Please verify the following trigonometric identities.
1. [tex]\frac{\tan x + \tan y}{\cot x + \cot y} = \tan x + \tan y[/tex]
2. [tex]\frac{\sin^3x + \cos^3x}{\sin x + \cos x} = 1 - \sin x \cos x[/tex]
3. [tex]\tan(\frac{x}{2}) + \cos x \tan(\frac{x}{2}) = \sin x[/tex]
Seems like there is a correction in the first question (RHS is tanx.tany)
(i) For convenience: let tanx = a ; tany = b
Thus, tanx + tany = a + b
Moreover, cotx = 1/tanx = 1/a ; coty = 1/b
Thus,
cotx + coty = 1/a + 1/b = (a + b)/ab
Hence,
=> (tanx + tany)/(cotx + coty)
=> (a + b) / { (a + b)/ab }
=> ab(a + b)/(a + b)
=> ab => tanx.tany , proved.
(ii) For convenience: let sinx = a ; cosx = b
As we know, sin²x + cos²x = 1 => a²+b²=1
=> (a³ + b³)/(a + b)
=> (a + b)(a² + b² - ab) / (a + b)
=> (a² + b² - ab)
=> 1 - ab => 1 - sinx.cosx , proved
(iii): let x/2 = A
=> tan(x/2) + cosx.tan(x/2)
=> tanA + cos2A.tanA
=> tanA [1 + cos2A]
=> tanA (2cos²A) {1+cos2A = 2cos²A}
=> (sinA/cosA) (2cos²A)
=> sinA (2cosA)
=> 2sinAcosA
=> sin2A
=> sin2(x/2)
=> sinx proved
Letting x/2 = A is not mandatory. I did it to decease words*(in a line).
Indentities used:
• sin²A + cos²A = 1
• (a³ + b³) = (a + b)(a² + b² - 1)
• 1 + cosA = 2 cos²(A/2)
• tanA = sinA/cosA.
• 2sinAcosA = sin2A
Jason launched a rocket for a physics experiment. This equation can be used to find
the height (h), in feet, of the rocket after t seconds.
h = -16t2 + 288t + 8
How many seconds will it take for the rocket to reach a height of 1,304 feet?
Answer:
5.063 seconds
Step-by-step explanation:
Use a graphing calculator to graph, then use the table functions to solve for 1304
or say
1304= rest of equations and solve for X
An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter
5.7 inches. In the new design, the chamber is scaled by a factor of 1.5.
The volume of the original chamber is
V cubic inches. This i
v cubic inches less than the volume of the new
chamber.
Answer:
the original volume is lesser than the new volume by 242.47 in³
Step-by-step explanation:
Volume of a cone is;
V = ⅓πr²h
Where;
r is radius
h is height
For the original chamber;
r = 5.7/2 = 2.85 inches
h = 12 inches
Volume of this original chamber is;
V_orig = ⅓ × π × 2.85² × 12
V_orig = 102.02 in³
In the new design, the chamber is scaled by a factor of 1.5.
Thus;
r_new = 2.85 × 1.5 = 4.275 inches
h_new = 12 × 1.5 = 18 inches
V_new = ⅓ × π × 4.275² × 18
V_new = 344.49 inch³
V_new - V_orig = 344.49 - 102.02 =
Thus, the original volume is lesser than the new volume by 242.47 in³
HELP PLEASE DUE IN 3 MINUTES
Answer:
the last answer... i hope this helps
Step-by-step explanation:
Answer:
Twice as many students had 3 brothers or sisters as students who had 1 brother or sister
Step-by-step explanation:
Im certain. Pls mark brainliest
what is the probability of flipping a coin and it lands on heads
50/50 since there are 2 sides, and 1 is heads
---
hope it helps
Find the area of the figure. 8.5 cm 9.5 cm 24 cm The area of the figure is_______cm2
Answer:
432 is the blank
Step-by-step explanation:
I just did this problem
can someone help I need to fill in the blank
Answer:
240
Step-by-step explanation:
Which algebraic expression is a polynomial with a degree of 5?
3x5 + 8x4y2 – 9x3y3 – 6y5
2xy4 + 4x2y3 – 6x3y2 – 7x4
8y6 + y5 – 5xy3 + 7x2y2 – x3y – 6x4
–6xy5 + 5x2y3 – x3y2 + 2x2y3 – 3xy5
if sinθ = A, find cos(π/2-θ)
(using trigonometric identities to fine the value)
Answer:
Cos(π/2 - θ) = A
Step-by-step explanation:
We know that:
Sin(θ) = A
And we want to find the value of Cos(π/2 - θ)
Here we can use the cosine relationship:
Cos(a - b) = Cos(a)*Cos(b) + Sin(A)*Sin(B)
Then:
Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ)
We know that:
Cos(π/2) = 0
Sin(π/2) = 1
Then:
Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ) = 0*Cos(θ ) + 1*Sin(θ)
= 1*Sin(θ) = A
Cos(π/2 - θ) = A
HELP ME ASAP PLEASEEEEEE!!!!!!!!!!!!!!
Answer:
D
Step-by-step explanation:
please give brainliest
Answer:
A
Step-by-step explanation:
Because there is 4 packs that have 72 in total and after the picnic is done there is 48 plates left.
point b is 8 units away for the origin
Answer:
ok
Step-by-step explanation:
Help please due in 25 minutes !!!
Answer:
Option B is correct from question point of view..знайдіть розв'язок системи лінійних рівнянь 10x-6y = 18 9x+6y=39
Answer:
(-21, -38)
Step-by-step explanation:
Given the simultaneous equation
10x-6y = 18 ... 1
9x+6y=39 ...2
Using the Elimination method
Subtract
10x - 9x = 18 - 39
x = -21
substitute x = -21 into 1;
From 1:
10x-6y = 18
10(-21)-6y = 18
-210 - 6y = 18
-6y = 18+210
-6y = 228
y = 228/-6
y =-38
Hence the solution to the system is (-21, -38)
1/3 divided by 4? Fractions
Answer:
1/12
Step-by-step explanation:
1+1=???????????????????
Answer:
I.d.k I think 1 :)
Step-by-step explanation:
have a great day
A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below.
If the farmer has 234 feet of fencing, what are the dimensions of the region which enclose the maximal area?
9514 1404 393
Answer:
58.5 ft by 39 ft
Step-by-step explanation:
Let x represent the length of the two horizontal segments. Then the three vertical segments will be ...
(234 -2x)/3
The total enclosed area is the product of these dimensions:
A = (x)(234 -2x)/3
A = (2/3)(x)(117 -x)
This is the equation of a downward-opening parabola with zeros at x=0 and x=117. The maximum of the parabola will be on the line of symmetry, halfway between these zeros. The value of x there is ...
x = (0 +117)/2 = 58.5
The lengths of the vertical segments are ...
(2/3)(117 -58.5) = 2/3(58.5) = 39
The dimensions of the region enclosing the maximum area are 58.5 ft by 39 ft. The additional vertical segment is 39 ft.
_____
Comment on maximum area problems
You may have noticed that the total length of the fence allocated to the long sides (2×58.5 = 117) is half the total length of fence and is equal to the total length of fence allocated to the short sides (3×39 = 117).
This relationship is true in all rectangular fencing problems where the area is being maximized for a given total fence length. It doesn't matter how many partitions there are in either direction: the total of horizontal lengths is equal to the total of vertical lengths.
Hurry please WILL GIVE BRAINLIST
Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table:
Color of Tile Purple Pink Orange
Number of times the tile is drawn 6 18 26
What is the experimental probability that Jenny will pull out an orange tile?
fraction 18 over 26
fraction 24 over 26
fraction 24 over 50
fraction 26 over 50
Answer:
26/50 bc she did it 26 out of 50 times ??
I GIVE BRAINLIEST FOR RIGHT ANSWER AND EXPLANATION
10 x 3 thousands how many thousands are in the answer
Answer:
30 thousands, or 30,000 units.
Step-by-step explanation:
Since the question refers to 10 x 3 thousands, to determine how many thousands are in the answer, the following calculation must be performed:
10 x 3 = 30
So there are 30 thousand in the answer, which is equal to 30,000.
On a map, a museum is located at (15, -2). A library is located at (15, -17). If each unit on the map is a city block, how many city blocks is the museum from the library?
Answer:
15 blocks
Step-by-step explanation:
The distance between the two points on the grid is 15 units, so they're 15 blocks away.
(ґ◎♭łøϰ ❡їḟт¢αґⅾ ωнεη)
(♭ґαḯηłḯℯ﹩⊥ ẘℌℯη)
kek
WILL GIVE BRAINLST
HAVE A AMAZING DAy !!
Answer:
12.16
Step-by-step explanation:
I used the Pythagorean theorem
2 squared is 4
12 squared is 144
added together gets 148
the radical is 12.16 rounded
A 80-ounce bottle of apple juice contains 32 ounces of water. Which juice has the greater percent of water? What percent of the bottle of apple juice is water
Answer:
Only 1 juice is listed.....
So apple juice has the greatest percent of water
40%
Step-by-step explanation:
Answer:
40%
Step-by-step explanation:
Just did it on iready
Use the values listed in the table to answer the question.
Which expression is equivalent to 0?
Answer:
B. (b x d) - c
Step-by-step explanation:
i. -(a x d) + b
= -(6 x [tex]\frac{1}{2}[/tex]) + 8
= -3 + 8
= 5
ii. (b x d) - c
(8 x [tex]\frac{1}{2}[/tex]) - 4
= 4 - 4
= 0
iii. 2(b x f) + a
= 2(8 x [tex]\frac{1}{4}[/tex]) + 6
= 4 + 6
= 10
iv. (a x e) - c
= (6 x [tex]\frac{1}{3}[/tex]) - 4
= 2 - 4
= -2
Thus, the expression which is equivalent to 0 is that of option B.
2. Three pairs of jeans and six shirts cost $104.25. The cost of 4 pairs of jeans and 5 shirts
is $112.15. Find the cost of each pair of jeans and each shirt.
Answer:jeans = x = 16.85
shirts = y = 8.95
Step-by-step explanation:
That’s the answer bud
is this a function ???????
CAN YOU ANSWE QUESTION 1 and 2 please??
Answer:
B. $700
Step-by-step explanation:
The answer is A because.....
Step 1: Find the 7% of 2000.
a.) 7% of 2000 is 140.
b.) Check- So: 140/2000= 0.07 (7%)
Step 2: Multiply 140x5 which equals $700.
Although, I can’t really see the second question‘s options, as the calculations made for the previous question, she paid $140 each year.
I rlly hope this is helpful! If so, please, please, please mark brainliest! Thanks! :)
Answer:
c
Step-by-step explanation:
8. The dimensions of a lawn shaped like a trapezoid are given in meters.
18 m
4 m
5 m
12 m
The dimensions of a lawn shaped like a trapezoid are given in meters. What is the
area of the lawn?
108 m2
60 m2
72 m2
120 m2
Answer:
60m²
Step-by-step explanation:
Area of the trapezoid attached = 1/2(a+b)*h
a and b are the opposite sides
h is the height
Given
a = 18m
b = 12m
h = 4m
Substitute
Area of the trapezoid = 1/2(18+12)*4
Area of the trapezoid = 1/2 * 30 * 4
Area of the trapezoid = 120/2
Area of the trapezoid = 60m²
Hence the area of the lawn is 60m²
Locate and label each point on the number line. Use the diagram to answer the questions. lives one block north of the pizza shop. Jonette's house is block post bar's house. blocks south of the pizza shop Jeffrey and Olivia are in the park Jenny's Jazzy Jewelry Shop is located halfway between the pizza shop and the park. Describe an appropriate scale to show all the points in this situation. What number represents the location of Jenny's Jazzy Jewelry Shop? Explain your reasoning
Answer: dog human
Step-by-step explanation: dog eat dog food
The directions says determine weather each rate of change is consistent. If it is, find the rate of change and explain what it represents.
I will give you tons of brainlist
Da.mn that sucks for you
Can someone explain how to do this for me!
Answer:
x = 90 degrees
Step-by-step explanation:
the above figure is of a circle, so the sum of the measures of angles will be 360 degrees.
measure of arc = measure of the angle inscribed by the arc
therefore, the measure of arc JK will also be x...... ( vertically opposite angles)
therefore, x + x + 30 + (2x - 30) = 360 .....(1)
therefore, 2x + 30 + 2x - 30 = 360
therefore, 4x = 360.....( as -30 and +30 will be cancelled)
therefore, x = 90 degrees
Cross correction:-
by putting in x = 90 in (1)
90 + 90 + 30 + 2*90 - 30 = 360
180 + 30 + 180 - 30 = 360
180 + 180 = 360
so, x= 90 degrees is verified.