriate number line representation for the inequality -1/2x ≥ 4. It clearly conveys that all values of x less than or equal to -8 are part of the solution set.
The correct answer is option B.
To represent the solution set of an inequality, we employ a number line with various markings to indicate the values that satisfy the inequality's criteria. In this case, we're dealing with the inequality -1/2x ≥ 4.
The inequality symbol ≥ signifies that the value on the left-hand side is greater than or equal to the value on the right-hand side. When we rewrite the inequality as x ≤ -8, we're essentially saying that any value of x less than or equal to -8 satisfies the inequality.
Option B accurately represents this solution set through a solid circle at -8, indicating that -8 is a direct solution to the inequality. The shaded region extending to the left of -8 further emphasizes that all values of x less than -8 also satisfy the inequality.
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You pick one card from each set, spin the spinner, and find the sum. How many different sums are possible
It depends on how many different options there are on the spinner
9 different sums are possible from the given data
To calculate the number of different sums possible, let's break down the problem step by step:
1. Determine the number of cards in each set:
- Set 1: 1, 2, 3, 4, 5 (5 cards)
- Set 2: 6, 7, 8, 9, 10 (5 cards)
2. Find the total number of combinations by multiplying the number of cards in each set:
- Total combinations = 5 (cards in Set 1) × 5 (cards in Set 2) = 25 combinations
Now, let's consider all the possible sums:
- The lowest possible sum is when we pick the lowest card from each set: 1 + 6 = 7.
- The highest possible sum is when we pick the highest card from each set: 5 + 10 = 15.
To find all the possible sums, we consider the range from the lowest sum to the highest sum, inclusive:
7, 8, 9, 10, 11, 12, 13, 14, 15
There are 9 different sums in total.
So, the correct answer is: 9 different sums are possible.
The key to solving this problem lies in understanding the concept of combinations and the range of possible sums. We find the number of combinations by multiplying the number of cards in each set. Then, by considering the lowest and highest cards from each set, we determine the range of possible sums. Finally, by listing out all the sums within that range, we find that there are 9 different sums possible. This method ensures a systematic approach to solving the problem, providing a clear and accurate answer.
Complete question:
You pick one card from each set, spin the spinner, and find the sum. How many different sums are possible
Please please help me
Answer:
18 in^2.
Step-by-step explanation:
The ratio of their areas = the ratio of the squares of corresponding sides. So:
9^2 / 12^2 = x / 32
81/144 = x / 32
x = (81 * 32) / 144
= 18 in^2.
A survey of 225 students showed the mean number of hours spent studying per week was 20.6 and the standard deviations was 2.7
Answer:
The margin of error is approximately 0.3
Step-by-step explanation:
The following information has been provided;
The sample size, n =225 students
The sample mean number of hours spent studying per week = 20.6
The standard deviation = 2.7
The question requires us to determine the margin of error that would be associated with a 90% confidence level. In constructing confidence intervals of the population mean, the margin of error is defined as;
The product of the associated z-score and the standard error of the sample mean. The standard error of the sample mean is calculated as;
[tex]\frac{sigma}{\sqrt{n} }[/tex]
where sigma is the standard deviation and n the sample size. The z-score associated with a 90% confidence level, from the given table, is 1.645.
The margin of error is thus;
[tex]1.645*\frac{2.7}{\sqrt{225}}=0.2961[/tex]
Therefore, the margin of error is approximately 0.3
Answer:
.3 is the answer.
Step-by-step explanation:
Factor –8x3 – 2x2 – 12x – 3 by grouping. What is the resulting expression?
The answer is (-4x-1)(2x^2+3) when factoring this expression by grouping
Answer:
The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]-8x^3-2x^2-12x-3[/tex]
The above expression can be written as:
[tex](-8x^3-2x^2)+(-12x-3)[/tex]
Take out the greatest common factor from each group.
[tex]-2x^2(4x+1)-3(4x+1)[/tex]
Further solve the above expression.
[tex](4x+1)(-2x^2-3)[/tex]
Hence, the required expression is
[tex](4x+1)(-2x^2-3)[/tex]
The resulting expression is [tex](4x+1)(-2x^2-3)[/tex]
Find the sum of the series. Include each term that leads to the final sum and show the expression for finding that term. ∑5k=3(−2k+5)
Answer:
[tex]\large\boxed{\sum\limits_{k=3}^5(-2k+5)=-9}[/tex]
Step-by-step explanation:
[tex]\sum\limits_{k=3}^5(-2k+5)\to a_k=-2k+5\\\\\text{Put}\ k=3,\ k=4\ \text{and}\ k=5:\\\\a_3=-2(3)+5=-6+5=-1\\a_4=-2(4)+5=-8+5=-3\\a_5=-2(5)+5=-10+5=-5\\\\\sum\limits_{k=3}^5(-2k+5)=-1+(-3)+(-5)=-9[/tex]
What is the ordered pair for point B?
The answer is C. (5,3)
Explanation:
(X,Y) is how ordered pairs should be set up.
Answer:
C (5,3)
Step-by-step explanation:
The first point in an ordered pair is the x coordinate.
We move 5 units to the right, so it is +5
The second coordinate is the y coordinate.
We move 3 units up, so it is +3
(5,3)
Which theorem(s) can be used to prove that the given triangles are congruent to each other with only the information shown? Select all that apply.
A. ASA similarity
B. AA similarity
C. SAS similarity
D. SSS similarity
PLEASE HELP FAST!! I apologize for the pictures being sideways.
Answer:
a) 180
b) CJ= 5.83095189485
CK= 9.89949493661
CL= 8.0622577483
c) All angles formed by a point and its image, with the vertex at the center of rotation, are congruent. Each point on the original figure is the same distance from the center of rotation as its image.
Step-by-step explanation:
Write the equation of the ellipse in standard form
Answer:
h=1 K =2 a =6 b=2
Step-by-step explanation:
look this solution :
Answer:
h = 1, k = 2, a = 6 and b = 2.
Step-by-step explanation:
Start by grouping the terms in x and y together:
4x^2 - 8x + 36y^2 - 144y = -4
Factor out the coefficient:
4(x^2 - 2x) + 36(y^2 - 4y) = -4
Complete the squares:
4 [(x - 1)^2 - 1] + 36 [y - 2)2 - 4] = -4
4(x - 1)^2 - 4 + 36(y - 2)^2 - 144 = -4
4(x - 1)^2 + 36(y - 2)^2 = 144
Divide through by 144:
(x - 1)^2 / 36 + (y - 2)^2/ 4 = 1
(x - 1)^2 / 6^2 + (y - 2)^2 / 2^2 = 1 (answer).
Simplify.
(2w)^4
Write your answer without parentheses.
Answer:
16w^4
Step-by-step explanation:
(2w)^4 is just 2w mulitplied by itself 4 times. we can do this step by step and multiply the 2 by itself 4 times first:
2 x 2 x 2 x 2 or 2^4 = 16
next we can multiply w by itself 4 times:
w x w x w x w or w^4 = w^4
our answer would be 16w^4
you can also multiply it without breaking it down like this:
2w x 2w x 2w x 2w = 16w^4
The simplification of an expression [tex](2w)^{4}[/tex] without parentheses is [tex]16w^{4}[/tex].
What is the simplification of an expression [tex](2w)^{4}[/tex]?Given:
An expression that is given is [tex](2w)^{4}[/tex].Find:
The simplification of the given expressionSolution:
The given expression is [tex](2w)^{4}[/tex].
This means that 2w has to be multiplied itself by 4.
So, 2*2*2*2 = 16
and w*w*w*w = [tex]w^{4}[/tex]
So, the expression [tex](2w)^{4}[/tex] = [tex]16w^{4}[/tex]
Therefore, The simplification of the expression [tex](2w)^{4}[/tex] is [tex]16w^{4}[/tex]
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A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. Which sentence about the points is true? A. A, B, C, and D lie on the same line. B. And are perpendicular lines. C. And are parallel lines. D. And are intersecting lines but are not perpendicular. E. And are parallel lines
Answer with explanation:
Coordinates of A, B, C, and D are (-8, 1), (-2, 4), (-3, -1), and (-6, 5).
Plotting the points on two dimensional plane
1. You will find that, the four points, A , B , C and D do not lie on the dame Line.
[tex]\text{Slope of AB}=\frac{4-1}{-2+8}=\frac{3}{6}=\frac{1}{2}\\\\\text{Slope of CB}=\frac{4+1}{-2+3}=\frac{5}{1}=5\\\\\text{Slope of CD}=\frac{5+1}{-6+3}=\frac{6}{-3}=-2\\\\\text{Slope of AD}=\frac{5-1}{-6+8}=\frac{4}{2}=2\\\\\text{Slope of BD}=\frac{5-4}{-6+2}=\frac{1}{-4}=\frac{-1}{4}\\\\\text{Slope of AC}=\frac{-1-1}{-3+8}=\frac{-2}{5}[/tex]
→→None of the two lines are Parallel nor they are perpendicular,because neither product of slopes of two lines is equal to ,-1, nor the slope of two lines are equal.
It means they are Intersecting Lines .
Option D:⇒ And are intersecting lines but are not perpendicular.
Answer:
line AB and line CD are perpendicular lines
Step-by-step explanation:
Elsie says that the question "Do you have any siblings?" is a statistical question. Mark says that "How many siblings do you have?" is a statistical question. Who is correct?
Make because it’s statistical and his question is more specific
In the given question, Mark is correct.
What is a statistical question?A statistical question is one that can be answered by collecting data from several sources.
The question Elsie asked is a yes/no question, you can't answer the question in terms of data/numbers, but the question mark asked has to be answered in terms of data/numbers, hence it is a statistical question.
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70 POINTS!!!!
Find the focus, directrix, and equation of the parabola in the graph.
Answer:
Option B
Part a) The focus is [tex](1/28,0)[/tex]
Part b) The directrix is [tex]x=-1/28[/tex]
Part c) The equation is [tex]y^{2}= (1/7)x[/tex]
Step-by-step explanation:
step 1
Find the equation of the parabola
we know that
The parabola in the graph has a horizontal axis.
The standard form of the equation of the horizontal parabola is
[tex](y - k)^{2}= 4p(x - h)[/tex]
where
p≠ 0
The vertex of this parabola is at (h, k).
The focus is at (h + p, k).
The directrix is the line x= h- p.
The axis is the line y = k.
If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left
In this problem we have that the vertex is the origin
so
(h,k)=(0,0)
substitute in the equation
[tex](y - 0)^{2}= 4p(x - 0)[/tex]
[tex]y^{2}= 4p(x)[/tex]
The points (7,1) and (7,-1) lies on the parabola-----> see the graph
substitute the value of x and the value of y in the equation and solve for p
[tex](1)^{2}= 4p(7)[/tex]
[tex]1= 28p[/tex]
[tex]p=1/28[/tex]
The equation of the horizontal parabola is
[tex]y^{2}= 4(1/28)(x)[/tex]
[tex]y^{2}= (1/7)x[/tex]
step 2
Find the focus
we know that
The focus is at (h + p, k)
Remember that
[tex](h,k)=(0,0)[/tex]
[tex]p=1/28[/tex]
substitute
[tex](0+1/28,0)[/tex]
therefore
The focus is at
[tex]F (1/28,0)[/tex]
step 3
Find the directrix
The directrix is the line x = h- p
Remember that
[tex](h,k)=(0,0)[/tex]
[tex]p=1/28[/tex]
substitute
[tex]x=0-1/28[/tex]
[tex]x=-1/28[/tex]
Answer:
B
Step-by-step explanation:
Confirmed on E D G 2021
consider the given right triangle. If a=20 and b=20, then angle B=
Answer:
Angle B is 45°
Step-by-step explanation:
Since a and b are both of length 20, this is an isosceles right triangle, and the angle opposite side b must be 45°.
The Angle B is 45°
What are isosceles triangles?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Given
Since a and b are both of length 20, this is an isosceles right triangle, and the angle opposite side b must be 45°.
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Please help me out!!!!!!!
In the triangle:
Y= 4.4 centimeters
what is the surface area of a triangular prism container that would be needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm?
Answer:
if this is geometry nation, the answer is c, 4671 sq cm
Step-by-step explanation:
Final answer:
The surface area of the triangular prism container needed to enclose the rolled document with a diameter of 10 cm and a length of 85 cm is 1695 cm².
Explanation:
To find the surface area of a triangular prism container, we need to consider the three rectangular faces and two triangular faces of the prism. The rectangular faces have the same dimensions as the rolled document, which is 10 cm in diameter and 85 cm in length. So, the area of each rectangular face is 10 cm x 85 cm = 850 cm².
For the triangular faces, we need to calculate the base and height. The base of the triangle is the same as the diameter of the rolled document, which is 10 cm. The height of the triangle can be found using the Pythagorean theorem, where the hypotenuse is the length of the rolled document (85 cm) and the base is half the diameter (5 cm). The height is then calculated as √(85 cm)² - (5 cm)² = 84.5 cm.
The area of each triangular face is 1/2 x base x height = 1/2 x 10 cm x 84.5 cm = 422.5 cm². Since there are two triangular faces, the total area of the triangular faces is 2 x 422.5 cm² = 845 cm².
Finally, to find the surface area of the triangular prism container, we add the areas of the rectangular faces and triangular faces: 850 cm² + 845 cm² = 1695 cm².
Please HELP!
Pedro needs a 2 on the roll of die in order to win a game. What is his probability of failure?
A-1
B-1/6
C-0
D-5/6
The answer is D, he has to hit 1/6 sides so the chances are 5/6 hit hits 1,3,4,5, or 6
Answer:
D
Step-by-step explanation:
there are six sides on a die and only one side with a 2 so you have 1 side witha two 6-1=5 =5/6
Two cyclists left simultaneously from cities A and B heading towards each other at constant rates and met in 5 hours. The rate of the cyclist from A was 3 mph less than the rate of the other cyclist. If the cyclist from B had started moving 30 minutes later than the other cyclist, then the two cyclists would have met 31.8 miles away from A. What is the distance between A and B, in miles?
Answer:
75 miles
Step-by-step explanation:
Let x mph be the cyclist A rate, then x+3 mph is the cyclist B rate.
1. In 1 hour they both traveled x+x+3=2x+3 miles. In 5 hours they traveled
[tex]5(2x+3)=10x+15\ miles.[/tex]
2. Cyclist A spent [tex]\frac{31.8}{x}[/tex] hours to travel 31.8 miles. If the cyclist from B had started moving 30 minutes (1/2 hour) later than the cyclist A, then he spent [tex]\frac{31.8}{x}-\frac{1}{2}[/tex] hours to travel the rest of the distance. In total they both traveled the whole distance 10x+15 miles, thus
[tex]31.8+\left(\dfrac{31.8}{x}-\dfrac{1}{2}\right)\cdot (x+3)=10x+15[/tex]
Solve this equation. Multiply it by 2x:
[tex]63.6x+(63.6-x)(x+3)=2x(10x+15)\\ \\63.6x+63.6x+190.8-x^2-3x=20x^2+30x\\ \\-x^2+124.2x+190.8-20x^2-30x=0\\ \\-21x^2+94.2x+190.8=0\\ \\210x^2-942x-1908=0\\ \\35x^2-157x-318=0\\ \\D=(-157)^2-4\cdot 35\cdot (-318)=69169\\ \\x_{1,2}=\dfrac{-(-157)\pm\sqrt{69169}}{2\cdot 35}=\dfrac{157\pm263}{70}=-\dfrac{106}{70},\ 6[/tex]
The rate cannot be negative, thus, x=6 mph.
Hence, the distance between cities A and B is
[tex]10\cdot 6+15=60+15=75\ miles.[/tex]
Please help me out!....
Check the picture below.
Drag each tile to the correct box. Consider the given functions f, g, and h.
h(x)=x²+x-6
Place the tiles in order from least to greatest according to the average rate of change of the functions over the interval [0, 3].
function H function f function g
Answer:
g, f, h
Step-by-step explanation:
By definition, the average rate of change of a function f over an interval [a,b] is given by
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
So, in your case, we want to compute the quantity
[tex]\dfrac{f(3)-f(0)}{3}[/tex]
for all the three function
Average rate of change of f:
We will simply use the table to check the values for f(3) and f(0):
[tex]\dfrac{f(3)-f(0)}{3}=\dfrac{10-1}{3} = 3[/tex]
Average rate of change of g:
We will use the graph to to check the values for g(3) and g(0):
[tex]\dfrac{g(3)-g(0)}{3}=\dfrac{8-1}{3} = \dfrac{7}{3}[/tex]
Average rate of change of h:
We can plug the values in the equation to get h(3) and h(0):
[tex]h(3)=3^2+3-6=9+3-6=6,\quad h(0)=0^2+0-6=-6[/tex]
And so the average rate of change is
[tex]\dfrac{h(3)-h(0)}{3}=\dfrac{6-(-6)}{3} = 4[/tex]
Answer:
g,f,h
I just took the test and was right
Step-by-step explanation:
Ian's parents asked him to creat a budget for his $ 1,000 monthly income . He determines that he would like to save the remaining amount. What percent of his budget will go towards saving. Expense : Amount ($) Car payment $ 350 Car insurance $ 100 Fuel $ 120 Cell phone $ 80
35%
First, we need to find the amount of money that is being spent. Add all of the amounts together.
$350 + $100 + $120 + $80
$450 + $120 + 80
$570 + $80
$650
So, Ian spends $650 of his budget each month. How much does that leave for savings? Just subtract $650 from $1,000 to find that he saves $350 each month.
Now, you just need to find the percentage. The percentage is the same as the numerator in a fraction with a denominator of 100, so x% = x/100. For example, 1% = 1/100. $350 / $1000 = x / 100
How do we turn 1,000 into 100? Divide it by 10. And if you do something to the denominator of a fraction, you have to do it to the numerator as well. So, divide $350 by 10 and divide $1000 by 10, leaving you with $35 / $100 = x / 100
Multiply both sides by 100 to get x by itself. This leaves you with 35 = x, so 35% of Ian’s budget with go towards saving.
Kylie and Ethan have each saved some money. I’m their savings, each coin is worth leas then 50 cents and each bill is less then $10. Kylie has saved more money than Ethan, but he has more bills and coins than Kylie. She has one bill and seven coins. What is the amount of money each person could have?
Answer:
Kylie could have a $5 bill and seven quarters while Ethan could have two $1 bills and forty pennies.
Step-by-step explanation:
Since Kylie has seven quarters, that is seven multiplied by the value of the quarter, a quarter is 25 cents. So 7 x 25 = 125 OR $1 and 25 cents. Leaving Kylie with a total of $7 and 25 cents with the addition of the $5 bill.
Ethan has two $1 bills and forty pennies, forty multiplied by the value of the penny, a penny is 1 cent. So 40 x 1 = 40 OR 40 cents. Leaving Ethan with $2 and 40 cents with the addition of the two $1 bills from earlier.
Ethan has more bills and coins than Kylie and yet still has less money than Kylie.
Which statement is correct about y = cos^–1 x?
Answer:
A) If the domain of y=cos(x) is restricted to [0, π], y=cos^-1(x) is a function.
Step-by-step explanation:
In order for the inverse function to be a function, the original must pass the horizontal line test: a horizontal line must intersect the function in only one place.
As you can see from the attached graph, restricting the cosine function to the domain [0, π] allows it to pass the horizontal line test, so its inverse will be a function.
__
Restricting the domain to [-π/2, π/2] does not limit cos(x) to something that will pass the horizontal line test.