find the value of each variable using sine and cosine. round your answers to the nearest tenth
Answers
Answer:
x=9.5 and y=15.3
Step-by-step explanation:
to find x you do sine of 32 = x/18 because the sine is opposite/hypotenuse
you put in a calculator sine (32) x 18 and get 9.538546756
so x equals 9.538546756 but it says to round to the nearest tenth so x equals 9.5
to find y you do the cosine of 32 = y/18 because cosine is adjacent/hypotenuse
cosine of (32) x 18 = 15.26486573 so you equals 15.26486573 but since you have to round to the nearest tenth y = 15.3
The value of x is 9.54.
The value of y is 15.3.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
From the figure,
Sin 32 = x / 18
Cos 32 = y / 18
Now,
Sin 32 = 0.53
Cos 32 = 0.85
Now,
0.53 = x / 18
Multiply 18 on both sides.
x = 0.53 x 18
x = 9.54
0.85 = y / 18
Multiply 18 on both sides.
y = 0.85 x 18
y = 15.3
Thus,
The value of x is 9.54.
The value of y is 15.3.
Learn more about trigonometric identities here:
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Related Questions
You may need to use the appropriate technology to answer this question. The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good, and fair categorical scale. Assume the sample data for 200 respondents below applies to this study.
Quality of Management Reputation of Company
Excellent Good Fair
Excellent 40 25 8
Good 35 35 10
Fair 25 10 12
Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.
a. State the null and alternative hypotheses.
b. Find the value of the test statistic. (Round your answer to three decimal places.)
c. Find the p-value. (Round your answer to four decimal places.)
Answers
Answer:
Step-by-step explanation:
The null and alternative hypothesis:
[tex]H_o \text{: Quality of management and reputation of company are independent}[/tex]
[tex]H_a \text{: Quality of management is not independent of the reputation of company }[/tex]
The observed values:
Excellent Good Fair Total
Excellent 40 25 8 73
Good 35 35 10 80
Fair 25 10 12 47
Total 100 70 30 200
The expected values = (Row total/column total)/grand total)
Excellent Good Fair
Excellent 36.5 25.55 10.95
Good 40 28 12
Fair 23.5 16.45 7.05
O E (O - E)²/E
40 36.5 0.3356
35 40 0.6250
25 23.5 0.0957
25 25.55 0.0118
35 28 1.7500
10 16.45 2.5290
8 10.95 0.7947
10 12 0.3333
12 7.05 3.4755
9.951
[tex]X^2 = \sum \dfrac{(O-E)^2}{E} \\ \\ \mathbf{X^2 = 9.951}[/tex]
Degree of freedom [tex]df = (r-1)(c-1)[/tex]
[tex]df = (3 - 1 ) (3 - 1)[/tex]
[tex]df = (2)(2)[/tex]
[tex]df = 4[/tex]
Using Excel formula =CHIDIST(x²,d.f)
The P-value = 0.0413
Help plzzzz helppp heppppdidjjdhjrbrbfnd meeee
Answers
Answer:
The large one
Step-by-step explanation:
If she used the WHOLE thing in the large one and HALF in the smaller one then that means there is more in the large one and that it is more choclete.
Answer:
The larger one!
Step-by-step explanation:
Which of the following is the correct factorization of -y²+y+6?
Answers
Answer:
(−y−2)(y−3)Step-by-step explanation:
I'm just going to factor it for you.
Factor −y^2+y+6
−y^2+y+6
=(−y−2)(y−3)
Answer:
(−y−2)(y−3)
Can someone please help me understand this and the answer
Answers
Answer:
x ≤ 2
Step-by-step explanation:
1
Add or subtract and simplify. *
(3d + 5) + (40 – 1)
Answers
How to:
Combine like terms
A 31-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 33 m. Find the length of the shadow. If necessary,
round your answer to the nearest tenth.
B
5
?
Answers
Answer:
Step-by-step explanation:
[tex]\text{By the Pythagorean Theorem the hypotenuse of a right triangle squared is equal to the sum of the squared sides.}\\ \\ h^2=x^2+y^2\\ \\ 33^2=31^2+x^2\\ \\ x^2=33^2-31^2\\ \\ x^2=128\\ \\ x=\sqrt{128}\\ \\ x\approx 11.3m[/tex]
what was the main difference between the French and British armies in the French and Indian War
Answers
Hope this helps :)
Solve these with work shown please.
Answers
Step-by-step explanation:
substitute the value in the value of x and u will get the result.
(2a+5)³ is equal to 8a³+60a²+________?
Answers
the answer is will be +50a+125
What types of numbers are Irrational numbers? A)Whole Numbers (positive and negative) B)Repeating Decimals C)Decimals that Terminate D)Decimals that never end
Answers
Answer:
Whole numbers, repeating decimals, and decimals that never end
Step-by-step explanation:
A line passes through the points (-5, 2) and (10,-1). Which is the equation of the line?
o y--3x+1
oys
O y=-5x - 23
O y = 5x + 27
Answers
Answer:
0
Step-by-step explanation:
what happened that 0 ok live bistro 2.52 and 10 1 which is the quality of the line or 3 x + 100 s y if x = 25
Cruz is the editor of a magazine.
The magazine has 40 pages.
The magazine must have:
20% of the pages for adverts
1/4 of the pages for photos
the remaining pages for articles.
Work out the number of pages for articles in the magazine.
Show your working out.
Answers
Answer:
22
Step-by-step explanation:
20% * 40 = 20 / 100 * 40 = 800 / 100 = 8
1/4 * 40 = 40 / 4 = 10
So far we have use 8 + 10 = 18
There are 40 - 18 pages left
articles = 22
If f(x) = (3+x)/ (x-3),what is f(a+ 2)?
Answers
f(a + 2) = (3 + a + 2) / (a + 2 - 3)
Simplifying the function generated above,
f(a + 2) = (5 + a) / (a - 1)
Fill in the blank to make the two fractions equivalent.
4/7 = ?/28
Answers
Answer:
16
Step-by-step explanation:
28/7 = 4
4 x 4 = 16
16/28 = 4/7
What Reasoning could you use to prove the two triangles shown below are congruent?
AAS
SAS
ASA
SSS
Answers
I KNOW ITS SAS....................
you need to use SAS
Step-by-step explanation:
so first you write PQ=QR
PQS=SQR
PS=SR
I need help on 21 and 22
Answers
Answer:
Q-22 (a) area of each face (square) = sxs
= 10 x 10
= 100 inches²
Total surface area = 6a²
= 6 x 10 x 10
= 600 inches²
Suppose a student carryinga virus returns toan isolated college campus o 1000 students. Determine a differential equation for the number x(t) who have contracted the fluif the rate at which the disease spreads is proportional to the number of interactions between the number of students who have the fluand the number of students show have not been exposed to it.
Answers
Answer:
[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ;
where k is the proportionality constant
Step-by-step explanation:
Let
The number of people who are infected with the flu = x(t)
Total number of students = 1000
So,
Total number of student who do not expose with the flue = 1000 - x(t)
As given,
We have to find the differential equation such that
The rate at which the disease spreads is proportional to the number of interactions between the number of students who have the flu and the number of students show have not been exposed to it.
⇒[tex]\frac{dx}{dt}[/tex] ∝ x(t) . [ 1000 - x(t) ]
⇒[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ; where k is the proportionality constant
x^2 and -x^2 for x =-3
Answers
Answer:
9 and -9
Step-by-step explanation:
x^2:
all you have to do is (-3)^2 = -3 * -3 = 9
-x^2:
this would be -(-3)^2
the order of operations says to do exponents first, so you would have:
-(9) or -9
cuál es el número entero de 2° bajo Cero
Answers
Answer:
-2 °C.
Step-by-step explanation:
Usa el signo + para representar temperaturas arriba de cero y el signo – para representar temperaturas bajo cero.
Find the equation of this line
Answers
Answer: y=1x+1
Step-by-step explanation:
Rise/Run = 1/1 = 1 = slope
y-intercept : 1
Answer:
y=-2x+1 is the answer
Step-by-step explanation:
3x+2=14 what number makes the equation true?
Answers
Answer:
Step-by-step explanation:
3x+2=14 subtract 2 from both sides
3x=12 divide both sides by 3
x=4
Dave divided 3/5 of a gallon of plant fertilizer evenly among 6 smaller bottles. How many gallons did he put in each bottle?
Whoever answers first gets brainliest please help
Answers
Answer:
Brothers Sorry I don't
Step-by-step explanation:
Please give thanks to all my answers and please mark as brilliant and please follow me
prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers
Answers
Answer:
Proved
Step-by-step explanation:
Given
[tex]a_n = 2n[/tex]
Required
Prove that [tex]S_n = n(n+1)[/tex]
The given sequence is an arithmetic sequence.
The Sn of this sequence is:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
Calculate a1
[tex]a_n =2n[/tex]
[tex]a_1 =2*1[/tex]
[tex]a_1 =2[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
[tex]S_n = \frac{n}{2}(2 + 2n)[/tex]
Factor out 2
[tex]S_n = \frac{n*2}{2}(1 + n)[/tex]
[tex]S_n = n(1 + n)[/tex]
[tex]S_n = n(n + 1)[/tex] --- Proved
15 PTS !!
NEED ASAP HELP !!
Answers
Answer:
314.16 m^2
Step-by-step explanation:
Julissa earns $13 per hour. If her regular hours are 40 hours per week, and she receives double time overtime,
find her total pay for a week in which she works 45 hours.
Answers
Answer:
1,040 dollars
Step-by-step explanation:
which orded pair is a solution of the equation 2x+4y=6x-y
Answers
$26,088,808.74 +
$34,311,887.98 =
Answers
Answer:60,400,696.72
Step-by-step explanation:
it just is...
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. where traffic flow in vehicles per hour vehicle speed in miles per hour The following data were collected during rush hour for six highways leading out of the city. Traffic Flow () Vehicle Speed () 1257 36 1329 45 1227 30 1336 50 1349 55 1124 25 a. Use the data to compute the coefficients of this estimated regression equation (to decimals). Enter negative value as negative number. (Create the variable first using Data/Transform
Answers
Answer:
ŷ = 0.1286X - 123.2175 ;
R = 0.9465
R² = 0.8958
Step-by-step explanation:
Given the data:
Traffic Flow, X : ()
1257
1329
1227
1336
1349
1124
Vehicle speed, Y () :
36
45
30
50
55
25
The estimated regression equation using a linear regression calculator is given thus:
ŷ = 0.1286X - 123.2175
According to the general linear regression formula :
y = mx + c
Where ; y = predicted variable (vehicle speed)
x = predictor variable (traffic flow)
Slope, m = 0.1286
Intercept, c = 123.2175
The correlation Coefficient, R = 0.9465, This depicts a strong positive relationship between traffic flow and vehicle speed.
The Coefficient of determination, R² = 0.9465² = 0.8958 ; This means about 89.5% of variation in Vehicle speed can be explained by the regression line.
What is the probability that the red die shows a six or the green die shows a six?
Answers
Answer:
[tex]\frac{11}{36}[/tex]
Step-by-step explanation:
= 1/6 + 1/6 - 1/6^2
Calculate the distance between the points A=(-5, 6) and J = (1, -1) in the coordinate plane.
Answers
Answer:
7 cubic meters away
Step-by-step explanation:
