Answer:
b) 270 ≥ 40.18d + 3.75
Step-by-step explanation:
Per day is a variable, so it's 40.18d
Per mile is also a variable so 0.05m
40.18d + 0.05m ≤ 270
40.18d + 0.05(75) ≤ 270
40.18d + 3.75 ≤ 270
Answer: 270 ≥ 40.18d + 3.75
division answer in feet and inches 8 divided by 34ft 8in
Answer:
since 12inches=1foot
x inches=34feet
34feet converted to inches =408inches
total inches=408+8
T=416inches
dividing 416 by 8 we have
52 inches left
converting back to feet we get
4ft 4in
Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random variable that is widely used by researchers to model real data.
Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation.
When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable can serve as a model.
There are several reasons why researchers might not use the normal distribution to model real data which are due to assumptions of normal distribution.
First, the normal distribution assumes that the data is symmetric and is distributed around the mean. However, in some cases, the data may be skewed, making the normal distribution an inappropriate model.
Second, the normal distribution assumes that the data is homoscedastic, meaning that the variance is constant across the sample. However, in some cases, the variance may be heteroscedastic, meaning that the variance changes across the sample. This makes the normal distribution an inappropriate model for this type of data.
One situation in which researchers should not use the normal distribution approximation is when modeling financial data. Financial data often follows a power-law distribution, which is not normal. Therefore, researchers should use a power-law distribution to model this type of data.
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NO LINKS!!
The inverse function of the exponential function f(x) = a^x is the (a. transcendental, b. logarithmic, c. rational, d. polynomial, e. algebraic) function with base a.
Answer:
The inverse function of the exponential function f(x) = a^x is the logarithmic function with base a.
The inverse function of a function f is a function that "undoes" the original function, meaning that it reverses the transformation applied by the original function. In the case of the exponential function, the inverse function is the logarithmic function, which "undoes" the transformation applied by the exponential function.
For example, suppose we have the exponential function f(x) = 2^x. The inverse function of this function is the logarithmic function with base 2, which is written as y = log_2 x. If we apply the inverse function to 2^x, we get:
y = log_2 (2^x)
Solving for x gives:
x = 2^y
This means that the inverse function of the exponential function f(x) = a^x is the logarithmic function with base a, which is written as y = log_a x.
The other options (a. transcendental, c. rational, d. polynomial, e. algebraic) are not correct, since they do not describe the inverse function of the exponential function.
Answer:
b. logarithmic
Step-by-step explanation:
Given exponential function:
[tex]f(x)=a^x[/tex]
The inverse of the given function is the logarithmic function with base a.
To find the inverse of a function, replace f(x) with y:
[tex]\implies y=a^x[/tex]
Swap the x and y:
[tex]\implies x=a^y[/tex]
Take logs with base a of both sides of the equation:
[tex]\implies \log_ax=\log_aa^y[/tex]
Apply the log power law: logₐ xⁿ = n logₐ x
[tex]\implies \log_ax=y\log_aa[/tex]
Apply the log law: logₐ a = 1
[tex]\implies \log_ax=y[/tex]
[tex]\implies y=\log_ax[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\log_ax[/tex]
Thus proving that the inverse of the exponential function f(x) = aˣ is the logarithmic function with base a.
Is (6, 8) a solution to this system of equations?
y =1/6x+5
y=5/6x+3
Yes
No
Answer:No
Step-by-step explanation:
When we substitute x=6 into the first equation we get
y=1/6 *6+5=6 so we get (6, 6)
When we substitute x=6 into the second equation we get
y=5/6*6+3=8 so we get (6, 8) . it works for the second equation but not the first. It must be true for both equations
A composite figure is represented in the image.
What is the total area of the figure?
A: 192 m2
B: 216 m2
C: 288 m2
D: 336 m2
The total area of the figure is equal to 192 square meters. The correct option is A.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Calculate the area of the rectangle by the formula written below,
Area of the rectangle = L x W
Area of the rectangle = 8 x 18
Area of the rectangle = 144 square meters
The area of the triangle will be calculated by the formula written as,
Area of triangle = 1/2 x B x H
Area of triangle = 1/2 x ( 18 - 6 ) x 8
Area of triangle = 1 / 2 x 12 x 8
Area of triangle = 48 square meters
Total area = 144 + 48
Total area = 192 square meters
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The following graph shows a system of inequalities. Is the point (-4,-4) a solution to the system?
Yes, the point is a solution.
No, the point is not a solution.
Please answer my quistion in math the quistions are in the picture
Step-by-step explanation:
i hope this helps u get an idea how to solve the problems, sorry for the bad handwriting though
Good luck!!
Trey makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.
Answer:
p=8h
Step-by-step explanation:
P is the total pay, so it will be on one side of the equation. 8 represents the fact that Trey receives 8 dollars per hour. It's multiplied by h to represent the number of hours he works.
find the interval of convergence of the power series. (be sure to include a check for convergence at the endpoints of the interval.) (7x)^n/(10n)!
The interval of convergence of the power series is (-10/7, 10/7).
What does Interval of convergence tell you?
A group of x-values on which a power series converges is known as the interval of convergence. In order to create a convergent series, you can plug in this interval of x-values.
The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence of the given power series, we can use the ratio test.
The ratio test states that if the series [tex]∑ a_nx^n[/tex] has a positive radius of convergence R, then the series converges for |x| < R and diverges for |x| > R. The radius of convergence is given by the formula
[tex]R = 1/limsup|a_n+1/a_n|.[/tex]
In the given power series, the coefficient [tex]a_n[/tex] is given by [tex]a_n = (7x)^n/(10n)!.[/tex]
We can rewrite this as [tex]a_n = x^n(7/10)^n/n!.[/tex]
Taking the limit of the ratio [tex]a_n+1/a_n[/tex] as n goes to infinity, we get:
[tex]limsup|a_n+1/a_n| \\\\= limsup|x^(n+1)(7/10)^(n+1)/(n+1)!/(x^n(7/10)^n/n!)|\\\\= limsup|x(7/10)/(n+1)|\\\\= |x(7/10)|[/tex]
Therefore, the radius of convergence R is [tex]1/|x(7/10)|[/tex].
This means that the interval of convergence is [tex]|x| < 1/|7x/10| = 10/7.[/tex]
We can check the endpoints of the interval to see if the series converges at these points. At x = 10/7, the series becomes [tex](7(10/7))^n/(10n)! = 1^n/(10n)!.[/tex]
This series is a geometric series with first term 1 and common ratio 1/10, and it converges because [tex]|1/10| < 1.[/tex]
At x = -10/7, the series becomes[tex](7(-10/7))^n/(10n)! = (-1)^n/(10n)![/tex]. This series is an alternating series with first term 1 and common ratio (-1/10), and it also converges because [tex]|-1/10| < 1.[/tex]
Therefore, The interval of convergence of the power series is (-10/7, 10/7).
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If x = 29°, find the measures of angles 1, 2, and 3.
Answer:
75.5
Step-by-step explanation:
There are three different sections to sit at a stadium. The number if people who can sit in each section is described below.
~ Red section seats 200 people
~ Blue section seats 20 fewer people than the red section
~ Green section seats 2 times as many people as the blue section
What is the total number of people who can sit in the stadium when it is full?
How did you get your answer?
Answer:
740
Step-by-step explanation:
R = 200
Blue = 200-20 = 180
Green = 2(200-20) = 2( 180) = 360
200 + 180 + 360
740
Answer:
Red section (full)=200 people
Blue section (full)=200-20=180 people
Green section (full)=2×blue section ( full)=2×180=360 people
Stadium (full)=(200+180+360) people=740 people
The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−1, 4) and goes to S(5, 4) and continues to T(5, −2). What is the total walking trail of units?
Answer:
Exact answer 12 + 6[tex]\sqrt{2}[/tex]
Answer rounded to the nearest whole number 20
Step-by-step explanation:
Write a fraction in simplified form that expresses the ratio of 0.27 to 0.06.
Answer: 9/2
Step-by-step explanation:
To express 0.27 and 0.06 as fractions, we first need to convert them to fractions with denominators that are powers of 10. We can do this by multiplying 0.27 by 100 to get 27/100, and multiplying 0.06 by 100 to get 6/100. The ratio of 0.27 to 0.06 is then equal to the ratio of 27/100 to 6/100, which simplifies to 27/6. To express this ratio in simplest form, we can divide both the numerator and denominator by the greatest common factor of 27 and 6, which is 3. This gives us a simplified fraction of 27/6 = 9/2.
-7 x 3^0.25x = -10
Which of the following is the solution of the equation?
There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean
B. Because the standard deviation is unaffected by a change in a single data value, it will remain unchanged.
A change in a single data value has no impact on the standard deviation, which measures the spread of a data collection. As a result, even if the single data value changes, the standard deviation won't.
The variability of a data set is measured by the standard deviation. It is calculated by taking the square root of the average of the sum of the squares of the differences between each value in a data set and the mean. When a single value in a data set is changed, the mean of the data set will change, but the standard deviation will not be affected. This is because the standard deviation is not calculated based on individual data points, but on the overall variability of the data set. Therefore, when a single data value is changed, the standard deviation of the data set will remain the same.
Let x be one of the students in the class
Mean = (76.9 + 82)/2 = 79.4
Standard Deviation = sqrt(((76.9 - 79.4)^2 + (82 - 79.4)^2)/2) = 3.2
The complete question is : There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean D. The standard deviation will increase because the change moved an exam score further from the mean
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find the k-value so that the point is on the line
kx+3y=7; (1,-k)
Answer:
k = -7/2
Step-by-step explanation:
You want the k-value so that the point (1, -k) is on the line kx+3y=7.
EquationThe point will be on the line when its coordinates make the equation true. Using (x, y) = (1, -k), we have ...
k(1) +3(-k) = 7
-2k = 7 . . . . . . . . simplify
k = -7/2 . . . . . . . divide by -2
The value of k = [tex]\frac{-7}{2}[/tex] so the point is on the line kx+3y=7
what is line?A line is an endlessly long object without breadth, depth, or curvature in geometry. Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.
given
the point of the line = ( 1 ,-k )
the line = kx + 3y = 7
the coordinates make the equation true when its points are on the line
so putting the values of x and y in equation of line
k( 1 ) + 3 ( -k ) = 7
k - 3k = 7
-2k = 7
k = [tex]\frac{-7}{2}[/tex]
The value of k = [tex]\frac{-7}{2}[/tex] so the point is on the line kx+3y=7
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A researcher is examining the effects of income (X1) and number of friends (X2) on personal happiness (Y) and finds an R2 of 0.45. Which of the following is a correct interpretation of this result?A.Friends are more important than money for happiness. B.Money CAN buy happiness. C.Taken together, income and number of friends explain 0.45% of the variance in happiness. D.Taken together, income and number of friends explain 45% of the variance in happiness.
Correct interpretation of this result is together, income and friend count account for 45% of the variation in happiness.
Define variation.Variation refers to this relationship between the change in a variable's value when the values of the linked variables change. An example of a straightforward equation, y = mx, in which m is a constant, can be used to show this. The equation becomes y = 5x if we suppose that the value of m is 5. A function in which the variables are related by how they alter in relation to one another is known as a variation function. In this function, for instance, if x rises or falls, D follows suit. Direct and inverse variation functions are the two different categories of variation functions.
Given
A researcher is examining the effects of income (X1) and number of friends (X2) on personal happiness (Y) and finds an R2 of 0.45.
Here, the independent variables of income (X₁) and friend count account (X₂) for 45% of the variation in happiness.
Correct interpretation of this result is:
D) Together, income and friend count account for 45% of the variation in happiness.
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A two-part question....
(i). Set up, but do not evaluate, a triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0.
(ii). Set up, but do not evaluate, a triple integral that gives the volumes of the right circular cylinder above with a hemisphere sitting atop the cylinder.
(i) The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
(ii) The triple integral that gives the volume of the right circular cylinder with a hemisphere sitting atop the cylinder is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10, and 0 ≤ r ≤ sqrt(x^2 + y^2).
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Cooper has 35 video games in his collection, and Maria has 15 in hers. Cooper decides to add 10 video games to his collection each month. Maria decides to add 8 video games to her collection each month. Part A Drag the values to the positions in the table to show how many video games each of them will have at the ends of months 1, 2, 3, and 4. 314533436529 Month Cooper Maria Start 35 15 1 23 2 55 3 39 Part B Which of the following is a true statement about the relationship between the number of video games collected by Cooper and Maria after each month? A. Cooper will always have 20 more video games than Maria. B. Maria will always have 20 more video games than Cooper. C. Cooper will always have 28 more video games than Maria. D. There is no constant relationship between the number of video games collected by Cooper and Maria.
From the values that we have here, the statement that can be said to be true here would be that: There is no constant relationship between the number of video games collected by Cooper and Maria. Last option
What is a constant relationship?A relationship with a fixed ratio between two quantities is referred to as proportionate. The graph will therefore be linear, or straight.
When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.
The values between these two does not show any constant relationship hence the last option
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Answer: part a
cooper- 35 45 55 65
maria 15 23 31 39
part B
there is no constant relationship between the number of video games collected by coopeer and maria
Step-by-step explanation:
How many liters are in 4 quarts of milk? Round to the nearest tenth if needed. 1 quart = 0.95 liters.
Answer:
3.8
Step-by-step explanation:
4 x 0.95 = 3.8
PLEASE HELP ASAP
A line that passes through the points (-1, -4) and (4, 2) is shown.
Which equation is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7) ?
The equation of the line that is perpendicular to the line that passes through the points (-1, -4) and (4, 2): D. 5x + 6y = 27.
How to Write the Equation of Perpendicular Lines?Perpendicular lines have slopes with a product of -1, or are negative reciprocals.
First find the slope of the line that passes through (-1, -4) and (4, 2):
Slope (m) = change in y / change in x = (2 -(-4)) / (4 -(-1))
m = 6/5
The negative reciprocal of 6/5 is -5/6. This means that the perpendicular line is, m = -5/6.
To write the equation of the line that is perpendicular to the given line, substitute m = -5/6 and (a, b) = (-3, 7) into y - b = m(x - a):
y - 7 = -5/6(x - (-3))
y - 7 = -5/6(x + 3)
6(y - 7) = -5(x + 3)
6y - 42 = -5x - 15
6y = -5x - 15 + 42
6y = -5x + 27
5x + 6y = 27
The answer is: D. 5x + 6y = 27.
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tessa needs 1,450 yards of yarn to knit a blanket. she buys 9 balls of yarn, which are each 185 yards long. tessa hopes there will be enough leftover yarn to knit a scarf for her younger brother. a childs scarf takes 125 yards of yarn.
There will be enough leftover yarn to knit a scarf for her younger brother If the child scarf takes 125 yards of yarn.
What is Unit conversion ?
Unit conversion is a necessary step in many mathematical problems. Calculations must be performed using mathematical conversions.
Tessa has bought 9 balls of yarn which are each 185 yards long.
So, She has total 1665 (185 × 9) yards of yarn.
She needs 1450 yards of yarn to knit a blanket.
So, The leftover yarn = 1665 - 1450
= 215.
She needs 125 yards of yarn to knit a scarf for her brother.
So, She has enough yarn to knit the scarf for her brother because the leftover yarn is greater than the yarn needed for scarf.
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9. If point Q is reflected across x = 1, what are the coordinates of its reflection image?
The coordinates of reflection image are (-1, -2).
What is point reflection?
A particular kind of Euclidean space isometry is known as a point reflection in geometry. A thing is said to have point symmetry if it is invariant under a point reflection; if it is invariant under a point reflection through its center, it is said to have central symmetry or to be centrally symmetric.
Given:
point Q is reflected across x = 1.
From graph the point Q is (3, -2).
We have to find the coordinates of its reflection image.
x = 1 is a vertical line passing through all points with an x- coordinate of 1.
(3, - 2) is 2 units to the right of x = 1 ( 3 - 1 ), thus
The reflection is 2 units to the left of x = 1 ( 1 - 2 = - 1 )
Q(3, - 2 ) → Q'(- 1, - 2 )
This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.
Hence, the coordinates of reflection image are (-1, -2).
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Question 5 of 20:
Select the best answer for the question.
5. What's the sum of 667 and 23?
OA. 644
OB. 29
OC. 690
D. 15,341
Mark for review Will be highlighted on the review pagel
Answer:
C). 690
Step-by-step explanation:
When you see the word "sum" that means you add the numbers together
667 + 23 = 690
Answer:
OC. 690
Step-by-step explanation:
To find the sum of 667 and 23, you need to add the two numbers together. When you do this, you get 690 as the result. Therefore, the sum of 667 and 23 is 690.
This can be written as an equation: 667 + 23 = 690. The symbol "+" is used to represent the operation of addition, and the equals sign "=" is used to show that the value on the right side of the equation is the result of the operation on the left side.
In general, when you add two or more numbers together, you find their sum by combining their values and counting the total. For example, to find the sum of the numbers 3 and 4, you would add them together to get 7. To find the sum of the numbers 5, 6, and 7, you would add them together to get 18.
I hope this helps to clarify the concept of addition and the meaning of the term "sum." Let me know if you have any further questions.
Ravi sells real estate. Based on previous data, he knows that 5% of home tours result in a sale. Assume that the results of these tours are independent from each other. Which of the following choices are binomial random variables? Choose all answers that apply: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale. C. Take a random sample of 3 tours and let M = the amount of sales (in dollars) generated by the tours
The following choices are binomial random variables: A. Take a random sample of 30 tours and let L = the number of tours that result in a sale. B. Take a random sample of 3 tours and let K = the number of tours that result in a sale.
Choice A is a binomial random variable because it represents the number of tours that result in a sale in a random sample of 30 tours. The trials are independent, as the results of one tour do not affect the results of other tours, and the probability of success (a sale) is constant at 5%.
Choice B is also a binomial random variable because it represents the number of tours that result in a sale in a random sample of 3 tours. The trials are independent and the probability of success is constant at 5%.
Choice C is not a binomial random variable because it represents the number of sales generated by a random sample of 3 tours, which is a continuous variable. Binomial random variables are always discrete, as they represent the number of successes in a sequence of trials.
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James was also measured at 23 inches long. How many centimeters long was he at birth
The length of the birth in centimeters will be 58.42 centimeters.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
James was also measured 23 inches long.
We know that, in one inch, there are 2.54 centimeters.
The length of the birth in centimeters is calculated as,
⇒ 23 inches
⇒ 23 x 2.54 centimeters
⇒ 58.42 centimeters
The number of birth in centimeters will be 58.42 centimeters.
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The equation y−k = a(x−h) ^2 has graph a parabola with vertex (h, k).
Suppose a > 0. A horizontal line 1 unit above the vertex intersects the
graph at two points. Find the distance between these two points.
The distance between these two points is given as follows:
[tex]d = 2\sqrt{1 - a}[/tex]
How to obtain the distance between these two points?The equation of the parabola is given as follows:
y - k = a(x - h)².
Hence:
y = a(x - h)² + k.
The horizontal line one unit above the vertex has the equation given as follows:
y = k + 1.
(as k is the y-coordinate of the vertex).
Then the intersection of this line with the graph is obtained as follows:
k + 1 = a(x - h)² + k.
a(x - h)² = 1
(x - h)² = 1 - a
[tex]x - h = \pm \sqrt{1 - a}[/tex]
[tex]x = \pm \sqrt{1 - a} + h[/tex]
Then the points are given as follows:
[tex]x = -\sqrt{1 - a} + h[/tex][tex]x = \sqrt{1 - a} + h[/tex]The distance between these two points is of:
[tex]d = \sqrt{1 - a} + h - (-\sqrt{1 - a} + h)[/tex]
[tex]d = 2\sqrt{1 - a}[/tex]
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Write an inequality for the graph
The inequality that represents the line in the figure will be y > - (2/3) x + 3.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
From the figure, the points of the line are (0, 3) and (3, 1). And the region above the line is a consideration. Then the equation of the line is given as,
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
Simplify the equation, then we have
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
(y - 3) > - (2/3)x
y > - (2/3) x + 3
The disparity that addresses the line in the figure will be y > - (2/3) x + 3.
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Evaluate (if possible) the six trigonometric functions of the angle (0).
-5pi/6
Answer:
sin(-5π/6) = -1/2cos(-5π/6) = -√3/2tan(-5π/6) = √3/3csc(-5π/6) = -2sec(-5π/6) = -2√3/3cot(-5π/6) = √3Step-by-step explanation:
You want the 6 trig functions of the angle -5π/6.
QuadrantThe angle is in the 3rd quadrant, so all trig functions are negative except the tangent and cotangent. The reference angle is -5π/6 +π = π/6.
Trig functionsSince you have memorized the values of the trig functions for multiples of π/6, you know ...
sin(-5π/6) = -1/2
cos(-5π/6) = -√3/2
tan(-5π/6) = sin/cos = √3/3
csc(-5π/6) = 1/sin = -2
sec(-5π/6) = 1/cos = -2√3/3
cot(-5π/6) = 1/tan = √3
Answer/Step-by-step explanation:
Use a Unit Circle, you may have access to (hopefully) or have been asked to memorize.
To find -5pi/6 count clockwise the sixths to 5. Or add:
-5pi/6 + 2pi
= -5pi/6 + 12pi/6
= 7pi/6
-5pi/6 is the same as 7pi/6 on the Unit Circle.
Use the coordinates at that spot
(-root3/2 , -1/2)
to find the six trig ratios.
The Unit Circle is a big, giant, Answer Key. It has all the trig answers on it all in one place. It looks like a scary math pizza, but really its all the answers all in one place.
Once you find your angle, the sine is the y-coordinate.
sin theta = -1/2
The cosine is the x-coordinate.
cos theta = -root3/2
Tangent theta is the sine over the cosine, sin/cos,
= y/x
= (-1/2) / (-rt3/2)
Use Keep-Change-Flip to simplify this.
see image.
= root3/3
Sec is cos flipped over. Csc is sin flipped over. Cot is tan flipped over (the math word is reciprocal)
Yes, just flip over sin to get csc:
sintheta = -1/2
csctheta = - 2/1 = -2
Flip over cos to get sec:
costheta = -rt3/2
sectheta = 2/-rt3
Then rationalize, see image.
= -2rt3/3
Flip over tan to get cot.
tantheta = 1/rt3
Use a form that's easy to flip.
cottheta = rt3/1 = rt3
see image.
Two members of the Math Competition Team solve 13 problems in 1 hour. Assume all team members solve problems at the same rate. How many team members are needed to solve in 1 hour 39 problems
Two members of the maths competition team solve 13 problems in 1 hour.
Person=13
Time=1 hour
Then.
Rate=13/1 (person/time)
With the help of question,
Let us consider,
x team members are needed to solve in 1 hour 39 problems,
2M×1/13=1×xM/39
2M/13=x M/39
2M=x M/13
M=26
26 team members are needed to solve in 1 hour 39 problems,
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