32 rows are needed in the truth table that we would use to evaluate a logical statement in five variables
As per the given data:
If we have a logical statement in five variables then we have to determine how many rows we need in the truth table that you would use to evaluate it.
It is calculated by both from truth table and by using the formula.
A table with rows and columns is created for a compound statement, and the number of rows depends on the number of statements.
As we know that the formula for number of rows need in the truth table.
Number of rows = [tex]2^{n}[/tex]
Where n = Number of variables
Here given number of variables are 5.
n = 5
[tex]2^{n}[/tex] = [tex]2^{5}[/tex]
= 32
Therefore 32 rows are needed in the truth table.
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Total consumption of fruit juice in a particular country in 2006 was about 1.78 billion gallons. The population of that country in 2006 was 500 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? Use pencil and paper. Using the per person amount from this problem, about how many gallons would your class consume?
The average number of gallons of fruit juice consumed per person in the country in 2006 is 3.56 gallons per person
What is average number?The average value in a set of numbers is the middle value calculated by dividing the total of all the values by the number of values.
Given:
Total consumption of fruit = 1.78 billion gallons
= 1,780,000,000
Total population = 500 million
= 500,000,000
Average number of gallons of fruit juice consumed per person = 1,780,000,000 ÷ 500,000,000
= 3.56 gallons per person
About how many gallons would your class consume?
Assume, there are 7 students in your class
Average number of gallons of fruit juice consumed per person = 3.56 gallons / 7
= 0.50 gallons per student
Therefore, the average number of gallons of fruit juice consumed per person in the country in 2006 is 3.56 gallons per person
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a typical person has an average heart rate of 73.0 beats/min. how many beats does she have in 2.0 years? in 2.00 years? and finally how many beats in 2.000 years?
(a) The number of beats she have in 2.0 years is 7.6 × [tex]10^7[/tex].
(b) The number of beats she have in 2.00 years is 7.57 × [tex]10^7[/tex].
(c) The number of beats she have in 2.000 years is 7.574 × [tex]10^7[/tex].
In the question, a typical person has an average heart rate of 73.0 beats/min.
(a) We have to determine number of beats she have in 2.0 years.
This is a rounding off issue. Pay attention to the fact that 72.0 has three important figures, 2.0 has two, 2.00 has three, and 2.000 has four.
Conversion of 72 beats per minute to beats per year.
72 beats/min = [tex]\left(\frac{1 \text{ min}}{72.0 \text{ beats}}\right)\times\left(\frac{1.00 \text{ hr}}{60.0 \text{ min}}\right)\times\left(\frac{1.00 \text{ day}}{24.0 \text{ hr}}\right)\times\left(\frac{1 \text{ year}}{365.25 \text{ days}}\right)[/tex]
Now simplify
72 beats/min = 3.7869×[tex]10^7[/tex] beats/year
The average person's heart beats in two years are
= 3.7869 × [tex]10^7[/tex] beats/year × 2 years
= 7.5738 × [tex]10^7[/tex] beats
The answer is only two significant digits, or 2.0. The response is 7.6 × [tex]10^7[/tex] beats.
(b) We have to determine number of beats she have in 2.00 years.
The answer is three significant digits, or 2.00. The response is 7.57 × [tex]10^7[/tex] beats.
(c) We have to determine number of beats she have in 2.000 years.
The answer is 4 significant digits, or 2.0. The response is 7.574 × [tex]10^7[/tex] beats.
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X
Joe is buying 4 tires for his truck The table shows the prices and the advertised sales for the same type of tire at 4 tire stores.
Based on the advertised sales, at which store will Jimmy get the lowest price on 4 tires?
es ))
A)
B)
9)
D)
Store A: Buy 3 tires and get the 4th tire free
Store B: Buy 4 tires and receive $60 off the price of each tire
Store C: Buy 4 tires and receive $200 off the total price
Store D: Buy 4 tires and receive 20% off the total price
Answer:
C
Step-by-step explanation:
not D because B is better than D. not A, still expencive. C is the most reasonable for getting $200 off. unless total is over $600.
Answer:A Store A: Buy 3 tires and get the 4th tire free
Step-by-step explanation:its A
Find y and x in the following figure
The measure of x is 105° and the measure of y is 45°.
What is a square?A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
The given quadrilateral is square.
The diagonals of a square are angle bisectors. Therefore, the diagonals split the right angles of the square into two 45° angles.
Here, y°=45°
Here, a+60° =180°
a=120°
In quadrilateral y°+x°+a°+90°=360°
45°+x°+120°+90°=360°
x°+255°=360°
x°=105°
Therefore, the measure of x is 105° and the measure of y is 45°.
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Can someone please help me on this ASAP?!
A graph is said to represent a function if a vertical line drawn anywhere on the graph of a relation only intersects the graph once by Slope of 3.75b + 5: 3.75
How do you know that a graph represents a function?A graph is said to represent a function if and only if any vertical line intersects it at one precise location. The vertical line only ever crosses the graph D, as seen when looking at the graphs.The graph does not represent a function if a vertical line can cross it at two or more places.In order to represent a function, you often use a function rule, such as y=2.50x, where x is the independent variable and y is the dependent variable. By creating a graph, you may visualize your function. Making a table of inputs and their matching outputs before creating a graph is the simplest way to create a graph.Example:
F(b) = 3.75b + 25
Axis interception points of 3.75b + 25:
X intercepts :(-20/3).
Y intercepts :(0.25)
Slope of 3.75b + 5:
3.75.
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Part A
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000. Was the change in price a positive or negative change?
Answer:
Positive
V
Part B
What was the percentage of change in the price of the house?
Answer:
%
There was a 125% change in the price of the house.
The answer can be deduced to be above 100% because the revised price represented an increase from the initial 100,000.
Tom's house cost $100000 in the year 2000.
In 2008 he sold his house for $125000.
Whatever the case, in order to solve this problem,
you must divide 100,000 by 125,000 to discover the answer. 125,000/100,000=1.25.
Then 1.25 can be converted to 125%.
So, There was a 125% change in the price of the house.
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Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h at time t seconds after launch is h(t) = -16(t)^2 +80t. Find the domain of the function.
The domain of the function h(t) = -16(t)² + 80t is,
⇒ (- ∞, ∞)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation for this object's height h at time t seconds after launch is,
⇒ h(t) = -16(t)² + 80t
Now, The function is shown a Quadratic equation.
Hence, The domain of the function h(t) = -16(t)² + 80t is,
⇒ (- ∞, ∞)
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Mr.Honkenberg I planning for hi Superbowl party.If he he buy 18 chicken wing for $15 what i the cot of the wing in wing per dollar?
The cost of the wings per dollar is 1.2 wings per dollar ($15 / 18 wings = $0.83 per wing). The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18).
1. Divide the total cost of the wings ($15) by the number of wings (18).
2. The result of this calculation is the cost of each wing ($15 / 18 = $0.83).
3. Divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar).
The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18). This calculation will give the cost of each wing ($15 / 18 = $0.83). To find the number of wings per dollar, divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar). This means that for every dollar spent, 1.2 wings can be purchased.
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I need help with question 7 part (ii)
Answer:
18 years old
Step-by-step explanation:
H=17- A/
H=8hours
8=17- A/
-9=- A/
A=18years
what’s the answer??? please
The rational inequality is not provided, so it is not possible to determine the next smallest critical value, b. To determine the critical values, or the values of x that make the denominator of the rational inequality equal to zero, you would need to set the denominator equal to zero and solve for x.
What is rational inequality?Once you have the critical values, you would then need to determine the sign of the numerator and denominator around each critical value to determine which side of the critical value the solution is on. The next smallest critical value, b, would then be the next lowest value of x that is a solution to the inequality.To solve the inequality, you can follow these steps:Set the denominator of the inequality equal to zero and solve for xFactor the numerator and denominatorDetermine the critical values by finding the zeros of the denominatorTest each critical value by plugging it back into the inequalityExamine the signs of the numerator and denominator around each critical value to determine which side of the critical value the solution is on.The next smallest critical value, b, would then be the next lowest value of x that is a solution to the inequality.Graph the inequality on a number line and shade the solution setIdentify the solution set in interval notation.To learn more about rational inequality refer:
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Joel needs to make 200 milliliters of a solution that is 35% sulfuric
acid for science class.
In the cabinet there is a 15% sulfuric acid solution and a 55% sulfuric
acid solution.
How much of the 15% solution and how much of the 55% solution
does Joel need?
Round to the nearest milliliter if necessary.
The amounts of each solution are given as follows:
15% solution: 100 milliliters.55% solution: 100 milliliters.How to obtain the amounts?The amounts are obtained solving a system of equations, for which the variables are given as follows:
Variable x: amount of the 15% solution.Variable y: amount of the 55% solution.Joel needs to make 200 milliliters, hence:
x + y = 200.
x = 200 - y.
The rate is of 35%, hence:
0.15x + 0.55y = 0.35 x 200
0.15x + 0.55y = 70.
The solution for y is given as follows:
0.15(200 - y) + 0.55y = 70
0.4y = 40
y = 40/0.4
y = 100.
The solution for x is given as follows:
x = 200 - y
x = 100.
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In which situation is the distance traveled proportional to time?
Answer:
Step-by-step explanation:
honolululuulu
If I take a loan of 4500€ at 6.5% and pay it back in 4 years, how much interest will i pay?
The required simple interest would be the amount of 1,170€ on a 4500€ principal deposited for four years at a rate of 6.5%
We have been given data as:
Principal (P) = 4500€
Rate of Interest (R) = 6.5% = 6.5/100 = 0.065
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 4500 × 6.5% × 4
⇒ Simple interest = 4500 × 6.5/100 × 4
⇒ Simple interest = 4500 × 0.065 × 4
Apply the multiplication operation, and we get
⇒ Simple interest = 1,170€
Therefore, the required simple interest would be the amount of 1,170€.
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The graph represents the function f(x). Which set of points lie on its inverse f^-1(x)?
Answer:
Third choice: (1, -3); (2, 2); (3, 7)
Step-by-step explanation:
There are two ways to solve this
The easiest way to solve this is to understand that the inverse of a function f(x), denoted by f⁻¹(x) is nothing but a reflection of the function about the line y = x
What that means is that if (x, y) is a specific point on the line, then the inverse point will be (y, x). Basically we are swapping the x, y values
The 3 points on f(x) and the corresponding points on f⁻¹(x) are given below:
f(x) f⁻¹(x)
------ --------
(-3, 1) (1, -3)
(2, 2) (2, 2)
(7, 3) (3, 7)
From the options given we see that the 3rd choice gives the correct values
So answer:
Third choice: (1, -3); (2, 2); (3, 7)
I have not taken the trouble of finding the equation for the line and finding the inverse of that equation since it is not needed in this question
I'LL WRITE A GOOD REVIEW AND 5 STARS!
The original length is 250 meters and the scale drawing width is 0.67 cm
The original length of the landFrom the question (see attachment), we have the following parameters that can be used in our computation:
Scale length = 0.5 meters
So, we have
Original length = 0.5/(1/500)
Evaluate
Original length = 250
This means that the original length is 250 meters
The scale drawing widthHere, we have
Scale drawing width = 335 cm * 1/500
Scale drawing width = 0.67 cm
Hence, the scale drawing width is 0.67 cm
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What type of equation does the flight of a volleyball make on a serve?
Inverse Variation
Linear
Exponential
Quadratic
Answer:
Step-by-step explanation:
dedede duehdueheuhd it a
may u answer this with equation im very confused pls
Answer:
See explanation below.
Step-by-step explanation:
1. (-1, -1) and (2, -2)
m = -2+1 / 2+1
m = -1/3
2. (-1, -4) and (0, -1)
m = -1+4 / 0+1
m = 3/1
m = 3
3. (-4, 0) and (-2, -3)
m = -3-0 / -2+4
m = -3/2
4. (2, 0) and (0, -3)
m = -3-0 / 0-2
m = -3/-2
m = 3/2
5. (-1, 2) and (-4, -3)
m = -3-2 / -4+1
m = -5/-3
m = 5/3
6. (4, 3) and (1, -4)
m = -4-3 / 1-4
m = -7/-3
m = 7/3
solve these proportion for the variable x. Use the reasoning of scalling to solve
The value of x from the given proportion is given as x = 10 after scalling both side of the equation.
What is Ratio and Proportion ?A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is often read as "x is to y" but may also be written as "x: y" or "x/y." The proportion equation, on the other hand, states that two ratios are equal.
The equality of two ratios is referred to as proportion. There is never a difference between two comparable ratios. The ratio sign (::) is used to express proportions, which aid in solving problems with ambiguous amounts. To put it another way, a percentage is an equation or a claim that shows the equality of two ratios or fractions. If a: b = c: d, then four non-zero values, a, b, c, are said to be in proportion. Let's now compare the two ratios, 3:5 and 15:25. In this case, 3:5 and 15:25 may both be written as 3:5 = 3/5 and 0.6, respectively. We may argue that these two ratios are proportionate because they are both equal.
There are two types of proportions :
Direct ProportionInverse ProportionThe proportion is given by ,
x/12 = 15/18
⇒ multipling both side with 12 we get ,
x = (12*15)/18
⇒ x = 5 * 2 = 10
The value of x from the given proportion is given as x = 10.
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The value of x from the given proportion is given as x = 10 after scalling both side of the equation.
What is meant by equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.An equation that expresses a significant relationship between two or more variables is called a formula.There are two types of proportions :
==>Direct Proportion
==>Inverse Proportion
The proportion is given by ,
x/12 = 15/18
⇒ multipling both side with 12 we get ,
x = (12*15)/18
⇒ x = 5 * 2 = 10
The value of x from the given proportion is given as x = 10.
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What is 3.5 as a fraction in simplest form
Answer:
Mixed Number: [tex]\frac{7}{2}[/tex]
Regular [tex]3\frac{1}{2}[/tex]
Explantion \/ \/
A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale
What is the volume of the file cabinet?
The volume of file cabinet is equal to 26 / 3 cubic feet.
How to determine the volume of the file cabinet
The statement let us infer that file cabinet has the form of right prism with rectangular base, whose formula is shown below:
V = b · h · l
Where:
V - Volume, in cubic feet.b - Base width, in feet.h - Height, in feet.l - Base length, in feet.If we know that b = 2 1 / 6 ft (13 / 6 ft), h = 1 1 / 2 ft (3 / 2 ft) and l = 2 2 / 3 ft (8 / 3 ft), then the volume of the file cabinet is:
V = (13 / 6 ft) · (3 / 2 ft) · (8 / 3 ft)
V = 26 / 3 ft³
RemarkStatement present an anomalous character "2", correct statement is introduced below:
A locker measurement at the bottom as 2 1 / 6 ft wide, 1 1 / 2 ft high and 2 2 / 3 ft long.
Picture is missing but question can be solved by inferential approach.
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Salma is interested in purchasing a portable speaker. The regular price is $118, but the online store is having a 40% off sale. Which expression represents how to calculate the sale price?
The expression represents the :
40% of 118 = Answer - Regular price
The sale price is = $70.8
Now, According to the question:
"Information available from the question"
The regular price is $118,
but the online store is having a 40% off sale.
To find the sale price.
Now, 40% of 118 = 47.2
And the sale price will be:
$118 - $47.2
= 70.8
The expression represents the :
40% of 118 = Answer - Regular price
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The given point lies on the terminal side of an angle θ in standard position. Find the values of the six trigonometric functions of θ. 3. (−4, −3)
The six trigonometry ratios are:
sinθ = 3/5, cosθ = 4/5, tanθ = 3/4, cotθ = 4/3, secθ = 5/4, cosecθ = 5/3
The point is (4, 3).
Perpendicular = 3
Adjacent Side = 4
Using the Pythagorean Theorem we find the value of Hypotenuse.
h = [tex]\sqrt{4^2 + 3^2}[/tex]
h = √(16 + 9)
h = √25
h = 5
The value of six trigonometric functions are
sinθ = Perpendicular/Hypotenuse
sinθ = 3/5
cosθ = Adjacent Side/Hypotenuse
cosθ = 4/5
tanθ = Perpendicular/Adjacent Side
tanθ = 3/4
cotθ = Adjacent Side/Perpendicular
cotθ = 4/3
secθ = Hypotenuse/Adjacent Side
secθ = 5/4
cosecθ = Hypotenuse/Perpendicular
cosecθ = 5/3
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The complete question is:
The point (4,3) is on the terminal side of an angle in standard position, how do you determine the exact values of the six trigonometric functions of the angle?
The density of titanium is 4. 5 g/cm3. A titanium object is accelerating at a rate of 800 cm/s2. The mass of the object can be modeled by the function m(v) = 4. 5v, where v is the volume in cubic centimeters. Additionally, the force of the object can be found using the function F(m) = 800m. Which composite function can be used to find the force of the object based on its volume?
Which composite function can be used to find the force of the object based on its volume?
F(m(v)) = 177. 8v
F(m(v)) = 795. 5v
F(m(v)) = 804. 5v
F(m(v)) = 3,600v
F(m(v)) = 3,600 v composite function can be used to find the force of the object based on its volume. So the option d is correct.
We have to determine which composite function can be used to find the force of the object based on its volume.
The density of titanium is 4. 5 g/cm^3.
A titanium object is accelerating at a rate of 800 cm/s^2.
The mass of the object can be modeled by the function m(v) = 4.5v, where v is the volume in cubic centimeters.
The force of the object can be found using the function F(m) = 800m.
F(m(v)) = 800 × 4.5 v
F(m(v)) = 3600 v
As a result, the function that can be utilized to simulate the force depending on volume is 3600 v.
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adding and subtracting fractions with whole numbers
The steps for adding and subtracting fractions with whole numbers:
- Write the whole number in the form of a fraction.
- Convert the fractions to like fractions.
- Add/Subtract the numerators while the denominator remains the same.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part of fraction is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
In case of adding and subtracting fractions with whole numbers:
Let us assume that 'a' represents the whole number and [tex]\frac{x}{y}[/tex] be fraction
First we write the whole number in the form of a fraction.
So, a = [tex]a = \frac{a}{1}[/tex]
Now we find the LCM of the denominators of fractions [tex]\frac{a}{1} ,\frac{x}{y}[/tex] and then convert the given fractions to like fractions.
Let m be the LCM of the denominators of fractions [tex]\frac{a}{1} ,\frac{x}{y}[/tex]
So, the fractions becomes [tex]\frac{a}{m} ,\frac{x}{m}[/tex]
Last we Add/Subtract the numerators while the denominator remains the same.
i.e., [tex]\frac{a\pm x}{m}[/tex]
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The complete question is:
How to add /subtract fractions with whole numbers?
Jerry baked 5 apple pies to share equally among 3 of his friends. Jerry thinks each friend will get 3/5 of an apple pie. Do you agree? Support your answer
Yes, 3 apple pies divided among 5 people
Now, According to the question:
"Information available from the question"
Apple shared equally
Portion of each person = 3/5
A possible way that shows how the pies were shared.
7/5 is the ration of the pie to each individual (Jerry and his friends).
Provided that each individual got equal ration....
The ration can be divided into two
The numerator = 3
The denominator = 5.
The numerator shows the number of things that were shared.
Hence, 3 apples were shared.
The denominator shows the number of people involved.
Hence, 5 people were involved.
So, we can conclude that 3 apples were divided among 5 people.
Hence, 3 apple pies divided among 5 people.
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4hk/20h^2k in simplest form
The simplified form of the expression 4hk/20h²k is 1/5h.
What is the simplified form of the expression?Given the expression in the question;
4hk / 20h²k
To simplify, first cancel out the common factor of 4 and 20.
4hk / 20h²k
4(hk) / 4(5h²k)
hk / 5h²k
Next, cancel out the common factor of h and h²
h(k) / h(5hk)
k / 5hk
Now, cancel out the common factor of k
k(1) / k(5h)
1/5h
Therefore, the simplified form is 1/5h.
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Tenisha Gist has a sheet of brass that is 36 inches wide and cuts two pieces that are each 8 3/4 inches wide. What is the width of the leftover brass?
The width of the leftover brass is 18 1/2 inches.
How to determine the width of the leftover brass?From the question, we have the following parameters that can be used in our computation:
Initial length = 36 inches
Length of each piece = 8 3/4 inches
The width of the leftover brass is then calculated as
Width = Initial length - 2 * Length of each piece
substitute the known values in the above equation, so, we have the following representation
Width = 36 - 2 * (8 3/4)
Evaluate
Width = 18 1/2
hence, the width is 18 1/2 inches
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work out 16^3/2 ??????????????????????
Answer:
2048
Step-by-step explanation:
Find out what [tex]16^{3}[/tex] is:
16x16x16 =
4096.
Now lets divide it by 2:
4096/2 =
2048.
2048 would be your answer to your problem.
v = 14.2(12.5 - s) The velocity, , in meters per second, of an airplane seconds after landing is given by the equation above. What is the best interpretation of 14.2 as shown in the equation above? HURRYYYY TIMEDDD TESTTT
The best interpretation of 14.2 as shown in the equation above is the constant acceleration of the airplane.
What is the constant acceleration?A particle's acceleration is the rate at which its velocity changes over time. The term "constant acceleration" refers to the rate at which a particle's velocity changes. When acceleration is constant, the rate of change in velocity is also constant. In the absence of any acceleration, velocity remains constant.
When acceleration is positive, velocity becomes more significant. Acceleration causes a decrease in velocity. The value 14.2 in the equation above represents the constant acceleration of the airplane in meters per second squared (m/s^2). It is the rate at which the velocity of the airplane is changing with respect to time.
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Angle
x
= 076° and angle
y
= 111°.
Find the bearing of point A from point O.
The bearing of point A from point O is 256°.
What are bearings?In mathematics, a bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.
Given that, angle x= 076° and angle y = 111°.
Now, the bearing of point A from point O is
180°+ 076°
= 256°
Therefore, the bearing of point A from point O is 256°.
Learn more about the bearings here:
https://brainly.com/question/27962362.
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