The six trigonometric functions of theta for the point (-4, -4) is
sin Θ = -1/√2
cos Θ = -1/√2
tan Θ = 1
cosec Θ = -√2
sec Θ = -√2
cot Θ = 1
Trigonometric Functions:
Trigonometric functions are defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle.
The six trigonometric functions are,
Sin Θ =Opposite/Hypotenuse
Cos Θ = Adjacent/Hypotenuse
Tan Θ = Opposite/Adjacent
Sec Θ = Hypotenuse/Adjacent
Cosec Θ = Hypotenuse/Opposite
cot Θ = Adjacent/Opposite
Given,
Let (-4,-4) be a point on the terminal side of theta in standard position.
Here we need to find the exact values of six trigonometric functions.
Here the give point (-4,-4) represents the values of (opposite, adjacent).
So, the opposite = -4
and adjacent = -4
Now we have to find the hypotenuse of the point,
For that, we have to use the Pythagoras theorem,
hypotenuse = √oppostie² + adjacent²
Therefore,
=> hypotenuse = √(-4)² + (-4)²
=> hypotenuse = √16 + 16
=> hypotenuse = √32
it can be written as,
=> hypotenuse = √2 x 16
=> hypotenuse = 4√2
Now the six trigonometric functions are based on the formula,
sin Θ = -4/4√2 => sin Θ = -1/√2
cos Θ = -4/4√2 => cos Θ = -1/√2
tan Θ = -4/-4 => tan Θ = 1
cosec Θ = 4√2/-4 => cosec Θ = -√2
sec Θ = 4√2/-4 => sec Θ = -√2
cot Θ = -4/-4 => cot Θ = 1
So, all the six trigonometric values are identified.
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The formula for the area of a trapezoid is given. Solve this equation for h, height. a=H(B1+B2)/2
The solution of the equation for h is H = 2a/(B1 + B2)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to solve the equation for h?The equation is given as
a=H(B1 + B2)/2
The above means that the variable h is represented by the variable H
Multiply both sides of the equation by 2
So, we have
2a = H(B1 + B2)
Divide both sides of the equation by (B1 + B2)
H = 2a/(B1 + B2)
Hence, the solution of the equation for h is H = 2a/(B1 + B2)
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Write and simplify an expression for the ratio of the volume of the cylindrical tank to its surface area (including the bases).
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
Let r be the radius and h be the height of the cylinder.
Then the volume of the cylinder will be
V = π r²h cubic units
Then the surface area of the cylinder will be
SA = 2πrh square units
Then the ratio of the volume of the cylindrical tank to its surface area will be
V / SA = π r²h / 2πrh
V / SA = r / 2
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
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factor the expressions:
1234567890123456789012345678901234567890
Write an equation of the line satisfying the given conditions. the line passes through (25,24)(25,24) and is perpendicular to y=6y=6.
The equation of the line is x = 25, in accordance with the given conditions.
What is the equation of a line?It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Given:
Line passes through (25,24)Line is perpendicular to y =6.To find: Equation of the line.
Finding:
Let the equation of the line be: (y - y') = m (x - x'),
where, (x',y') = point through which the line passes and m = slope of the line.
Since the given line is perpendicular to y = 6; the slope of this line = 0.The slope of the first line = [tex]\frac{1}{0}[/tex] , i.e., the y-intercept of this line does not exist and it is a vertical line.
Hence, the equation of the line is 0 = 1 (x - x')
Since the line passes through (25,24), x' = 25Thus, the equation of the line => 0 = 1 (x - 25)
=> x = 25.
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The half-life of phosphorus-32 is about14 days. there are 6.6 grams present initially.a.express the amount of phosphorus-32 remaining as a functionof time t.b.when will there be 1 gram remaining?
a. The expression of the amount of phosphorus-32 remaining as a function of time t is A(t) = [tex]6.6\left(\frac{1}{2}\right)^{t / 14}[/tex].
b. The time when 1 gram remaining is 38.1145 days.
What is the half-life?The half-life is the amount of time it takes for half of a unstable nuclei to decay. Each substance has its own half-life.
Now, as per the question;
Exponential growth is given by the formula;
[tex]A(t)=A_0(1+r)^t[/tex]
Where,
A(t) = amount at time t.
A₀ = Initial amount of the nuclei (= 6.6)
r = rate of increasing( = -1/2; as decay is always negative)
t = time (= t/14)
Part a. Calculate the expression for the amount of phosphorus-32 remaining as a function of time t as-
Substituting all the values in the equation;
[tex]\begin{aligned}&A(t)=6.6\left(1+\left(-\frac{1}{2}\right)\right)^{t / 14} \\&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
This is the requires expression.
Part b. Calculate the time there be 1 gram remaining as;
This time can be written as A(t) = 1.
Substitute the value in the equation.
[tex]\begin{aligned}&A(t)=6.6\left(\frac{1}{2}\right)^{t / 14} \\&1=6.6\left(\frac{1}{2}\right)^{t / 14}\end{aligned}[/tex]
[tex]\left(\frac{1}{2}\right)^{t / 14}=\frac{10}{66}[/tex]
Further solving;
t = 38.1145 days.
Thus, the time taken by phosphorus-32 to remain as 1 gram is 38.1145 days.
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Please help! Need answers fast
A manufacturing company has decided to be carbon free by 2030. what can it do to achieve this goal?
The manufacturing company has decided to be carbon free by 2030. so, it can reduce its pollution rate by using environmentally friendly equipment to achieve this goal.
Pollution:
The term pollution refers any substance that negatively impacts the environment or organisms that live within the affected environment.
Given,
A manufacturing company has decided to be carbon free by 2030.
Here we need to find the solution to achieve this goal.
To achieve this goal the company can take many measures this includes,
To completely switching to alternative sources of energy. The company can reduce its pollution rate by using environmentally friendly equipment.
By making maximum use of renewable energy in the company, in which energy can be emitted using solar energy, windmill etc.
And by planting more and more trees, the amount of oxygen in our environment should be increased.
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The brady family received 31 31 pieces of mail on april 22. the mail consisted of bills, letters, magazines, and ads. how many bills did they receive if they received the same number of bills as magazines, five more ads than letters, and three more letters than magazines?
The number of bills received by brady family are 781.
What is Linear equation in one variable?A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable with the form an x + b = 0 are solved utilizing basic algebraic operations.
Let x equal the number of letters obtained,
(x - 3) equal the number of bills obtained,
(x + 5) equal the number of advertisements received, and also
the number of magazines did receive is also given (x - 3).
The following equation can be derived:
x + (x - 3) + (x + 5) + (x - 3) = 3131
4x - 1 = 3131
4x = 3132
x = 784
Thus, number of bills received are-
(x - 3) = 784 - 3
number of bills received = 781.
Therefore, the number of bills obtained by brady family are 781.
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The finances of a group of pet owners were analyzed to determine how much they were spending on their pet(s) each year. A graph of that data is shown:
A graph with Number of Owners on the x axis and Yearly Cost of Pets, in hundreds, on the y axis. The x axis has a scale from 1 to 10 with an increment of 1. The y axis has a scale of 5 to 15 with increments of 1. A curved line connecting 1, 15, approx 3, 7, and 10, 0 is drawn.
Would (3, 7.2) be a realistic solution for the function? Explain.
Group of answer choices
Yes, it is realistic to have 7.2 owners who spend $300 dollars on their pet(s).
No, it is not realistic to have 3 owners.
Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
No, it is not realistic that owners spend $720 a year on their pet(s).
It is realistic that 3 owners spend $720 a year on their graph
C) Yes, it is realistic that 3 owners spend $720 a year on their pet(s).Given that
In the displayed graph, the y-axis shows the annual cost of pets in hundreds of dollars, while the x-axis shows the number of pet owners.The graph's path through the points(1,15),(3,7), and (10,0).To find
Would (3, 7.2) be a realistic solution for the function?So, according to the question
We can say that,
3 owners are present and,
A pet's annual cost is $720.
So, the option C (Yes, it is realistic that 3 owners spend $720 a year on their pet(s) ) is correct explanation of it.
Because no fractional value can represent the number of owners. Therefore, having 7.2 owners is not feasible and other options showing only one value. So A, B, and D are wrong answer.
C) Yes, it is realistic that 3 owners spend $720 a year on their pet(s).
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Please help thank youuu
Answer:
f(-7) = -15
g(-3) = 27
Step-by-step explanation:
We see that the functions defined are:
f(x) = 2x - 1
AND
g(x) = 2x^2 - 3x
This problem asks to find f(-7) and g(-3). To find this, we have to plug the respective numbers into the respective functions.
f(-7) = 2 (-7) - 1
f(-7) = - 14 - 1
f(-7) = -15
g(-3) = 2(-3^2) - 3(-3)
g(-3) = 2(9) + 9
g(-3) = 18+9
g(-3) = 27
FINAL ANSWER: f(-7) = -15, g(-3) = 27
Given last periods forecast of 65, and last periods demand of 62, what is the simple exponential smoothing forecast with an alpha of. 4 for the next period?.
The exponential smoothing forecast for next period is 63.2.
What is exponential smoothing?A time series forecasting technique called exponential smoothing can be expanded to support data with a systematic trend or seasonal component.
Now,
Given:
Last period forecast = 65Last period demand = 62α = 0.4To find: Simple exponential smoothing forecast with α = 0.4 for next period.
Finding:
Now, by the concept of exponential smoothing, forecast for next period will be given by:
Ft + 1 = α Dt + (1 - α)F,
where,
Ft+1 = the next forecast,
α = weighing factor,
Dt = actual value for this period,
F = forecast value for the current period,
Substituting the values in the above expression:
=> Ft + 1 = 0.4 (65) + (1 - 0.4) 62
=> Ft + 1 = 26 + 37.2
=> Ft + 1 = 63.2
Hence the exponential smoothing forecast for next period is 63.2.
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use mathematical symbols to write 3 different expressions to represent three groups of five
The different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3
How to write different expressions to represent three groups of five?The mathematical statement is given as:
three groups of five
The statement three groups of five means
Three multiplied by 5
i.e. 3 * 5
This can also be written as
5 + 5 + 5
Also, it can be expressed as
3 + 3 + 3 + 3 + 3
Hence, the different expressions to represent three groups of five are 3 * 5, 5 + 5 + 5 and 3 + 3 + 3 + 3 + 3
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Two customers spent the same total amount of money at a resturant.
* The first customer bought 8 hot wings and left a $4 tip.
* The second customer bought 10 hot wings and left a $2.80 tip.
* Both customers paid the same amount per hot wing.
How much does one hot wing cost at this resturant in dollars and cents?
Considering the definition of an equation and the way to solve it, the cost of one hot wing is $0.6.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the cost of one hot wing, and knowing that:
The first customer bought 8 hot wings and left a $4 tip. → First customer payment= 8x +4The second customer bought 10 hot wings and left a $2.80 tip. → Second customer payment= 10x + 2.80Both customers paid the same amount per hot wing.the equation in this case is:
First customer payment= Second customer payment
8x +4= 10x +2.80
Solving:
4 - 2.80= 10x - 8x
1.2= 2x
x= 1.2 ÷ 2
x=0.6
Finally, the cost of one hot wing is $0.6.
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Consuelo is buying flavored coffee and plain coffee. the total amount of money she spends on coffee is t = 5.50p + 7f, where p represents the cost of a package of flavored coffee.
Answer is
(a) She can buy 7 packages of plain coffee or 5 packages of coffee.
(b) f = [tex]\frac{T- 5.50 p}{7}[/tex]
(c) she can buy 3 packages of flavoured coffee
(a) she spent on coffee is $ 40
amount of money she spends on coffee is 5.50
then, packages of plain coffee = [tex]\frac{40}{5.50}[/tex] ≈ 7.2
so she buy 7 packages of plain coffee.
she spent on coffee is $ 40 and amount spends on flavoured coffee is 7
then , packages of flavoured coffee = [tex]\frac{40}{7}[/tex] ≈ 5.7
so she can buy 5 packages of flavoured coffee.
(b)According to question ,
T = 5.50 + 7f
so 7f = T - 5.50
then , f = [tex]\frac{T - 5.50}{7}[/tex]
(c) we get the value of f = [tex]\frac{T - 5.50}{7}[/tex]
given that , f is equal to 3
then, f = [tex]\frac{T - 5.50}{7}[/tex]
= [tex]\frac{T - 5.50}{7}[/tex]×3
we get = [tex]\frac{T - 16.5}{7}[/tex]
when T is equal to 40
then , f = [tex]\frac{40 - 16.5}{7}[/tex] ≈ 3.35
so she can buy 3 packages of flavoured coffee.
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Rearrange the formula to make x the subject y=4(x-1)
By rearranging the formula using algebraic operations, the value of x is [tex]\frac{y}{4}[/tex] - 1.
What is an Algebraic Expression?When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
To find the value of x, use the same operations on both sides of the equation.
For making x the subject
Divide by 4 on both sides
[tex]\frac{y}{4}[/tex] = (x-1)
On both sides of the equation, add 1.
[tex]\frac{y}{4}[/tex] - 1 = x
As a result, by rearranging the equations, the value of x is [tex]\frac{y}{4}[/tex] - 1.
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Write an expression that represents the total owed for 4 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $35?
Answer:
4c + 35
Step-by-step explanation:
What every the monthly amount is (c) you would multiply that by 4 to find the cost for 4 months and then you have to add in the one time cost of 35
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 2), (negative 1, 4), (1, 1), (1, 3), (2, negative 3).
Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?
We need to remove either (1, 4) or (1, 1) to create a function.
How to alter a relation in order to obtain a function
Relations are formed by two sets, an input set known as domain and an output set known as range and relationships between these sets. A relation is a function if and only if each element from domain is related to only one element of the range. Mathematically speaking, we must satisfy the following proposition:
x → f(x), x → f'(x) ⇒ f(x) = f'(x)
Based on this definition, there are two possibilities to create a function:
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1,3 is the answer I believe. :)
A school has 360 students, 4/9 of whom are boys. How many of the students are boys? How many are girls?
Answer:
There are 160 boys and 200 girls
Step-by-step explanation:
its a proportion
You have one box that is 1 3 11 feet tall and a second box that is 1.27 feet tall. Write the decimal expansion for 1 3 11. If you stack the boxes, about how tall will the stack be?
Answer:
Step-by-step explanation:
Anyone 10-11 grade? Ig or S?
i am 11th grade
but why?
How much of a(n) 70% orange juice drink must be mixed with 18 gallons of a 30% orange juice drink to obtain a mixture
that is 50% orange juice?
Answer:
18 gallons
Step-by-step explanation:
Start with x gallons of 70% juice and 18 gallons of 30% juice.
Result: x + 18 gallons of 50% juice
0.7x + 0.3 × 18 = (x + 18)(0.5)
0.7x + 5.4 = 0.5x + 9
0.2x = 3.6
x = 18
Answer: 18 gallons
which answer???????
plss
Answer:
I am not sure myself but I think the answer is 2.3 hours per week.
a) down payment, b) amount of the loan, c) monthly payment, and d) finance charge.
Shelly Lemony obtains a small business equipment loan for $120,000. Her down payment is 20% and the APR is 8% for 12 months.
a) Shelly Lemony's down payment is $24,000.
b) The loan amount is $96,000.
c) The monthly payment is $8,350.89.
d) The finance charge is $4,210.68.
What is the down payment?The down payment represents the initial up-front partial payment for the purchase of the equipment on loan.
The down payment reduces the cost of the equipment to the loan amount. Finance companies demand a down payment to ascertain the buyer's willingness and ability to proceed with the loan arrangement.
It is a sign of commitment to meet the loan contract obligations.
Data and Calculations:Monthly Pay: $8,350.89
Total Loan Amount = $96,000.00
Upfront Payment $24,000.00
Equipment loan = $120,000
Number of periods = 12 months
APR = 8%
Total of 12 Loan Payments = $100,210.68
Total Loan Interest = $4,210.68
Total Cost (price, interest, tax, fees) = $124,210.68
Thus, Shelly will make a down payment of $24,000 or 20% of the equipment loan.
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The functions are defined:
f(x) = -2x
g(x) = 2x + 5
h(x) = x² + 3x-10
Calculate the indicated function values.
ƒ(6²)
The indicated function value is f(6²) = -72
How to calculate the indicated function values?The function definitions are given as
f(x) = -2x
g(x) = 2x+ 5
h(x) = x^2 + 3x - 10
The function f(6²) means that x = 6² in f(x)
So, we have
f(6²) = -2(6²)
Evaluate
f(6²) = -72
Hence, the indicated function value is f(6²) = -72
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Find the rate of change for each set of ordered pairs. What is
the average rate of change of all the sets?
(2,3.5), (6,5.5)
(-1,0), (0, 3)
(3,-3), (4,4)
Write your answer to the average rate of change as a fraction,
a/b.
Enter the answer
SCRATCHPAD
Check it
Improve this question
The rate of change for each set of ordered pairs is:
a. 1/2
b. 3
c. 7
How to Find the Average Rate of Change?The average rate of change = change in y / change in x.
Average rate of change for (2,3.5), (6,5.5):
Average rate of change = (5.5 - 3.5)/(6 - 2) = 2/4 = 1/2
Average rate of change for (-1,0), (0, 3):
Average rate of change = (3 - 0)/(0 - (-1)) = 3/1 = 3
Average rate of change for (3,-3), (4,4):
Average rate of change = (4 -(-3))/(4 - 3) = 7/1 = 7
Therefore, the rate of change for each set of ordered pairs is:
a. 1/2
b. 3
c. 7
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Two players are playing chess and usually player a wins 65 percent of games. they will play 3 games and the winner is:_________
In each game, the probability that player A wins the game is 13/20 and player B wins the game is 7/20.
What is probability?Probability is a branch of mathematics with numerical characterizations of how likely an event is really to occur or how probable a proposition is to be true. The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.To find the probability:
To find the probability that player a wins the game and by what probability player b wins the game.So, 65/100 = 13/20.So, the probability of player b will be 7/20.Therefore, in each game, the probability that player A wins the game is 13/20 and player B wins the game is 7/20.
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please help,, will mark branliest if its right!!
Answer:
1. DNE
2. DNE
3. (-2, inf)
4. (-3,-2)
Step-by-step explanation:
Multiplying and dividing Decimals
In qualifying for an auto race, one driver had lap speeds of 195.3 mph, 190.456 mph,193.557 mph, and 192.575 mph. What was the driver's average speed for the laps driven?
Answer:
193.0 mph
Step-by-step explanation:
The average is defined as the sum of the items divided by the number of items. In this case the sum is 771.888. If we divide that by the number of items (4) we get 192.972. However, our answer typically cannot have more significant digits than the element having the least number of significant digits. Since one of the numbers has only one digit to the right of the decimal point, we would usually want to round our answer to one place as well. So 192.972 will round to 193.0.
(PLEASE HELP!) A car travels 76 km due north and then 25 km due east.
(a) What is the cars current bearing from the starting point correct to the nearest degree?
(b) How far is the car from the starting point correct to the nearest km?
Answer:
Step-by-step explanation:
Look at the File I attached. The Question says that a car travels 76 km north then 25 km east. Now think of this as the Right angled triangle I attached in the file.
a) Bearing from the staring point to the means the degrees of the part i marked with a question mark.
Now SOH CAH TOA
76 km is the ADJACENT
25 km is the OPPOSITE
and x is the HYPOTENUSE
We have the values of the ADJACENT and the OPPOSITE.
Now see which rule has both, It is TOA(tan rule) which is:
tan(y) = OPPOSITE/ADJACENT (y is the degrees we will get)
tan(y) = 25/76 ( opposite of the degree we need is 25 and adjacent is 76)
tan inverse(25/76) = y (inverse will be given as to the power -1 on the calculator)
FINAL ANSWER OF (a) = 18.21°
b) This part is asking for the length of the hypotenuse, which i denoted as x in the attached file.
For this part, you will use the Pythagoras Theorem
Which is :
a² + b² = c²
Where c is the hypotenuse and a and b are the opposite and adjacent.
So
76² + 25² = x²
6401 = x²
√6401 = x
x = 80.01
Shifting data, by adding a constant to each data value, does not change the _________.
A. quartiles
B. mean
C. standard deviation
D. median
The standard deviation is a measure of a collection of values' variance or dispersion. The correct option is C, standard deviation.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Shifting data, by adding a constant to each data value, do not change the standard deviation. This is because the standard deviation is a measurement of how much a group of values varies or is dispersed.
Hence, the correct option is C, standard deviation.
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