Answers
Your question has been heard loud and clear/
we know,
4cos³x = 3cosx + cos3x
put here, x = 20°
then, 4cos³20° = 3cos20° + cos3 × 20°
= 3cos20° + cos60°
cos³20° = (3cos20° + cos60°)/4 -------(1)
similarly ,
4sin³x = 3sinx - sin3x
put here, x = 10°
4sin³10° = 3sin10° - sin30°
sin³10° = (3sin10° - sin30°)/4 -----------(2)
now,
LHS = cos³20° + sin³10°
put equations (1) and (2)
= 1/4(3cos20° + cos60°) + 1/4 ( 3sin10° - sin30°)
= 1/4( 3cos20° + cos60° + 3sin10° - sin30°)
we know,
cos60° = sin30° = 1/2
= 1/4 ( 3cos20° + 3sin10°)
= 3/4(cos20° + sin10°) = RHS
hence proved
Thank you
Answer: see proof below
Step-by-step explanation:
Use the following identities & Unit Circle calculations:
4cos³x = 3cos x + cos 3x
--> cos³x = (1/4)[3cos x + cos 3x]
4sin³x = 3sin x - sin 3x
--> sin³x = (1/4)[3sin x - sin 3x]
cos 60° = sin 30° = (1/2)
Proof: LHS → RHS
Given: cos³ 20° + sin³ 10°
Triple Angle Identity: (1/4)[3cos 20° + cos 3·20°] + (1/4)[3sin 10° - sin 3·10°]
Simplify: (1/4)[3cos 20° + cos 60° + 3sin 10° - sin 30°]
(1/4)[3cos 20° + (1/2) + 3sin 10° - (1/2)]
(1/4)[3cos 20° + 3sin 10°]
Factor: (3/4)[cos 20° + sin 10°]
Proven: (3/4)[cos 20° + sin 10°] = (3/4)[cos 20° + sin 10°] [tex]\checkmark[/tex]
Related Questions
Solve the following equation.
3(5x+4)−20=13x−4
A. -2
B. 2
C. 8
D. 4
Answers
Answer:
B
Step-by-step explanation:
Hi!
3(5x+4)−20=13x−4
15x+12-20=13x-4 Distribute the 3 to the 5x and 4
15x-8=13x-4
2x-8=-4 Subtract 13x from both sides
2x=4 Add 8 to both sides
x=2 Divide both sides by 2
So 2 is the answer :)
On a coordinate plane, a piecewise function has 2 lines. The first line has an open circle at (0, negative 2) and continues up through (negative 5, 3) with an arrow instead of an endpoint. The second line has a closed circle at (0, 0) and continues down with a negative slope through (4, negative 2) with an arrow instead of an endpoint. Which defines the piecewise function shown?
Answers
[tex]\bold{\text{Answer:}\quad f(x)=\bigg\{\begin{array}{ll} -x-2&;x<0\\ -\frac{1}{2}x&;x\geq0 \end{array}}[/tex]
Step-by-step explanation:
Find the equation of each line in Slope-Intercept form: y = mx + b
Line 1 passes through (-5, 3) and (0, -2) --> m = -1, b = -2
--> y = -x - 2
Line 2 passes through (0, 0) and (4, -2) --> m = -1/2, b = 0
--> y = -(1/2)x + 0
Now that you have the equations, evaluate which x-values are included.
Line 1: open dot at x = 0 and line goes to the left --> x < 0
Line 2: closed dot at x = 0 and line goes to the right --> x ≥ 0
Now you have all the information you need to write the piecewise function:
[tex]\large\boxed{f(x)=\bigg\{\begin{array}{ll} -x-2&;x<0\\ -\frac{1}{2}x&;x\geq0 \end{array}}[/tex]
The piece wise function can be written as
[tex]f(x) = -x-2 \; for\; x < 0[/tex]
[tex]f(x) = \dfrac{-1}{2}x \; for\; x \geq 0[/tex]
The Equation of line passing through [tex](x_1,y_1)\; and \; (x_2,y_2)[/tex] can be given by equation (1)
[tex]y -y_1 = \dfrac{y_2 -y_1 }{x_2 - x_1} (x-x_1) ........(1)[/tex]
The equation of line passing through (0,-2) and (-5,3) =
[tex]y-(-2) = \dfrac{3-(-2)}{-5-0}\times (x-0)[/tex]
[tex]y +2 = -x\\y = -x -2 ......(2)[/tex]
Similarly the line passing through (0,0) and (4,-2) =
[tex]y- 0 = \dfrac{-2 -0}{4-0} (x-0)\\y = \frac{-1}{2} x......(3)\\2y =-x \\x +2y =0[/tex]
The first line has an open circle at (0, -2) and continues up through (-5, 3) with an arrow instead of an endpoint.
The second line has a closed circle at (0, 0) and continues down with a negative slope through (4, -2) with an arrow instead of an endpoint. [tex]f(x) = \dfrac{-1}{2}x \; for\; x < 0[/tex]
Hence the piece wise function can be defined by equations (2) and (3)
[tex]f(x) = -x-2 \; for\; x < 0[/tex]
[tex]f(x) = \dfrac{-1}{2}x \; for\; x \geq 0[/tex]
For more Information please refer to the link below
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solve by showing work -15 - (-12)
Answers
Answer:
-3
Step-by-step explanation:
-15 - (-12) = -15 + 12 = -3
Pls help me ooo Pls it's urgent : Solve:a-(7-a)=5
Answers
Answer: a=6
Step-by-step explanation:
a-(7-a)=5
a-7+a=5
2a-7=5
2a=12
a=6 :)
Answer:
[tex]\Huge \boxed{a=6}[/tex]
Step-by-step explanation:
[tex]a-(7-a)=5[/tex]
We need to isolate the [tex]a[/tex] variable on one side of the equation to find the value.
Distribute the negative sign.
[tex]a-7+a=5[/tex]
Combine like terms.
[tex]2a-7=5[/tex]
Add 7 to both sides of the equation.
[tex]2a=12[/tex]
Divide both sides of the equation by 2.
[tex]a=6[/tex]
Solve for y.
4y - 4= 4.
Answers
Answer:
y=2
because 4x2 =8 then 8-4 equals to 4 which is what your trying to get
4y=8
Y=2 the answer is y=2
Find the answer please
Answers
1st set = 4 letters
2nd set = 4x 4 = 16 letters
3rd set = 16 x 4 = 64 letters
4th set = 64 x 4 = 256 letters
5th set = 256 x 4 = 1,024 letters
6th set =1024 x 4 = 4,096 letters
7th set = 4096 x 4 = 16,384 letters
8th set = 16,384 x 4 = 65,536 letters
Each letter cost 2
Total cost = 65,536 x 2 = 131,072
how many terms are in the equation 14x^2 - 12x + 5
Answers
Essentially any like term is a variable with the same letter at the end or the same letter and power.
In this equation, we are given:
a variable, a letter, and a powera variable, and a lettera variableThey are all different, so there are 3 different terms in the equation
Best of Luck!
if a square + b square + c square is equal to 50 and AB+ BC + CA equal to 3 find a + b + c
Answers
Step-by-step explanation:
Taking LHS of the identity:
(a + b +c)2
This can also be written as:
= (a + b + c) (a + b + c)
Multiply as we do multiplication of trinomials and we get:
= a(a + b + c) + b(a + b + c) + c(a + b + c)
= a2 + ab + ac + ab + b2 + bc + ac + bc + c2
Rearrange the terms and we get:
= a2 + b2 + c2 + ab + ab + bc + bc + ac + ac
Add like terms and we get:
= a2 + b2+ c2 + 2ab + 2bc + 2ca
Hence, in this way we obtain the identity i.e. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
what is the distance between the points ( - 1 , -3 ) and ( 5 , -2 )
Answers
Step-by-step explanation:
let the point A( - 1 , -3 ) and B( 5 , -2 )
here, x1 = -1; x2 = 5
y1 = -3; y2 = - 2
Now, the distance between A and B
[tex]AB = \sqrt{(x _{1} - {x}_{2} ) {}^{2} + (y _{1} - y _{2}) {}^{2} } [/tex]
[tex]AB = \sqrt{( - 1 - 5) {}^{2} + ( - 3 ( - 2) {}^{2} }[/tex]
[tex]AB = \sqrt{36 + 1} = \sqrt{37} [/tex]
Thus, The Distance between AB is
[tex] \sqrt{37} [/tex]
Jacques determines the remainder of −17x53+12x9−5x2−11x+1, using the remainder theorem. How does he proceed to the correct answer? A- Jacques evaluates the numerator of the expression when x=−1. He finds the remainder of the division to be −11. B- Jacques evaluates the numerator of the expression when x = 1. He finds the remainder of the division to be −21. C- Jacques evaluates the numerator of the expression when x = 1. He finds the remainder of the division to be −11. D- Jacques evaluates the numerator of the expression when x=−1. He finds the remainder of the division to be −21.
Answers
Answer:
Jacques evaluates the numerator of the expression when x=−1. He finds the remainder of the division to be −11.
Step-by-step explanation:
Got 100% on the test.
Which names accurately describe figure PQRS? Select three options.
parallelogram
pentagon
rectangle
rhombus
trapezoid
Answers
Answer:
parallelogram, rectangle, rhombus
Step-by-step explanation:
Answer:
heyooo i am here to clarify the answer is {parallelogram, rectangle and rhombus}
Step-by-step explanation:
in short, the answer is
A.
C.
D.
i hope you do good on your test !!
-cookie <3
Solve the equation. x/8=0.625
Answers
Answer:
X = 5
Step-by-step explanation:
x in (-oo:+oo)
x/8 = 0.625 // - 0.625
x/8-0.625 = 0
1/8*x-0.625 = 0 // + 0.625
1/8*x = 0.625 // : 1/8
x = 0.625/1/8
x = 5
x = 5
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
:)
Answer:
x = 5
Step-by-step explanation:
[tex] \frac{x}{8} = 0.625[/tex]First convert the decimal to an improper fraction
That's
[tex]0.625 = \frac{5}{8} [/tex]So we have
[tex] \frac{x}{8} = \frac{5}{8} [/tex]Multiply through by 8
That's
[tex]8 \times \frac{x}{8} = \frac{5}{8} \times 8[/tex]We have the final answer as
x = 5Hope this helps you
13 upon 5, 11 upon 6, 17 upon 8....write in decimal form
Answers
Answer:
[tex]\large \boxed{\mathrm{see \ below}}[/tex]
Step-by-step explanation:
13 upon 5 is 13/5
13/5 in decimal form is 2.6
11 upon 6 is 11/6
11/6 in decimal form is 1.833333...
17 upon 8 is 17/8
17/8 in decimal form is 2.125
3 Which property can be used to expand the expression
[tex] - 2( \frac{3}{4} \times + 7)[/tex]
Answers
Answer: Distributive Property
Step-by-step explanation:
[tex]-2\bigg(\dfrac{3}{4}x+7\bigg)\\\\\\\text{DISTRIBUTE -2 to both terms:}\\-2\bigg(\dfrac{3}{4}x\bigg)+(-2)7\\\\\\\text{Simplify:}\\-\dfrac{3}{2}x-14[/tex]
Gasoline prices are given to the nearest thousandth of a dollar. If a gallon of gasoline costs $3.49 and increases $0.09, what is the price of gasoline after the increase?
Answers
Answer:
$3.58
Step-by-step explanation:
Since the cost is increasing, you need to add the two values together.
$3.49 + $0.09 = $3.58
The price of gasoline after the increase is $3.58.
A petroleum laboratory technician can perform 56 tests on samples in 7 hours. At this rate, how many of the same
tests could the technician perform in 8 hours?
49
57
64
105
120
Answers
Answer:
64
Step-by-step explanation:
56/7 = 8
8*8 = 64
64 tests
-5x - 5y + 4x - (2y + 3)
Answers
Step-by-step explanation:
-5x - 5y + 4x - (2y + 3)
= - 5x + 4x - 5y - (2y + 3)
= - x - 5y - 2y - 3
= - x - 7y - 3 ( Answer )
Answer:
-x-7y-3
Step-by-step explanation:
distribute parentheses:
-(2y)-(3)= -2y-3
= -5x-5y+4x-2y-3
simplify
group like terms= -5x+4x-5y-2y-3
add similar elements= -x-5y-2y-3
add similar elements= -x-7y-3
Therefore, simplest expression is -x-7y-3
I hope this helps!!!
Calculate the area
Answers
[tex]A=a\cdot b\cdot \sin\angle AB\\\\A=5\cdot8\cdot\sin63^\circ\\\\A=40\cdot0.891\\\\\boxed{A=35.64}[/tex]
Answer:
[tex]\huge \boxed{\mathrm{35.64 \ units^2 }}[/tex]
Step-by-step explanation:
The adjacent side lengths and an angle is given.
We need to find the height of the parallelogram.
A small right triangle is formed with an angle of 63 degrees and an hypotenuse of 5 units.
We can use trigonometric functions to solve for the height.
sin θ = opp/hyp
sin 63 = h/5
Multiplying both sides by 5.
h = 5 sin 63
h ≈ 4.45503262
Area of parallelogram = base × height
A = 8 × 4.45503262
A = 35.640261
The deepest point of Lake Titicaca in South America is -922 feet relative to its surface. The deepest point is 11,542 feet above sea level. What is the elevation of the surface of the lake? Use absolute value to explain.
Answers
Answer: 12464 feet
Step-by-step explanation:
Given: The deepest point of Lake Titicaca in South America is -922 feet relative to its surface.
We use absolute function, then the deepest point of Lake Titicaca in South America is |-922|=922 feet.
The deepest point is 11,542 feet above sea level.
That means, the elevation of the surface of the lake is the sum of 922 feet and 11,542 feet which is given by (922+ 11,542) feet =12464 feet
Hence, the elevation of the surface of the lake = 12464 feet
please help on 7 to be marked the brainliest
Answers
Answer:
D) 3.57%
Step-by-step explanation:
The percentage change is given by ...
percent change = ((new value) -(old value))/(old value) × 100%
= (3.19 -3.08)/3.08 × 100% = 0.11/3.08 × 100% = (11/3.08)% ≈ 3.57%
__
When dealing with percentages, you need to be clear about what number represents 100%, the reference value against which errors or changes are measured. Here, it is the π of the mug, 3.08.
please help me on this i’ll mark u the brainliest
Answers
Answer:
x = 14Step-by-step explanation:
(4x - 2)° + [180° - (7x - 3)°] + 41° = 180°
(4x)° - 2° + 180° - (7x)° + 3° + 41° = 180°
+2°-180°-3°-41° +2°-180°-3°-41°
- (3x)° = - 42°
÷(-3) ÷(-3)
x° = 14°
x = 14
A deep sea diver descends below the surface of the water at a rate of 60 feet each minute. What is the depth of the diver after 10 minutes.
Answers
Answer:
600 feet
Step-by-step explanation:
60 feet per minute
m = minute
60m
60(10)
600 feet
Find x.
help i have no idea
Answers
Answer:
18
Step-by-step explanation:
The triangle on the left is a 30-60-90 triangle.
The ratio of the lengths of the sides is:
short leg : long leg : hypotenuse
1 : √3 : 2
The short leg of the left triangle is half the hypotenuse.
12√6 / 2 = 6√6
The long leg of the left triangle measures √3 times the short leg.
6√6 * √3
The triangle on the right is a 45-45-90 triangle.
The ratio of the lengths of the sides is:
short leg : long leg : hypotenuse
1 : 1 : √2
The length of the leg is the length of the hypotenuse divided by √2.
6√6 * √3 / √2 = 18
What is the upper quartile value of the data summarized on the box plot?
A) 30
B) 40
C) 95
D) 100
Answers
Answer:
95
Step-by-step explanation:
what two numbers multiply to -18 and and add to -7
Answers
Answer:
2 and -9
Step-by-step explanation:
what makes a great society in china
Answers
Please please please please help
Answers
Answer: x^2+4x+3
Step-by-step explanation:
f(g(x)) >>> replace the g(x) with the given information
f(x+2) >>> replace every (x) in the given f(x) with (x+2)
(x+2)^2-1 >>> foil it out
x^2+4x+4-1 >>> simplify
x^2+4x+3 >>> ANSWER!! :)
Read the question and help me with that, please.
Answers
Answer:
B. -1
Step-by-step explanation:
examples:
1 and -1
1/2 and -2
Answer:
B=-1
Step-by-step explanation:
diagonals are perpendicular line, the slope of perpendicular line are opposite reciprocal.
example if the slope line AC =3
the slope of BD=-1/3
-1/3*3=-1
Find the total monthly cost of owning and maintaining a car given the information shown. Monthly car payment Monthly insurance cost Average cost of gasoline per month Average maintenance cost per month $274.96 $ 77.00 $ 89.20 $ 16.38
Answers
Answer:
$457.54 total
Step-by-step explanation:
Just add the numbers altogether:
274.96
77.00
89.20
16.38
$457.54 total
The required total monthly cost of owning and maintaining a car, given the information shown, is $457.54.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
To find the total monthly cost of owning and maintaining a car, we need to add up the monthly car payment, the monthly insurance cost, the average cost of gasoline per month, and the average maintenance cost per month.
Adding these values, we get:
Total monthly cost = Monthly car payment + Monthly insurance cost + Average cost of gasoline per month + Average maintenance cost per month
= $274.96 + $77.00 + $89.20 + $16.38
= $457.54
Therefore, the total monthly cost of owning and maintaining a car, given the information shown, is $457.54.
Learn more about arithmetic here:
https://brainly.com/question/11424589
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Approximately how much dirt is needed to fill a cone with a diameter of 6 in. and a height of 3 in.?
Answers
Answer:
Amount of dirt needed to fill the cone = 28.28 in³ (Approx)
Step-by-step explanation:
Given:
Diameter = 6 in
Radius (r) = 6 / 2 = 3 in
Height (h) = 3 in
Find:
Amount of dirt needed to fill the cone
Computation:
Volume of cone = (1/3)πr²h
Volume of cone = (1/3)(22/7)(3)(3)(3)
Volume of cone = 28.28 in³
Amount of dirt needed to fill the cone = 28.28 in³ (Approx)