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]
We know that,
[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]
Using the trigonometric ratios, we get
[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]
Hence, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].
An arithmetic sequence has a first term of 0 and the 9th term of 12. If 27 is an output of the sequence, which term number is it? Show all steps of calculations and explain in a sentence at the end how you know you have the correct term number.
Giving 100 points to first correct answer
Answer:
Step-by-step explanation:
[tex]a_{n}=a_{1}+(n-1) d\\n=9\\12=0+(9-1)d\\8d=12\\d=\frac{12}{8}=\frac{3}{2}\\again\\27=0+(n-1)*\frac{3}{2}\\n-1=27*\frac{2}{3}=18\\n=18+1=19[/tex]
A store gives reward points for every dollar
spent. The number of reward points varies
directly with the total amount spent.
Sofia spends $300 and receives 15 reward
points.
Juan spends $900. He receives reward points
at the same rate as Sofia.
How many more reward points will Juan
receive than Sofia?
Please help me I give u 14 points please only correct answers ,!!!
One marble is picked at random and NOT replaced from a box that has 3 red marbles, 4 green marbles 2 blue marbles and one yellow marble. Find the probability of selecting a red and a red marble.
Answer:
3/9
Step-by-step explanation:
because there are total 9 marbles. 3 red, 4 green and 2 blue.so the probability is 3/9.
Use a net to find the surface area of the cone to the nearest
square centimeter. Use 3.14 for it.
23 cm
(The figure is not drawn to scale.)
The surface area of the cone is about cm2.
(Round to the nearest whole number as needed.)
Answer:
[tex]V=497.16\ cm^3[/tex]
Step-by-step explanation:
The attached figure shows a cone of radius 5 cm and height 19 cm. The formula for the volume of a cone is given by :
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Substitute all the values,
[tex]V=\dfrac{1}{3}\times 3.14\times 5^2\times 19\\\\V=497.16\ cm^3[/tex]
So, the volume of the cone is equal to [tex]497.16\ cm^3[/tex].
Can you solve it on paper
Answer:
28/15
Step-by-step explanation:
find the slope of each line
helppp!!
Answer:
-3/4
Step-by-step explanation:
The slope is -3/4
The line goes down three and four left.
GIVING BRAINLIEST!!!!!!!!
1/2 x(6X4)+3+2
SHOW UR WORK PLS
Answer: 1/2 times 6x equals 3x and then you do 1/2 times 4 and that equals 2 then multiply the 3 and 4 in the parenthesis and that is 12 then add 12 to the 3 and 2 and your answer is 17.
Step-by-step explanation:
what percent of 98 is 74
Answer:
75.51%
Step-by-step explanation:
hopefully this helps
x/100 = 74/98
98x = 7,400
x = 7,400/98
× = 75.51 % of 98
PLS HELP ME GRADES ARE DUE TODAY! Fill in the chart below based on the graphs. Remember: Slope is vertical change divided by horizontal change.
Answer:
VC , HC , S
A) 6 , 3 , 2
b) 8 , 2 , 4
c) 40 , 20 , 2
Answer:
Graph Vertical Horizontal Slope
A 6 3 2
B 2 8 .25
C 40 20 2
Step-by-step explanation:
Graph A
vertical...
9-3=6
horizontal...
4-1=3
slope...
6/3=2
Graph B
vertical...
3.5-1.5=2
horizontal...
10-2=8
slope...
2/8=.25
Graph C
vertical...
75-35=40
horizontal...
30-10=20
slope...
40/20=2
????????????????????????????????????????????????
Answer:
Second one to the top right i think
Step-by-step explanation:
HELP ASAPPPPP PLZZZZ Question in pic!!!!!
Step-by-step explanation:
Given
5y + 68 = 3y + 96 (vertically opposite angles) and
3x + 18 = 5x + 2 (vertically opposite angles)
Now solve for x.
[tex]3x + 18 = 5x + 2 \\ 3x + 18 - 5x = 2 \\ - 2x + 18 = 2 \\ - 2x = 2 - 18 \\ - 2x = - 16 \\ x = - 16 \div - 2 \\ = 8[/tex]
Now Solve for y.
[tex]5y + 68 = 3y + 96 \\ 5y + 68 - 3y = 96 \\ 2y + 68 = 96 \\ 2y = 96 - 68 \\ 2y = 28 \\ y = 14[/tex]
Help me please I will give Brainliest!
Answer:
n = 4.5
Step-by-step explanation:
I think it is 4.5 because n is 3 units ahead of 1.5 on the number line:
1.5+3=4.5
The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units
Answer:
The area of a triangle is 1/2BH, or 1/2 times the base times the height.
If the area = 6, and B and H must both be whole numbers.
The area of the triangle ΔSTU is given by A = 12 units²
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the area of the triangle ΔSTU be represented as A
Now , the area of triangle ΔQTU is 6 square units, and the area of triangle ΔRSU is 6 square units
So , the base of the triangle ΔSTU = 6 units
The height of the triangle ΔSTU = 4 units
So , area of the triangle = ( 1/2 ) x Length x Base
On simplifying , we get
The area of triangle ΔSTU = ( 1/2 ) x 4 x 6
The area of triangle ΔSTU = 12 units²
Therefore , the value of A is 12 units²
Hence , the area of the triangle is 12 units²
To learn more about triangles click :
https://brainly.com/question/16739377
#SPJ3
The complete question is attached below :
The area of triangle QTU is 6 square units, and the area of triangle RSU is 6 square units. The dimensions in the figure below are labeled in units. What is the area of triangle STU in square units?
What is the value of x?
X
Answer:
30°
Step-by-step explanation:
Solve 3x2−3x=0 by factoring.
Answer:
3x(x-1) = 0
x= 1
Step-by-step explanation:
is 3x2 supposed to mean 3x^2 i dont know
Can someone help me with this triangle??
Find missing side lengths
Answer:
Y=75 x=75
Step-by-step explanation:
This is a scalene triangle and the total of the degrees will always be 180. So 180-30=150
since there are two sides split 150 in 2. 150 divided by 2 = 75
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
describe and correct the error in the factoring polynomial. x^2+4x-96=(x-12)(x+8)
Answer:
100.03
Step-by-step explanation:
i think it is correct
Using the pattern of blocks below, how many blocks does Figure 26 have?
Mhanifa please help i will mark brainliest :)
Answer:
If figures are similar, corresponding sides have same ratio.
Similar polygonsSide IJ x is corresponding with QR, and side HK with PS:
x/6.5 = 25.5/8.5x = 6.5*3x = 19.5 Similar trianglesRatio of corresponding sides:
x/7 = 18/6x = 7*3x = 21What value of x will make line m parallel to line n?
The value of x that will make line m parallel to line n is?
what is the opposite of 1/7
Answer:-1/7
Step-by-step explanation:
i could be wrong but i tink it going to negative would be the opposite
What are the measurements of FGT plssss?
Answer:
The Foster–Greer–Thorbecke indices are a family of poverty metrics. The most commonly used index from the family, FGT2, puts higher weight on the poverty of the poorest individuals, making it a combined measure of poverty and income inequality and a popular choice within development economics.
Step-by-step explanation:
0000000
8.47÷6 in 2 decimal place
Answer:
1.41
Step-by-step explanation:
8.47÷6 = 1.4116
I need help with this please
Answer:
27
Step-by-step explanation:
2 is vertical to 1, making it 27 as well. then, 4 is corresponding to 4, making it 27
Answer:
27°
Step-by-step explanation:
angle 1 is vertically opposite to angle 2
angle 2 is correspondence to angle 4
vertically opposite and corresponding angles are equal
NEED HELP QUICK!!!!! A set of data includes the point (17,3.8) and has the regression equation y=-25x+436. What is the residual for this point
Given:
The regression equation is:
[tex]y=-25x+436[/tex]
The given point is (17,3.8).
To find:
The residual for the given point.
Solution:
We have,
[tex]y=-25x+436[/tex]
Substituting [tex]x=17[/tex], we get
[tex]y=-25(17)+436[/tex]
[tex]y=-425+436[/tex]
[tex]y=11[/tex]
The predicted value at [tex]x=17[/tex] is 11.
The given point is (17,3.8). It means the observed value at [tex]x=17[/tex] is 3.8.
Formula for residual:
Residual = Observed value - Predicted value
Residual = [tex]3.8-11[/tex]
Residual = [tex]-7.2[/tex]
Therefore, the residual for the given point is -7.2.
Which of the following is the concept illustrated with the misentered data? A. The procedure for constructing the confidence interval is robust. The larger the sample size, the more resistant the mean. Therefore, the confidence interval is less robust. B. The procedure for constructing the confidence interval is robust. The larger the sample size, the more resistant the mean. Therefore, the confidence interval is more robust. C. The procedure for constructing the confidence interval is not robust. The smaller the sample size, the less resistant the mean. Therefore, the confidence interval is more robust.
Answer: B. The procedure for constructing the confidence interval is robust. The larger the sample size, the more resistant the mean. Therefore, the confidence interval is more robust.
Step-by-step explanation:
Large sized data samples usually have more stability than data with small samples, they yield a mean value which edges closer to the value of the population data. This means that large size data samples will have a mean which is more resistant to change than samples with a lower sample size. The confidence interval gives robustness while constructing a model by giving te leverage for a range of values based in a certain level of confidence upon which a statistical vale can be tested for validity.
Need help once again!!!
Answer:
the answer to this question is seven
help? i need this done by the end of the day
I need help on 19 and 20. Please help me. Please don’t put a link. Please help me.
Answer:
19:
4 < third side < 14
20:
3 < third side < 13
Step-by-step explanation:
hint: go to http://www.17 28.org/trianinq.htm
(fix the space between 17 and 28)
you're welcome xx