Answers
[tex]\dfrac{\sin \alpha}{\cos \alpha + \sin \alpha} - \dfrac{\cos \alpha}{\cos \alpha - \sin \alpha}\\\\\\=\dfrac{\sin \alpha(\cos \alpha - \sin \alpha) - \cos \alpha(\cos \alpha + \sin \alpha)}{(\cos \alpha + \sin \alpha)(\cos \alpha -\sin \alpha)}\\\\\\=\dfrac{\sin \alpha \cos \alpha - \sin^2 \alpha - \cos^2 \alpha - \cos \alpha \sin \alpha}{\cos^2 \alpha - \sin^2 \alpha}\\\\\\=\dfrac{-(\sin^2 \alpha + \cos^2 \alpha)}{\cos 2 \alpha}\\\\\\=-\dfrac{1}{\cos 2 \alpha}\\[/tex]
[tex]=-\left(\dfrac{1}{\tfrac{1- \tan^2 \alpha}{1 + \tan^2 \alpha}} \right)~~~~~~~~~~~~~~~~~~; \left[\cos 2\theta = \dfrac{1 - \tan^2 \theta}{1+ \tan^2 \theta} \right]\\\\\\\ = -\left(\dfrac{1+ \tan^2 \alpha}{1- \tan^2 \alpha}\right)\\\\\\= \dfrac{1+\tan^2 \alpha}{\tan^2 \alpha -1}[/tex]
Related Questions
The annual snowfall in city A is 45.8 inches. This is 14.2 inches more than 4 times the snowfall in city B. Find the annual snowfall for city B.
Answers
Answer: 7.9inches
Step-by-step explanation:
45.8-14.2=31.6
31.6/4=7.9
simplify the following 6b-8(46 - 9) + 3b
Answers
The value of 6b-8(46 - 9) + 3b is 9b - 296.
The equation given is 6b-8(46 - 9) + 3b, the calculation will go thus:
= 6b-8 (46 - 9) + 3b
= 6b-8 (46 - 9) + 3b
= 6b - 8(37) + 3b
= 6b - 296 + 3b
= 6b + 3b - 296
= 9b - 296
Answer: 9b-296
Step-by-step explanation:
Subtract the numbers 6−8 (46−9)+3 6−8(37)+3 2
Multiply the numbers 6−8⋅37+3 6−296+3
Combine like terms 6b−296+3b
Ur answer
9b−296
Pls help me with this!!
Answers
Answer:
76 quarters, 3 dimes
Step-by-step explanation:
if the whole number is 19, you would have to figure out how many quarters would be in 19$. 76 quarters are in 19$. then you would have to figure out how many dimes are in 30 cents, there are 3 dimes in 230 cents
Answer:
66 Quarters and 28 dimes
Step-by-step explanation:
.10d + .25Q = 19.3Q
d + Q = 94
so d = 94 - Q
Substitution method:
.10(94 - Q) + .25Q = 19.30
9.4 - .10Q + .25Q = 19.30
9.4 + .15Q = 19.30
.15Q = 9.9
Q = 66 so d = 94 - 66 = 28
A weather station on the top of a mountain reports that the temperature is currently 0°C and has been falling at a constant rate of 3°C per hour. What was the temperature 4.5 hours ago ?
Answers
Answer:
10.5 degrees Celsius
Step-by-step explanation:
Answer: 13.5
Step-by-step explanation:
This is because 3x4.5=13.5
I WILL GIVE BRAINLIEST!! PLS HELP
Answers
Answer:
Angle PRQ is the same as NRM so therefore one of the three angles for both triangles is the same. Angle QPR and NMR are both 90 degrees and so the last angle must be the same in order for the three angles to be 180 degrees in total.
Step-by-step explanation:
Hope This Helps!!!
???
Philip Schofield bench presses 200N over a distance of 0.5m. calculate the work done
Answers
Answer:
100J
Step-by-step explanation:
work done = force x distance
= 200 x 0.5
= 100J
Analyze the diagram below and complete the instructions that follow.
Answers
Answer:
this question is a very simple. you should start with the biggest triangle then follow the steps to find each side of other triangles. THE ANSWER İS ROOT FORTY ONE
Step-by-step explanation:
these are all right-angled triangles. even the smallest one with the x side.
so, we need to apply Pythagoras to get the missing sides and finally x.
c² = a² + b²
c is the Hypotenuse, the baseline of the triangle opposite of the 90 degree angle. a and b are the legs of the triangle enclosing the 90 degree angle.
so,
52² = 48² + side1²
2704 = 2304 + side1²
400 = side1²
side1 = 20
20² = 12² + side2²
400 = 144 + side2²
256 = side2²
side2 = 16
13² = 5² + (larger part of side2)²
169 = 25 + (larger part of side2)²
144 = (larger part of side2)²
larger part of side2 = 12
that means the smaller part of side 2 = 16-12 = 4.
x² = 5² + 4² = 25 + 16 = 41
x = sqrt(41)
So, D is the right answer option.
Work out the percentage change to 2 decimal places when a price of £198 is increased to £209.99.
Answers
Answer:
6.06%
Step-by-step explanation:
198 + 6.06%=209.9988
i need to know the answer to number one
Answers
Answer:
If the slope of the line is 3, it either decreases or increases by 3 everytime. (3x) If the y-intercept is 0, then when the line intercepts with the graph, it will intercept with (0, 0)
Step-by-step explanation:
Basically, the slope means how much the line increases or decreases. The y-intercept means where the line will intercept or start on the y-axis. If the y-intercept was 5, it would be (0, 5)
A coach purchased a soccer ball for each of his 18 players. If each soccer ball cost $12.99, how much did the coach spend before sales tax was added?
Answers
Answer:
$233.82
Step-by-step explanation:
$12.99 a ball times 18 players (12.99x18) equals 233.82$
If x = 5, find the value of
a) x2
b) (x + 3)^2.
the 2 is meant to be squared
Answers
Answer:
a)since x=5
x²= 5×5
=25
b)(x+3)²
x=5
5+3=8
8²=8×8
=64
Soo :
a) x² = 5² = 5•5 = 25
b) (x + 3)² = (5 + 3)² = 8² = 8•8 = 64
a man earn $6 in two hours. how much does he earn in 5 hours
Answers
Answer:
$15
Step-by-step explanation:
6 divided by 2 is 3
3 multiplied by 5 is 15
In Richmond, Chloe ordered $40 worth of sushi. She knew that when the bill came, she would need to pay Richmond sales tax of 5% and would want to leave a 20% tip on the original $40. Including tax and tip, how much did Chloe's meal cost?
Answers
Answer:
50$$$
Step-by-step explanation:
(she has the same name as me lol)
Chloe has to pay 40$
5% of 40 is 2
20% of 40 is 8
Add the extra money together
2+8=10
Add original price
40+10=50
You get 50$ for the final price
PLEASE HELP
Find the current value of a car bought for new at $18300 which depreciates at 8% per annum over 4 years
Answers
Answer:
12, 444
Step-by-step explanation:
•First find out what is 8% of 18300
=8\100 ×18300\1 = 146400\100 =1464. [\ means ÷]
• Next multiply 1464 by 4 years =5,856
•Finally calculate 18300- 5856 = 12,444 (we are saying 18300 - 5856 because the money
decreased & 5856 represnt 8% of 18300 in 4 years)
Note :~ Appreciation is when money increases
~Deperciation is when money decreases
Hope this helps !!!PLEASE HELP 60 POINTSSSS
Answers
Answer:
x = 6.5 units
Step-by-step explanation:
The 2 given squares are the on the legs of the right triangle with hypotenuse x
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 legs , then
x² = 13 + 29.25 = 42.25 ( take square root of both sides )
x = [tex]\sqrt{42.25}[/tex] = 6.5 units
Find the positive root of x^2+2x-35=0 in math Please.
Answers
Answer:
x2+2x−35=0
Step 1: Factor left side of equation.
(x−5)(x+7)=0
Step 2: Set factors equal to 0.
x−5=0 or x+7=0
x=5 or x=−7
Step-by-step explanation:
<=> x^2 - 5x + 7x - 35 = 0
<=> x(x-5) + 7(x-5)=0
<=> (x+7)(x-5)=0
<=> x+7=0 or x-5=0
<=> x = -7 or x = 5
Ok done. Thank to me :>
How to do question 10 a?
Answers
Answer:
23 hgrghhgfggggggghhhhh
Answer:
I looked at all those numbers and they all say d=0
Step-by-step explanation:
(X-3)(X-1)
Expand and simplify
Answers
[tex](x-3)(x-1)\\\\=x(x-1) -3(x-1)\\\\=x^2 -x -3x +3\\\\=x^2 - 4x+3[/tex]
someone please help me i'll mark brainliest
Answers
Answer:
4-9/5
Step-by-step explanation:
I think so but if not sorry
Consider the graph shown below.
What are the coordinates of point C after a dilation with a scale factor of 5,centered at the origin
Answers
Answer:
10,5
Step-by-step explanation:
After a dilation of 5, it should become 10 and 5 because it was 2,1 before.
find the slope of the line through these pair of points. (17, –6), (–11, 7)
Answers
m = (Y2 - Y1)/(X2 - X1)
m = (7 - (-6))/(-11 - 17)
m = (7 + 6)/(-28)
m = 13/(-28) = -(13/28)
Find the value of x in the triangle shown below.
102
48
Answers
Answer:
The sum of the angles of a triangle is always 180, so the answer is
180-102-48=30
Step-by-step explanation:
What is the slope of the line through points J and L?
Answers
Answer:
Slope: 2/3
Step-by-step explanation:
Lucy can type 300 words in 5 minutes. How many words can Lucy type in 27 minutes?
Answers
Answer:
1620 wordsStep-by-step explanation:
Given,
Number of words Lucy can type in 5 minutes
= 300 words
So,
Number of words Lucy can type in 1 minute
[tex] = \frac{300}{5} \: words[/tex]
= 60 words
Therefore,
Number of words Lucy can type in 27 minutes
= (60 × 27) words
= 1,620 words
Hence, Lucy can type 1620 words in 27 minutes.
Which answer choice correctly identify the missing information in the problem?
is 23 years old and just graduated from college. He accepted a job as the manager of a amusement park. His major decision was to offer family memberships to the public for $200 a year. The single admission to the amusement park is $25 per family each visit. How many shows can a family see if they have a limited budget?
A) there is no missing information; to find the answer you divided 200 by 25
B) you need to know how many people are in the family
C) you need to know how many times the family will go to the amusement park
D) you need to know the amount of the family budget to solve the problem
Answers
Answer:The missing information to answer the question: "How many shows can a family see if they have a limited budget?" is the amount of the family budget.
Let's suppose that we know that information and one family has $100. If each visit costs $25 dollars, the family can see:
100/25 =4 shows
So if we do not have this info, we are not going to be able to solve the problem. The correct answer is the letter D!
Step-by-step explanation:
A committee consisting of three people is to be selected from ten members. How many ways are there to select the committee of three people
Answers
Answer:
120
Step-by-step explanation:
10 choose 3
theres really no simple way to do that with work unless you have a fancy calculator.
A lines slope is 1/10, and it’s y - intercept is 9 what is its equation in slope intercept form
Answers
Answer:
[tex]y=\frac{1}{10}x +9[/tex]
Step-by-step explanation:
y = mx + b
where m is slope (1/10)
c is y intercept (9)
I need help asap!!!!
What is the slope of the line on the graph below?
2 IV
-2 -1
1
2
3
4
5
6.
7
8
х
-2
4
45
-6
-7
48
1
Answers
Answer:
Slope is 1/3
Step-by-step explanation:
This is because the line is positive (moving upwards), and it moves up 1 unit and to the right 3 units. That means if you write it in the form of rise/run, where rise is the up or down movement and run is the left or right movement, 1 will be on top and 3 will be at the bottom.
Bonus: The line is y = 1/3x -5 (where 1/3 is slope and -5 is the y-intercept).
Hope this helps :)
round 87,255 to the nearest ten thousand.
Answers
Answer:
90,000
Step-by-step explanation:
What is the volume?????