Answer:
When x = 10, or when f(x) = 1024, or any value greater than that.
Step-by-step explanation:
For f(x): 1x = 2, 2x = 4, 3x = 8, 4x = 16, 5x = 32, 6x = 64, 7x = 128, 8x = 256, 9x = 512, 10x = 1024
for g(x) 1x = 10, 2x = 19 3x = 38, 4x = 72, 5x = 128, 6x = 230, 7x = 358, 8x = 528, 9x = 746, 10x = 1018
Answer:
When x = 10, or when f(x) = 1024, or any value greater than that.
Step-by-step explanation:
What is g(x)?
5-
X
10
-10
Answer: g(x)= -x^2
Step-by-step explanation:
BRO THIS IS THE MOST BASIC ALGEBRA 1 !?!?!?!?!?!?!?!
Brand name producers of aspirin claim that one advantage of their aspirin over generic aspirin is that brand name aspirin is much more consistent in the amount of active ingredient used. This in turn means that users can expect the same results each time they use the brand name aspirin, while the effects of the generic aspirin can be a lot more variable. A random sample of 200 brand name aspirin tablets had a mean and standard deviation of active ingredient of 325.01 and 10.12 mg. A second independent sample of 180 generic aspirin tablets was measured for the amount of active ingredient, and the mean standard deviation were 323.47 and 11.43 mg. Given that the amount of active ingredient is normally distributed for both the brand name and the generic aspirin, do these data support the brand name producers claim? Let alpha = 0.025.
Answer:
Step-by-step explanation:
The claim here is that the brand name aspirin is more consistent in the amount of active ingredient used than the generic aspirin.
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean amount of active ingredients in brand name aspirin and μ2 be the mean amount of active ingredients in generic name aspirin
The random variable is μ1 - μ2 = difference in the mean amount of active ingredients between the brand name and generic aspirin
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 ≥ μ2 H0 : μ1 - μ2 ≥ 0
The alternative hypothesis is
H1 : μ1 < μ2 H1 : μ1 - μ2 < 0
This is a left tailed test
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
x1 = 325.01
x2 = 323.47
s1 = 10.12
s2 = 11.43
n1 = 200
n2 = 180
t = (325.01 - 323.47)/√(10.12²/200 + 11.43²/180)
t = 1.24
1.237877
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [10.12²/200 + 11.43²/180]²/[(1/200 - 1)(10.12²/200)² + (1/180 - 1)(11.43²/180)²] = 1.53233946713/0.00537245359
df = 285
We would determine the probability value from the t test calculator. It becomes
p value = 0.108
Since alpha, 0.025 < than the p value, 0.108, then we would fail to reject the null hypothesis. Therefore, at 2.5% level of significance, these data support the brand name producers claim
There are 5 gallons of distilled water in science supplies. If 8 students each use an equal amount of distilled water and there is 1 gallon left in supplies, how much will each student get?
Answer:
0.5 gallon
Step-by-step explanation:
let x refer to students
5 = 8x + 1
8x = 4
x= 0.5 gallon
Which fraction is equivalent to 2/-6? -2/6 2/6 -2/-6 6/2
how many nickels equal $18.45? (show your work)
Answer:
369
Step-by-step explanation:
One nickel = 0.05
0.05x=18.45
x=369
12x - y = -4
4x - 3y = -6 (1 point)
Answer:
Step-by-step explanation:
12x - y = -4 ----------------------(I)
4x - 3y = -6 ---------------------(II)
Multiply equation (I) by (-3)
(I)*(-3) -36x + 3y = 12
(II) 4x - 3y = - 6 {Add and y will be eliminated}
- 32x = 6
x = 6/-32
x = -3/16
Plugin the value of x in equation (I)
[tex]12*\frac{-3}{16} -y=-4\\\\3*\frac{-3}{4}-y=-4\\\\\frac{-9}{4}-y = -4\\\\-y=-4+\frac{9}{4}\\\\-y=\frac{-4*4}{1*4}+\frac{9}{4}\\\\-y=\frac{-16}{4}+\frac{9}{4}\\\\-y=\frac{-7}{4}\\\\y=\frac{7}{4}\\\\y=1\frac{3}{4}[/tex]
this is a grade 4 maths question. i need help with doing a model from this question as well. thank you! —————————————————- a rope was cut into 2 pieces. The first piece was twice the length of the second piece. If the first piece was 5m 50cm long what was the length of the rope before it was cut
Answer:825cm
Step-by-step explanation:550cm/2=275cm
275*3=825cm
Solve for b. -11b+7 = 40 Two step equations
Step-by-step explanation:
-11b + 7 = 40
-11b = 40 - 7
-11b = 33
b = 33/-11
b = - 3
All the angles in the diagram are measured to the nearest degree. Work out the upper bound and lower bound of angle x 59 degree 108 degree 81 degree X degree ??????
Answer: lower bound, x = 110.5°
upper bound, x = 113.5°
Step-by-step explanation:
There is no diagram but I am going to assume it is a quadrilateral since it has 4 angles. The sum of the angles of a quadrilateral is 360°.
Upper Lower
59° 58.5° ≤ a < 59.5
108° 107.5° ≤ b < 108.5°
81° 80.5° ≤ c < 81.5°
Total: 246.6° ≤ x < 249.5°
Subtract the lower and upper bound totals from 360° :
360.0 360.0
- 246.5 - 249.5
x = 1 1 3.5 1 1 0.5
↓ ↓
upper lower
bound bound
by what rational number should we divide 22/7 so as to get the number -11/13?
Answer:
7/54
Step-by-step explanation:
let thenumber be x
then 22/7 /x = -11/27
= 22x/7 = -11/27
= x = -11*7/27*22 = 7/54
Hope it helps!!
The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 3 years, how long will it take to triple
When $\frac{1}{1111}$ is expressed as a decimal, what is the sum of the first 40 digits after the decimal point?
Answer:
90
Step-by-step explanation:
1/1111= 0. (0009) cycles of 0009 after decimal point (one 9 per 4 digits)
Number of digits 9:
40/4= 1010*9= 90Answer:
90
Step-by-step explanation:
george cut a cake into 8 equal pieces. what is the unit fraction for the cake
Answer: 1/8
Step-by-step explanation:
Unit Fractions: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Example of Unit Fractions: 1/1, 1/2, 1/3, 1/4 ,1/5, etc.
Hope this helps! Please mark as brainliest!
The unit fraction of the cake is 1/8
What is a unit fraction?A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc.
Given that, George cut a cake into 8 equal pieces, we need to find the unit fraction for the cake
Since, George cut the cake in 8 equal pieces so, 1 part will be shown by 1/8 of the cake, that mean 1/8 is one unit of the cake, we can say that 1/8 is the unit of the whole cake.
Hence, the unit fraction of the cake is 1/8
Learn more about unit fractions, click;
https://brainly.com/question/15326565
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A piece of wire of length 7070 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square?
Answer:
a.x=39.2
b.Use whole wire as a circle
Step-by-step explanation:
We are given that
Length of piece of wire=70 units
Let length of wire used to make a square =x units
Length of wire used in circle=70- x
Side of square=[tex]\frac{perimeter\;of\;square}{4}=\frac{x}{4}[/tex]
Circumference of circle=[tex]2\pi r[/tex]
[tex]70-x=2\pi r[/tex]
[tex]r=\frac{70-x}{2\pi}[/tex]
Combined area of circle and square,A=[tex](\frac{x}{4})^2+\pi(\frac{70-x}{2\pi})^2[/tex]
Using the formula
Area of circle=[tex]\pi r^2[/tex]
Area of square=[tex](side)^2[/tex]
a.[tex]A=\frac{x^2}{16}+\frac{4900+x^2-140x}{4\pi}[/tex]
Differentiate w.r.t x
[tex]\frac{dA}{dx}=\frac{x}{8}+\frac{2x-140}{4\pi}[/tex]
[tex]\frac{dA}{dx}=0[/tex]
[tex]\frac{x}{8}+\frac{2x-140}{4\pi}=0[/tex]
[tex]\frac{\pi x+4x-280}{4\pi}=0[/tex]
[tex]\pi x+4x-280=0[/tex]
[tex]x(\pi+4)=280[/tex]
[tex]x=\frac{280}{\pi+4}[/tex]
x=39.2
Again differentiate w.r.t x
[tex]\frac{d^2A}{dx^2}=\frac{1}{8}+\frac{1}{2\pi}[/tex]>0
Hence, the combined area of circle and the square is minimum at x=39.2
b.When the wire is not cut and whole wire used as a circle . Then, combined area is maximum.
All math teachers are smart. Ms. Smith is your math teacher, so she is smart. What type of reasoning is this? inductive or deductive
Answer:
I believe it is Inductive Reasoning.
Step-by-step explanation:
Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.
Deductive Reasoning is a basic form of valid reasoning.
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 228 customers on the number of hours cars are parked and the amount they are charged.
Number of Hours Frequency Amount Charged
1 21 $4
2 36 6
3 53 9
4 40 13
5 22 14
6 11 16
7 9 18
8 36 22
228
A. Convert the information on the number of hours parked to a probability distribution. Is this a discrete or a continuous probability distribution?
B. Find the mean and the standard deviation of the number of hours parked. How would you answer the question: How long is a typical customer parked?
C. Find the mean and the standard deviation of the amount charged.
Answer: A. This is a discrete probability distribution.
hours probability
1 0.09
2 0.16
3 0.23
4 0.17
5 0.09
6 0.05
7 0.04
8 0.16
B. E(X) = 4.12; σ = 2.21
C. μ = 12.75; s = 6.11
Step-by-step explanation: Probability Distribution is an equation or table linking each outcome of an experiment with its probability of ocurrence. For this case, since the experiment is performed a high number of times and in a long run, the relative frequency of the event is its probability. Therefore:
A. To convert to a probability distribution, find the probability through the frequency by doing:
Hour 1
P(X) = [tex]\frac{21}{228}[/tex] = 0.09
Hour 2
P(X) = [tex]\frac{36}{228}[/tex] = 0.16
Hour 3
P(X) = [tex]\frac{53}{228}[/tex] = 0.23
Hour 4
P(X) = [tex]\frac{40}{228}[/tex] = 0.17
Hour 5
P(X) = [tex]\frac{22}{228}[/tex] = 0.09
Hour 6
P(X) = [tex]\frac{11}{228}[/tex] = 0.05
Hour 7
P(X) = [tex]\frac{9}{228}[/tex] = 0.04
Hour 8
P(X) = [tex]\frac{36}{228}[/tex] = 0.16
The table will be:
hours probability
1 0.09
2 0.16
3 0.23
4 0.17
5 0.09
6 0.05
7 0.04
8 0.16
This is a discrete distribution because it lists all the possible values that the discrete variable can be and its associated probabilities.
B. Mean for a probability distribution is calculated as:
E(X) = ∑[[tex]x_{i}[/tex].P([tex]x_{i}[/tex])]
E(X) = 1*0.09 + 2*0.16+3*0.23+4*0.17+5*0.09+6*0.05+7*0.04+8*0.16
E(X) = 4.12
Standard Deviation is:
σ = √∑{[x - E(x)]² . P(x)}
σ = [tex]\sqrt{(1-4.12)^{2}*0.09 + (2-4.12)^{2}*0.16 + ... + (7-4.12)^{2}*0.04 + (8-4.12)^{2}*0.16}[/tex]
σ = [tex]\sqrt{4.87}[/tex]
σ = 2.21
The average number of hours parked is approximately 4h with a standard deviation of approximately 2 hours, which means that a typical costumer parks between 2 to 6 hours.
C. Mean for a sample is given by: μ = ∑[tex]\frac{x_{i}}{n}[/tex] , which is this case is:
μ = [tex]\frac{4+6+9+13+14+16+18+22}{8}[/tex]
μ = 12.75
Standard Deviation of a sample: s = √[tex]\frac{1}{n-1}[/tex]∑([tex]x_{i}[/tex] - μ)²
s = [tex]\sqrt{ \frac{(4-12.75)^{2} + (6-12.74)^{2} + ... + (18-12.75)^{2} + (22-12.75)^{2} }{8-1}}[/tex]
s = 6.11
The average amount charged is 12.75±6.11.
You are standing 5 miles away from the peak. You look up at a 47-degree angle to the peak. How tall is the mountain? Hint: 5280 feet = 1 mile. Round your answer to the nearest foot.
Answer:
19272 feet
Step-by-step explanation:
We are given that the distance between the person and peak is 5 miles.
and angle is [tex]47^\circ[/tex] when we look up at the mountain peak.
The given situation is best represented as a right angled triangle as shown in the attached figure.
[tex]\triangle[/tex]IKJ where [tex]\angle K = 90^\circ[/tex]
IK is the mountain.
J is the point where we are standing.
Distance JI = 5 miles
[tex]\angle J = 47^\circ[/tex]
To find: Distance IK = ?
We can use trigonometric identities to find IK.
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]sinJ = \dfrac{IK}{JI}\\\Rightarrow sin47 = \dfrac{IK}{5}\\\Rightarrow IK = sin47^\circ \times 5\\\Rightarrow IK = 0.73 \times 5\\\Rightarrow IK = 3.65\ miles \\\Rightarrow IK = 3.65 \times 5280\ ft\\\Rightarrow IK = 19272\ ft[/tex]
Hence, height of mountain = 19272 ft
Jalisa earned $71.25 today babysitting, which is $22.50 more than she earned babysitting yesterday. The equation d + 22.50 = 71.25 can be used to represent this situation, where d is the amount Jalisa earned babysitting yesterday. Which is an equivalent equation that can be used to find the amount Jalisa earned babysitting yesterday? 71.25 minus 22.50 = d 71.25 + 22.50 = d d + 71.25 = 22.50 d minus 22.50 = 71.25
Answer:
71.25 - 22.50 = d
Step-by-step explanation:
To find how much she earned yesterday, we subtract how much she earned today by the amount more she earned.
Answer:
A
Step-by-step explanation:
Find the value of x and the value of y.
A r= 15, y = 10/3
B. r=20, p=10/3
C. x=20/3, y = 513
D. r=15, y =53
Answer:
Step by step solution:
Teaching descriptive statistics. A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam.
a. What are the hypotheses for evaluating if the average test scores are different for the different teaching methods?
b. What are the degrees of freedom associated with the F-test for evaluating these hypotheses?
c. Suppose the p-value for this test is 0.0168. What is the conclusion?
Answer:
Step-by-step explanation:
a. The hypotheses are:
Null hypothesis: the average test scores are the same for the different teaching methods.
Alternative hypothesis: the average test scores are different for the different teaching methods.
b. To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample
c. With a p value of of 0.0168 and using a standard significance level of 0.05, we will reject the null hypothesis as 0.0168 is less than 0.05 and conclude that the average test scores are different for the different teaching methods.
How do I solve 24-27?
Answer:
-3
Step-by-step explanation:
You find the difference between the numbers, which is 3. Then you make it negative since 24 is less than 27.
Rearrange the following steps in the correct order to locate the last occurrence of the smallest element in a finite list of integers, where the integers in the list are not necessarily distinct.
a. return location
b. min ≔a1 and location ≔1
c. min ≔ai and location≔i
d. procedure last smallest(a1,a2,...,an: integers)
e. If min >= ai then
Answer:
The rearranged steps is as follows:
d. procedure last smallest(a1,a2,...,an: integers)
b. min ≔a1 and location ≔1
e. If min >= ai then
c. min ≔ai and location≔i
a. return location
Step-by-step explanation:
The proper steps to perform the task in the question above is dbeca
Here, the procedure (or function) was defined along with necessary parameters
d. procedure last smallest(a1,a2,...,an: integers)
The smallest number is initialized to the first number on the list and its location is initialized to 1
b. min ≔a1 and location ≔1
The next line is an if conditional statement that checks if the current smallest number is greater than a particular number
e. If min >= ai then
If the above condition is true, the smallest value is assigned to variable min; it's location is also assigned to variable location
c. min ≔ai and location≔i
The last step returns the location of the smallest number
a. return location
Please answer this correctly
Answer:
yes
Step-by-step explanation:
not every person is going to have the same opinion, so it is yes.
// have a great day //
Answer:
Yes, because if Pedro asked them the question "what do you think of public transportation?" the majority would probably say that they like it or something along those lines. This is biased because there may be other city inhabitants who don't think very highly of public transportation. Basically, what I'm trying to say is that not everyone will have the same opinion.
The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot.
What does h(3.2) represent?
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
Answer:
h(3.2) represents the height of the rock 3.2 seconds after it is propelled. Remember, h(t) represents the height of a rock t seconds after it is propelled.
Answer:
D
Step-by-step explanation:
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
please help and please show your work
Answer:
The volume of all 9 spheres is 301.6 [tex]in^3[/tex]
Step-by-step explanation:
Notice that three of the identical spheres fit perfectly along the 12 in side box, therefore we know that the diameter of each is 12 in/3 = 4 in.
Then the radius of each sphere must be 2 inches (half of the diameter). Now that we know the radius of each sphere, we use the formula for the volume of a sphere to find it:
[tex]V=\frac{4}{3} \pi R^3\\V=\frac{4}{3} \pi (2\,in)^3\\V=\frac{4}{3} \pi\, 8\,\,in^3\\V=\frac{32}{3} \pi\,\,in^3[/tex]
Now, the total volume of all nine spheres is the product of 9 times the volume we just found:
[tex]V_{all \,9}=9\,*\frac{32}{3} \pi\,\,in^3\\V_{all \,9}=96 \pi\,\,in^3\\V_{all \,9}\approx \,301.6\,\,in^3[/tex]
Find the common ratio for this geometric sequence. 243, 27, 3, 1/3, 1/27.
Answer:
1/9
Step-by-step explanation:
Since each next term is 1/9 of the last, the common ratio is 1/9. This can be confirmed by the fact that 243*1/9=27, 27*1/9=3, 3*1/9=1/3, and so on. Hope this helps!
Benny is trying to learn how to ride a bike, but is terrified of falling. He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1; if he learns to ride a bike by using a bike without training wheels, his probability of falling is 0.5, and if he uses a unicycle, his probability of falling is 0.8. Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.
a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?
b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?
Answer:
a) 7.14% probability that Benny was learning to ride a bike using the training wheels
b) 28% probability that Benny was learning to ride a bike using the training wheels
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.
a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?
So
Event A: Benny fell
Event B: Benny was using training wheels.
The probability that Benny was using each of these 3 methods is equal
This means that [tex]P(B) = \frac{1}{3}[/tex]
He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;
This means that [tex]P(A|B) = 0.1[/tex]
Probability of falling:
1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.
1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5
1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then
[tex]P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667[/tex]
So
[tex]P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714[/tex]
7.14% probability that Benny was learning to ride a bike using the training wheels
b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?
Similar as above, just some probabilities change.
Event A: Benny fell
Event B: Benny was using training wheels.
The probability that he was using training wheels is 0.7
This means that [tex]P(B) = 0.7[/tex]
He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;
This means that [tex]P(A|B) = 0.1[/tex]
Probability of falling:
0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.
0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5
0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then
[tex]P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25[/tex]
So
[tex]P(B|A) = \frac{0.7*0.1}{0.25} = 0.28[/tex]
28% probability that Benny was learning to ride a bike using the training wheels
Brainliest to whoever gets this correct Which of the following is equal to the rational expression when x ≠ -3? x^2-9/x+3
Answer:
see below
Step-by-step explanation:
We presume you want to simplify ...
[tex]\dfrac{x^2-9}{x+3}=\dfrac{(x-3)(x+3)}{x+3}=\boxed{x-3}[/tex]
__
The numerator is the difference of squares, so is factored accordingly. One of those factors cancels the denominator.
can 10/12 be simplified
Answer:
5/6
Step-by-step explanation:
10/12
Divide the top and bottom by 2
10/2 = 5
12/2 =6
the fraction becomes 5/6
Answer :
10/12
Reduce the fraction
= 5/6
4. Rational, irrational (4 points) (1) (2 points) Prove or disprove that if x y is an irrational number, then x or y is also an irrational number. (2) (2 points) Prove that if x 2 is irrational, then x is irrational. (Hint: try a proof by contrapositive)
Answer:
See explanation below
Step-by-step explanation:
1) Prove or disprove that if [tex] x^y[/tex] is an irrational number, then x or y is also an irrational number.
Let's take the following instances:
i) When x= 2 and y=[tex] \sqrt{2} [/tex] we have: [tex] 2^\sqrt^{^2^} [/tex]
ii) When [tex] x=2\sqrt{2} [/tex] and y=3, we have: [tex] (x=2\sqrt{2})^3 [/tex]
iii) When [tex] x=2\sqrt{2} [/tex] and [tex] y = \sqrt{2}[/tex], we have: [tex] (2\sqrt{2})^\sqrt^{^2^}[/tex]
It is proven because, in scenario
i) x is rational and y is irrational
ii) x is irrational and y is rational
iii) x and y are irrational
2) Prove tha x² is irrational, then x is irrational.
Use contradiction here.
Thus, x² is irrational and x is rational.
[tex] x =\frac{b}{a} [/tex] when x is rational, a & b are integers.
Therefore, [tex] x^2 =\frac{b^2}{a^2} [/tex]. This x² is rational.
This contradicts the statement that x² is irrational.
Therefore, if x² is irrational, x is also irrational.