Find sin2x, cos2x, and tan2x if sinx=-15/17 and x terminates in quadrant III
Given:
[tex]\sin x=-\dfrac{15}{17}[/tex]
x lies in the III quadrant.
To find:
The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].
Solution:
It is given that x lies in the III quadrant. It means only tan and cot are positive and others are negative.
We know that,
[tex]\sin^2 x+\cos^2 x=1[/tex]
[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]
[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]
[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]
x lies in the III quadrant. So,
[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]
[tex]\cos x=-\dfrac{8}{17}[/tex]
Now,
[tex]\sin 2x=2\sin x\cos x[/tex]
[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]
[tex]\sin 2x=-\dfrac{240}{289}[/tex]
And,
[tex]\cos 2x=1-2\sin^2x[/tex]
[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]
[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]
[tex]\cos 2x=\dfrac{289-450}{289}[/tex]
[tex]\cos 2x=-\dfrac{161}{289}[/tex]
We know that,
[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]
[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]
[tex]\tan 2x=\dfrac{240}{161}[/tex]
Therefore, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].
please help me do it
Answer:
D) FJ is a perpendicular bisector
15 tractors each working 8 hours a day take to take eight days to Plough a piece of land how many days will it take 24 tractors each working 10 hours a day to plough the same piece of land
It will take 24 tractors, each working 10 hours a day, a total of 4 days to plough the same piece of land.
To determine how many days it will take 24 tractors, each working 10 hours a day, to plough the same piece of land, we can use the concept of man-hours.
Given that 15 tractors, each working 8 hours a day, took 8 days to complete the task, we can calculate the total man-hours required to plough the land.
Total man-hours = Number of tractors * Hours per tractor * Number of days
Total man-hours = 15 tractors * 8 hours/tractor * 8 days
Total man-hours = 960
Now, let's calculate the number of days required for 24 tractors, each working 10 hours a day, to complete the task.
Number of days = Total man-hours / (Number of tractors * Hours per tractor)
Number of days = 960 / (24 tractors * 10 hours/tractor)
Number of days = 960 / (240)
Number of days = 4
As a result, ploughing the same plot of land will require 24 tractors to labour for a total of 4 days at 10 hours per day each.
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Which one? Do i chose
Answer:
226 inches cube
Step-by-step explanation:
The volume of the cylinder is the area of the base X height therefore it would be 3^2 * 3.14 * 8 = 72 * 3.14 = 226.08.
Answer:
151 in^3
Step-by-step explanation:
pi x 3^2 x 5.5 (the approximate water level)
= 155
151 is the closest answer
A water bottle company is designing a new larger cylindrical water bottle that is intended to hold 4 times as much water as the original cylindrical water
bottle. Which of the following methods would work to create the larger water bottle with the intended volume?
1. Double the radius of the original water bottle. Keep the height the same.
II. Double the height of the original water bottle. Keep the radius the same.
III. Double the height and double the radius of the original water bottle
IV. Quadruple the height of the original water bottle. Keep the radius the same
o I and IV
O I and 11
O I, II, III, and IV
O III and IV
Answer:
option 3, double the height and with of original bottle
The methods which will create the larger water bottle with the intended volume is 1 and IV.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
A water bottle company is designing a new larger cylindrical water bottle that is intended to hold 4 times as much water as the original cylindrical water bottle.
Volume of a cylindrical shape = π r² h
Let V be the original volume.
If radius is doubled, then the new volume is,
V' = π (2r)² h = 4(π r² h) = 4V
So 1 is an option.
When the height is Quadrupled,
V' = π r² 4h = 4(π r² h) = 4V
Hence the correct options are 1 and IV.
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Does the mean or median best describe a typical value in the data set shown?19, 18, 19, 18, 19, 19, 1, 19, 18, 19, 18
Answer:
Probably mean.
Step-by-step explanation:
The median is the middle number (in this case, 19) and the mean is the average of all the numbers
Find the value of x please and fast!!
Answer:
B) 5
Step-by-step explanation:
2 1/5+6 4/5 6 5/12 -2 1/12 11 8/9+4 1/3 7 1/6-5 3/4 11/18+ 6 1/10 15 1/3- 2 5/8 mixed numbers
Answer:
2 1/5+6 4/5 = 9
6 5/12 -2 1/12 = 4 1/3
11 8/9+4 1/3 =16 2/9
7 1/6-5 3/4 = 1 5/12
11/18+ 6 1/10 = 6 64/90
15 1/3- 2 5/8 = 12 17/24
Step-by-step explanation:
Using the technique of mixed numbers to add the fractions
2 1/5+6 4/5
=2+6 + 1/5+4/5 add the whole numbers separately and then the fractions
=8 5/5= 9
6 5/12 -2 1/12
=6-2 + 5-1/12
=4 4/12
= 4 1/3
11 8/9+4 1/3
=11+4 +8/9+1/3 adding the whole numbers separately
=15 + 8+3/9
= 15+11/9 adding the fractions separately
= 15+1+2/9
= 16+2/9
=16 2/9
7 1/6-5 3/4
= 7-5 +1/6 -3/4 subtracting the whole numbers separately
= 2+ 2-9/12 subtracting the fractions separately
= 2-7/12
= 24-7/12
= 17/12
=1 5/12
11/18+ 6 1/10
= 11/18 + 61/10
= 110 +1098/180
= 1208/180
= 6 128/180
= 6 64/90
15 1/3- 2 5/8
=15- 2 + 1/3- 5/8
=13 + 8- 15/24
= 13 + -7/24
= 312-7/24
= 12 17/24
Taylor is producing graphic T-shirts that
will come in three different colors. He
randomly surveys 100 people, asking which
one of the three colors they prefer. Of the
100 people surveyed,55 say that they prefer
the white T-shirt. If Taylor is going to produce
500 graphic T-shirts, about how many should
be white?
If Taylor is producing graphic T-shirts that will come in three different colors then about 275 graphic T-shirts should be white.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Since Taylor randomly surveyed 100 people and 55 of them said they prefer the white T-shirt
we can estimate the proportion of people who prefer the white T-shirt as:
p = 55/100 = 0.55
We can assume that this proportion is a good estimate of the true proportion of people who will prefer the white T-shirt among all potential customers.
To estimate the number of people who will prefer the white T-shirt among 500 potential customers
The formula for the expected value of a binomial random variable is
E(x) = np
Substituting the values, we get:
E(x) = 500 × 0.55 = 275
Therefore, about 275 graphic T-shirts should be white.
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I need help please ........ on 6.
Answer:
Step-by-step explanation:
Remark
His pay gets income tax deducted at a rate of 18% = 18/100
That means you multiply is weekly wage by 18/100 to get what the government takes off.
Solution
18/100 * 495 = 80.10
The government takes $80.10
His take home pay is 495 - 80.10 = $405.90
Note:
There is a short way of doing his take home pay if that is all you are interested in. His take home pay is 82% of his gross pay which is 82/100 * 495.
82/100 * 495 = 405.90
You charge $2 per evening plus $5 per hour to babysit and you only charge for whole hours. You have a goal to earn at least $121 for 8 evenings of babysitting. What is the least amount of hours in total you need to babysit for the evenings?
Answer:
8 hours
Step-by-step explanation:
Answer:
21 hours
Step-by-step explanation:
8 evenings x $2 per evening = $16
$121 - $16 = $105
$105 / $5 per hour = 21 hours
to check:
21 hours x $5 per hour = $105
8 evenings x $2 per evening = $16
$105 + $16 = $121
The strength of a rectangular beam varies jointly as its width and the square of its depth. If the strength of a beam 2 inches wide by 10 inches deep is 1000 pounds per square inch, what is the strength of a beam 4 inches wide and 8 inches deep?
Answer:
yes
Step-by-step explanation:
i know this
M∠E + m∠S=______° (plzzz help me )
Trina collects 56 oak leaves,38 maple leaves,and 46 birch leaves. what percent of trina's leaf collection is made up of oak leaves?
Answer:
40% of 140 because 56+38+46= 140
Is 32 + 33 equal to 35 ? Explain.
!!! help
Answer:
no
Step-by-step explanation:
32+33=65
5. The circumference of the earth is about 24,855miles. Find the surface area of the Western Hemisphere of Earth.
Answer:
oh my answer is in the explanation
Step-by-step explanation:
it
is
quite
big
Andresssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
Anderess?
Step-by-step explanation:
What expression is equal to (5^4)²
Answer:
5^8
Step-by-step explanation:
multiply the exponents = 4x2 = 8
At 2:45 in the afternoon, the tree cast a 9-foot shadow. Just after sunrise, the shadow had been 24 feet. What was the % change in the shadow’s length?
What is -8w-4 simplified?
[tex]\huge\red{\boxed{\tt{\colorbox{pink}{ANSWER:}}}}[/tex]
[tex] - 4(2w + 1)[/tex]
[tex]\huge\red{\boxed{\tt{\colorbox{pink}{Solution:}}}}[/tex]
[tex] - 8w - 4[/tex]
Bind the expression with the common factor -4
[tex] - 8w - 4[/tex]
#❀CARRY ON LEARNING❀#❀KEEP ON LEARNING❀#❀LEARNING IS FUN❀#❀LETS LEARN❀#❀NoToCopyPaste❀❀hope it helps(◕ᴗ◕✿)❀❀Keep safe!❀シ︎Answer: −4(2w+1)
Step-by-step explanation: Hope this help :D
The ratio of 3 to 8 is equivalent to which
of these ratios?
A 16 to 6
B. 18 to 48
C. 48 to 6
D. 18 to 16
Answer:
B
Step-by-step explanation:
18:48
divide both sides by 6
3:8
HELP ASAP PLS!!! I WILL MARK BRAINLIEST, PROMISE!!!
Select the correct answer.
Which number is a rational number?
this is for PLATO, btw
Answer: 17.156
Step-by-step explanation:
A rational number is any number that has a pattern (in decimals) and can be written as a fraction. 17.156 is a terminating decimal. So its a predicting pattern therefore is a rational number.
Solve. Round to the nearest hundredth.
(Help! Will give brainliest)
what is a discriminant? (maths definition)
Discriminant: in mathematics, a parameter of an object or system calculated as an aid to its classification or solution.
Answer: Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2
Hope this helped!
Sending U you good luck!
Which expression is equivalent to
-32 3/5?
O -8
O -3√32^5
O 1/3√32^5
O 1/8
Answer:
-8 is the final answer
Step-by-step explanation:
-(2⁵)^3/5
-2³
-8
3. The width of a rectangle is 4 feet less than the length. The area is
12 ft. Find the dimensions of the rectangle.
Answer:
L = 6, w = 2
Step-by-step explanation:
Let w = width of rectangle
Let L = length of rectangle
w = L - 4
Area of rectangle = Lw
L (L - 4) = 12
L^2 - 4L = 12
L^2 - 4L - 12 = 0
(L - 6)(L + 2) = 0
L - 6 = 0
L = 6 (the other option doesn't work because dimensions can't be negative)
w = L - 4
w = 6 - 4
w = 2
Double check
A = Lw
A = 6 x 2
A = 12
It matches so we are right.
Divide: 1213 ÷ 9 = A)
134 R7
B)
134 R8
C)
135 R7. D)
135 R8
The circle graph shows the result of a survey of 1500 middle school students.
How many students save their money?
Answer:
Theres no pic
Step-by-step explanation:
I cant solve this
PLEAS HELP PLEASE ASAP
Answer:
9 it is
Step-by-step explanation:
Write an equation through the point (0,13) with a slope 11/3
Answer:
13=11/3(0)+c
c=13
y=11/3X+13
Step-by-step explanation:
please like and brainliest mee