Answers
The Linear inequality holds true for 21 ≥ x;
What is Linear Inequality?
The mathematical expression with unequal sides is known as inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to a symbol (), less than or equal to a symbol (), or not equal to a symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics. The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities.
In the given question, the given inequality given is:
-3(2x-11) ≥ 8x-9;
Solving the Inequality:
⇒-6x + 33 ≥ 8x - 9;
⇒33 + 9 ≥ 8x - 6x;
⇒ 42 ≥ 2x;
⇒ 21 ≥ x;
Hence,
The Linear inequality holds true for 21 ≥ x;
To learn more about Linear Inequality, visit:
https://brainly.com/question/24372553
#SPJ1
Related Questions
A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Answer:
When a die is rolled, here it's Total possible outcome is= 6
and sample space is = 2 ( i.e. 1 & 2)
So. Probability of getting less than 3 = 26
=13
That's it.
Step-by-step explanation:
A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum. About how much did the Tyrannosaurus rex weigh?
Answers
Tyrannosaurus rex weighs about 0.14 times the weight of Patagotitan mayorum
How to determine by how much Tyrannosaurus rex weigh
In solving the proportion of the weights we use multiplication of fractions
Multiplication is a mathematical operator to handle such operation
A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum
This is is written mathematically as
Tyrannosaurus rex weight, x = 1.4 * 1/10 * Patagotitan mayorum weight, y
x = 1.4 * 1/10 * y
x = 0.14 *y
x = 0.14y
Learn more about multiplication here:
https://brainly.com/question/29401139
#SPJ1
Using information provided please answer the following
Answers
1. The bank discount on the note of $6,000, which will mature in 160 days at 3.5%, is $93.33.
2. The noteholder will receive total proceeds of $5,906.67 after the 3.5% discount.
What is a bank discount?Bank discount is the difference between the discounted and face (par) values.
For example, if the bank discounts a note, the holder receives a smaller amount than the face value they would have received had they held the note till its maturity.
The bank discount represents the finance charge for cashing the note earlier than its due date.
Amount due at maturity = $6,000
Discount rate = 3.5%
Time (period) = 160 days
Days in the year for ordinary interest = 360 days
Bank discount = $93.33 ($6,000 x 3.5% x 160/360)
The proceeds = $5,906.67 ($6,000 - $93.33)
Thus, the bank discount refers to the difference between the face value and the discounted value resulting from receiving cash from a note before maturity.
Learn more about discounting notes at brainly.com/question/29399811
#SPJ1
Find the value of x (desperately need help with this please! Due today!)
Answers
Answer:
x=48
Step-by-step explanation:
the 2 given angles if added together we know it’ll be 180 degrees
3x-12+x=180
4x-12=180
+12. +12
4x=192
x=48
Hopes this helps please mark brainliest
a track coach creates an obstacle course for his team. the coach plots the locations of the three obstacles on the coordinate plane shown to the right. each unit on the coordinate plane represents three yards. a student starts at Obstacle A. Then runs south to obstacle b, and then runs west to obstacle c. what is the total distance, in yards, the student runs to get from obstacle a to obstacle c?
Answers
The Total Distance is 51 yards.
What are Coordinates?Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).
Given:
As, A and B have same x- coordinate
AB = | (y- coordinate of A) - (y- coordinate of B)|
= |5 - (-2)|
= 7
and, B and C have same y- coordinate
AB = | (x- coordinate of B) - (x- coordinate of A)|
= |3 - (-7)|
= 10
Then, Total distance= 7+ 10= 17
and, Total distance in yards = 17 x 3= 51 yards
Learn more about Coordinates here:
https://brainly.com/question/27749090
#SPJ1
can someone simplify 2\sqrt(6 and 3\sqrt(54))ft
Will mark brainliest
Answers
Answer:
2/sqrt6 = sqrt6/3
3/sqrt54 = sqrt6/6
2/sqrt6 + 3/sqrt54
= sqrt6/2
Step-by-step explanation:
Simplifying when there are radicals involved usually means "rationalizing".
Rationalizing means getting rid of the square root on the bottom of a fraction.
See image.
Part of the pride of being an American comes from the fact that most people that want jobs have jobs. However, this is not always the case. Sometimes, as happened in 2008, the economy slows down, and jobs become harder to find or keep. Businesses make less money and so can keep fewer people employed. Those people who lost their jobs then have less money to spend. Because they have less money to spend, other businesses make less money, and then they, too, have to cut workers. In the United States, these cycles always end and the economy recovers, but it can take a while. People have to get creative about making money if they lose their jobs. Sometimes, they can use the skills they used at their old jobs to make money independently. For example, people don’t buy many car stereos when the economy is bad. So, car stereo stores have to layoff some of their stereo installers. If an installer has a place to work, that person can install stereos without a store. Often, this person will charge less than the store where he or she used to work. Also, the installer will get to keep all of the money he or she charged. At the store where the installer used to work, the store would have made most of the money. During hard times, it is important to be open-minded. There are always ways to make money outside of a formal job, if a person is willing to do things he or she wouldn’t normally do. A computer programmer, for example, might not be able to find work as a computer programmer. However, if the programmer is good with his or her hands, he or she may be able to find work in construction. Lawns never stop growing, and many aspects of life do not stop just because the economy has slowed down. A person who lost a job at a supermarket may be able to mow lawns for money, or do many other things. Most importantly, a person who loses a job must not give up. One’s attitude is very important in determining if he or she will be successful. A hopeful person is more likely to find a new job. Also, a hopeful person will
Answers
The sentence which supports the idea that people can use the skills they used at their old jobs to make money independently is "If an installer has a place to work, that person can install stereos without a store."
The correct answer option is option C
A summary about employees and American economy down timeThe essay is about American employees where people who actually needs a job gets a job. Although, this is not always the case especially when the economy slows down.
This slow down in the economy causes businesses to make less profit, thereby, making most people to lose their jobs. The purchasing power of the unemployed (people who lost their job) will reduce causing a decrease in the amount of money made by businesses. This is like a vicious cycle.
However, people who are skilled can still earn a living by doing other available jobs or those who are creative can create new jobs for themselves. For instance, an accountant can become a sales person in a supermarket if he or she lost their job.
In conclusion, a person who lost their job must be determined, hopeful and hard-working and must never give up, most importantly, they should never be idle because an idle mind is the devil's workshop.
Complete question:
Which sentence supports the idea that people can use the skills they used at their old jobs to make money independently?
Answer choices
A"So, car stereo stores have to layoff some of their stereo installers."
B"Often, this person will charge less than the store where he or she used to work."
C. "If an installer has a place to work, that person can install stereos without a store."
D. "At the store where the installer used to work, the store would have made most of the money."
Read more on supporting sentences:
https://brainly.com/question/12809344
#SPJ1
(a) Write an equation representing the fact that the product of two consecutive odd Integers is 143. Use x to represent the smaller
integer.
(b) Solve the equation from part (a) to find the two integers.
(a) The equation is
Answers
The equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
According to the question,
We have the following information:
The product of two consecutive odd Integers is 143.
Now, let's take the smaller integer to be x.
Now, next consecutive odd integer:
(x+2)
So, we have the following expression:
x(x+2) = 143
[tex]x^{2} +2x = 143\\[/tex]
[tex]x^{2} +2x -143 = 0[/tex]
[tex]x^{2}[/tex]+13x-11x-143 = 0
Taking x as the common factor from first two terms and -11 from the last two terms:
x(x+13)-11(x+13) = 0
(x-11)(x+13) = 0
x-11 = 0 and x+13 = 0
x = 11 or x = -13
Next odd integer = 13 or -11
Hence, the equation representing the fact that the product of two consecutive odd Integers is 143 is x(x+2) = 143 where x represents the smaller number and the value of x is 11 or -13.
To know more about consecutive odd integer here
https://brainly.com/question/4249096
#SPJ1
You have 100 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.
Note: The length of the sum of three sides is 100. Let w be the width, find the length in terms of w, setup an equation for the area, then find the vertex (maximum) of your equation. Area of rectangle is length * width.
Answers
The length and width of the rectangular plot that will maximize the area are 50 feet and 25 feet respectively.
The vertex (maximum) of this equation is equal to 1,250 square feet.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = lw
Where:
A represents the area of a rectangle.w represents the width of a rectangle.l represents the length of a rectangle.Since one side of this rectangular plot along the river does not require fencing, the perimeter equation is given by:
P = 2(l + w)
100 = 2w + l
Making length the subject of formula, we have:
l = 100 - 2w
Therefore, the area of this rectangular plot would now be:
A = (100 - 2w)w
A = 100w - 2w²
Next, we would take the first derivative and equate to zero in order to obtain the maximum area:
dA/dw = 100 - 4w
0 = 100 - 4w
4w = 100
Width, w = 25 feet.
For the length of this rectangular plot, we have:
Length, l = 100 - 2w
Length, l = 100 - 2(50)
Length, l = 50 feet.
Now, we can find the vertex (maximum) of this equation is given by:
Maximum area = 50 × 25
Maximum area = 1,250 square feet.
Read more on area of a rectangle here: brainly.com/question/25292087
#SPJ1
Square of 10^4 is ?
Answers
As proof 10^2 times 10^2=10^4
Refer to this exponent sheet for future problems
There are three consecutive odd integers.Three times the largest is seven times the smallest. What are the integers?
Answers
The three consecutive odd intergers are 3,5 and 7
What do you mean by algebraic expression ?
An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.
An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.
Let the three consecutive odd integers are x, x+2 and x+ 4
Here x is the smallest odd integer and x+4 is the largest odd integer
According to the question:
3(x +4) = 7x
3x + 12 = 7x
7x - 3x = 12
4x = 12
x = 12/4
x = 3
Three consecutive odd integers become:
x = 3
x + 2 = 3 +2 = 5
x + 4 = 3 + 4 = 7
Hence, the three consecutive odd intergers are 3,5 and 7
To learn more about the algebraic expression from the given link.
https://brainly.com/question/28036476
#SPJ4
The arithmetic mean of the ages of 30 pupils is 15.3 years. One boy leaves the class and one girl is enrolled and the new average age of 30 pupils in the class becomes 15.2 years. How much older is the boy than the girl
Answers
The answer will be 3 years.
1st 30 pupils at average age of 15.3 yrs. give total age of 15.3 x 30 = 459yrs
2nd group of 30 pupils at average age of 15.2 yrs
give total age of 15.2 x 30 = 456yrs
Difference in age = 459 - 456
= 3 years.
SOMEONE PLS HELP ME!!!!!!Match the statements with their correct reason to complete the proof.
Given: AB = BC and AD = CD
Prove: Triangle ABD Triangle CBD
Answers
Proved that Triangle ABD ≅ Triangle CBD
Consider the triangle ABD and the triangle CBD
The length of the side AB = The length of the side BC
The length of the side AD = The length of the side cd
The third side is common
According to the SSS rule congruent . If the three side of the triangle is equal to the three sides of the another triangle then the both triangles are congruent
Then three sides of the triangle ABD is equal to the three sides of the triangle CBD, Therefore the triangle ABD and triangle CBD are congruent
Hence, proved that Triangle ABD ≅ Triangle CBD
Learn more about congruent here
brainly.com/question/22062407
#SPJ1
If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements. A. The x-intercept of the function is 3.
Answers
The true statement about the function is that (b) the y-intercept of the function is 3
How to determine the true statement?The mathematical statement of the representation of the function is given as
The function f(x) is the absolute value of 3 more than the value of x.
Mathematically, this can be represented as
f(x) = |x + 3|
To determine the y-intercept, we set the x value of the function to 0
This means that we calculate f(x) when x = 0
i.e. f(0)
Substitute the known values in the above equation, so, we have the following representation
f(0) = |0 + 3|
Evaluate the sum
This gives
f(0) = |3|
Remove the absolute bracket
f(0) = 3
Hence, the y-intercept is 3
Read more about absolute value functions at
https://brainly.com/question/10538556
#SPJ1
Possible question
If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements.
A. The x-intercept of the function is 3.
B. The y-intercept of the function is 3.
find slope intercept form and graph (-3,0) and (-3,-7)
Answers
Answer:
x = -3
Step-by-step explanation:
Slope = Rise/Run
Slope = Difference in y/Difference in x
Slope = -7/0
Slope = undefined (can not divide by 0)
This means that this is a vertical line
How many 2/5 can go into 1/2?
Answers
Part 1 A new bank customer with $5,000 wants to open a money market account. The bank is offering a simple interest rate of 1.9% a. How much interest will the customer earn in 20 years? b. What will the account balance be after20 years?
Answers
The account balance after20 years will be $6900 and the simple interest for 20 years is $1900
The Principal amount = $5,000
Rate of Interest (r) = 1.9 %
Time Period (t) = 20 years
The Simple Interest is given by
[tex]S.I. = \frac{P*r*t}{100}[/tex]
Now, putting the values on the formula, we get:
[tex]S.I. = \frac{5000*1.9*20}{100} = 1900[/tex]
Hence, the interest will be $1900
Now, The Account Balance after 20 years = $ (1900 + 5000) = $6900
To read more about Simple Interest, visit https://brainly.com/question/25663053
#SPJ1
Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year. Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Answers
Adam earned $100.12 more interest than the Sophie
Consider Sophie
The principal amount = $3330
The interest rate = 7.4%
The time period = 5 years
Simple interest = PRT
Where P is the principal amount
R is the interest rate
T is the time period
Substitute the values in the equation
Simple interest = 3330× (7.4/100) × 5
= $1232.1
Consider Adam
The principal amount = $2795
The interest rate = 8.1%
The time period = 5 years
Simple interest = 2795 × (8.1/100) × 5
= $1131.98
The difference = 1232.1 - 1131.98
= $100.12
Hence, the Adam earned $100.12 more interest than the Sophie
Learn more about simple interest here
brainly.com/question/11564235
#SPJ1
15.75 + .5x = 16.53 - .13x
Answers
Subtract 15.75 from both sides
.5x= 0.78-.13x
Add .13x to both sides
0.63x= 0.78
Divide .63 to both sides
x equals approximately 1.238
For a segment of a radio show, a disc jockey can play 5 records. If there are 7 records to select from, in how many ways can the program for this segment be arranged?
Answers
There are 2520 possible ways to arrange the programs
How to determine the ways the program can be arranged?From the question, we have
Total number of jockey records, n = 7
Total number of disc jockey records to select, r = 5
To determine the ways the program can be arranged, we make use of permutation
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 7 and r = 5
Substitute the known values in the above equation
So, we have the following representation
Total = ⁷P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)!
So, we have
Total = 7!/2!
Evaluate
Total = 2520
Hence, the number of ways is 2520
Read more about permutation at
brainly.com/question/11732255
#SPJ1
Solve one sixth times quantity x plus 24 end quantity equals negative 6
Answers
The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.
What is an expression?The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, the expression given will be illustrated as:
1/6x + 24 = -6
Collect like terms
x / 6 = -6 - 24
x/6 = -30
Cross multiply
x = -30 × 6
x = -180
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
What is –11 + |-5|-|-15|?
-1
-11
-9
-26
-21
Answers
Answer:
-1
Step-by-step explanation:
you would do -11 + (-5) which will be -16. Then do -16 - (-15) which will get you -1.
IXL Please Help Fast!
Answers
Answer:
Step-by-step explanation:
should be both line GJ and JK as well as line HK and JK
Guidance Missile System A missile guidance system has eight fail-safe components. The probability of each failing is 0.35
Assume the variable is binomial. Find the following probabilities. Round your answers to at least four decimal places.
Part: 0/4
Part 1 of 4
com Rem
(a) Exactly six will fail.
P(exactly six will fail) =
Answers
The probability of exactly six will fail = 0.0808
What is Probability?
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.
In the given question, we have:
We know that Probability in binomial distribution with total components ' n ', probability of success ' p ', and the number "of successes " = [tex]{ }^n c_k p^k(1-p)^{n-k}[/tex]
we know that:
[tex]{ }^n c_k=\frac{n !}{(n-k) ! k !}[/tex]
[tex]\begin{aligned}P(\text { success }) &=P(\text { a part fails })=0.35 \text {. So, } \\P(x=5) &={ }^8 C_5 \times(0.35)^5(0.65)^3 \\&=56 \times(0.005252) \times(0.274625) \\&=0.0808 \\& \text { (Round to } 4 \text {-decimals) }\end{aligned}[/tex]
Hence,
The probability of exactly six will fail = 0.0808
To learn more about Probability, visit:
brainly.com/question/24188569
#SPJ1
Please help. Find X and Y. NEED ASAP
Answers
Answer:
x=1.25 y=1.75
Step-by-step explanation:
8/10=5/5+x
50=8(5+x)
50=40+8x
50-40=8x
10=8x
x=10/8
x=1.25
while Y=8/10=7/7+y
70=8(7+y)
70=56+8y
70-56=8y
14=8y
y=14/8
y=1.75
How much should be deposited in an account paying 4.5% interest, compounded semiannually, in order to have a balance of $ 5,000 after 19 years and 6 months?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Principal ≈ $ ________
Answers
The amount that should be deposited in the account to earn a balance of $5, 000 after 19 years and 6 months is $2, 099.43
How to find the amount?First, find the periodic rate:
= 4.5% / 2 semi annual periods per year
= 2.25%
Find the number of periods:
= 19 years and 6 months = 19.5 years
= 19.5 years x 2 semi annual periods per year
= 39 periods
The amount to deposit in the account can be found by the future value formula:
Future value = Deposit x ( 1 + rate) ^ number of periods
5, 000 = Deposit x ( 1 + 2.25%)³⁹
Deposit = 5,000 / ( 1 + 2.25%)³⁹
= $2, 099.43
Find out more on semiannual compounding at https://brainly.com/question/14845705
#SPJ1
Match the equations with the value of x that makes them true. 2(2x − 3) = 6 5x − 2x − 4 = 5 x + 2x + 3 = 9 5(x + 3) = 25 4x − (2x + 1) = 3 5x − (3x − 1) = 7
Answers
Each of the equations should be matched with the value of x that makes them true as follows:
x = 2; x + 2x + 3 = 9, 5(x + 3) = 25, and 4x − (2x + 1) = 3.
x = 3; 2(2x − 3) = 6, 5x - 2x - 4 = 5, and 5x − (3x − 1) = 7.
How to determine the true equations?In order to determine which x-values are true solutions based on the given equations, we would have to test each of the values of x by substituting them into the equations as follows;
When x = 2, we have:
2(2x − 3) = 6
4x − 6 = 6
4(2) - 6 = 6
8 - 6 = 6
2 = 6 (False).
When x = 3, we have:
2(2x − 3) = 6
4x − 6 = 6
4(3) - 6 = 6
12 - 6 = 6
6 = 6 (True).
When x = 2, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(2) - 4 = 5
6 - 4 = 5
1 = 5 (False).
When x = 3, we have:
5x - 2x - 4 = 5
3x - 4 = 5
3(3) - 4 = 5
9 - 4 = 5
5 = 5 (True).
When x = 2, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(2) + 3 = 12
9 = 12 (False).
When x = 3, we have:
x + 2x + 3 = 9
3x + 3 = 9
3(3) + 3 = 12
12 = 12 (True).
5(x + 3) = 25
5x + 15 = 25
5x = 25 - 15
5x = 10
x = 2 (True).
4x − (2x + 1) = 3
4x - 2x - 1 = 3
2x = 3 + 1
2x = 4
x = 2 (True).
5x − (3x − 1) = 7
5x - 3x + 1 = 7
2x = 7 - 1
2x = 6
x = 3 (True).
Read more on equation here: https://brainly.com/question/24291977
#SPJ1
Five hours and 20 minutes after a raft left a dock, a patrol boat left the dock and traveled in the same direction as the raft. The boat caught up to the raft 20 km away from their starting point. What was the speed of the raft if the speed of the patrol boat was 12km/hr ?
Answers
The speed of the raft was 2.86 km/hr.
What is speed?Speed is defined as the rate of change of position of an object in any direction.
Given that, a patrol boat with speed of 12 km/hr caught a raft after travelling for 20 km and patrol boat left the dock after 5 hours and 20 minutes the raft left,
The time taken by the patrol boat to catch the raft is;
t = 20/15 = 5/3 hours
5/3 hours = 1 hour 40 minutes
Thus, it took 1 hour 40 minutes for the patrol boat to catch the raft
Thus, the raft was travelling for 5 hours 20 minutes plus 1 hour 40 minutes which 7 hours,
The speed of raft = 20/7 = 2.86 km/hr
Hence, The speed of the raft was 2.86 km/hr.
For more references on speed, click;
https://brainly.com/question/7359669
#SPJ1
please check the image
Answers
The trigonometric measures in the context of this problem are given as follows:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex][tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex][tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]How to obtain the trigonometric measures?We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.
To find the measure for half the angle, the cosine is needed to apply the identities, and the cosine is calculated by the following identity:
sin²(x) + cos²(x) = 1
[tex]\left(\frac{2}{3}\right)^2 + \cos^2{x} = 1[/tex]
[tex]\cos^2{x} = 1 - \frac{4}{9}[/tex]
[tex]\cos{x} = \pm \sqrt{\frac{5}{9}}[/tex]
The angle is in the first quadrant, in which the cosine is positive, hence:
[tex]\cos{x} = \sqrt{\frac{5}{9}}[/tex]
[tex]\cos{x} = \frac{\sqrt{3}}{3}[/tex]
Then, applying an identity, the sine for half the angle is given as follows:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]
Considering the calculated value for the cosine:
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]
[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex]
The identity for the cosine is:
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]
Hence:
[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex]
The tangent is obtained by the division of the sine and the cosine. The entire division can be placed into a single square root, and the common denominators of six are simplified, hence:
[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]
More can be learned about trigonometric measures at https://brainly.com/question/24349828
#SPJ1
The compression ratio in a certain engine is 7.5 to 1. If the expanded volume of a cylinder is 45 cu in., what is the
compressed volume?
Answers
If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .
In the question ,
it is given that ,
the compression ratio in a certain engine is 7.5 : 1 .
the expanded volume of a cylinder is = 45 in³ .
we have to find the compressed volume of the cylinder ,
let the compressed volume of the cylinder be = v .
the above situation can be represented as
7.5 : 1 = expanded volume : compressed volume
7.5/1 = 45/v
7.5 = 45/v
v = 45/7.5
v = 6 cubic inches .
Therefore , If the expanded volume of a cylinder is 45 in³ , then the compressed volume is 6 in³ .
Learn more about Ratio here
https://brainly.com/question/1865618
#SPJ1