tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)
• rewrite tan = sin/cos
… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))
• expand the functions of 2A using the double angle identities
… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))
• factor out sin(A) cos(A)
… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))
• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)
… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))
• rearrange terms in the product
… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)
• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)
… = 4 sin(A) cos(A) / (2 - 1/cos²(A))
• rewrite cos = 1/sec, i.e. sec = 1/cos
… = 4 sin(A) cos(A) / (2 - sec²(A))
• divide through again by cos²(A)
… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))
• rewrite sin/cos = tan and 1/cos = sec
… = 4 tan(A) / (2 sec²(A) - sec⁴(A))
• factor out sec²(A) in the denominator
… = 4 tan(A) / (sec²(A) (2 - sec²(A)))
• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)
… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))
• simplify
… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))
• condense the denominator as the difference of squares
… = 4 tan(A) / (1 - tan⁴(A))
(Note that some of these steps are optional or can be done simultaneously)
help me find m and b
Answer:
m = 2/3
b = -1
y = 2/3x - 1
Step-by-step explanation:
Answer:
y=2/3x-1
Step-by-step explanation:
. William fills 1/3 of a water bottle in 1/6 of a minute. How much time will it
take him to fill the bottle?
Answer:
1/2 minute
Step-by-step explanation:
We can use a ratio to solve
1/3 bottle 1 bottle
------------ = --------------
1/6 minute x minutes
Using cross products
1/3x = 1/6 *1
1/3 x = 1/6
Multiply each side by 3
3 * 1/3x = 3 * 1/6
x = 3/6
x = 1/2
1/2 minute
Answer:
30 seconds (1/2 minute)
Step-by-step explanation:
We are given that,
Amount of water filled in 1/6 minute = 1/3
Now, Let the time taken to fill the whole bottle with water be x
Hence,
Through the ratio method we get,
1/3:1/6 : : 1:x
Hence, we need to multiply the extremes and the means together and equalize them.
Hence,
x/3=1/6
x=(1/6)×3
x=(1/2) minute or 30 seconds
Question 3 (2 points)
Use the figure below to answer the following questions. Find the measure of each angle.
Answer:
∠ 1 = 70°, ∠ 2 = 140
Step-by-step explanation:
110° and the adjacent angle inside the triangle are supplementary, then
angle = 180° - 110° = 70°
Since 2 sides of the triangle are congruent, then the triangle is isosceles
Thus the 2 base angles are congruent, then
∠ 1 = 70°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ 2 is an exterior angle of the triangle, thus
∠ 2 = 70° + 70° = 140°
integral 1-rootx/x dx
picture above
give the right answer and i’ll literally give 75 extra points and brainliest x2 , please help i can’t fail
Answer:
False :)
Step-by-step explanation:
Answer:
Not a function, therefore false.
Step-by-step explanation:
Maybe this attachment can help.
You notice a hot air balloon descending. The elevation h (in feet) of the balloon is modeled by the function h(x)=−6x+330, where x is the time (in seconds) since you first noticed the hot air balloon. ANSWER FASTTTTT!!!
Answer:
55 secsStep-by-step explanation:
Given the elevation h (in feet) of the balloon modeled by the function h(x)=−6x+330, we can calculate the time it takes the balloon to reach the ground. The hot air balloon hits the ground at h(x) = 0.
Substitute h(x) = 0 into the modeled expression and find x as shown;
h(x)=−6x+330
0 = −6x+330
6x = 330
Divide both sides by 6
6x/6 = 330/6
x = 55 seconds
Hence the hot air balloon hits the ground after 55 seconds
Rosalina is driving to visit her family which live 150 km away her average speed is 60 km/h the cars tank is 20 L of fuel at the beginning of the drive and its fuel efficiency is 6 km perL fuel cost $.60 per liter how long can Roselene drive before she runs out of fuel
Answer:
With the amount of fuel she has, she can drive 120 km which will take 2 hours.
Step-by-step explanation:
You need to figure out which information is necessary for this problem and which is not.
The fuel tank has 20 L.
The car drives 6 km per L.
20 L * 6 km/L = 120 km
She can drive 120 km with the amount of fuel she has.
She is driving at 60 km/h.
speed = distance/time
time * speed = distance
time = distance/speed
time = (120 km)/(60 km/h) = 2 hours
Answer: With the amount of fuel she has, she can drive 120 km which will take 2 hours.
A woman sold a typewriter for Rs 13718 in the system of compound depriciation at the rate of 5 percent .If she had purchased it 3 years before how much did she pay for it by that time?
Answer:
Rs 16000
Step-by-step explanation:
Given that :
Price at which typewriter was sold = Rs 13718
Compound Depreciation rate = 5%
Time = 3 years
Amount paid for typewriter 3 years ago
Using the relation :
Final amount = Initial amount(1 - r/n)^nt
n = number of compounding times per period
Rate = r = 5% = 0.05
t = time
A = Final amount = 13718
Initial amount = original purchase price (p)
Therefore ;
13718 = p(1 - 0.05)^3
13718 = p(0.95)^3
13718 = p * 0.857375
13718 = 0.857375p
p = 13718 / 0.857375
P = Rs 16000
Amount paid at the time of purchase = 16000
What is the greatest cornron foctor (Gc) of 15 and 64?
The GCF of 15 and 64 is 1.
Mikhail has $4.15. If he buys one pack of candy canes, how much money does he have left? (the candy canes are $2.45 FOR A PACK OF 4 candy canes)
Answer:
1.70$
Step-by-step explanation:
$4.15-$2.45
=1.70$
Answer:
$1.70
Step-by-step explanation:
If you subtract the price of one pack of candy canes from how much money he has you get $1.70
(hope this helps)
A color printer prints 21 pages in 9 minutes. How many pages does it print per minute? Round your answer to the nearest hundredth.
? = pages per minute
Answer:
2.33 = x
Step-by-step explanation:
pages minutes
21 9
x 1
Cross multiply.
21×1 = 9×x
21 9x
9 9
9 cancels 9 leaving x. and 21 divided by 9 equals 2.33 pages. NB. both sides are divided by 9 because we want x by itself and what you do to one side, you have to do to the other.
The height of a room is 10 feet. You are installing floor-to-ceiling shelving, and each shelf is 8 inches tall. Write and solve an inequality for the number of shelves you could possibly build.
10 feet = 120 inches
120 divided by 8 = 15
you can have 15 shelves in the room
What will be the distance from the center of dilation, P, to the image S'?
2 units
4 units
6 units
8 units
Answer:
the answer is 6 units..
Find the value of x.
Answer:
x = 78
Step-by-step explanation:
180 - 60 - 42 = 78
Pardon me if i'm wrong :/
PLZ do all of it plz i will give brainlest and thanks to best answer
Answer:
1. -4
2. 10
3. -19
4. 5
Step-by-step explanation:
1. 5 + -9= -4
2. -3 + 13 = 10
3. -8 + 11 = -19
4. 6 + -1 = 5
20 POINTS and BRAINLIEST
Solve the simultaneous equation!
Answer:
x=7 y=-2
Step-by-step explanation:
The diagonals of rhombus ABCD intersect at E. Given that m∠CAD=20° and CE=4, find the m∠CDA.
Given :
The diagonals of rhombus ABCD intersect at E.
∠CAD = 20°.
To Find :
The angle ∠CDA.
Solution :
We know, diagonals of a rhombus bisects each other perpendicularly.
So, ∠DEA = 90°.
In triangle ΔEAD :
∠EAD + ∠AED + ∠EDA = 180°
20° + 90° + ∠EDA = 180°
∠EDA = 70°
Now, we know diagonal of rhombus also bisect the angle between two sides .
So, ∠CDA = 2∠EDA
∠CDA = 2×70°
∠CDA =140°
Therefore, ∠CDA is 140°.
what fraction is 3/4 equivalent to?
Answer:
6/8
Step-by-step explanation:
double both of them lol
Answer:
3/4 is equivalent to 6/8 and 12/16
Step-by-step explanation:
please help me !!!!!!!!!!!!!!!!
5Step-by-step explanation:
sin 40 cos 50 + cos 40 sin 50 find the value
Answer:
= 1
Step-by-step explanation:
0.4131 + 0.5868 = 0.999 --> 1
Please help me out!!!!!
Answer:
To find a degree 3 equation you must find and take the roots.You have the roots at x=0 Now plug those into the equation for example: (x-4) would result in x1=4Hope this helps!50 points!!! If your good at math please help! :) will give brainlest
Y is directly related to X, and Y is 81 when X is 27.
The constant of variation is ___
(there are no answer choices, it's just a type in box so i need an exact answer please! :))
Answer:
y=3x or x=y/3
Step-by-step explanation:
81, y divided by 3 is equal to 27.
Please help me, TYSM !!❣
Answer:
A
Step-by-step explanation:
thats my best guess, but im not positive sorry if im wrong!
The scores on a test are normally distrubuted with a mean of 60 and a standard deviation of 12. What is the score that is 2 1/2 standard deviations above the mean?
Answer:
?
Step-by-step explanation:
Find the measure of the indicated angle. Round to the nearest tenth of a
degree.
Step-by-step explanation:
Using trignometry, we have cosθ = Adjacent / Hypotenuse = 3/5.
Hence θ = cos-1(3/5) = 53.1° (A).
If the temperature outside increases by 3 1/2 degrees every 1 1/2 hours, by how much will the temperature increase after 4 hours?
please answer in fractions.
Part 1:
What is the rate per hour of the temperature increase?
Part 2:
How much will the temperature increase after 4 hours?
Answer:
Part 1: 7/3 degrees/hour
Part 2: 28/3 degrees
Step-by-step explanation:
Part 1:
3 1/2 degrees per 1 1/2 hours =
= (3 1/2)/(1 1/2)
= (7/2) / (3/2)
= 7/2 * 2/3
= 7/3 degrees/hour
The rate is 7/3 degree per hour
Part 2:
In 4 hours, the temperature goes up 4 times what it goes up in 1 hour.
4 hours * 7/3 degree/hour = 28/3 degrees
The yellow turtle country covered 33 cm in six minutes her speed as a unit rate is blank a country walk blank in one minute
Answer:
5.5 cm/minute
Step-by-step explanation:
Given that,
The yellow turtle country covered 33 cm in six minutes.
To find unit rate, divide distance covered by the time.
Here, distance = 33 cm
Time, t = 6 minutes
[tex]R=\dfrac{33\ \text{cm}}{6\ \text{minutes}}\\\\=5.5\ \text{cm/minutes}[/tex]
Hence, the unit rate is 5.5 cm/minute. It means, Courtney covered 5.5 cm in one minute.
Answer I will mark branliest
Answer:
D 50
Step-by-step explanation:
Answer:
55
Step-by-step explanation:
5y^2+4x
5(3)^2+4(2.5)
5(9)+4(2.5)
45+4(2.5)
45+10
=55
three fourths times two thirds .
a
five twelfths
b
six twelfths
c
five sevenths
d
six sevenths
Answer: 1/2
Step-by-step explanation: 3/4x2/3= 6/12=3/6=1/2. Hope this helps! Have a wonderful day/night! PLz mark me as brainliest!
Answer:
b) six twelfths
Step-by-step explanation:
(3/4)*(2/3) = 0.50.5 = 1/2 = 6/12 = six twelfthsA pair of designer blue jeans is on sale for $51. This is 75% of the original price. What was the original price of the jeans?