Two triangles with the same corresponding side lengths will be congruent.
True
False
Two triangles with the same corresponding side lengths will be congruent - False
False. Two triangles with the same corresponding side lengths are not guaranteed to be congruent. They may still be similar triangles with equal corresponding angles but different sizes.
Rewrite the expression below.
-2a (a + b - 5) + 3 (-5a + 2b) + b (6a + b - 8)
Final answer:
The simplified expression is [tex]-2a^2 + 4ab - 5a - 2b + b^2[/tex]
Explanation:
The expression -2a (a + b - 5) + 3 (-5a + 2b) + b (6a + b - 8) needs to be rewritten by expanding and combining like terms using the distributive property. To expand the expression, multiply each term inside the parentheses by the term outside the parentheses. Then, combine the like terms to simplify the expression.
Let's expand each term as follows:
-2a * a = -2a²
-2a * b = -2ab
-2a * (-5) = +10a
3 * (-5a) = -15a
3 * 2b = +6b
b * 6a = +6ab
b * b = b²
b * (-8) = -8b
Now, combine the like terms:
[tex]-2a^2 - 2ab + 10a - 15a + 6b + 6ab + b^2 - 8b[/tex]
The simplified expression is -
[tex]-2a^2 + 4ab - 5a - 2b + b^2[/tex]
What assumption must be made about the sun rays if you use this method of determining the circumference of a large sphere?
Which of the following is the expansion of (3c + d2)6?
A) 729c6 + 1,458c5d2 + 1,215c4d4 + 540c3d6 + 135c2d8 + 18cd10 + d12
B) 729c6 + 1,458c5d + 1,215c4d2 + 540c3d3 + 135c2d4 + 18cd5 + d6
C) 729c6 + 1,215c5d2 + 810c4d4 + 270c3d6 + 90c2d8 + 15cd10 + d12
D) 729c6 + 243c5d2 + 81c4d4 + 27c3d6 + 9c2d8 + 3cd10 + d12
E) c6 + 6c5d2 + 15c4d4 + 20c3d6 + 15c2d8 + 6cd10 + d12
Answer: Option A) [tex]729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}[/tex] is the correct expansion.
Explanation:
on applying binomial theorem, [tex](a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r[/tex]
Here a=3c, [tex]b=d^2[/tex] and n=6,
Thus, [tex](3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r[/tex]
⇒ [tex](3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6[/tex]
⇒[tex](3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}[/tex]
⇒[tex](3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}[/tex]
⇒[tex](3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}[/tex]
Answer:
Option (a) is correct.
[tex](3c+d^2)^6=729c^6+1458c^5d^2+1215c^4d^4+540c^3d^6+135c^2d^8+18cd^{10}+d^{12}[/tex]
Step-by-step explanation:
Given : [tex]\left(3c+d^2\right)^6[/tex]
We have to expand the given expression and choose the correct from the given options.
Consider the given expression [tex]\left(3c+d^2\right)^6[/tex]
Using binomial theorem ,
[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
We have [tex]a=3c,\:\:b=d^2[/tex]
[tex]=\sum _{i=0}^6\binom{6}{i}\left(3c\right)^{\left(6-i\right)}\left(d^2\right)^i[/tex]
also, [tex]\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}[/tex]
for i = 0 , we have,
[tex]\frac{6!}{0!\left(6-0\right)!}\left(3c\right)^6d^2^0=729c^6[/tex]
for i = 1 , we have,
[tex]\frac{6!}{1!\left(6-1\right)!}\left(3c\right)^5d^2^1=1458c^5d^2[/tex]
for i = 2 , we have,
[tex]\frac{6!}{2!\left(6-2\right)!}\left(3c\right)^4d^2^2=1215c^4d^4[/tex]
for i = 3 , we have,
[tex]\frac{6!}{3!\left(6-3\right)!}\left(3c\right)^3d^2^3=540c^3d^6[/tex]
for i = 4 , we have,
[tex]\frac{6!}{4!\left(6-4\right)!}\left(3c\right)^2d^2^4=135c^2d^8[/tex]
for i = 5 , we have,
[tex]\frac{6!}{4!\left(6-4\right)!}\left(3c\right)^2d^2^4=18cd^{10}[/tex]
for i = 6 , we have,
[tex]\frac{6!}{6!\left(6-6\right)!}\left(3c\right)^0d^2^6=d^{12}[/tex]
Thus, adding all term together, we have,
[tex](3c+d^2)^6=729c^6+1458c^5d^2+1215c^4d^4+540c^3d^6+135c^2d^8+18cd^{10}+d^{12}[/tex]
Thus, Option (a) is correct.
HELP PLEASE?!
Multiply: 3x4(4x4 − x5 + 2)
A.) 7x8 − 3x9 + 6x4
B.) 12x8 − 3x9 + 6x4
C.) 12x4 − x9 + 6x4
D.) 12x16 − 3x20 + 6x4
Answer:
[tex]12x^8-3x^9+6x^4[/tex]
B is the correct option.
Step-by-step explanation:
We have to multiply the expression
[tex]3x^4(4x^4-x^5+2)
Using the distributive property a(b+c)=ab+ac
[tex]3x^4\times4x^4+3x^4\times(-x^5)+3x^4\times2[/tex]
Now, using the exponent rule [tex]x^a\times x^b=x^{a+b}[/tex]
[tex]12x^{4+4}-3x^{4+5}+6x^4[/tex]
On simplifying, we get
[tex]12x^8-3x^9+6x^4[/tex]
B is the correct option.
1. What is the apparent solution to the system of equations graphed above?
(0,-1)
(0,3)
(1,2)
(2,1)
Answer:
the answer is (,2)
Step-by-step explanation:
the system of solutions is the point that two equations/line cross
the two lines cross at (1,2)
4. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle at the peak. What angle does each side form with the ground? (1 point)
156°
146°
73°
78°
True or False
5. All right triangles are isosceles. (1 point)
true
false
14. What does CPCTC represent and when would you use it? (4 points)
1) 2x + 35 = 180° so x= 180 - 35 / 2 =73°
the answer is 73°
2)
3) In geometry, "Corresponding parts of congruent triangles are congruent" (CPCTC) is a succinct statement of a theorem regarding congruent trigonometry, defined as triangles either of which is an isometry of the other. CPCTC states that if two or more triangles are congruent, then all of their corresponding angles and sides are congruent as well. CPCTC is useful in proving various theorems about triangles and other polygons.
If triangles ABC and DEF are congruent, denoted as
Final answer:
Each congruent side of the A-frame house forms a 73° angle with the ground, and the statement that all right triangles are isosceles is false. CPCTC is a geometric theorem that states corresponding parts of congruent triangles are congruent.
Explanation:
Angles in an A-frame house
The given A-frame house forms an isosceles triangle with a peak angle of 34°. Using the theorem that the sum of angles in a triangle is 180°, we can calculate the angles each side forms with the ground. Since the two congruent sides are equal, the angles they form with the ground are also equal. There are two steps to solve this:
Subtract the peak angle from 180° to find the sum of the two base angles: 180° - 34° = 146°.
Divide the sum of the base angles by 2 (since they are equal in an isosceles triangle): 146° / 2 = 73°.
Therefore, each side forms a 73° angle with the ground.
All right triangles are isosceles - True or False?
This statement is false. Not all right triangles are isosceles. A right triangle is defined as having one 90° angle, but it doesn't necessarily have two sides of equal length, which would make it isosceles.
What does CPCTC represent?
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It is a theorem used in geometry to conclude that the corresponding parts (angles or sides) of two triangles are congruent, given that the triangles themselves are proven to be congruent based on certain criteria like side-angle-side (SAS) or angle-side-angle (ASA).
Which algebraic expression represents “the product of a number and five”?
Answer:
5n
Step-by-step explanation:
group of answer chances below
A. n - 5
B. 5n
C. 5 + n
D. 5/n
1. The Spokesman-Review wants to know the public opinion on the construction of a new library downtown. It is decided that 48 people will be surveyed using a simple random sample. Which of the following will produce a simple random sample?
Number the residents using the latest census data, then use a random number generator to pick 48 people.
Record the opinion of the first 48 people who visit the newspaper's website.
Survey every fourth person who enters the current library until 48 have responded.
Randomly select 48 people from the phone book.
Randomly select 12 people each from the downtown, south hill, northwest, and hillyard parts of the city.
2. The Morning News radio station is interested in predicting the proportion of registered voters who support an increase in the state sales tax. Listeners were asked to go to the station's website and indicate whether they favored an increase in the tax in order to support the State Park system. 1744 listeners logged on and 922 were against the increase. The population of interest is:
All people who listen to the station
The 1744 listeners who logged in and indicated their preference
The 922 listeners who were against the issue
All registered voters
Only the portion of the 1744 listeners who voted that are actually registered to vote
Answer:
(a) Number the residents using the latest census data, then use a random number generator to pick 48 people.
(b) The 1744 listeners who logged in and indicated their preference
Step-by-step explanation:
(a) Sampling method is said to be Simple Random Sampling if unit from the population are drawn randomly without any criteria, such that each unit as same chance of selection.
Since, In only first option each unit has same chance of selection. Thus, method of selection is Simple Random Sample.
(b) Since, population of interest is asked and 1744 listeners logged on in the support of State Park.
Thus, first option is correct.
Katie cut out a rectangular piece of wrapping paper that was 2 times as long and 3 times as wide as the box that she was wrapping. the box was 5 inches long and 4 inch's wide. what is the perimeter of the wrapping paper that katie cut?
Steve is buying a home worth $275000. His closing costs will amount to 6%, & his down payment is 15%. How much is each fee.
A. The closing cost are $16,500, & the down payment is $41,250.
B. The closing cost are $16,500, and the down payment is $42,000
C. The closing cost are $42,500, & the down payment is $165,000
Answer: For Plato users
A. The closing costs are $16,500 ,and the down payment is $41,250
Step-by-step explanation:
Just took the test
The closing costs are $16,500, & the down payment is $41,250.Option A is correct.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol. The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages.
It is given that, Steve is buying a home worth $275000. His closing costs will amount to 6%, & his down payment is 15%
Closing cost = 6 % of $275000
Closing cost = 6/100 × $275000
Closing cost = $16500
Down payment = 15% of $275000
Down payment = 15/100 × $275000
Down payment = $41,250.
Thus closing costs are $16,500, & the down payment is $41,250.Option A is correct.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ5
Intr un oras sunt 235 de blocuri cu 8 etaje si cu 177 mai multe blocuri cu 4 etaje.Formuleaza intrebarea pentru a rezolva problema astfel
Which ordered pairs are solutions to the inequality 2x + y > −4?
Select each correct answer.
A. (−3, 0)
B. (0, 1)
C. (−1, −1)
D. (5, −12)
E. (4, −12)
The probability that it will rain today is 0.4, and the
probability that it will rain tomorrow is 0.3. The
probability that it will rain both days is 0.2.
Determine the probability that it will rain today or
tomorrow
Final answer:
The probability that it will rain today or tomorrow, given the individual probabilities and the joint probability for both days, is calculated using the addition rule of probability, resulting in a probability of 0.5 or 50%.
Explanation:
The student is asking how to calculate the probability that it will rain today or tomorrow given the individual probabilities for rain on each day and the joint probability that it will rain on both days. This is a typical question involving the addition rule of probability.
To find the probability of either event A (rain today) or event B (rain tomorrow) occurring, we use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Where:
P(A) is the probability that it will rain today, which is 0.4,
P(B) is the probability that it will rain tomorrow, which is 0.3, and
P(A and B) is the probability that it will rain on both days, which is 0.2.
Substituting the given values, we get:
P(A or B) = 0.4 + 0.3 - 0.2
P(A or B) = 0.5
Therefore, the probability that it will rain today or tomorrow is 0.5, or 50%.
What statement makes the open sentence 3x + 20 = 5x + 6 true? x = 13 x = 2 x = 4 x = 7
Complete these ordered pairs for this equation.
How old will Bill be in 10 years if he is x + 2 years old now?
Which expression represents this?
(x + 2) - 10
(x + 2) + 10
10(x + 2)
The gray area is the sidewalk. the area of the sidewalk is ___________ square units.
Answer:
72
Step-by-step explanation:
Each student wrote a two step equation. peter wrote the equation 4x - 2 =10, and andres wrote the equation 16x - 8 = 40. the teacher looked at their equations and asked them to compare them. describe one way in which the equations are similar
Both equations are two-step equations involving a variable term multiplied by a constant and then subtracting another constant. Peter's is 4x - 2 = 10 and Andres's is 16x - 8 = 40.
One way in which Peter's equation 4x - 2 = 10 and Andres's equation 16x - 8 = 40 are similar is that they both involve a variable term multiplied by a constant and then subtracting another constant.
In Peter's equation, 4x represents four times a variable x, and then subtracting 2 from the result.
Similarly, in Andres's equation, 16x represents sixteen times a variable x, and then subtracting 8 from the result.
This common structure of multiplying a variable term by a constant and then subtracting another constant makes both equations two-step equations, even though the specific values and constants differ.
One estimate of the population of the world on January 1, 2005, is 6,486,915,022. The population is estimated to be increasing at the rate of 1.4 percent per year. At this rate, what will the population of the world be on January 1, 2024? Round your answer to the nearest whole number. ...?
The gift shop at manatee mall was having a clearance sale. everything was marked down 30%. the original price of a manatee hat was $18. what is the clearance price?
Answer
Find out the what is the clearance price .
To prove
As given
The gift shop at manatee mall was having a clearance sale.
everything was marked down 30%.
The original price of a manatee hat was $18.
30% is written in the decimal form
[tex]= \frac{30}{100}[/tex]
= 0.30
Than
The clearance price = 18 - 0.30 × 18
= 18 - 5.4
= $12.6
Therefore the clearance price be $12.6 .
If f(x) = √x + 12 and g(x) = 2√x, what is the value of (f-g)(144)?
-84
–60
0
48
we have
[tex]f(x)=\sqrt{x}+12[/tex]
[tex]g(x)=2\sqrt{x}[/tex]
we know that
[tex](f-g)(144)=f(144)-g(144)[/tex] -------> equation A
Step 1
Find the value of [tex]f(144)[/tex]
For [tex]x=144[/tex]
substitute in f(x)
[tex]f(144)=\sqrt{144}+12[/tex]
[tex]f(144)=12+12[/tex]
[tex]f(144)=24[/tex]
Step 2
Find the value of [tex]g(144)[/tex]
For [tex]x=144[/tex]
substitute in g(x)
[tex]g(144)=2\sqrt{144}[/tex]
[tex]g(144)=2(12)[/tex]
[tex]g(144)=24[/tex]
Step 3
Find [tex](f-g)(144)[/tex]
Substitute the values in the equation A
[tex]24-24=0[/tex]
therefore
the answer is the option
[tex]0[/tex]
Hailey has a summer job at the water slide park. She earns $9.50 an hour as a lifeguard, but never works more than 25 hours in a week. She determines that her salary is modeled by the function s = 9.5h. What is the domain of this function in this situation? A) s ≤ 237.50 B) all real numbers C) {0 ≤ h ≤ 25} D) {0 ≥ h ≥ 25}
Answer: C) {0 ≤ h ≤ 25}
Step-by-step explanation:
The domain of a function is the set of all values for independent variable for which the function must be defined.Given: The amount earned by Hailey for one hour work =$9.50
She determines that her salary is modeled by the function [tex]s = 9.5h[/tex].
Here h is the independent variable such that 's' is dependent on 'h'.
Since she never works more than 25 hours in a week.
Therefore, the maximum hours she will work = 25
Hence, the domain of this function in this situation is {0 ≤ h ≤ 25}, where h is number of hours she works.
how many 16s go into 57
*Need Help??!!
Which table is a probability distribution table?
Photo is attached.
Answer: Hi!
in a probability table, the x represents a given event, and p is the probability of such event.
There are two rules if you have n events; then p₁ + p₂ + ... + pₙ = 1, this is because the probability is normalized.
whit this info you can discard the third option, because there is a probability bigger than 1, and then the addition of al the probabilities is bigger than 1.
The second rule is that there do not exist negative probabilities (because they don't have sense) then you can also discard the second option.
Now we need to check the first and the fourth options, we need to add the 4 probabilites in each and see if the result is 1.
for the first options we have :
0.2 + 0.35 + 0.15 + 0.25 = 0.95
this is not normalized, this is not a probability distribution table.
for the fourth option we have:
0.4 + 0.15 + 0.25 + 0.2 = 1
this is normalized, then this is a probability distribution table.
Then the only right answer is option 4.
At what value(s) of x does f(x)=x^4-18x^2 have a critical point where the graph changes from decreasing to increasing?
The values of x at which f(x) = x^4 - 18x^2 has a critical point and changes from decreasing to increasing are x = 3 and x = -3.
Explanation:To determine at what values of x the function f(x) = x^4 - 18x^2 has critical points where the graph changes from decreasing to increasing, we must find the first derivative of f(x), set it to zero, and solve for x. The first derivative of f(x) is f'(x) = 4x^3 - 36x. Setting the derivative to zero gives us 4x^3 - 36x = 0, which can be factored as 4x(x^2 - 9) = 0. The solutions to this are x = 0, x = 3, and x = -3.
Next, to determine if these points are minima (where the graph changes from decreasing to increasing), we must examine the second derivative, or use the first derivative test. The second derivative f''(x) is 12x^2 - 36. Entering our critical points into this equation, we find that for x = ±3, the second derivative is positive, indicating a minima, whereas for x = 0, the second derivative is negative, which indicates a maxima.
Thus, the values of x at which f(x) has a critical point and the graph changes from decreasing to increasing are at x = 3 and x = -3.
The critical points of the function [tex]f(x) = x^4 - 18x^2[/tex], we need to find the derivative f'(x) and set it equal to zero. The critical points are x = 0, -3, and 3. At x = -3, the graph changes from decreasing to increasing.
The critical points of the function[tex]f(x) = x^4 - 18x^2,[/tex] we need to find the derivative f'(x) and set it equal to zero. Let's find the derivative:
[tex]f(x) = x^4 - 18x^2[/tex]
[tex]f'(x) = 4x^3 - 36x[/tex]
Now, set f'(x) equal to zero and solve for x:
[tex]4x^3 - 36x = 0[/tex]
Factor out 4x:
[tex]4x(x^2 - 9) = 0[/tex]
Now, set each factor equal to zero:
4x = 0 → x = 0[tex]x^2 - 9 = 0[/tex] x = ±3So, the critical points are x = 0, -3, and 3.
To determine whether each critical point corresponds to a minimum, maximum, or an inflection point, we can use the second derivative test. The second derivative is:
[tex]f''(x) = 12x^2 - 36[/tex]
Evaluate f''(x) at each critical point:
At x = 0, f''(0) = -36 (negative), so x = 0 corresponds to a local maximum.At x = -3, f''(-3) = 72 - 36 = 36 (positive), so x = -3 corresponds to a local minimum.At x = 3, f''(3) = 108 - 36 = 72 (positive), so x = 3 corresponds to a local minimum.Therefore, at x = -3, the graph changes from decreasing to increasing.
If cosx=4/5,cscx<0, then sin2x=
cos2x=
tan2x= ...?
Given cosx = 4/5 and cscx < 0, we can find sin2x = -24/25, cos2x = 7/25, and tan2x = -3/8 using trigonometric identities.
Explanation:To find sin2x, cos2x, and tan2x given cosx = 4/5 and cscx < 0, we can use trigonometric identities. First, let's find sinx using the Pythagorean identity: sinx = sqrt(1 - cos^2x) = sqrt(1 - (4/5)^2) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5. Since cscx < 0, we know that sinx is negative. Therefore, we have sinx = -3/5.
Next, we can use the double angle identities to find sin2x, cos2x, and tan2x. The double angle identities state that sin2x = 2sinxcosx, cos2x = cos^2x - sin^2x, and tan2x = 2tanx / (1 - tan^2x).
Using the values we found earlier, we can calculate:
sin2x = 2(-3/5)(4/5) = -24/25
cos2x = (4/5)^2 - (-3/5)^2 = 16/25 - 9/25 = 7/25
tan2x = 2(-3/5) / (1 - (-3/5)^2) = -6/5 / (1 - 9/25) = -6/5 / (16/25) = -6/16 = -3/8
Learn more about Trigonometry here:https://brainly.com/question/11016599
#SPJ3
The correct values for sin2x, cos2x, and tan2x given that cosx = 4/5 and cscx < 0 are as follows:
sin2x = -24/25
cos2x = 7/25
tan2x = -24/7
To find these values, we will use trigonometric identities and the given information.
First, since cosx = 4/5 and cosx is positive, we know that x must be in the first or fourth quadrant. However, because cscx < 0 (which means sinx is negative), x must be in the fourth quadrant since cscx is the reciprocal of sinx.
In the fourth quadrant, sinx is negative, so we can find sinx using the Pythagorean identity:
sin^2x + cos^2x = 1
sin^2x = 1 - cos^2x
sin^2x = 1 - (4/5)^2
sin^2x = 1 - 16/25
sin^2x = 25/25 - 16/25
sin^2x = 9/25
Since sinx is negative in the fourth quadrant, sinx = -3/5.
Now, we can use the double-angle identities to find sin2x, cos2x, and tan2x:
sin2x = 2sinxcosx
sin2x = 2 * (-3/5) * (4/5)
sin2x = -24/25
cos2x = cos^2x - sin^2x
cos2x = (4/5)^2 - (-3/5)^2
cos2x = 16/25 - 9/25
cos2x = 7/25
tan2x = sin2x/cos2x
tan2x = (-24/25) / (7/25)
tan2x = -24/7
p=3h+3u solve for h
...?
p=3h + 3u subtract 3u from both sides
p-3u=3h now divide both sides by 3
h = p/3 - u
Mike’s weekly wages are $685.20. What is the amount after a 4.2% Social Security tax and a 15% Federal Withholding income tax are deducted? Round to the nearest cent.
Answer:
553.64 rounded to the nearest cent
or
553.65
Step-by-step explanation:
if cos2X=1/3 and 0<=2X<=pi, find cosX ...?
When cos2X=1/3 and 0<=2X<=pi, you can use the double angle formula for cosine to solve for cosX. The result is sqrt(6)/3.
Explanation:To solve for cosX given that cos2X=1/3 and 0<=2X<=pi, you need to use the double angle formula for cosine, which is:
cos2X = 2cos²X - 1
Plugging in 1/3 for cos2X, we get:
1/3 = 2cos²X - 1
Solving this equation for cos²X gives us :
cos²X = 2/3
The square root of this is ±sqrt(2/3), or ±sqrt(2)/sqrt(3). However, since X falls in the range 0<=X<=pi/2 (because 0<=2X<=pi), cosX is positive. Therefore:
cosX = sqrt(2)/sqrt(3) = sqrt(6)/3
Learn more about Trigonometry here:https://brainly.com/question/11016599
#SPJ12