The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
What is mean of rational zero ?
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.
Have given ,
f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex]
This is a fourth degree polynomial.
Using the rational root theorem, the possible zeros of the polynomial are the factors of 15.
We know that
Factors of 15 = ± 1, ±3, ±5, ±15
Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
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The graph of the equation y = x^2 − x − 6 is shown below
For what value or values of x is y=0?
x=−2 and x=3
x=2 and x=−3
x=−6 only
x=−2 only
For the equation y=0, there is much less math involved. This is because, no matter what, for any value of x, y must always be equal to zero.
What does y-intercept 0 mean?This is so because the y-intercept occurs at x = 0. X = 0, mx = 0, and Y = B at this point. When y = 0, we solve the equation for x to determine the x-intercept. The line crosses the x-axis at y=0,
Is the Y axis at Y = 0?You can mistakenly think of the line y = 0 as the y-axis, be aware of this. It's not right. Simply put, the line y=0 indicates that the y coordinate is always 0 for all locations (x, y) in the x-y plane, indicating that the line y=0 represents the x-axis.
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HELP ME PLEASE,IM DOING A FINAL.
Relation between base and height of parallelograms is a function [tex]f(x)=\frac{48}{x}[/tex].
What is a function?Relations called functions provide an output for each input. The characteristic that every input is associated to exactly one output defines a function as a relation between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
Calculation:Based on the values listed in the table for the parallelograms' base length and height, you can see that the base length grows by one unit, giving you the numbers 1, 2, 3, and 4. When base length increases by one unit, height reduces by 1/x, as shown in the following example:
Height and base length have the following relation:
[tex]f(x)=\frac{48}{x}[/tex]
where x is the base length and f(x) is the height.
[tex]f(1)=\frac{48}{1}= 48\\f(2)=\frac{48}{2}=24\\f(3)=\frac{48}{3}=16\\f(4)=\frac{48}{4}=12\\f(6)=\frac{48}{6}==6[/tex]
Relation between base and height of parallelograms is a function [tex]f(x)=\frac{48}{x}[/tex].
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Write y=-5/8x+3 in standard form using integers.
Answer:
5x + 8y = 24
Step-by-step explanation:
y = [tex]\frac{-5}{8}[/tex]x + 3 Add [tex]\frac{5}{8}[/tex]x to both sides
[tex]\frac{5}{8}[/tex]x + y = [tex]\frac{-5}{8}[/tex]x + [tex]\frac{5}{8}[/tex]x + 3
[tex]\frac{5}{8}[/tex]x + y = 3 Multiply all the way through by 8 to clear the fraction
[tex](\frac{8}{1})[/tex][tex](\frac{5}{8})[/tex]x + (8)y= (8)(3)
5x + 8y = 24
Work out the area of this shape.
3cm
4cm
7cm
6cm
Answer: the area of the shape=25.5 cm²
Step-by-step explanation:
This shape is composed of a rectangle and a trapezoid
The area of the rectangle= 3(4)
The area of the rectangle= 12 cm²
[tex]\displaystyle\\The\ area\ of\ the\ trapezoid=\frac{3+6}{2} (7-4)\\\\The\ area\ of\ the\ trapezoid=\frac{9}{2} (3)\\\\The\ area\ of\ the\ trapezoid=4.5(3)\\\\The\ area\ of\ the\ trapezoid=13.5 \ cm^2[/tex]
The area of the shape=12+13.5
The area of the shape=25.5 cm²
How can I grow my height?
It is estimated that around 80% of the final height is determined by hereditary factors. Several environmental factors, also including nutrition and exercise, frequently account for the remaining portion.
Explain the meaning of the term height?A variety of factors affect your overall height.
1. Consume a diet rich in fresh, fruits, and vegetables.
proteins from whole grains.
2. Use caution when using supplements:
Few situations call for the use of supplements to help children grow taller and elderly persons stop shrinking.
3. Get the appropriate amount of rest:
On occasion skipping sleep won't have a long-term impact on your height. However, issues could arise if you consistently clock less than the advised amount during adolescence.
4. Keep moving:
Regular exercise has a lot of advantages. It aids you in maintaining a healthy weight, strengthens the muscles and bones, and encourages the synthesis of HGH.
5. Take care of your posture:
You could appear shorter than they actually are if you have poor posture.
Additionally, slouching or slumping over time might change your actual height.
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Micah's gym is moving into a bigger space, where he can have more stationary bicycles and treadmills. Micah needs both stationary bicycles and treadmills in his gym. Let x be the number of bicycles and y be the number of treadmills. The number of new bicycles must be more than 13 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650. Select all of the constraints for this situation.
The constraints for this situation are x>0, y>0, 340x + 670y < 5650 and x>1/3y
Let the number of bicycles = x
and the number of treadmills = y
Since the number of new bicycles must be more than 1/3 times of the new treadmills.
Inequality representing the statement will be,
x>1/3y
Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,
Inequality will be,
340x + 670y < 5650
And the number of bicycles and treadmills should be greater than 0.
x > 0
y > 0
Therefore, constraints for this situation are, x>0, y>0, 340x + 670y < 5650 and x>1/3y
(Refer to the image attached for the complete question)
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Let the number of bicycles = x
and the number of treadmills = y
Inequality representing the statement will be,
x>1/3y
Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,
Inequality will be,
340x + 670y < 5650
And the number of bicycles and treadmills should be greater than 0.
x > 0
y > 0
Therefore, constraints for this situation are, x>0, y>0, 340x + 670y < 5650 and x>1/3y
a tile store charges $747.50 to install 115 square feet of tile. assuming they charge the same rate per square foot regardless of the amount of tile installed, how much would they charge to install 970 square feet of tile?
With the help of simple mathematical operations, we know that the cost of installing 970 ft² will be $6,305.
What are mathematical operations?A method of calculation: The most popular ones are (+, −, ×, ÷) for add, subtract, multiply, and divide.
However, there are many more, like square roots, logarithms, and squares.
It is most likely an operation if it isn't a number.
Example: The operation in 25 + 6 = 31 is added.
So, we know that:
The store charges $747.50 to install 115 ft² of tiles.
Then, the amount that will come to install 970 ft² tiles:?
Cost of installing 1 ft² of tiles:
747.50/115
$6.5
So, the cost of installing 1 ft² of tiles: is $6.5.
Now, the cost of installing 970 ft² tiles will be:
6.5 × 970
$6,305
Therefore, with the help of simple mathematical operations, we know that the cost of installing 970 ft² will be $6,305.
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Which graph is a histogram?
Answer: The second one.
How do you write a factor of 5?
On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
The factors of 5 are -
5
and 1
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Determine whether the pair of lines is parallel, perpendicular, or neither.
Answer:
Neither
Step-by-step explanation:
It is not opposite to each other (perpendicular) or the same slope (parallel)
How do you write more than 3 in math?
The way to write 'more than 3' is >3.
We have to find a way to write "more than 3" in a mathematical form.
The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number.
Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.
We can use this mathematical symbol here, in order to denote "more than 3" mathematically.
> 3 denotes that a number is more than 3.
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Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.
We can use this mathematical symbol here, in order to denote "more than 3" mathematically.
> 3 denotes that a number is more than 3.
If lambda belong to R and the domain of f(x) = log lambda x-2/x i [1,2) union (2,3], then lambda belong to
the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1. Then λ belongs to (0,1).
In the given question, if λ∈R and the domain of f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex] is [1,2)∪(2,3], then λ belong to
The given function is
f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex]
The function is belong in between [1,2)∪(2,3]. So
|x-2| ≠ 0 and |x| > 0
x ≠ 2 and x > 0
Since the value of x can not be equal to 2 and x value is always greater than 0. So
[tex]log_{\lambda}|x-2|\geqslant 0[/tex]
The value of |x-2| should be lies between 0 and 1 because x cannot be equal to 2 and greater than 1.
So 0< |x-2| < 1
If the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1.
Hence, 0 < λ < 1.
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Consider the economy whose data appear in the table below. Working-age population 100,000 Labor force 60,000 Unemployed 12,000 Instructions: Round your answers to one decimal place.
a. The unemployment rate is ___%.
b. The labor-force participation rate is ___ %.
a. The unemployment rate is 20%.
b. The labor-force participation rate is 60%.
According to the question,
Working age population- 100,000
Labour force - 60,000
Unemployed - 12000 instructions
a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:
Unemployment Rate = [tex]\frac{Number of unemployed People}{Labor force}[/tex] × 100
When an unemployed population is 12,000 and the labor force is 60,000,
the unemployment rate is = [tex]\frac{12000}{60000}[/tex] × 100 = 20%
b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:
Labor Force Participation Rate = [tex]\frac{Labor force}{working age population}[/tex] × 100
When the labor force is 60,000 and the working-age population is 100,000
Labor Force Participation Rate = [tex]\frac{60000}{100000}[/tex] × 100 = 60%
So, a. The unemployment rate is 20%.
b. The labor-force participation rate is 60 %.
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lucia is renting a stand up paddleboard from sunrise lake rentals. she is charged an initial rental fee and an additional cost per hour she rents the paddleboard.
this situation can be modeled as linear relationship
what does the slope of the line tell you about the situation?
A. including the initial rental fee, the toal cost to rent the paddleboard for 5 hours is $70
B. after the initial rental fee, the paddleboard costs an additional $12 every hour
C. lucia rents the paddleboard for 5 hours
D. the inital rental fee is $10
The slope of the situation means: B. after the initial rental fee, the paddleboard costs an additional $12 every hour
What is the Slope of a Linear Equation?If a situation is modeled as a linear relationship between two variables, the slope of the relationship is a measure of the strength and direction of the relationship between the two variables in that particular situation.
The slope is calculated as the change in the value of one variable (the "rise") over the change in the value of the other variable (the "run").
For example, consider a situation in which the number of hours that a student studies is related to their grades in a class. The slope of this relationship would indicate the strength and direction of the relationship between hours of study and grades in this particular situation.
A positive slope would indicate that as the number of hours of study increases, the grades also increase, while a negative slope would indicate that as the number of hours of study increases, the grades decrease.
To find the slope of the situation that is represented in the graph given, use two points on the line to calculate the slope.
Using (0, 10) and (2.5, 40)
Slope (m) = change in y / change in x = (40 - 10) / (2.5 - 0)
= 30/2.5
Slope (m) = 12
Therefore, this means that, B. after the initial rental fee, the paddleboard costs an additional $12 every hour.
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Write an equation in slope-intercept form of the line that passes through the given points. $x$ $y$ $-4$ $9$ $-2$ $4$ $0$ $-1$ $2$ $-6$ $y=$
The equation of the line that passes through the given points in the slope-intercept form is y = (-5/2)x - 1
Writing equation of a lineFrom the question, we are to determine the equation of the line that passes through the given points
We will pick two value pairs from the table
Picking (-4, 9) and (-2, 4)
Using the formula,
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
Then,
(y - 9) / (x - (-4)) = (4 - 9) / (-2 - (-4))
Simplify
(y - 9)/(x + 4) = -5/(-2 + 4)
(y - 9)/(x + 4) = -5/2
Cross multiply
2(y - 9) = -5(x + 4)
2y - 18 = -5x - 20
2y = -5x -20 + 18
2y = -5x - 2
Divide through by 2
y = (-5/2)x - 1
Hence, the equation is y = (-5/2)x - 1
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What is the x and y intercepts of -4x+5y=20 and is (5,8) a solution?
Answer: Yes, (5,8) is a solution.
x=-5, y=4
x-intercept (-5,0)
y-intercept (0,4)
Step-by-step explanation:
To find the x-intercept, make y equal to 0 and solve
-4x+5(0)=20
-4x=20
x=-5
To find the y-intercept, make x equal to 0 and solve
-4(0)+5y=20
5y=20
y=4
To see if 5,8 is a solution, sub in and solve
-4(5)+5(8)=20
-20+40=20
20=20
Yes, (5,8) is a solution.
Hi can someone fully answer the question down below
Answer:
x= -10
Step-by-step explanation:
since its > not ≥, your only answer would be -10.
at the point -6, it would be =
when x= -10,
[tex]\frac{-10+3}{6}[/tex]>[tex]\frac{-10}{4}[/tex]+1
-7/6>-3/2
which is correct
When a truckload of oranges arrives at a packing plant, a random sample of 125 is selected and examined. The whole truckload will be rejected if more than 8% of the sample is unsatisfactory. Suppose that in fact 10% of the oranges on the truck do not meet the desired standard. What is the probability that the shipment will be rejected?.
The probability that the shipment will be rejected is 0.724.
Given :
Since we have given that
n = 125
p' = 8 % = 0.08
p = 10 % = 0.10
Test statistic value :
z = p' - p / [tex]\sqrt{p(1-p)/n}[/tex]
= 0.08 - 0.10 / [tex]\sqrt{0.10 * 0.90 / 125}[/tex]
= -0.75
p value at z = -0.75
p = 0.226
What is probability ?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Probability of shipment will be rejected = 1 - 0.226
= 0.724
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A rectangle has a height of 1 1/4 inches and a base of 5/6 inches. What is the area of the rectangle?
How many 5 digit numbers can be formed using all the digits with repetition the digits being 0,1,2,3,4?
The number of 5 digit numbers that can be formed is 3125
How to determine the number of 5 digit numbers that can be formed?From the question, we have the following parameters that can be used in our computation:
Digits = 0, 1, 2, 3, 4
These digits can be repeated
So, we have
n = 5 i.e. the count of digits in 0, 1, 2, 3, 4
The number of 5 digit numbers is then calculated as
Count = n⁵
So, we have
Count = 5⁵
Evaluate
Count = 3125
Hence, the count is 3125
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Andy bought 300 shares of a corporation that manufactures kitchen cabinets. He
bought the stock years ago for x dollars. He recently sold this stock for y dollars.
Express his capital gain as a percent of the original purchase price algebraically.
The equation for capital gain as a percent of the original purchase price will be equal to a = (y - x)/x × 100.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. A mathematical operation like reduction, addition, multiplication, or division is used to include terms in an expression.
As per the given information in the question,
Use the equation for capital gain,
Let the selling price be y and the purchase price is x dollars.
Capital gain = Selling price - Purchase
Substitute the values,
Capital gain = y - x
Now, let's find out the percent increase.
Let's assume that 'a' is the percent increase.
So, the equation will be,
(a)(x) = y - x
ax = y - x
Divide both sides by x.
(ax)/x = (y - x)/x
a = (y - x)/x
Multiply the equation by 100 to show in percentage form,
a = (y - x)/x × 100
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What are the types of expression?
There is major 3 types of expression. Numerical expression, algebraic expression and fractional expression.
What is numerical expression?This expression contains only two or more numbers along with symbols or operator. There is no variable present.
such as 226÷113+2×22-11
or (44÷88) ×100%
the above sign is percentage sign we can determine a percent value
or∛ (64)
the above sign represents a cubic root
we get the value 4
What is fractional expression?The expression having two or more fractional terms along with symbols are called fractional expression. There are numerator and denominator from which we need to determine a common denominator to obtain a result.
such as, 4/5+3/4
we have 2 different denominators 5 and 4. we need to find a common denominator by multiplying both. 5x4
20
In the next, common denominator is divided by each denominator and the result is multiplied with each numerator.
(4×4+3×5)/20
hence, the result is 31/20
What is algebraic expression?
The expression contains both variables and numbers along with symbols are called algebraic expression. The algebraic expression having equal sign are termed as equation. Tha main purpose of using equation is to determine unknown value.
Algebraic expression are different types such as linear expression
2x+3-4y
2 and 4 are coefficient, 3 is constant
Polynomial expression as example 2x²-3y+4
Besides, we have other algebraic expression such as 3y+4 or x/4+y/3
and so on.
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What are the 4 forms of quadratic equations?
The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.
write the equation of the line that is parallel to the graph of 3x-y=5 whose y-intercept is (0,4)
Answer:
3x -y = -4
Step-by-step explanation:
You want the equation of the line parallel to 3x-y=5 through point (0, 4).
Parallel lineThe equation for the parallel will differ only in the constant. To find the new constant, use the given point coordinates for x and y.
3x -y = 3(0) -(4) = -4
The equation of the line is ...
3x -y = -4
How old should a kid count to 10?
Children who are 4 years old frequently count up to 1,0and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.
What is Counting?
In order to calculate the size of a set, or the number of items in a finite set, one must count. Calculating the amount or total number of items in a collection or group is what is meant when we say we are counting in arithmetic. To count, then, is to speak numbers in sequence while giving each item in a group a value based on a one-to-one correlation. Objects are counted using counting numbers.
Children who are eight years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.
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When Deema begins her drive, she is 400 mi from home. She drives at an average rate of 50 mph until she gets home. Draw a graph to represent this situation?
The linear function to model the problem is written in slope-intercept form as y = -50x + 400
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b
m = slope of lineb = y-interceptIn the question given, we can model a linear function to represent this.
Let x represent the distance covered.
The function can be written as;
f(x) = -50x + 400
This function represents the distance left till she gets home
Plotting this on a graph, we would have a straight line intercpeting the x-axis at (8, 0) and the y- axis at (0, 400)
Kindly find attached graph below.
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find k so that a and b will be orthogonal
Answer:
k = -5
Step-by-step explanation:
The scalar product of vectors a and b is zero when the vectors are orthogonal (perpendicular):
[tex]\boxed{\begin{aligned}\vec a \cdot \vec b & = |a||b| \cos \theta\\& = |a||b| \cos 90^{\circ}\\& = 0 \end{aligned}}[/tex]
[tex]\textsf{Therefore, $\vec a$\; and \;$\vec b$\; are orthogonal when\; $\vec a\cdot \vec b=0$}[/tex]
Given:
a = ⟨2, -2⟩b = ⟨−5, k⟩Substitute the given vectors into the formula and solve for k:
[tex]\implies \langle 2, -2 \rangle \cdot \langle-5, k \rangle=0[/tex]
[tex]\implies (2)(-5) +(-2)(k)=0[/tex]
[tex]\implies -10-2k=0[/tex]
[tex]\implies 2k=-10[/tex]
[tex]\implies k=-5[/tex]
After researching many different shoes, chris narrows down his choice to these two. Which shoes are the best deal?.
Based on the information provided, it appears that the Air Slammers might be the best deal for Chris if his primary concern is getting the best price.
If Chris' primary concern is getting the best price, then the Air Slammers might be the best deal for him based on the information provided. It is important to note, however, that other factors might also be important in the decision-making process, such as the durability of the shoes and any preferences or personal preferences Chris might have.
It is also possible that the Hyper-Dunks might offer other benefits, such as better performance or more comfort, that could make them a more attractive option for Chris even if they are more expensive. Ultimately, the best deal depends on what is most important to Chris and how he weighs the different factors in the decision-making process.
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A wheelchair ramp is 20 feet long. It rises 5.1 feet above the ground. What is its angle of inclination (angle of elevation), to the nearest degree
Answer:
θ = 15°
Step-by-step explanation:
The wheelchair ramp creates a right triangle figure. Look at the image I have attached to this response to see the figure.
⭐ What is the "angle of inclination"?
The angle of inclination is the base angle adjacent to the 90-degrees. The angle of inclination is often denoted as θ.
To solve for the angle of inclination, θ, we have to use the inverse of a trigonometric function.
⭐ What trigonometric function do we use?
Look at the side lengths you are given. Are they opposite of θ? Are they adjacent to θ? Are they the hypotenuse of the triangle? Whatever combination of 2 side lengths you have, see what trigonometric function uses those 2 side lengths.
We are given the side length opposite of θ and a side length that is the hypotenuse of the triangle. Therefore, we are going to use the sine function.
⭐ What is the sine function?
sin(θ) = opposite/hypotenuse
Now, we are going to create an equation of the wheelchair ramp using the sine function.
sin(θ) = 5.1/20
Next, find the inverse of the equation. Here is the inverse of the sine function:[tex]sin^{-1} (opposite/hypotenuse) =[/tex]
Let's substitute the opposite and hypotenuse into the inverse of the sine function and solve using a scientific calculator. Make sure to round to the nearest degree.
[tex]sin^{-1}(5.1/20) =[/tex]
∴ [tex]sin^{-1}(5.1/20)[/tex] ≈ 15°
What is discontinuity example?
Example of discontinuity in mathematical function is given by :
f(x) = ( x - 1 )/ ( x - 2) at x = 2.
Discontinuous function is defined as:
A function is said to be discontinuous if its left hand side limit is not equal to right hand side limit.It does not show the continuity of a function.Example of discontinuous function is given by :f(x) = ( x - 1 ) / ( x - 2 )
When x = 2 function does not defined .
Hence it is not continuous at x = 2.
Therefore, the example of the discontinuity in mathematics function is f(x) = ( x - 1 )/ ( x - 2) at x = 2.
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