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].
Expand and Simplify: (x-5)(x+7)
In October sally drove 560 miles in her car.
the car travelled 34.5 miles for each gallon of petrol used
Petrol cost £1.08 per litre.
1 gallon = 4.55 litres.
Work out the cost of the petrol the car used in October
The cost of petrol the car used in October is;
Amount spent on fuel in October = £79.76
Distance sally drove in October = 560 miles
She used 1 gallon of petrol for every 34.5 miles she drove.
Thus, number of gallons of petrol she used for the month of October on the car = 560/34.5 gallons
Now, we are told that;
1 gallon = 4.55 litres
Thus; 560/34.5 gallons = (560/34.5) × 4.55/1
Quantity of petrol she used for the month in liters = 73.855 litres
Petrol costs £1.08 per liter.
Thus;
Amount spent on fuel in October = 1.08 × 73.855
Amount spent on fuel in October = £79.7634 ≈ £79.76
Read more at; https://brainly.com/question/22940138
Use this picture to name one pair of ALTERNATE EXTERIOR angles: *
Answer:
angle 4 is congruent to angle 7
angle 8 is congruent to angle 3
angle 2 is congruent to angle 5
angle 1 is congruent to angle 6
Step-by-step explanation:
alternate exterior angles are congruent, which means identical
Can I get some help?
not sure about these either...
If 8 + 4 = 12, then 12 = _ + _
Answer:
8 + 4
Step-by-step explanation:
It is a fact family.
Answer:
12= 4+8
Step-by-step explanation:
When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. Select all of the values that the number could be.
Answer:
(1/2,0) is one solution
(-4/3,0) is the other solution.
Step-by-step explanation:
i hope this helps you it might not be right
which sets of three lengths can be used to form a triangle?
A. 7ft, 5ft, 2ft
B. 6ft, 4ft, 8ft
C. 15cm, 18cm
D. 72 in, 10 in, 90 in
E. 6m, 2m, 12m
F. 6 yd, 21 yd, 25yd
Plz no links and explain what your doing not just the answer thank you!
Answer:
I’m confused
Step-by-step explanation:
there is no pic .. :/
PQRS is a parallelogram with PQ=26cm and QR=20cm . If the distance between the longer-sides is 12.5cm , Find
Answer:
Below.
Step-by-step explanation:
I am guessing you want the area of the parallelogram.
Take the longer side to be the base.
Area = base * distance between base and opposite side
= 26 * 12.5
= 325 cm^2.
3/5 = 12/x find the missing numbers in the equivalent ratios
Answer:
x=20
Step-by-step explanation:
Well just cross multiply if its easier
x(3)=3x
12*5=60
60=3x
x=20
2/3x - 1/9x + 5 = 20
Answer:I think the answer is x=27
Step-by-step explanation:
Cendrick D'Amitrano works Friday and Saturday delivering pizza. He delivers 8 pizzas on Friday. How many pizzas must he deliver on Saturday to average (mean) 11 pizzas per day?
Answer:
Number of pizza deliver on Saturday = 14 pizza
Step-by-step explanation:
Given:
Number of delivery day (Friday, Saturday) = 2
Number of pizza deliver on Friday = 8
Average of delivery (Mean) = 11 pizza
Find:
Number of pizza deliver on Saturday
Computation:
Mean = Sum of pizza / Number of delivery day
11 = [8 + Number of pizza deliver on Saturday] / 2
22 = 8 + Number of pizza deliver on Saturday
Number of pizza deliver on Saturday = 22 - 8
Number of pizza deliver on Saturday = 14 pizza
I need help on this question plsss help
Paulette wrote the equation below to show f, the amount of framing she needs for a square frame with a side length of s centimeters. f=4s How many centimeters of framing does Paulette need for a square frame that has a side length of 15.3 centimeters. Pls help this is a test A. 61.2 centimeters B. 60.3 centimeters D. 19.3 centimeters C. 11.3 centimeters
Answer: 61.2 centimeters
Step-by-step explanation:
Since the equation given to show the amount of framing that she needs for a square frame with a side length of s centimeters is:
f = 4s
Therefore, the number of centimeters of framing needed by Paulette for a square frame that has a side length of 15.3 centimeters will be:
f = 4s
f = 4 × 15.3
f = 61.2 centimeters
Which of the following best describes the shape of the
distribution?
A) skewed to the left
B) bimodal symmetric
C) skewed to the right
D) unimodal symmetric
The shape of the data distribution in the dot plot is: A. skewed to the left.
What is a Left-Skewed Data Distribution?A data distribution that is left-skew will have the longest tail at your far left, compared to your right.
The dot plot shows similar pattern, therefore, the shape of the data distribution represented by the dot plot is: A. skewed to the left
Learn more about left-skewed data on:
https://brainly.com/question/3252860
#SPJ6
please help ! I’m so confused
Answer:
2/7 is the scale factor.
Step-by-step explanation:
All you have to do is get two sides that are equal to each other. Let's say Side SR and YX. 3 and 10.5. Do 3/10.5, which is 30/105, which simplified is 6/21, which again simplified is 2/7. So, the scale factor is 2/7.
I’ll give u BRANLIEST if u get it right
Answer:
c
Step-by-step explanation:
Step-by-step explanation:
I think its A plz give me brainliest
Find the value of x.
x=74°
look at the given picture for stepwise
Help please!!! I need it!
Answer:
1300.62
Step-by-step explanation:
thank me later lolol.
London in column bought 1/2 pound of peanuts they are sharing the nuts equally how many pounds of nuts do each person get
Answer: 1/4 pounds
Step-by-step explanation:
Full question is:
Landon and Colin bought a 1/2 pound of peanuts. They are sharing the nuts equally. How many pounds of peanuts will each person get?
There are 2 people here - London and Colin - and they are to share 1/2 pounds of nuts equally amongst themselves.
They should therefore divide the nuts in 2:
= Amount of nuts / Number of people
= 1/2 ÷ 2
= 1/2 * 1/2
= 1/4 pounds
Note: When dividing a fraction, multiply the inverse of the divisor.
I don’t. Think I posted this one
Answer:
The volume of the ice cream cone is 528.1 cubic centimeters.
Step-by-step explanation:
The formula for finding the volume of a cone is V = [tex]\pi r^2\frac{h}{3}[/tex].
Substitute values now:
V = [tex]\pi* 5.8^2*\frac{15}{3}[/tex]
V ≈ 528.1
6. If Aliya can make 10 bracelets in 2 days, how long will it take her to make 35 bracelets? WILL GIVE EXTRA 10 POINTS WILL MARK AS BRAINLIST
a) 175 days
b) 70 days
c) 7 days
d) 5 days
Answer:
C
Step-by-step explanation:
Answer:
7 days
Step-by-step explanation:
We need to find bracelets per day.
1 day 2 days
5 bracelets 10 bracelets
since we know how many bracelets she can make per day, all we have to do is divide 35 by 5.
to get 7 days.
f(7)=
g(7)=
The equation for f(x) is
The equation for g(x) is
Answer: f(7) = -128
g(7) = 26
Equation of f(x): f(x)= -11x-51
Equation of g(x): g(x)=3x+5
Step-by-step explanation:
Rate of change of a function: [tex]\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
From the table. Rate of change in f(x)= [tex]\dfrac{f(1)-f(0)}{1-0}=\dfrac{-62+51}{1}=-11[/tex]
Rate of change in g(x)= [tex]\dfrac{g(1)-g(0)}{1-0}=\dfrac{8-5}{1}=3[/tex]
Also, the rate of change throughout the function is the same, hence both are linear functions.
Equation of linear function: [tex]f(x)=mx+c[/tex], where m= rate of change of function, c = f(x) at x=0.
From table, f(0)= -51 , g(0)=5
Equation of f(x): f(x)= -11x-51
Equation of g(x): g(x)=3x+5
f(7) = -11(7)-51 = -77-51 = -128
g(7) = 3(7)+5 = 21+5 = 26
f(7) = -128
g(7) = 26
Please help! I really don't understand...
Beth purchased her car for $18,400. Three years later the car was worth $15,200. Find the percent change in the value of her car.
Answer:
17.39%.
Step-by-step explanation:
As a percentage (rounded to two decimal places):
A decrease of 17.39%.
What is the middle value of the following data set? 33, 36, 24 31, 39,44,32
Cendrick D'Amitrano works Friday and Saturday delivering pizza. He delivers 8 pizzas on Friday. How many pizzas must he deliver on Saturday to average (mean) 11 pizzas per day?
Answer:
14
Step-by-step explanation:
there are two days whose mean is 11.for you to get the mean of 11 you had divided by 2
multiply 11 by 2 which is 22
then minus fridays which is 8
Describe the error in the work shown.
Answer:
where is the question
Step-by-step explanation:
Can somebody please answer this for me will give
Brainliest