The force the road exerts on the car as the car passes the highest point of the bump n=mg−mv²/R
Newton's second law of motion defines the behavior of objects for which all existing forces are not balanced.
The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.
The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.
The free-body diagram given below shows the forces on the car in the vertical direction. Newton’s second law then gives
∑F y=may = mv²/R
mg−n=mv²/R
n=mg−mv²/R
When n=0, mg=mv²/R
Then, v= √gR
A more gently curved bump, with a larger radius, allows the car to have a higher speed without leaving the road. This speed is proportional to the square root of the radius.
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Time to walk 3 1/3 miles on Saturday and 2 4/5 mile on Sunday how much farther does Tonya walk on Saturday then on Sunday
The distance that Tonya walk on Saturday more than on Sunday would be = 8/15 miles
What is distance?Distance is defined as the quantity that describes the space that exists between two locations in a field.
The number of miles Tonya covered on Saturday = 3 ⅓ miles
The number of miles that Tonya covered on Sunday = 2 ⅘
Therefore the distance that Tonya walk on Saturday more than on Sunday would be the difference between the distance covered in Saturday and Sunday.
That is; 3⅓ - 2⅘ ( change to single fraction form)
= 10/3 - 14/5
= 50-42/15
= 8/15
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Two fractions with the same denominator that have numerators 5 and 7 what would the denominator be?
The denominator could be any real value
How to determine the possible denominatorFrom the question, we have the following parameters that can be used in our computation:
Fraction = same denominator
Such that the numerators are 5 and 7
This means that the fractions can be represented as
Fractions = 5/x and 7/x
There is no restriction on the possible value of x
hence, the denominator is any value
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Let f(x)= x^2 + 7 and g(x)= x^2+2. Find the following functions, and simplify each as much as possible: your final answer should be a polynomial with only one term in each power of x. (a) f(x) + g(x) = (b) f(x) - g(x) = (c) f(x).g(x)= (c) f(x)/g(x)= (For part (d), you need not simplify as you did in (a)-(c).)
For function f(x)= x² + 7 and g(x)= x² + 2,
a) f(x) + g(x) = 2x² + 9
b) f(x) - g(x) = 5
c) f(x) . g(x) = x⁴ + 9x² + 14
d) [tex]\frac{f(x)}{g(x)} =\frac{x^2 + 7 }{ x^2+2}[/tex]
Consider given functions f(x)= x² + 7 and g(x)= x² + 2
a) To find addition of functions: f(x) + g(x)
f(x) + g(x)
= (x² + 7) + (x² + 2)
= x² + x² + 7 + 2 .............(associative property of addition)
= 2x² + 9 ................(combine like terms)
b) to find subtraction of functions : f(x) - g(x)
f(x) - g(x)
= ( x² + 7 ) - (x² + 2)
= 7 - 2
= 5
c) To find multiplication of functions: f(x).g(x)
f(x) . g(x)
= ( x² + 7 ).(x² + 2)
= x² (x² + 2) + 7(x² + 2)
= x⁴ + 2x² + 7x² + 14
= x⁴ + 9x² + 14 ................(combine like terms)
d) To find division of functions: f(x)/g(x)
[tex]\frac{f(x)}{g(x)}\\\\ =\frac{x^2 + 7 }{ x^2+2}[/tex]
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Find the slope of the line graphed below.
The slope of the given graph is 3/8 .
What is Graph ?
Graph can be defined as the visual representation in which we can represent the data.
Given in the graph,
We are given two points: (4, 5) and ( -4, 2 ). Slope is calculated as the change in y over the change in x, or rise over run.
The change in y is the difference of the two y coordinates (it doesn't matter the order): 5- (2) = 3
The change in x is the difference of the two x coordinates (this order depends on the order that you subtracted the y coordinates; they must be the same order): 4 - (-4) = 4+4 = 8.
So, the slope is 3/8
Therefore, The slope of the given graph is 3/8 .
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Figure out the polynomial being multiplied on top and then fill in the missing boxes
In order to factor your quadratic polynomials, the box method, as its name suggests, uses a box. You can divide your quadratic into its factors by using the box, which is essentially a square divided into four equal parts.
What is box method ?Be aware that not all quadratics can be factored. Some just lack relevant components. But if a quadratic polynomial does have components, you can utilize the box approach to simplify the operation.Drawing a square divided into four equal sections or a two-by-two grid is the first step. You then enter your first squared term into the upper left box and your final term into the lower right box. the product of your final term and first term.These new term's contributing components are found. You're seeking for a specific combination of elements that, when added together, give you your middle word. Write these elements in the two remaining empty boxes once you've identified this group of components. Your answer will remain the same no matter which empty box each term is entered into. Find the largest common factor for each row and column to determine the quadratic factors. The factors of your polynomial will then be determined by finding the biggest common factors from your columns and rows, respectively.Employing the Box Method
For our first quadratic, 6x2 - x - 12, let's utilize the box approach to solve it.
The first step is to create a two by two grid, as shown here:
using a box
Following that, we place the first term in the upper left box and the last term in the lower right box.
The Complete Question.
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A group of meteorologists recorded the
temperature in some cities at noon on one
day.
They recorded the temperature in Leeds using
a thermometer that measures to the nearest
0.1 °C and found that the temperature was
16.8°C.
The temperature in Copenhagen was 12 °C
colder than in Leeds, to the nearest degree.
The temperature in Valletta was 23 °C warmer
than the temperature in Copenhagen, to the
nearest degree.
Work out the lower and upper bounds of the
temperature at noon in Valletta.
Give your answer in °C.
The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.
What is Temperature?A physical number known as temperature expresses the concepts of hotness and coolness in numerical form. With a thermometer, the temperature is measured.Thermometers are calibrated using a number of temperature scales that have defined distinct reference points and thermometric substances. The most widely used scales are the Kelvin scale (K), which is mostly used for scientific reasons, the Fahrenheit scale (°F), and the Celsius scale (°C), formerly known as centigrade, with the unit symbol °C. In the International System of Units, one of the seven base units is the kelvin.The upper bound of Valletta = Upper bound of Leeds - Copenhagen +23
upper bound of Valletta = 16.8 -12+23
upper bound of Valletta = 27.8 °C
Lower bound of Valletta = 0.1 -12+23
Lower bound of Valletta = 10.9 °C
Hence, The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.
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Allison can sew three scarves in 75 minutes. How many scarves can she sew in four hours?
The number of scarves in 4 hours is 9.6
How to determine the number of scarves in 4 hoursFrom the question, we have the following parameters that can be used in our computation:
Rate = 3 scarves in 75 minutes
Time = 4 hours
The number of scarves is then calculated as
Scarves = Rate * Time
substitute the known values in the above equation, so, we have the following representation
Scarves = (3/75 minutes) * 4 hours
Evaluate the product
Scarves = 9.6
Hence, the number of scarves is 9.6
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A 20.00 g milk chocolate bar is found to contain 12.00 g of sugar.
A) How many milligrams of sugar does the milk chocolate bar contain?
B) What will be the amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g?
The amount of sugar present in the milk chocolate bar is, 12000 milligrams.
Given,
Amount of milk chocolate bar = 20.00 grams
Amount of sugar = 12.00 grams
The conversion used for grams to milligram is :
1 gram = 1000 milligram
As per question we are given that, 12 grams of sugar
As, 1 gram of sugar = 1000 milligram of sugar
So, 12.00 grams of sugar = (12/1) x 1000
= 12000 milligrams of sugar
Therefore, the amount of sugar present in the milk chocolate bar is, 12000 milligrams.
(b) THe reduced size is 3 g
3 g bar has 12x3/20 g of sugar
i.e 7.2 g
hence , he amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g is 7200mg.
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Find the unit vector perpendicular to the plane of given vectors.P =i−2j+ k^Q =2i+j−k^
The unit vector perpendicular to the plane of given vectors P =i−2j+ k and Q =2i + j − k is ( i + 3j + 5k )/√35
The vector that perpendicular to the plane is equal to the cross product of:
P ⨉ Q
Remember the properties of cross product of two vectors:
i ⨉ i = j ⨉ j = k⨉ k = 0
i ⨉ j = k
j ⨉ i = - k
j ⨉ k = i
k⨉ i = j
i⨉ k = -j
Hence,
P ⨉ Q = (i−2j+ k) ⨉ (2i+j−k)
= k + j +4k + 2i +2j - i
= i + 3j + 5k
The magnitude of P ⨉ Q is:
|| P ⨉ Q || = √(1² + 3² + 5²)
= √35
Therefore, the unit vector = ( i + 3j + 5k )/√35
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Merle tiene una oferta de un emisor de tarjeta de crédito para una APR del 0
% durante los primeros 60 días y una APR del 23,19 % después, con
capitalización diaria. ¿Qué tasa de interés efectiva se ofrece Merle?
UNA 26.00%
La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.
¿Cómo determinar la tasa de interés efectiva anual?
En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.
Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:
I = (1 + r / 36500)ⁿ
Donde:
r - Tasa de interés anual.n - Número de días.I - Ganancia por interés.La situación es descrita por la siguiente expresión matemática:
1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵
Donde R es la tasa efectiva de interés anual.
Finalmente, despejamos la variable correspondiente:
R = 21,375
La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.
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pair of equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36
The slope of the given lines are representing that these lines are perpendicular.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36
Slope intercept form of both equations of a line
1) y = -7/8x - 1
it is already in a slope intercept form
2) 32x - 28y = -36
-28y = -32x -36
y = 8/7x + 9/7
Since their slope is inverse and had a negative constant.
The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.
Therefore, The slope of the given lines are representing that these lines are perpendicular.
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HELP!!!!!
Make a table for each equation
y=x-2
Chart:
x -2 -1 0 1 2
y ? ? ? ? ?
I basically just need he y row
Within the database environment, a data model represents data structures with the purpose of supporting a specific problem domain.a. Trueb. False
True. A data model is an abstract representation of the data structures used in a database.
It is typically used to represent the structure of the data and the relationships between different elements of the data. Data models are used to define the structure of the data in a database, as well as the relationships between different elements of the data. A data model is a combination of entities, attributes, relationships, and constraints. It is used to describe the data that is stored in a database and how the data can be accessed and manipulated. The data model also defines the relationships between the different elements of the data, such as which element of the data is related to which other element. The data model also defines the constraints that must be met in order to ensure the integrity of the data. A data model is also used to define the data types that are used in the database and the operations that can be performed on the data. For example, a data model may define data types such as integers, strings, and dates, as well as operations such as arithmetic, comparison, and sorting. A data model also defines rules for the structure and organization of the data, such as which fields must be present in a record, the order in which records must be stored, and the types of relationships that can exist between records.
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Determine the number of lines of symmetry for the figure.
The figure has ✓line(s) of symmetry.
Select the angles of rotation, if any, that map the figure onto itself.
O 30°
O 90°
☐ 180°
dh
O 45°
O 120°
Answer:
The figure has 4 lines of symmetry.Rotating through angles 90° or 180° will map the figure to itself.Step-by-step explanation:
You want the number of lines of symmetry of the 4-leaved rose shown in the figure.
Lines of symmetryThe figure is symmetrical about a line through opposite petals. It is also symmetrical about a line through the space between petals. The attachment shows the 4 lines of symmetry.
Rotational symmetryThe petals have the same geometry, but are rotated 90° from each other. That means any rotation that is a multiple of 90° will map the figure to itself. (180° is a multiple of 90°)
The figure maps to itself when rotated 90° or 180°.
how many four digit decimal number that has an estimated value of 10 when rounded off to the nearest tenths place
Answer:
There are 10,000 four-digit decimal numbers that have an estimated value of 10 when rounded off to the nearest tenths place. This is because each decimal number from 0.0001 to 0.9999 will have an estimated value of 10 when rounded off to the nearest tenths place.
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The president wants the carpet in the east room of the whits house replaced the east room is 79 feet long by 36 feet wide how much carpet should the decorator order
Answer: the decorator should order 2,844 square feet of carpet to replace the carpet in the east room of the White House.
Step-by-step explanation:
Area = Length x Width
Area = 79 feet x 36 feet
Area = 2,844 square feet
Please help!! It’s due in 10 minutes!!! Also please explain how you got the answer!
Answer: 22 vaccines
Step-by-step explanation:
first, reduce the amount that doctors leave out from the total amount of a vial
6 - 0.5 = 5.5
next divide 5.5 by the amount that is given to each person, which will give you the number of vaccinations the doctor can give
5.5/ 0.25 = 22 vaccines
Sasha ran at a constant speed of 3.8 meters per 1/2 hour.Then walked 1.3 meters per second for 1/2 hour. How far did she run and walk in 60 minutes.
Answer: 2343.8 meters
Step-by-step explanation: If 3.8 meters is walked in 1/2 hours then another 4680 meters per hour is ran for a half hour is 2340 meters add those 2 together
Which graph is defined by f(x) = x²-x-2|?
O A.
О в.
OC.
O D.
graph A
graph B
graph C
graph D
Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10* micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
IIn a case whereby Transistors are used to build computer chips and the size of the earliest transistors was about 1 x 10* micrometers and today, transistors can measure smaller than 1 × 10-2 micrometer the numbert of times the old is as great as the size of transistors today is 1 × 10^6.
How can the size of transistors be known?The concept that will be use here is division. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math.
We were told that the side of the earliest form of transistors for computer was 1 × 10⁴.
In another sentence, we were told that the size of the transistor today is expressed as 1 × 10^-2
We can then know the difference in size will which will be
= 1 × 10^4 / 1 × 10^-2
= 1 × 10^6
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complete question:
Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10^4 micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
What is 11 divided by 2.5 and can you show the work
If you divide 11 by 2.5 you will end up with 4.4. Answer = 4.4
Find the slope between the points:
(1,7) and (-5, -11)
Slope between the points (1,7) and (-5, -11) is m = 18/6 as a decimal m = 3
What is slope?The slope of a hill describes its steepness. The steepness of a line follows a similar pattern. The rise between two points, which is the vertical change, is divided by the run, which is the horizontal change between those same two points, to determine the slope.
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
step1:
calculate the slope m using the slope formula
slope m=y2-y1/x2-x1
with (x₁, y₁ )=(1,-5) and (x₂, y₂ ) =(-5,-11)
step2:
m=-11-7/-5-1=-18/-6=18/6
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is there a value of a that makes the statement |a| = - 2 true ? Explain your reasoning.
Answer:
No, there is no value of a that makes the statement |a| = -2 true.
Step-by-step explanation:
The absolute value of a number is the distance of that number from zero on the number line. It is always non-negative, so it can't be -2. The absolute value of a number is denoted by two vertical lines on either side of the number like this |a|.
For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. In both cases, the distance from zero is 5.
In the statement |a| = -2, the absolute value of a is -2, which is impossible as the absolute value can't be negative. Therefore, there is no value of a that makes the statement true.
Answer:
no
Step-by-step explanation:
You want to know if there's any value of the variable 'a' that would make its absolute value be -2.
Absolute valueThe absolute value of a number is always positive. There is no such thing as a number whose absolute value is negative, not -2 or any other negative number.
such a value of 'a' Does Not Exist (DNE)
Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³
The values of (f + g) (x), (f - g) (x), (fg) (x) and (f /g) (x) for the functions are x/(x + 9) + x³, x/(x + 9) - x³, x³/(x³ + 9) and 1/ [x² (x + 9)] respectively
How to determine the values for the functions?
A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Since f(x) = x/(x + 9), g(x) = x³
(a) (f + g) (x) will be the addition of f(x) and g(x). That is:
(f + g) (x) = x/(x + 9) + x³ or x³ + x/(x + 9)
(b) (f - g) (x) will be the subtraction of f(x) and g(x). That is:
(f - g) (x) = x/(x + 9) - x³
(c) (fg)(x) substitute x = x³ into f(x). That is:
f(x)= x/(x + 9), g(x) = x³
(fg)(x) = x³/(x³ + 9)
(d) (f/g)(x) will be the division of f(x) by g(x). That is:
(f/g)(x) = [x/(x + 9)] / x³ = x/ [x³ (x + 9)] = 1/ [x² (x + 9)]
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The vertices of triangle xyz are x=(-2,6), y=(4,10), and z=(14,6). Find the coordinates of the centroid of triangle xyz
The centroid of the given triangle is =(5.3 , 7.3)
What is Centroid of triangle?The centroid is the term for the object's geometric centre. We apply the centroid formula to find the triangle's centroid's coordinates. The intersection of a triangle's three medians yields the centroid, or centre, of the triangle. All of the medians are divided by the centroid of a triangle in a 2:1 ratio.
The centroid formula of a given triangle can be expressed as,
C = ((x1+x2+x3)/3 , (y1+y2+y3)3/3)
where,
C denotes the centroid of a triangle
x1,x2,x3 are the x-coordinates of the 3 vertices.
y1,y2,y3 are the y-coordinates of the 3 vertices
To find: Centroid of a triangle.
We are taking the Cordinates of the traiangle XYZ
as x1,y1,x1,y2,x3,andy3
so,Given parameters are,
(x1,y1)=(-2,6)
(x2,y2)=(4,10)
(x3,y3)=(14,6)
Using centroid formula,
The centroid of a triangle = ,
=-2+4+14/3 6+10+6/3
=5.3 7.3
The centroid of a triangle is ==(5.3 and 7.3)
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
0.325
0.625
0.750
0.875
Answer:
0.750
Step-by-step explanation:
Yellow sections: section 2 and section 3
Number of yellow sections: 2
Number of non yellow sections: 6
Total sections: 8
p(not yellow) = 6/8 = 0.75
Answer:
0.750
Step-by-step explanation:
you take a quarter and then you divide and think
Find the volume, V, of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of
y=x^2, x=y^4
To solve for the volume of the rotated region we will use the integration and its formula is V=π∫ba(r21−r22)h where r1 and r2 are the radii of the washer and h is the height. Note that the limits a and b is determined by finding the volume of the solid .
Using the washer method, the volume of the solid is
V=π∫ba[(x14)2−(x4)2]dx
Find the limits, equate the two equations in terms of x
4√x=x4
Raising both sides to fourth power,
x=x8x8−x=0
Factor out x
x(x7−1)=0
x=0,1
Thus, the limits is from x =
V=π∫10[(x^1/4)^2−(x4)^2]dx
Integrate this equation with in limits 0 to 1
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Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building, what is the height of the building? Show your work.
The height of the building that cast the shadow 98 feet will be 61.25 feet.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.
Let 'h' be the height of the building. Then the equation is given as,
h / (90 + 8) = 5 / 8
h / 98 = 5 / 8
h = 98 x 5 / 8
h = 12.25 x 5
h = 61.25 feet
The height of the building that cast the shadow 98 feet will be 61.25 feet.
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Mr. Hanson assigned his students a trigonometry project. Each student was to use a clinometer to determine the angle of elevation to the sun followed by trigonometry to determine the length of their shadows. James and Andy were partners in this assignment. James stood tall and Andy found that the distance from the ground to the clinometer that James was holding was 5.5 feet. James determined the angle of elevation to the sun to be 35 derajat. Draw a picture and write an equation to model this scenario. Then solve for the variable without using your calculator (hint: you should still have a trig function in your answer).
The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35). To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). The answer is y = 4.51 feet.
y = 5.5sin(35)
y = 4.816
arcsin(4.816) = 35
4.816 = 5.5sin(35)
y = 5.5 arcsin(35)
y = 4.51 feet
The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35), which is the length of the shadow. To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). We can then use the Pythagorean Theorem to solve for y: 4.816 = 5.5sin(35), so y = 5.5 arcsin(35). The answer is y = 4.51 feet, so the length of the shadow is 4.51 feet. This demonstrates how trigonometry can be used to calculate the length of shadows, with the help of a clinometer.
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match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. enter the appropriate letter (a,b,c,d, or e) in each blank.
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials.
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. These functions are often used in applications such as navigation and surveying, as they allow us to calculate angles and distances in the real world. Examples of trigonometric functions include sine, cosine, tangent, cotangent, secant, and cosecant. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials. These functions are often used in engineering and scientific applications, as they allow for more precise calculations than trigonometric functions. Examples of non-trigonometric functions include polynomial functions, exponential functions, logarithmic functions, and hyperbolic functions. In each case, the function being used must be appropriate for the type of problem being solved. By understanding the differences between trigonometric and non-trigonometric functions, it is possible to choose the right function for the right problem.
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