Answer:
Step-by-step explanation:
half the base times the height
Fill in the blanks.
X =
P
S
m
m
(12x+3)
O
(7x-13)
R
The measures in the parallelogram are given as follows:
x = 10.m < R = 57º.m < Q = 123º.How to obtain the measures?In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.
The angles of 12x + 3 and 7x - 13 are consecutive, meaning that the value of x is given as follows:
12x + 3 + 7x - 13 = 180
19x = 190
x = 190/19
x = 10.
Then the angle measures are given as follows:
m < R = 7(10) - 13 = 57º.m < Q = 12(10) + 3 = 123º.More can be learned about angle measures at https://brainly.com/question/30749938
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p(x)=-14+30x+26x^4 How many roots does this have
P(x) = -14 + 30x + 26x⁴ has four roots. The solution has been obtained by using properties of polynomials.
What is a polynomial?
The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
We are given a polynomial as P(x) = -14 + 30x + 26x⁴.
It is a polynomial of degree 4 as the highest power is 4.
We know that the number of roots is equal to the degree of the polynomial.
Here, since the degree is 4, so it has 4 roots.
Hence, P(x) = -14 + 30x + 26x⁴ has four roots.
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A square has an area of 400 square miles. What is the length of each side of the square? 10 mi 20 mi 30 mi 40 mi
Answer: The side of the square is 20 miles
Step-by-step explanation:
Since the area of square= side *side
given, area =400 square miles
400 = side *side
400= side²
√400=side
20 miles=side
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In Exercises 1 to 8, find the limit of each sequence that converges; if the sequence diverges, explain why 4. z" = Log ( 1 + θ fixed α fixed {i-co-C)-is nC)} fised θ fixed
The given sequence is
[tex]z_n = log(1 + (θ/(α + {i*cos(π/2) - i*sin(π/2)}))^n)[/tex]
First, we need to simplify the expression inside the log. The term [tex]{i*cos(π/2) - i*sin(π/2)}[/tex] can be simplified to 0, since cos(π/2) = 0 and sin(π/2) = 1.
Therefore, the expression inside the log becomes [tex](1 + (\theta/\alpha)^n)[/tex].
Now, we need to find the limit of this sequence as n approaches ∞.
If θ/α is less than 1, then (θ/α)^n will approach 0 as n approaches infinity, and the limit of the sequence will be log(1) = 0.
If θ/α is greater than 1, then (θ/α)^n will approach infinity as n approaches infinity, and the limit of the sequence will be log(infinity) = infinity.
If θ/α is equal to 1, then (θ/α)^n will always be 1, and the limit of the sequence will be log(2).
Therefore, the limit of the sequence depends on the values of θ and α. If θ/α < 1, the limit is 0. If θ/α > 1, the limit is infinity. If θ/α = 1, the limit is log(2).
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Brian b has a box of 96 forks for $4.98. what is the unit price for each brand?
Answer: To find the unit price for each fork, we need to divide the total cost of the box by the number of forks in the box.
The cost of the box is $4.98, and the box contains 96 forks. So the unit price for each fork is:
$4.98 ÷ 96 = $0.051875
Rounding to the nearest cent, the unit price for each fork is $0.05.
Step-by-step explanation:
Using the unitary method, we found that the cost of one fork of brand B is $0.051.
What is meant by the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. We typically utilise this technique for maths computations. This method allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.
The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or more items by multiplication.
Given,
The number of forks in a box of brand B = 96
Price of 96 forks = $4.98
The unit price of brand B = Cost of one fork
Using the unitary method,
96 forks = $4.98
1 fork = $4.98 / 96 = $0.051
Therefore using the unitary method, we found that the cost of one fork of brand B is $0.051.
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What is the factorization of the polynomial below? x2 - x - 42 A. (x + 7)(x + 6) B. (x + 7)(x - 6) C. (x - 7)(x + 6) D. (x - 7)(x - 6)
The factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.
What is factorization?The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
The given polynomial is:
x² - x - 42 = 0
Expand the quadratic equation:
x² + 6x - 7x - 42 = 0
Take the common terms out from the equation:
x(x + 6) - 7(x + 6) = 0
(x - 7)(x + 6) = 0
Hence, the factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.
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1) Ryan buys a sofa for £2500 plus VAT at 20%
a) What is the total price of the sofa?
The total price of the sofa is £3000.
Step-by-step explanation:1. Calculate the amount to pay for VAT.To calculate this, multiply the given amount by "0.2", which equals "20%".
[tex]2500*0.2=500[/tex]
2. Add up the two number to find the total amount due.[tex]2500+500=3000[/tex]
3. Conclude.The total price of the sofa is £3000.
-------------------------------------------------------------------------------------------------------
Alternative (and also easier) method.So if we want to add 20% of any amount to said amount, we may multiply it by (1+0.2), which equals "1.20", and it'll give us the result immediately:
[tex]2500*(1+0.2)\\ \\2500*1.2=3000[/tex]
Now, working on the opposite way, let's say we want to reduce that same number (2500) by 25%, maybe because there's a discount on the product. In that case, we must multiply by (1-0.25), which equals 0.75:
[tex]2500*(1-0.25)\\ \\2500*(0.75)=1875.[/tex]
Given :-
Ryan buys a sofa for £2500 .VAT is 20% .To Find:-
Total price of the sofa.Solution:-
Here we are given that Ryan purchases a sofa for £2500 . In order to find the cost of sofa after VAT , find 20% of the price of the sofa,
20% of £2500
20/100 * £2500
£500
Now add this to the original price of the sofa,
£2500 + £500
£3000
Hence the cost of the sofa after VAT is £3000 .
41 is what percent of 120
Answer: Approximately 34.17%.
Step-by-step explanation: Let's divide 41 by 120. Doing so, we get 0.3466666 looping forever. We can simplify that to .3417, and then turn that into a percentage giving us 34.17%
Here are the first four terms of an arithmetic sequence. 5 11 17 23 Write down an expression, in terms of n , for the nth term of the sequence.
To find the expression for the nth term of the sequence, we need to first find the common difference.
The common difference is the difference between any two consecutive terms in the sequence. We can see that the difference between each pair of consecutive terms is 6. Therefore, the common difference is 6.
To find the nth term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Substituting the values we have:
a1 = 5
d = 6
So the expression for the nth term of the sequence is:
an = 5 + (n - 1)6
Simplifying:
an = 6n - 1
In the figure ABC, ~ EDC, find the width of the olen river. (AB)
The width of the olen river is 16 yards
How to find the width of the olen river.From the question, we have the following parameters that can be used in our computation:
ABC, ~ EDC
The above means tha the triangles are similar triangles
Using the above as a guide, we have the following:
x : 32 = 20 : 40
Express as fraction
x/32 = 20/40
So, we have
x = 32 * 20/40
Evaluate
x = 16
Hence, the length is 16 yards
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Evaluating lim x approaching pi/3 [tex](sin(3\sqrt{2} /\pi -sec(3x/4)+\pi/6))[/tex]. Enter an exact answer.
The required value of the given expression of limit is 1/2.
What is the limit?In mathematics, a limit is a fundamental concept that describes the behavior of a function as its input approaches a certain value or point. In particular, the limit of a function at a point is the value that the function approaches as its input gets arbitrarily close to that point, whether from the left or the right.
Here,
Given expression,
[tex]=\lim_{x \to \\ \pi /3} sin(3\sqrt{2}x/\pi - sec(3x/4) + \pi/6)[/tex]
Put x = π/3
= sin (3√2 × π/3 × 1/π - sec (3/4 × π / 3) + π /6)
= sin(√2 - sec(π/4) + π/6)
= sin(√2 - √2 + π/6)
= sin(π/6)
= 1/2
Thus, the required value of the given expression of limit is 1/2.
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Lily makes a triangular car scratcher for her pet cat.. If two of its sides, measure 8 inches and 15 inches, which of the following is the possible measure of its third side? Choose two.Show your work.
A. 18 inches
B. 7 inches
C. 22 inches
D. 23 inches
E. 12 inches
It can't because 15 + 8=23 and the sum of the first 2 sides have to be greater than the third side
So the answer is 18
Prove the following statement by mathematical induction:
[tex]\sum_{i=1}^{n+1}{i*2^i = n * 2^{n+2} + 2}[/tex] for all integers n ≥ 0.
The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
What is mathmetical induction?Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.
The process involves two steps:
Base case: Prove the statement is true for some initial value, usually n = 1 or n = 0.Inductive step: Assume the statement is true for an arbitrary value of n, and use this assumption to prove that the statement is also true for the next value, n + 1.Here,
First, we need to prove the statement is true for the base case n=0,
When n=0, we have,
[tex]\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2[/tex]
and
[tex]n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2[/tex]
Therefore, the statement is true for n=0.
Next, we assume the statement is true for some arbitrary integer k, meaning:
[tex]\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2[/tex]
We want to show that the statement is also true for n=k+1,
[tex]\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2[/tex]
We can rewrite the left-hand side of the equation as,
[tex]=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2[/tex]
This last step used the assumption that the statement is true for n=k.
Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.
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Noise in a quiet room is 500 times as intense as the threshold of sound. What is the decibel measurement for the quiet room?
The decibel measurement for the quiet room is 54 dB.
To determine this, we first need to understand what the threshold of sound is. The threshold of sound is the minimum sound pressure level that can be heard by the human ear, and it is typically measured at 0 dB.
Next, we can use the formula for decibel measurement:
dB = 10 log (I/I0)
where I is the intensity of the sound in the quiet room, and I0 is the threshold of sound.
Since the noise in the quiet room is 500 times as intense as the threshold of sound, we can plug in the values into the formula:
dB = 10 log (500/1)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB. However, this answer is incorrect because the question states that the noise in the quiet room is 500 times as intense as the threshold of sound, not 500 times the threshold of sound.
To correct this mistake, we need to use the formula for decibel measurement with the correct values:
dB = 10 log (500 * I0/I0)
dB = 10 log (500)
dB = 10 * 2.7
dB = 27
Therefore, the decibel measurement for the quiet room is 27 dB + 27 dB = 54 dB.
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What is the range of possible lengths of the third side of triangle with side lengths of 5 and 8?
Answer:
I'm going to assume it's a right triangle, but if you're looking for the hypotenuse with the side lengths 5 and 8, then the answer is 9.434
A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.
x 0 1 2 3 4 5 6
p(x) 0.12 0.18 0.20 0.20 0.20 0.07 0.03
Calculate the cdf F(x).
x 0 1 2 3 4 5 6
f(x)
Use the graph to calculate the probabilities of the events given below.
(a) {at most three lines are in use}
(b) {fewer than three lines are in use}
(c) {at least three lines are in use}
(d) {between two and five lines, inclusive, are in use}
The probability of the event between two and five lines, inclusive, are in use is 0.85.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that,
x 0 1 2 3 4 5 6
p(x) 0.12 0.18 0.20 0.20 0.20 0.07 0.03
a) At most three lines are in use
Here we need to find the probability for x≤3.
P(x≤3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)
= 0.12+0.18+0.20+0.20
= 0.70
b) Fewer than three lines are in use
Here we need to find the probability for x<3.
P(x<3)=P(x=0)+P(x=1)+P(x=2)
= 0.12+0.18+0.20
= 0.50
c) At least three lines are in use
Here we need to find the probability for x≥3.
P(x≥3)=P(x=3)+P(x=4)+P(x=5)+P(x=6)
= 0.20+0.20+0.07+0.03
= 0.50
d) Between two and five lines, inclusive, are in use
Here we need to find the probability for 2≤x≤5.
P(2≤x≤5)= P(x=2)+P(x=3)+P(x=4)+P(x=5)
= 0.18+0.20+0.20+0.20+0.07
= 0.85
Therefore, the probability of the event between two and five lines, inclusive, are in use is 0.85.
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For the 12-km-long Bridge Run, officials set up a water table every 600 meters, starting at the start line. How many water tables are set up for the Bridge Run?
Answer:
Step-by-step explanation:
To determine the number of water tables set up for the Bridge Run, we need to divide the total length of the run by the distance between the water tables.
The total length of the run is given as 12 km.
The distance between the water tables is 600 meters.
To convert the units, we can express the total length of the run in meters:
12 km = 12,000 meters
Now we can divide the total length of the run by the distance between the water tables:
12,000 meters ÷ 600 meters = 20
So there are 20 water tables set up for the Bridge Run.
the radius of a circle is 3 inches. What is the lenght of a 180° arc?
The length of the 180° arc as required in the task content is; 22/21 inches.
What is the measure of the 180° arc's length?Recall that the length of an arc is given by the formula;
Length of arc = theta / 360 × 2 π r
Therefore, for a radius of 3 inches;
Length of arc = 180/360 × 2 × 22/7 × 3
Length of arc = 22/21 inches.
Ultimately, the length of the arc in discuss is; 22/21 inches.
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4. Aziz grows vegetables in his garden. of the vegetables grow underground. Of these underground vegetables, are potatoes. What fraction of all the vegetables are potatoes? 5 If there are 70 vegetables altogether, how many potatoes are there?
A fraction of [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.
If there are 70 vegetables altogether, then there are 10 potatoes.
What are Fractions?Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.
Here p, called the numerator and q, called the denominator, are real numbers.
Some of the values are missing here.
Given that,
Aziz grows vegetables in his garden.
Let the total number of vegetables be x.
Assuming [tex]\frac{1}{2}[/tex] of the vegetables grow underground.
Number of underground vegetables = [tex]\frac{1}{2}[/tex] x
Assuming, [tex]\frac{2}{7}[/tex] of these underground vegetables, are potatoes.
Number of potatoes = [tex]\frac{2}{7}[/tex] × ( [tex]\frac{1}{2}[/tex] x ) = [tex]\frac{1}{7}[/tex] x
So, [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.
If there are 70 vegetables altogether,
Number of potatoes = [tex]\frac{1}{7}[/tex] x = [tex]\frac{1}{7}[/tex] × 70 = 10
Hence of the total vegetables of 70, 10 are potatoes.
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Need help asap. Whoever helps gets 25 points
The value of the indicated trigonometric ratio cosβ is equal to 11/12.
How to determine the value of cosβ?From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:
Opposite side = 2√23.Hypotenuse = 24Adjacent side = 22.In order to determine the magnitude of cosβ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.
cos(θ) = Adj/Hyp
Where:
Adj represents the adjacent side of a right-angled triangle.Hyp represents the hypotenuse of a right-angled triangle.θ represents the angle.Therefore, we have the following cosine trigonometric function:
cosβ = 22/24
cosβ = 11/12
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Draw a graph for f(x)= 2^x-3
Answer:
graph linked
Step-by-step explanation:
You owe $378.12 on your credit card. Because you have not paid your bill on time, you have to add a past due charge of $25 , an over limit fee of $50 , and a service charge of 12% of the amount owed on the credit card (without the past due charge and over limit fees). If you wish to send a check for the full amount immediately, how much should you write the check for? Round your answer to the nearest cent, if necessary.
You can write a check for the full amount of $303.12 right away because you currently owe $378.12 on your credit card.
what is amount ?aggregating attempting to quantify the number, maximum count, or time needed. The sum in front of you or being contemplated about is quite active. the overall verdict, its impact, or its import. three accountings: initial, interest, and indeed the third. Word equivalents include amounts, amounting, and amount. supple noun How much something is, how many you have, what you're using, or even how much you get is its quantity. He needs as much cash to get by.
given
owe $378.12 on your credit card
past due charge of $25
limit fee of $50
$378.12- ($25 + $50 )
= $378.12 - $75
= $303.12
You can write a check for the full amount of $303.12 right away because you currently owe $378.12 on your credit card.
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Plot the points (-3, 8) and (5, -8) on the plane below. Determine the slope-intercept form of the equation of the line
through these points.
A graph of the points (-3, 8) and (5, -8) is shown on the plane below.
The slope-intercept form of the equation of the line through these points is y = -2x + 2.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-3, 8), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:
y - 8 = (-8 - 8)/(5 + 3)(x + 3)
y - 8 = -16/8(x + 3)
y = -2(x + 3) + 8
y = -2x - 6 + 8
y = -2x + 2
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Find domain Range Y-intercept X- intercept Vertical asymptote Horizontal asymptote Pic attached below note write domain and range in interval notation
Find domain
Range
Y-intercept
Xi intercept
Vertical asymptote
Horizontal asymptote
Pic attached below
The domain and range of the function f(x) = 3/x + 2 are (-∞, 0) ∪ (0, ∞) and (-∞, 2) ∪ (2, ∞). The vertical and horizontal asymptotes are x = 0 and y = 2 respectively
What is the domain and range of a functionIn mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.
To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.
The function f(x) = 3/x + 2
The domain of the function is (-∞, 0) ∪ (0, ∞)
The range of the function is (-∞, 2) ∪ (2, ∞)
The x - intercept is (-3/2, 0)
The y - intercept does not exist
The vertical asymptotes is x = 0
The horizontal asymptotes is y = 2
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two different points an a number line are bath 3 units from the point with coondinate .the solution to which of the following equations gives the coordinates of both points?
Answer: |x + 4| = 3
Step-by-step explanation:
If [x+(4+3i)] is a factor of a polynomial function f with real coefficients, then [x-(4+3i)] is also a factor of f.
A complex number is a number of the form a + bi, where a and b are real numbers
Given is that {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients.
Yes, the given statement -
" If {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients, then {x - (4 + 3i)} is also a factor of f " is true.
Therefore, the given statement -
" If {x + (4 + 3i)} is a factor of a polynomial function f with real coefficients, then {x - (4 + 3i)} is also a factor of f " is true.
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In this regular pentagon, all of the exterior
angles marked f are the same size.
Find the value of f.
Give your answer in degrees (°).
f
f
Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Nico Aditi Erick Raj Sandra
Nico and Aditi are not correct in their approach to solving the problem.
Describe Equation?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=).
The expressions on both sides of the equation can contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and others. The goal of solving an equation is to find the values of the variables that make the equation true.
Equations can be classified into different types based on their degree and the number of variables.
Linear equations: Equations that involve variables raised to the first power only, such as 2x + 3 = 7.
Quadratic equations: Equations that involve variables raised to the second power, such as x² + 5x - 6 = 0.
Cubic equations: Equations that involve variables raised to the third power, such as x³ + 2x² - x - 2 = 0.
Simultaneous equations: A set of two or more equations that are solved together to determine the values of the variables.
Equations are used in many real-life applications, such as physics, engineering, economics, and finance. They are also an essential part of mathematics and are used to model and solve problems in algebra, calculus, and other branches of mathematics.
The students who are correct in their approach to solving the problem are:
Erick: By multiplying both sides of the equation by 5/2, he eliminates the fraction on the left side and simplifies the equation.
Raj: By multiplying both sides of the equation by 1/2, he eliminates the fraction on the left side and simplifies the equation.
Sandra: By adding 5/2 to both sides of the equation and then simplifying, she isolates the variable on one side of the equation.
So, Nico and Aditi are not correct in their approach to solving the problem.
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Answer:
yo
Step-by-step explanation:
C D E
Which of the following best describes range, as the word is used in data interpretation?
Answer:
Range in data interpretation is described as the distance between the minimum value and the maximum value.
Step-by-step explanation:
Examples: 15 to 97.
Can someone help me with this problems with an explanation please? Thank you.
The values and heights obtained using the trigonometric ratios are as follows;
4. The six trigonometric ratios are;
cos(θ) = 15/17sec(θ) = [tex]1\frac{2}{15}[/tex]sin(θ) = 8/17csc(θ) = [tex]2\frac{1}{8}[/tex]tan(θ) = 8/15cot(θ) = [tex]1\frac{7}{8}[/tex]5. The two other ways to write cot(θ) are;
cot(θ) = 1/tan(θ)cot(θ) = cos(θ)/sin(θ)6. The six trigonometric function values are;
cos(x) = -3/5sec(x) = [tex]-1\frac{2}{3}[/tex]sin(x) = -4/5csc(x) = [tex]-1\frac{1}{4}[/tex]tan(x) = [tex]1\frac{1}{3}[/tex]cot(x) = 3/47. The function for the height of the tree is; H = 100·tan(θ)
The completed table is presented as follows;
θ [tex]{}[/tex] 10° 15° 20° 25°
H[tex]{}[/tex] 17.63 26.79 36.4 46.63
What are trigonometric ratios?Trigonometric ratios are functions that relate the ratio of two of the sides of a right triangle to an interior angle of the right triangle.
4. The length of the adjacent side to the angle θ according to the Pythagorean Theorem is; Adjacent = √(17² - 8²) = 15
The six trigonometric ratios are;
cos(θ) = 15/17, sec(θ) = 17/15 = 1 2/15
sin(θ) = 8/17, csc(θ) = 17/8 = 2 1/8
tan(θ) = 8/15, cot(θ) = 15/8 = 1 7/8
5. The 2 other ways to write cot(θ) are;
cot(θ) = 1/(tan(θ))
cot(θ) = cos(θ)/sin(θ)
6. The location of the point on the terminal side of the angle is; (-3, -4)
Length of the hypotenuse side = √((-3)² + (-4)²) = 5
Let x represent the angle, we get;
The six trig functions of the angle are;
cos(x) = -3/5sec(x) = -5/3 = -1 2/3sin(x) = -4/5csc(x) = -5/4 = -1 1/4tan(x) = -4/(-3) = 4/3 = 1 1/3cot(x) = 3/47. The length of the shadow of the tree = 100 m
Angle of elevation of the Sun = θ
Let h represent the height of the tree, we get;
tan(θ) = h/100
Therefore, the height of the tree, h = 100·tan(θ)
The values of the height of the tree at the different angle of elevation in the table are;
θ = 10°, h = 100 feet × tan(10°) ≈ 17.63 feet
θ = 15°, h = 100 feet × tan(15°) ≈ 26.79 feet
θ = 20°, h = 100 feet × tan(20°) ≈ 36.4 feet
θ = 25°, h = 100 feet × tan(25°) ≈ 46.63 feet
Learn more on trigonometric ratios here: https://brainly.com/question/30646429
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