Use identities to find tan, csc, sec, and cot. Where necessary, rationalize denominators
Answers
We are given:
[tex]sin\text{ }\theta=\frac{3}{5},cos\text{ }\theta=\frac{4}{5}[/tex]The tangent is defined as the ratio of the sine and the cosine:
[tex]tan\text{ }\theta=\frac{sin\text{ }\theta}{cos\text{ }\theta}[/tex]Calculating:
[tex]\begin{gathered} tan\text{ }\theta=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{5}\cdot\frac{5}{4} \\ \\ tan\text{ \theta}=\frac{3}{4} \end{gathered}[/tex]The cotangent is the reciprocal of the tangent:
[tex]\begin{gathered} \cot\theta=\frac{1}{\tan\theta} \\ \\ \cot\theta=\frac{1}{\frac{3}{4}}=\frac{4}{3} \end{gathered}[/tex]The secant is the reciprocal of the cosine:
[tex]\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{1}{\frac{4}{5}} \\ \\ \sec\theta=\frac{5}{4} \end{gathered}[/tex]The cosecant is the reciprocal of the sine:
[tex]\begin{gathered} \csc\theta=\frac{1}{\sin\theta}=\frac{1}{\frac{3}{5}} \\ \\ \csc\theta=\frac{5}{3} \end{gathered}[/tex]Related Questions
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answers
Answer:
A) there are no outliers in this distribution.
Assume the given function is one to one.Find the indicated values
Answers
To solve this question, you have to look for the answers in the table.
Let's analise each part of the question to solve it:
(a) f(1) =
f(1) means the output of the function [f(x)] when x = 1.
Looking for x =1 in the table, you can see that f(x) = 0.
f(1) = 0.
(b) f(x) = 3, x =
Now, you have to find the input (x) when the outpout [f(x)] is 3.
Looking for f(x) = 3, you can see that x = 7.
f(x) = 3, x = 7.
(c) f⁻¹(0) =
Now, you have to evaluate the inverse function.
To look for the values of the inverse function, x will be the output and f⁻¹ will be the input.
To look for f⁻¹(0), look for f(x) = 0 (input) and the output will be 1
f⁻¹(0) = 1.
(d) f⁻¹(x) = 7; x =
Again, you have an inverse function. So, 7 will be the input in the table (x). x is 7 (output).
f⁻¹(x) = 7; x = 3.
Please help me I don’t know it
Answers
Answer:
angle 4 and 5 are interior angles, and 3 and 6 as well
a communication system consists of n components, each of which will, independently, function with probability p. the total system will be able to operate effectively if at least one-half of its components function. (a) let x denote the number of functioning components out of the n components. what is the distribution of x? (b) what is the probability that a 5-component system will function? (c) for what values of p is a 5-component system more likely to operate effectively than a 3-component system?
Answers
A Communication system consists of n components.
a) Binomial distribution,
P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾
b) For 5-component system,
P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5
c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.
Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .
(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.
(b) Now , 5-component system is function . That is n=5
Probability that 5-components system will function is P(X= 5)
= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)
(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is
⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵
Whereas the corresponding probability for a 3-components system
³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3
³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³
5-Component system is better than 3-Components system if
10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³
=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²
Which reduce to
3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0
either p> ½ or p <1
=> p belongs to ( 0.5, 1)
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a=3,k=12,z=6,h=4 Evaluate the algebraic expression z+15=?
Answers
since z=6, so z+15 is equal to 21
or a+k+z=21
Use spinner and color key to find the indicated probabilities. Landing on green or a vowelNot landing on yellow or a constant
Answers
Solution:
The spinner has a total of 8 sections.
There are two green sections and 4 four vowel sections where one of the vowels is also green.
Then, the probability of landing on green or a vowel is;
[tex]\frac{5}{8}=0.625[/tex]Pleas help me !!!! Please!!!
Answers
The most appropriate choice for domain of a functions will be given by -
What is a domain of a function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
The set of values for which the function is defined is called domain of the function.
Here, from the graph, the set of values of x axis for which the graph is drawn is [tex]-6\leq x \leq 6[/tex].
And values of x - axis represents the domain.
So domain of function is {x ∈ [tex]\mathbb{R}[/tex], [tex]-6 \leq x \leq 6[/tex]}
Third option is correct.
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You had $21 to spend on five notebooks after buying them u had $6 dollars how much did each notebook cost.
Answers
Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:
[tex]5x[/tex]We had 21 dollars and we spent 5x on the notebooks, this can be express as:
[tex]21-5x[/tex]Finally we know that this is equal to the six dollars we had at the end, then we have the equations:
[tex]21-5x=6[/tex]Solving for x we have:
[tex]\begin{gathered} 21-5x=6 \\ 21-6=5x \\ 5x=15 \\ x=\frac{15}{5} \\ x=3 \end{gathered}[/tex]Therefore each notebook cost $3
The diagram below shows an equilateral triangle ABC, with each side 3 cm long. The side [BC] is extended to D so that CD = 4 cm.What is the length of side AD?Round your answer to two decimal places.
Answers
The triangle ABC is an equilateral triangle. This means that each angle equals 60°. Hence, the angle at B is 60°.
The length of each side of ABC is given to be 3 cm long.
We can get the length of side AD by solving the triangle ABD using the Cosine Rule given to be:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Since we're considering triangle ABD, and we have the measure of angle B, we can use the relationship:
[tex]b^2=a^2+d^2-2ad\cos B[/tex]Note that a, b, and d are the sides, such that:
[tex]\begin{gathered} a=BD=BC+CD=3+4=7\operatorname{cm} \\ b=AD \\ d=AB=3\operatorname{cm} \end{gathered}[/tex]Substituting these values, we have:
[tex]\begin{gathered} AD^2=7^2+3^2-2(7\times3\times\cos 60) \\ AD^2=49+9-42\cos 60 \\ AD^2=37 \\ AD=\sqrt[]{37} \\ AD=6.08\operatorname{cm} \end{gathered}[/tex]The length of AD is 6.08 cm to 2 decimal places.
Find the measure of the complement for the angle 1 degree
Answers
89 degrees
Explanations:
The sum of an angle and its complement is equal to 90 degrees.
Let the measure of the complement be "x"
Given the information below:
Angle = 1 degrees
Taking the sum of the angle and its complement will give:
[tex]x+1^0=90^0[/tex]Subtract 1 from both sides
[tex]\begin{gathered} x+1-1=90-1 \\ x+0=90-1 \\ x=89^0 \end{gathered}[/tex]Therefore the measure of the complement for the angle given is 89 degrees
Santiago's car used 15 gallons to travel 525 miles. How far can he travel on 19 gallons?
Answers
Answer:
665
Step-by-step explanation:
the reasoning is because you divide 525/15 and you get 35 with that you multiply by 19 because you are seeing how far you can get with 19 gallons of gas .
665 miles Santiago can travel on 19 gallons of fuel.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
Given, Santiago's car used 15 gallons to travel 525 miles. Since,
Santiago travels in 15 gallons = 525 miles
Santiago travels in 1 gallons = 525/ 15 = 35
Santiago travels in 19 gallons = 35* 19 = 665
Therefore, Santiago can travel 665 miles on 19 gallons of fuel.
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Given that f(x)=x^2-3x-54and g(x)=x-9 find (x)(f⋅g)(x)
Answers
Answer: [tex]x^4 - 12x^3 - 27x^2 +486x[/tex]
Step-by-step explanation:
[tex](f \cdot g)(x)=f(x)g(x)\\\\=(x^2 -3x-54)(x-9)\\\\=x^3 - 9x^2 - 3x^2 + 27x - 54x + 486\\\\=x^3 -12x^2 -27x+486\\\\\therefore x(f \cdot g)(x)=x(x^3 -12x^2 -27x+486)\\\\=x^4 - 12x^3 - 27x^2 +486x[/tex]
where is the center of dilation located in the image pictured below?
Answers
Answer:
V
Step-by-step explanation:
find the volume of a cone with a height of 100 feet and a radius of its base 100 feet use 3.14 for pi
Answers
The volume of a cone is given as follows;
[tex]\begin{gathered} \text{Vol}=\frac{1}{3}(\pi\times r^2\times h) \\ \text{The radius of the base r=100, h=100} \\ \text{Vol}=\frac{1}{3}\times3.14\times100^2\times100 \\ \text{Vol}=\frac{3.14\times10000\times100}{3} \\ \text{Vol}=1046666.67 \\ \text{Vol}\approx1046666.67ft^3\text{ (rounded to the nearest hundredth)} \end{gathered}[/tex]The volume of the cone with the given dimensions is
1,046,666.67 cubic feet (rounded to the nearest hundredth)
Without approximation, the answer would be,
1,046,666.6666 cubic feet
helpppppp math its hard for me
Answers
Step-by-step explanation:
You would start off with solving inside, the parenthesis, and you would get -8/27.
Then, your would solve the 1 1/4 - 3/4 and get 1/2.
You then have to multiply -8/27*1/2, which is -4/27.
Lastly, you divide by negative 4.
-4/27 divided by -4.
You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.
Since negative times negative is positive, the answer would be 1/27.
Answer:
1/27
Hope this helped! :)
{(7, 3), (4, 8), (-6, -5), (6, 6), (-1, 9) }
Domain:
Range:
Answers
Answer:
Domain: -6,-1,4,6,7
Range: -5,3,6,8,9
Step-by-step explanation:
The domain is the first element in each ordered pair. It is the x value. The range is the second element in each ordered pair. It is the y values.
Linear equations
Which ordered pair is a solution of this equation, -2x+9y=-26
A. (4,4)
B. (-4,-4)
C. (-5,-4)
D. (-4,-5)
Answers
The ordered pair which is a solution to the given linear equation is (-5, -4)
What are linear equations?Linear equations are equations that has a leading degree of 1. The standard linear equation is given as Ax + By = C.
Given the linear equation below;
-2x+9y=-26
We need to determine the ordered pair that gives a solution to the linear expression.
For the coordinate point (4, 4)
-2(4) + 9y = -26
9y = -26 + 8
9y = -18
y = -18/9 = -2
This shows that (4, 4) is not a solution.
For the coordinate point (-4, -4)
-2(-4) + 9y = -26
9y = -26 - 8
9y = -34
y = -34/9
This shows that (-4, -4) is not a solution.
For the coordinate (-5, -4)
-2(-5) + 9y = -26
9y = -26 - 10
9y = -36
y = -4
This shows that (-5, -4) is a solution of the linear equation.
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what is the probability that a card drawn randomly from a standard deck of 52 cards is a red three? express your answer as a fraction in lowest terms or a decimal number rounded to three decimal places, if necessary.
Answers
Answer:
1/26
Step-by-step explanation:
If the cards are all there, you can count there are 2 red threes. And there are 52 cards. The fraction is 2/52 or 1/26
Using positive integers between 1 and 9 and each positive integer at most once, fill in values
to get two constraints so that x = 7 is the only integer that will satisfy both constraints at
the same time.
☐ x+☐ < ☐ x + ☐
☐x+ ☐ > ☐ x+ ☐
Answers
Using positive integers between 1 and 9 and each positive integer at most once,
2 x+ 9 < 3 x + 1
6x+ 4 > 5 x+ 8
To get two constraints so that x = 7 is the only integer that will satisfy both constraints at the same time. Upon analysing it can be seen that to the coefficients of x in eaxh equation shouch be two consecutive number. The coefficient on the lesser than side should be lower than the coeffiecient present on the greater than side.
To make the equation in such a way that only 7 satisfy it, the lesser than sides are added with numbers higher than 7 that is 8 and 9.
Therefore, Using positive integers between 1 and 9 and each positive integer at most once,
2 x+ 9 < 3 x + 1
6x+ 4 > 5 x+ 8
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Please help me do my Math Homework ASAP, it is attached.
Answers
Answer:
Step-by-step explanation:
which measure of variability is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean? group of answer choices iqv interquartile range variance standard deviation
Answers
Standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.
What is measure of variability?
Measures of variability provide descriptive information about the dispersion of scores within data.
Standard deviation uses all the values in the distribution in it's calculation hence the standard deviation provides the most information.
Therefore standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.
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karem drives his car 96 miles per hour 1 1/2 hours how many miles will he drive in 2 1/2 hours
Answers
96/x=1 1/2/2 1/2
Cross multiply
1 1/2x= 96 * 2 1/2
Convert the equation
3/2x= 96*2*1/2
Cancel out the 2’s which is the greatest common factor
3/2x=96
Multiply both sides by 2/3
X= 64 miles
Given the image Q’(33, 36) and preimage Q(11, 12), by what scale factor was the point dilated?
22
3
24
1/3
Answers
Answer:
22
Step-by-step explanation:
A manufacturer has been selling 1250 television sets a week at $450 each. a market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
Answers
The demand function of the number of sets sold will increase by 130 per week is p(x) = (-1 ÷ 13)x + 550.
Determine the coordinates of two points mostly online. Estimate the difference in y-coordinates between these two places. Estimate the difference in x-coordinates between these two places. Divide the y-coordinate difference by the x-coordinate difference.
Let p(x) denote the demand function, with x denoting the number of TV sets desired. As stated in the issue, a $10 decrease in p(x) causes a 130 rise in x. As a result, the slope of the demand function graph is -13 ÷ 130 = -1 ÷ 10.
Given p(1250) = 450,
-1 ÷ 10 = (p(x) - 450) ÷ (x - 1250)
p(x) = (-1 ÷ 13)x + 550
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find the number of terms in the sequence 1,-4,16,...,65536
Answers
Answer:
9 terms
Step-by-step explanation:
The sequence given is a geometric sequence
In a geometric sequence, the nth term of the sequence can be found by the formula
[tex]a_n = a_1r^{n-1}[/tex]
[tex]\text{where }\\\\ a_n = \text {nth term}\\\\\text{$a_1 = $ first term}\\\\\text{$r = $ common ratio}[/tex]
In the given sequence,
a₁ = 1
r = -4
aₙ = 65536
So we get the relation:
65536 = 1· (-4)ⁿ⁻¹
65536 = (-4)ⁿ⁻¹
It is clear that n-1 has to be even so that the power of 4 is positive.
Substituting x = n -1 where x is even gives us
4ˣ = 65536
If we take logarithms to the base 4 on both sides we get
=> x = [tex]\log_465536 = 8\\\\[/tex]
Since x = n - 1 and x = 8, n = 9
So the 9th term in the series is 65536
find the product
6x/(-2)
Answer:
-12xy
Answers
The result of the expression given as 6x/(-2) is -3x
How to determine the product?From the question, the expression is given as
6x/(-2)
The above expression is a quotient expression
So, we start by rewritting it as a product
This is represented as
6x/(-2) = 6x * 1/(-2)
Remove the bracket
So, we have the following equation
6x/(-2) = 6x * 1/-2
Evaluate the product
6x/(-2) = -3x
Hence, the value of the expression is -3x
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Draw the preimage and image of the polygon with the vertices X(-1,4), Y (2,2), and Z(0,-1) translated using the vector <2,-37>
Answers
Answer:
12
Step-by-step explanation:
Which expression is equivalent to the given expression? (+2+6)-(- 2+3) x +9 O A I O B. - } +3 O C. x+3 OD. - *+9
Answers
Answer:
The equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]Explanation:
We want to simplify the expression;
[tex](\frac{1}{7}x+6)-(-\frac{4}{7}x+3)[/tex]we will first multiply the negative by every term in the bracket, then simplify by collecting the like terms.
[tex]\begin{gathered} \frac{1}{7}x+6-(-\frac{4}{7}x)-(+3) \\ \frac{1}{7}x+6+\frac{4}{7}x-3 \\ \text{collecting the like terms we have;} \\ \frac{1}{7}x+\frac{4}{7}x+6-3 \\ \frac{5}{7}x+3 \end{gathered}[/tex]Therefore, the equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]help me answer this question please
Answers
Answer:
sum = -15/2
Step-by-step explanation:
Given the formula for the n-th term of a sequence is n(n-8)/√(n+3), you want the sum of the 1st and 6th terms.
First termThe first term is found by substituting 1 for n:
1(1 -8)/√(1 +3) = 1(-7)/√4 = -7/2
Sixth termThe sixth term is found by substituting 6 for n:
6(6 -8)/√(6 +3) = 6(-2)/√9 = -12/3 = -4
SumThe sum of the first and sixth terms is ...
-7/2 +(-4) = -(7/2 +8/2) = -15/2
sum = -7 1/2
Taylor and Emily are painting banners for their Halloween Party. Taylor’s banner is 8 inches tall and 564 inches wide. The area of Emily’s banner is 10 times as large as the area of Taylor’s banner. What is the area of Emily’s banner, in square inches?
Answers
Answer:
[tex]45120 in^2[/tex]
Step-by-step explanation:
Area of Taylor's Banner (AT): [tex]A_T = 8*564=4512 in^2[/tex]
Area of Emily's Banner (AE): [tex]A_E=10*A_T[/tex]
Plugging in AT: [tex]A_E = 10 * 4512 = 45120 in^2[/tex]
The Area of Emily's Banner is 45120 inch²
What is Area of rectangle?The Area of rectangle is the product of its length to its width.
i.e., Area of rectangle= length x width
Given:
Taylor’s banner : 8 inches tall and 564 inches wide.
Area of Taylor's Banner= l x w
= 8 x 564
= 4512 inch²
and, area of Emily’s banner is 10 times as large as the area of Taylor’s banner.
So, Area of Emil's Banner= 10 x 4512
= 45120 inch²
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