write v as a linear combination of u1, u2, and u3, if possible. (enter your answer in terms of u1, u2, and u3. if not possible, enter impossible.
Answers
The v can be written as a linear combination of u1, u2, and u3 as:
v = -(1/9)u1 + (5/3)u2 - (4/3)u3
To find the linear combination of u1, u2, and u3 that equals v, we can use the method of solving a system of linear equations.
The equation for v in terms of u1, u2, and u3 is:
v = a1u1 + a2u2 + a3u3
where a1, a2, and a3 are the coefficients of the linear combination.
Plugging in the given values for v, u1, u2, and u3:
(-1,7,2) = a1(3,2,8) + a2(1,-3,-1) + a3(-2,1,-3)
We can solve this system of equations by equating the corresponding entries of the two vectors:
-1 = 3a1 + a2 - 2a3
7 = 2a1 - 3a2 + a3
2 = 8a1 - a2 - 3a3
We can then use any method to solve the system of equations, such as substitution, elimination or Cramer's rule.
By solving the system of equations we get:
a1 = -(1/9), a2 = (5/3), a3 = -(4/3)
Therefore, v can be written as a linear combination of u1, u2, and u3 as:
v = -(1/9)u1 + (5/3)u2 - (4/3)u3
It is possible to write v as a linear combination of u1, u2, and u3.
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Related Questions
Simplify. Need ASAP. show work
Answers
The simplified expressions that we have are;
a) 2∛16 - 12
b) (-375)^1/3x^8/3y^8/3
What is simplification?The term simplifications means that we have to write the expression is the easiest way that it can be written. In this case we have two expressions. We can be able to simplify them as we work through the steps that have been written below;
8) -2∛81 + 2∛16 - 2∛81
-4∛81 + 2∛16
-4(3) + 2∛16
2∛16 - 12
10) ∛-375x^8y^8
This simplifies to;
(-375)^1/3x^8/3y^8/3
This is the way that we can be able to simplify the expressions here.
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Let F(s)=5s2+4s+4 F ( s ) = 5 s 2 + 4 s + 4 . Find a value of d d greater than 0 0 such that the average rate of change of F(s) F ( s ) from 0 0 to d d equals the instantaneous rate of change of F(s) F ( s ) at s=1. s = 1.
Answers
The required value of d for the given function is given as d = 2.
The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol
Here,
F(s) = 5s²+ 4s +4
F'(s) = 10s + 4
F'(1) = f(d) - f(0)/ d
10(1) + 4 = 5d² + 4d / d
14 = 5d +4
d = 2
Thus, the required value of d is given as d = 2.
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A sum of £36000 is divided between ALex ,Bill and claire by the ratio of 2 ×3/4 : 1×1/2 : 2×1/4 what is the amount each individual gets
Answers
so hmm £36000 will be split, hmmm let's call the ratios "a,b and c", so the amount will be split in ratios of a : b : c, which means we'll be dividing the 36000 bucks by (a + b + c) and distribute accordingly, let's do that, hmm let's convert also all those mixed fractions to improper fractions.
[tex]\stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} ~\hfill \stackrel{mixed}{1\frac{1}{2}} \implies \cfrac{1\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{3}{2}} \\\\\\ \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} ~\hfill \boxed{\cfrac{11}{4}+\cfrac{3}{2}+\cfrac{9}{4}\implies \cfrac{13}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{36000}{~~ \frac{13 }{2 } ~~}\implies 36000\cdot \cfrac{2}{13}\implies \cfrac{72000}{13} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{Alex}{\cfrac{11}{4}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{3}{2}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Claire}{\cfrac{9}{4}\cdot \cfrac{72000}{13}}\implies \stackrel{Alex}{\cfrac{198000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{108000}{13}}~ : ~\stackrel{Claire}{\cfrac{162000}{13}} \\\\\\ ~\hfill \stackrel{Alex}{15230\frac{10}{13}}~~ : ~~\stackrel{Bill}{8307\frac{9}{13}}~ : ~\stackrel{Claire}{12461\frac{7}{13}}~\hfill[/tex]
A utility line runs underground through Shayne's rectangular backyard. Shayne is not allowed to dig within 3 feet of the
utility line. The diagram below shows the dimensions of Shayne's backyard in feet. The dashed line represents the utility
line.
What is the area in square feet of the part of the backyard in which Shayne is allowed to dig?
A) 102ft2
B) 59ft2
C) 374ft2
D) 272ft2
Answers
The area in square feet of the part of the backyard in which Shayne is allowed to dig is option D: 272 ft².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The length of the rectangle ADEH is 17 ft.
The breadth of the rectangle ADEH is 22 ft.
The length of the rectangle ABGH is 17 ft.
The breadth of the rectangle ABGH is -
GH = (EH - GE)
GH = [EH - (GF + EF)]
GH = [22 - (6 + 14)]
GH = [22 - 20]
GH = 2 ft
The formula for the area of a rectangle is -
Area = Length × Breadth
The area of part where Shayne is allowed to dig is -
Area = [Area of ABGH + Area of CDEF]
Area = [(17 × 2) + (17 × 14)]
Area = [34 + 238]
Area = 272 ft²
Therefore, the value for area is obtained as 272 ft².
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A heterozygous round pea is crossed with a purebred round pea. Predict the genotypic and phenotypic outcomes.
Answers
Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.
How do two heterozygous peas fare when they are bred?Punnet square analysis indicates that the progeny of two heterozygous pea plants (Yy) will be 75% (3/4) dominant and 25% (1/4) recessive. In the event that 1000 individuals are created, 750 will therefore be dominating.
Tt will be the genotype of a tall heterozygous plant. It will actually prevail over the recessive t allele because T is primarily the dominant allele. Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.
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5 math teachers, 6 science teachers, and 5 social studies teachers attending a conference break for lunch at the same time. During the lunch break, they randomly finish and return to the conference individually. Find the probability that the first two people to leave are science teachers.
Answers
The probability that the first two people to leave are science teachers is; 2/15
What is the probability of selection?The parameters about the subject teachers are;
Number of maths teachers = 5
Number of Science Teachers = 6
Number of Social Studies Teachers = 5
Total number of teachers = 5 + 6 + 5
Total teachers = 16
Thus;
Probability that first to leave is a science teacher = 6/15
Probability that after the first leaves, the second to leave will be a science teacher = 5/15
Thus;
P(first two to leave are science teachers) = (6/15) * (5/15)
= 2/15
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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
Answers
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
Moving vertically up from the origin is movement in the direction of positive z
The first hook will be hung at a point 4 feet east of the origin and 7.5 feet above the origin. The second hook will be hung at a point 5 feet east of the origin, 12
feet north of the origin, and 8 feet above the origin.
Provide the coordinates of the following points:
1. the first hook
2. the second hook
3.
the point on the string joining the hooks that is exactly halfway between the hooks
Answers
The coordinates of the hooks in three-dimensional space are found and the mid-point of the string is recognised as (4.5, 6, 7.75).
What is meant by three-dimensional space?
A three-dimensional space in geometry is a mathematical structure where a point's location depends on three different values.
For this question, we are considering the east of origin as the positive x-axis, the above origin as the positive z-axis and the north of the origin as the positive y-axis.
a) For the first hook there is no y-axis, it is hung in the xz plane.
So the coordinates are (4,0,7.5)
b) The second hook coordinates are given as (5, 12,8)
c) The point on the string which joins the hook, which is halfway between the hooks can be found using the mid-point formula.
x= (x1 + x2)/2 = (4+5)/2 = 4.5
y = (y1 + y2) /2 = (0+12) / 2 = 6
z = (z1+z2) / 2 = (7.5 + 8) /2 = 7.75
Therefore the mid-point of the string is (4.5, 6, 7.75).
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Consider the following sample data.
14 9 19 18 5
8
Calculate the z-score for the following values.
a. 12
b. 6
c. 15
d. 13
The z-score for a-d are?
(Round to two decimal places as needed.)
Answers
Take the original data and divide it by the standard deviation to determine the z-scores. X is a symbol for the relevant data point. For the population from which you selected your sample, mu and sigma stand in for the mean and standard deviation.
What are z-scores?In terms of standard deviations above or below the mean, a data point's z-score quantifies this exact distance.
A z-score is calculated using the following formula:
data point = mean standard deviation
Data point means with standard deviation equal to z
The same equation is given below in symbol form:
z= x−μ / σ
Some significant z-score details are as follows:
An elevated z-score indicates that the data point is.
When a data point has a negative z-score, it is below average.
The data point is considered to be roughly average if the z-score is near to 0.00.
If a data point's z-score is higher or lower than 3 33 or 3 3minus, the data point is deemed uncommon.
At Almond, the average score on a history midterm is
= 85 = 85mu, which is equivalent to 85 with a standard deviation of
= 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2
On the test, Michael received a score of 86.866.668.
Calculate Michael's exam grade in Z-score form.
His Grade = Mean Grade Standard Deviation
= 86 − 85 / 2
= 1 /2 = 0.5 z z z
= standard deviation of his grade and mean grade.
= 2 / 86−85
= 2 / 1 =0.5.
The z-score for Michael is 0.5, 0.50, and 5. He received a grade that was half a standard deviation higher than the mean.
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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
Answers
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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Alexandra invested 40% of his money in mutual funds, 40% in real estate, and 20% in stocks. If the value of the money that he invested in mutual funds, real estate, and stocks grew by 2%, 7%, and 11% respectively, what was the average growth on his total investment?
Answer is: 5.80%
I don't know the steps to get this answer
Answers
Answer:
5.80
Step-by-step explanation:
just to make the answer
Within the database environment, a data model represents data structures with the purpose of supporting a specific problem domain.a. Trueb. False
Answers
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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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.
Answers
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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The university of California health services committee has five members. two members are chosen to serve as the committee chair and the vice chair. each committee member is equally likely to serve in either of the positions. What is the probability of randomly selecting the chair and the vice chair?
Answers
Answer:
the probability of randomly selecting the chair and the vice chair is 10%.
Step-by-step explanation:
There are a total of 5 members on the health services committee, and 2 of them will be chosen to serve as the chair and vice chair, respectively.
The probability of randomly selecting the chair out of the 5 members is 2/5, or 40%.
Once the chair is selected, there are 4 members remaining, and only one of them can serve as the vice chair. Therefore, the probability of randomly selecting the vice chair out of the remaining 4 members is 1/4, or 25%.
To find the probability of randomly selecting the chair and the vice chair, we need to multiply the individual probabilities of selecting each position, which is (2/5) * (1/4) = 2/20 = 1/10 = 10%.
So, the probability of randomly selecting the chair and the vice chair is 10%.
Find the product of the complex number and its conjugate. 1/3 + 2i
Answers
Answer:
Step-by-step explanation:
1/3 + 2i is a complex number, with the real part equal to 1/3 and the imaginary part equal to 2i. It can be represented in a Cartesian coordinate system as a point (1/3, 2)
Find the slope of the line graphed below.
Answers
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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Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³
Answers
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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how many four digit decimal number that has an estimated value of 10 when rounded off to the nearest tenths place
Answers
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.
give me brainiest
Ethan's wallet contains 19 bills totaling to
$114. If Ethan's wallet only contains $20-
bills and $1-bills, how many $20 bills are in
Ethan's wallet?
Systems of linear equations applications
Answers
3 x 10 + 6 x1 + 1 + 8 x 1/1,000 in standred form
Answers
The expression in the standard form is 37.008
How to evaluate the expression in standard formFrom the question, we have the following parameters that can be used in our computation:
3 x 10 + 6 x1 + 1 + 8 x 1/1,000
Evaluate the products
This gives
30 + 6 + 1 + 8/1,000
Evaluate the quotients
30 + 6 + 1 + 0.008
Evaluate the sum
37.008
Hence, the number in standard form is 37.008
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Write an expression to represent:
3 minus the product of 2 and x
.
Answers
Answer: 3 - 2x
Step-by-step explanation:
Product = Multiplication
Product of 2 and x = 2*x
3 minus 2x
3-2x
Answer:
3−2×x or 3-(2xx)
Question 15 (2 points)
The equation 5x-11 = 6x-x-11 has infinite solutions.
O True
O False
Answers
Reason:
The 6x-x on the right hand side simplifies to 5x
This means the right hand side turns into 5x-11, which is an identical copy of the 5x-11 on the left side.
The equation 5x-11 = 5x-11 has infinitely many solutions because we can replace x with any real number to end up with a true statement.
What is 25% of R594180
Answers
Answer:
148545
Step-by-step explanation:
it's easy enough
When the function f(x) is divided by 2x + 1, the quotient is x² - 8x + 8 and the
remainder is 5. Find the function f(x) and write the result in standard form.
Please help
Answers
The expression for the function f(x) in standard form if the function f(x) is divided by x-2 is f(x) = 3x³ + 2x² - 20x + 17.
What will be the function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5?The function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5 is determined as follows:
f(x) = (2x + 1)(x² - 8x + 8) + 5
Simplifying the above gives the following:
f(x) = 2x³ - 16x² + 16x + x² - 8x + 8 + 5
f(x) = 3x³ - 15x² + 8x + 13
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What are the explicit equation and domain for an arithmetic sequence with a first term of 9 and a second term of 1?
Group of answer choices
an = 9 − 1(n − 1); all integers where n ≥ 1
an = 9 − 1(n − 1); all integers where n ≥ 0
an = 9 − 8(n − 1); all integers where n ≥ 0
an = 9 − 8(n − 1); all integers where n ≥ 1
Answers
The explicit equation and domain for an arithmetic sequence is a_{n}=9+(n-1)-8, the correct option is C
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given;
A first term of 9 and a second term of 1
a=9
D=1-9=-8
We know that the explicit equation of an AP is
a_{n}=a_{1}+(n-1)d
So, substituting the values
a_{n}=9+(n-1)-8
Therefore, the arithmetic sequence will be a_{n}=9+(n-1)-8.
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HELPPP PLEASEEE take your time , explanation please
Answers
Answer:
3 1/10 as a fraction
Step-by-step explanation:
3.3 as a fraction is 3 3/10. The first 3 is a whole number because it is to the left of the decimal point, and it represents 3 ''ones''. However, the second 3 to the right of the decimal point represents a decimal amount. Because this 3 is in the tenths place, we say it as ''3 tenths.
33 is repeating
When converting a percent in fraction form, you must know its place value of each number, and you can easily transform it to fraction.
EXAMPLE:3.3% - the place value is ones. It is a whole number and called as three.
3.3% - the place value is tenths. It is called as three-tenths.
ANSWER= 3 3/10 as this can't be simplified.PERCENT TO DECIMAL
When you convert a percent to decimal, you must divide it by 100.
SOLUTION (in the photo)3.3 ÷ 100
ANSWER= 0.33Find the unit vector perpendicular to the plane of given vectors.P =i−2j+ k^Q =2i+j−k^
Answers
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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PLEASE HELP!!!!!!!! i dont understand this at all
Answers
Answer:
4
--
3
Step-by-step explanation:
Rate of Change via a table should be
f(x2)-f(x1)
-------------
x2 - x1
In this problem they indicated X2 is 36 and X1 is 18
At 36, F(X) is 61 and for 18, it's 37
Now to plug in...
61 - 37
----------
36 - 18
That boils down to
24
----
18
If we want to simplify it;
4
--. or. 1.333
3
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
Answers
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).
Answers
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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