Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The terminal point is (1.33,−2).
What is the angle's measure (in radians)?
θ=
Answers
Answer:
5.3 or (4217pi/2500)
Step-by-step explanation:
Create a right triangle with the coordinates provided.
We can ignore the negative sign and create the equation
[tex]tan(x) = \frac{1.33}{2} [/tex]
x = 33.624
We then add 270 and x together because the coordinates are in the 4th quadrant.
angle = 303.624
To convert to radians, we multiply this number by pi/180
5.3 radians
The measure of the angle is approximately [tex]1.687\pi[/tex] radians.
By trigonometry we can determine the direction of the terminal ray ([tex]\theta[/tex]), in radians, by the following inverse trigonometric function:
[tex]\theta = \tan^{-1}\frac{y}{x}[/tex] (1)
Since [tex]x > 0[/tex], [tex]y <0[/tex] and angle is in standard position, the angle must have a direction greater than [tex]\frac{3\pi}{2}[/tex] radians and less than [tex]2\pi[/tex] radians. Hence, we conclude that direction of the angle is:
[tex]\theta = \tan^{-1} \left(\frac{-2}{1.33} \right)[/tex]
[tex]\theta \approx 1.687\pi\, rad[/tex]
The measure of the angle is approximately [tex]1.687\pi[/tex] radians.
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Related Questions
It takes 43 facial muscles to frown. This is 26 more muscles
than it takes to smile. How many muscles does it take to
smile?
Answers
Answer:
17
Step-by-step explanation:
43 - 26 = 17
Answer:
43 - 26 = 17 muscles
find the image of ( 1 , 2 ) after a reflection about y = x followed by a reflection about y = - x
PLS ONLY ANSWER IF YOU KNOW THE ANSWER.
Answers
1. (2,1)
2. (-1,-2)
Answer:
(-1,-2)
Step-by-step explanation:
Think of the line y=x as a mirror. The image of the point (1,2) is obtained by drawing a line through (1,2) perpendicular to the line y=x and finding the point on the perpendicular line that is equal distance from the line y=x but on the other side. This gets you to the point (2,1).
Similarly, from (2,1) find the mirror image using the line y=-x as the mirror. You travel diagonally 1.5 diagonal squares to reach y=-x and then continue another 1.5 diagonals to reach (-1,-2) which is your answer.
What is the area of this figure?
Answers
9514 1404 393
Answer:
54 square units
Step-by-step explanation:
One way to find the area is to divide the figure into 3 parts using a horizontal line at y=3.
The trapezoid below the line has bases 9 and 7, and height 6, so an area of ...
A = (1/2)(b1 +b2)h
A = (1/2)(9 +7)(6) = 48 . . . . square units
The left triangle above the line has a base of 3 and a height of 2, so an area of ...
A = (1/2)bh
A = (1/2)(3)(2) = 3 . . . . square units
The right triangle above the line has a base of 6 and a height of 1, so an area of ...
A = (1/2)(6)(1) = 3 . . . . square units
Then the total area is ...
figure area = trapezoid area + left triangle area + right triangle area
figure area = (48 + 3 + 3) square units = 54 square units
Two parallel lines are cut by a transversal. Find the value of x
Answers
Answer:
x = 18
Step-by-step explanation:
you set the 2 equations equal to eachother
you minus x on both sides to get x on one side
than find the answer
*URGENT* THERE CAN BE MORE THAN 2
Answers
Answer:
12.50p+50.00 and 50(0.25p + 1.00)
im positive of both answers
What is the fraction for 9 copies of 1/12
Answers
Answer:
9 x 1/12 = 4 1/2
Have a nice day
Together teammates Pedro and Ricky got 2671 base hits last season Pedro had 275 more hits Ricky hits did each player have
Answers
What is the function of the seed? (What does it provide the embryo?)
Answers
Answer:
Seeds serve several functions for the plants that produce them. Key among these functions are nourishment of the embryo, dispersal to a new location, and dormancy during unfavourable conditions.
Step-by-step explanation:
3. The Mathville Zoo only has tigers and
ostriches. The zoo keeper says they have 22
animals and the animals have a total of 70 feet.
Find the number of each kind of animal?
Answers
9514 1404 393
Answer:
13 tigers9 ostrichesStep-by-step explanation:
Let t represent the number of tigers. Then the number of feet is ...
4t +2(22 -t) = 70
2t = 26 . . . . . . . . . subtract 44, collect terms
t = 13 . . . . . . . divide by 2; number of tigers
22 -t = 9 . . . . number of ostriches
The zoo has 13 tigers and 9 ostriches.
Robert painted 4/8 of each tile with green paint. He painted 52 tiles. What is the total amount of tiles that he painted green?
Please show an explanation to solve this problem. Thank you.
Answers
Answer:
The answer is 26
Step-by-step explanation:
All we do is multiply 4/8 by 52.
52 = 52/1
52/1 * 4/8 = 208/8
208/8 = 26
So the answer is 26.
Hope this helps! :)
pablos pizza makes a profit of $495 each day for 12 days, what is the profit for the 12 days
Answers
Answer:
5940
Step-by-step explanation:
495 x 12 = 5940
What is 24 divided by 849, be sure to show your work.
Answers
Answer:
0.02826855123 or 35.37
Step-by-step explanation:
24/849 = 0.02826855123
849/24 = 35.37
Use the diagram below to find x and each missing angle
Answers
7x+5 = 180
7x = 175
x = 25°
Angle 1 is 127°
Angle 2 is 53°
U just sub in x=25 into your two equations. :)
Need help ! (algebra)
Answers
Austin walks 1/3 of the way to school and stopped to rest. Devyn walks 2/6 of the way to the school and stops to rest who traveled further
Answers
Answer:
Austin and Devyn.
Step-by-step explanation:
1/3 and 2/6 are equal fractions.
I need help on this question
Answers
Answer:
a = 62.5
b = 40
c =62.5
d = 70
Please help need answer!
Answers
Answer: About 513 feet
A more accurate value is roughly 512.575960394824
==============================================================
Explanation:
With many trig problems, a diagram should help steer you in the right direction. See below.
The red angle is the angle of depression. It's formed by starting off looking straight horizontal, then we look down 26 degrees. The blue angle adds to the red angle to get 90, so we can see that 26+64 = 90. Or you could say 90-26 = 64.
The goal is to find the value of x, which is the length from B (the lighthouse base) to point C (the ship's location).
The lighthouse is 250 ft tall, meaning AB = 250
We'll use angle BAC, or angle A for short, as the reference angle. This is the blue angle in the diagram.
We have a known adjacent side (AB = 250) and an unknown opposite side (BC = x). We use a tangent ratio to tie these sides together with the reference angle in question. This way we can solve for x.
-------------------
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(64) = x/250
250*tan(64) = x
x = 250*tan(64)
x = 512.575960394824
x = 513
The distance from B to C is roughly 513 feet.
I'm rounding to the nearest whole number because the other values given to you are whole numbers.
Dale has set up his own business. He now needs funds to buy a new machine to cater to those consumers whose needs could not be met earlier due to lack of infrastructure and funds. Which stage is his business in?
A.
seed stage
B.
growth stage
C.
maturity stage
D.
decline stage
The correct answer is growth stage
Answers
Answer:
The answer is B
Step-by-step explanation:
The preceding two stages are development stage and startup stage. In growth stage one should first focus on fine tuning the business model and by finding ways for operational inefficiencies. Dale has actually already identified the inefficiency which is new machines and non being able to cater to some customers due to lack of machines. In this exact stage businessman try to grow the business by analyzing the main profit drivers and the finding ways to grow the profit driver with less cost
porque una roca pequeña se hunde en el agua mientras los barcos no se hunden apesar de ser tan pesados
Answers
Answer:
Step-by-step explanation: una roca se unde porque aunq tiene una forma solida igualmente que un barco, la roca no tiene aire dentro de ella, a diferencia del barco que es hueco por dentro, contiene aire causando que flote y no pueda hundirse
Thank you all for helping me with every thing! I also need help with this one :)
Answers
Answer:
1.5/6
2.1/6
Step-by-step explanation:
Answer:
[tex]\frac{5}{6}[/tex] and [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
find x. :( i’ll mark brainlist and give thanks !
Answers
Answer:
tan15=x/300
0.267=x/300
0.267×300=x
x=80.01=80(approx)
Skyler getting a delivery from Chick-fil-A they charge $3 delivery fee plus $0.25 per mile write an equation to find the total cost y for a delivery that is X miles away
Answers
Answer:
y = 3 + 0.25x
Step-by-step explanation:
x represents the miles and if Skyler is charged $0.25 per mile, then x goes with the 0.25. The $3 is a flat fee and doesn't get added any more times then when it is first added.
Rewrite the expression by factoring out (x+3).
7x²(x + 3) + 5(x+3)
Answers
Answer:
(7x² + 5) ( x + 3)
Step-by-step explanation:
7x²(x + 3) + 5(x+3)
Factor out x + 3
(7x² + 5) ( x + 3)
7x³ + 21x² + 5x + 15
Factorize
7x²(x + 3) + 5(x + 3)
(7x² + 5) ( x + 3)
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected
from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli with mean weight of 15.26 grams and standard deviation of 2.56 grams. The margin of error (ME) to construct a 99% confidence interval for the true mean amount of cheese filling is
A) 2.064 B) 1.432 C) 3.745 D) 1.276 E) 1.797
b. A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected
from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find the 99% confidence interval of 14.16 to 15.84 grams. Which of the following is the correct interpretation?
I. We are 99% confident that the mean weight of cheese filling in all ravioli made by this process is between 14.16 and 15.84 grams.
II. 99% of all ravioli made by this process will have cheese filling weights between 14.16 and 15.84 grams.
III.We are 99% confident that the interval (14.16, 15.84) contains the mean weight of cheese filling in all ravioli made by this process.
IV. The weight of cheese filling in the ravioli is between 14.16 and 15.84 grams 99% of the time.
A) I only
B) III only
C)I and III.
D) II and III
E) I and IV
Answers
Answer: a. B) 1.432
b. E) I and IV
Step-by-step explanation:
a. Margin of error to construct a 99% confidence interval is calculated as
[tex]ME=t.\frac{s}{\sqrt{n}}[/tex]
where
t is the critical value expressed as t-score, which comes from t-distribution;
s is sample standard deviation
n is sample size
In this case, a t-score is used because the population standard deviation is unknown and the sample size is small, n < 30.
The way to find t-score is:
1) Define the degree of freedom, which is sample size minus 1: df = n - 1;
2) Compute alpha: [tex]\alpha=1-\frac{confidence}{100}[/tex];
3) Find the critical probability: [tex]p=1-\frac{\alpha}{2}[/tex]
With the df and critical probability, consulte the t-distribution table and find the score.
For the cheese filling:
df = 24
p = 0.995
t-score = 2.797
Calculating margin of error:
[tex]ME=2.797.\frac{2.56}{\sqrt{5}}[/tex]
ME = 1.432
The margin of error to construct a 99% confidence interval for the true mean amount of cheese filling is 1.432.
b. Confidence interval is an interval in which we have a percentage of certainty that the true population mean is. For example, with a 99% confidence interval of 14.16 to 15.84 grams, we are 99% confident that the true mean weight of cheese filling is between those numbers or that the weight of cheese filling is between 14.16 and 15.84 grams 99% of the time.
Enter the value of 3.4. (6 + 12).
Answers
Answer:
cool
Step-by-step explanation:
add the (6+12) and than multiply what you get by 3.4. you will get the answer
The value of the expression is 216.
What is a mathematical expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Quantities (operands), factors, operations, operations, braces, grammar, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features. In algebra, a value may be designated by an expression; this value may rely on the values given to the variables that the expression contains. The semantics associated with the symbols in the expression determine this value. The expression's context determines which semantics to use. Depending on the suggested sequence of operations by the context, the identical syntactic statement 1 + 2 3 might have multiple values (mathematically 7, but also 9).
The given expression is 3.4.(6+12)
And it can be solved as
3.4.(6+12) = 12.18 = 216
Hence, the value of the above expression is 216.
To know more about expressions, click on the link
https://brainly.com/question/18189573
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Base your answer on Ali opened a savings account with $100. He saves $25 per month.
Solve an inequality to find the least number of months it will take Ali to have $700.
Answers
Answer:
24
Step-by-step explanation:
700- 100 = 600 divided by 25 = 24
Help plz I’ll mark brainliest
Answers
3x+4y=10—2
Adding equation 1 and 2,
4x=20
x=5
Putting x in equation 2,
4y=-5
y=-5/4
Each month, a shopkeeper spends 5x+17 dollars on rent and electricity. If she spends 3x-4 dollars on rent how much does she spend on electricity?
Answers
Answer:
2x-13
Step-by-step explanation:
5x-3x=2x
17-4=13
The planning department of Abstract Office Supplies has been asked to determine whether the
company should introduce a new computer desk next year. The department estimates that $8,000
of new manufacturing equipment will need to be purchased and that the cost of constructing each
desk will be $200. The department also estimates that the revenue from each desk will be $600.
a. Determine the revenue function R(x) from the sale of x desks. R(x) =
Answers
8,000/800=10
So, the answer is 10
Evaluate (14 + x) = 2 when x = 4. A. 7 O B. 18 C. 11 D. 9
Answers
Answer:
14+4=18 have a good day Ahead