Answers
Answer:
The prove of the given identity is shown below:
Step-by-step explanation:
It seems that the question involves the proving of a trigonometric identity.
Therefore, we are going to work independently on each side of the equal sign.
We start by considering [tex]cos(\alpha)=cos(\frac{\alpha}{2} +\frac{\alpha}{2})[/tex] since the angle alpha is the same as the addition of two halves of it. Then we apply the identity for the cosine of an addition of angles: [tex]cos (\frac{\alpha}{2} +\frac{\alpha}{2})=cos(\frac{\alpha}{2})*cos(\frac{\alpha}{2})-sin(\frac{\alpha}{2})*sin(\frac{\alpha}{2})= cos^2(\frac{\alpha}{2})-sin^2(\frac{\alpha}{2})[/tex]
and now we use the Pythagorean identity to replace the cosine square expression:
[tex]cos^2(\frac{\alpha}{2})=1-sin^2(\frac{\alpha}{2})[/tex]
in the difference of square trig functions we had arrived to:
[tex]cos^2(\frac{\alpha}{2})-sin^2(\frac{\alpha}{2})=1-sin^2(\frac{\alpha}{2})--sin^2(\frac{\alpha}{2})=1-2\,sin^2(\frac{\alpha}{2})[/tex]
We have arrived at the exact same expression the original identity shown on the righthand side of the equal sign, so we have proved the identity.
Related Questions
f(x)=2x^7 find the domain and range
Answers
Answer:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
Step-by-step explanation:
It’s infinite both ways, so:
Domain:
-∞<x<∞, or (-∞,∞) in interval notation
Range:
-∞<f(x)<∞, or (-∞,∞) in interval notation
Mrs. Tollett's class is working on a
recycling project. The students
are collecting aluminum cans. Over
three days, they collected 88 cans,
113 cans, and 73 cans. How many
cans did they collect in all?
Answers
Answer:
274
Step-by-step explanation:
113+88+73
If DE = 5x, EF = x + 8, and DF = 20, what is EF? Simplify your answer and write it as a proper fraction, mixed number, or integer. Please if you could(or not) type the answer step by step.
Answers
Answer:
EF = 10
Step-by-step explanation:
DE + EF = DF
5x + x + 8 = 20
6x = 20 - 8
6x = 12
x = 12/6
x = 2
EF = x + 8 = 2 + 8 = 10
Zoe mows the lawn in the summer to earn extra money she usually charges $15 per week but she offers a special rate of $59.50 if a customer prepaid for 5 weeks. how much does a customer pay for each week with a special rate?
Answers
Answer:$11.90
Step-by-step explanation:
Divide 59.50 by 5
A factory manufactures tennis balls. Each tennis ball is stamped with the number 1, 2, 3, or 4. The table shown below lists the percent of tennis balls stamped with each number. What is the probability that a tennis ball selected at random is stamped with an even number? 1/35% 2/30% 3/20% 4/15%
Answers
Answer:
Step-by-step explanation:
the answer is .25 because i got it right and it makes alot of sense
In a volcano, erupting lava flows continuously through a tube system about 17 kilometers to the sea. Assume a lava flow speed of 0.5 kilometer per hou calculate how long it takes to reach the sea.
Answers
Answer:
Distance = rate x time or d = rt...that means time t = d/r...and we have
t = 21 km / .5 km/hr = 42 hr
Step-by-step explanation:
The amount of time taken by the lava to reach the sea will be 42 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. The speed is a scalar quantity it only requires magnitude to represent.
Given In a volcano, erupting lava flows continuously through a tube system about 17 kilometers to the sea. Assume a lava flow speed of 0.5 kilometers per hour.
The distance will be calculated as below:-
Distance = rate x time
d = r x t
t = d / r
t = 21 km / .5 km/hr
t = 42 hr
Therefore, the amount of time taken by the lava to reach the sea will be 42 hours.
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Kai had a gross weekly paycheck of $616 last week. Kai worked 6 hours for 4 of the days and 8 hours on 1 day. What is Kai's hourly rate of pay? a. $16.21 b. $19.25 c. $20.53 d. $25.67 Please select the best answer from the choices provided
Answers
The correct answer is B. $ 19.25
Explanation:
To calculate the hourly rate of pay, first, let's calculate the total number of hours Kai worked, and then divide the total earned into the number of hours.
6 hours x 4 days = 24 hours
8 hours x 1 day = 8 hours
24 hours + 8 hours = 32 hours
This shows Kai worked a total of 32 hours. Now to find the hourly rate of pay, follow this procedure:
$616 (total earned) ÷ 32 hours = $19.25 each hour
This means Kai earns $19.25 for each hour of work and therefore the hourly rate of pay is $19.25.
Answer:
B
Step-by-step explanation:
express the mass 6,200,000 kilograms using scientific notation in kilograms, and then in grams.
Answers
Answer:
620000000
Step-by-step explanation: 6.2 10^8
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form,62*10^5 is the scientific notation of 6,200,000 kilograms
We need to express 6,200,000 kilograms using scientific notation in kilograms.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
We need to express 6,200,000 kilograms into scientific notation
The format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.
Now 62*10^5 is the required scientific notation.
Therefore 62*10^5 is scientific notation of 6,200,000 kilograms.
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The inverse of f(x) = 2x + 3 is
O True
O False
Answers
The inverse of f (×) =2× + 3 is
yes it is true
You had $199, but you are spending $3 each day. What algebraic expression models this situation?
Answers
Answer:
y=199-3x
Step-by-step explanation:
you ave 199 and 3 pper day so is considered each day and whatever it equals it will be y
Answer:
A 199 -3d
Step-by-step explanation:
Plz choose mine as brainliest
Given that U = {1, 2, 3, 4, 5, 6), find the complement of the set A = {1, 3, 5).
Answers
Answer:
complement of set A={2,4,6}
hope it helps
plz mark as brainliest
Point V is on line segment UW, given VW = x + 7, UW = 3x - 9, and UV = 8, determine the numerical length of UW
Answers
Answer:
The numerical length of UW is 27
Step-by-step explanation:
I need two tickets to the movies. Each ticket costs $12. How much do I need to purchase 2 tickets to the movies?
Show Work!
Answers
Answer: 24$
multiply $12x$2 and get 24$
Step-by-step explanation: I need two tickets to the movies. Each ticket costs $12. How much do I need to purchase 2 tickets to the movies?
Shea bought x candy bars for $1.50 each. Write an
algebraic expression for the total amount Shea spent.
What’s the answer?
Answers
can someone do it :) Simplify 5(x - 6).
Answers
Answer:
5x - 30
Step-by-step explanation:
I used the distributive property and I think I got it.
Answer:
5 x minus -30
x is equal to -6
hope this helped you
please mark as the brainliest (ㆁωㆁ)
PLEASE HELPP!! Round each mixed number to the nearest whole number. Then, estimate the sum.
14 11/12 + 3 1/6
Answers
Answer:
Step-by-step explanation: 14 11/12 rounds up to 15 and 3 1/6 is closer to 3 so the answer would be 18
A dozen eggs cost $4.25 at the farm stand. Approximately how much does each egg cost (round to the nearest penny)
Answers
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line.
(6, −7), (6, 1)
Answers
Answer: undefined; vertical line
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]m=\frac{1-(-7)}{6-6} =\frac{8}{0}[/tex]
The slope is undefined because you cannot divide anything by 0.
The graph of the line is a vertical line at x=6. We know this because the points are both at x=6, with different y-values.
What is the area of the triangle?
20
16
12
units
Answers
Answer:
3840
Step-by-step explanation:
Hope this helps you out
8÷2(2+2) is 16 right or is it 1
Answers
the answers 16 if you need an explanation then ill comment one.....!
Answer:
16
Step-by-step explanation:
8 :2 ×(2 +2) =
4 ×4 =
16
Find an equation for the line with the given properties.
Parallel to the line 2x - y = - 4; containing the point (0,0)
y = 2x (Type your answer in slope-intercept form.)
Answers
Answer:
y = 2x
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
2x - y = -4
-y = -2x - 4
y = 2x + 4
Since the 2 lines are parallel, they have the same slope.
Step 2: Define variables
Slope m = 2
Origin (x-int and y-int) (0, 0)
Step 3: Write parallel linear equation
y = 2x + 0
y = 2x
Find the inverse transform by convolution: 4 (s-3)(s-2) C.27.
Answers
I suppose you're asking about the inverse Laplace transform of
[tex]F(s)=\dfrac4{(s-3)(s-2)}[/tex]
by way of the convolution theorem.
The theorem itself says that
[tex]\mathscr L^{-1}\{A(s)B(s)\}=(a*b)(t)[/tex]
where [tex]A(s)[/tex] and [tex]B(s)[/tex] are the Laplace transforms of [tex]a(t)[/tex] and [tex]b(t)[/tex], respectively.
Let [tex]A(s)=\frac1{s-3}[/tex] and [tex]B(s)=\frac1{s-2}[/tex]. Then
[tex]a(t)=\mathscr L^{-1}\left\{\dfrac1{s-3}\right\}=e^{3t}[/tex]
[tex]b(t)=\mathscr L^{-1}\left\{\dfrac1{s-2}\right\}=e^{2t}[/tex]
So we have
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=e^{3t}*e^{2t}[/tex]
Convolution is defined as
[tex](a*b)(t)=\displaystyle\int_0^t a(t-\tau)b(\tau)\,\mathrm d\tau[/tex]
The convolution of [tex]e^{3t}[/tex] and [tex]e^{2t}[/tex] is
[tex]e^{3t}*e^{2t}=\displaystyle\int_0^t e^{3(t-\tau)}e^{2\tau}\,\mathrm d\tau[/tex]
[tex]=\displaystyle e^{3t} \int_0^t e^{-\tau}\,\mathrm d\tau[/tex]
[tex]=e^{3t}(1-e^{-t})=e^{3t}-e^{2t}[/tex]
We end up with
[tex]\mathscr L^{-1}\left\{\dfrac4{(s-3)(s-2)}\right\}=\boxed{4(e^{3t}-e^{2t})}[/tex]
-2X=-42
What do I do to this problem
Answers
X= 21
In ΔXYZ, the measure of ∠Z=90°, YX = 37, ZY = 12, and XZ = 35. What ratio represents the sine of ∠X?
Answers
Answer:
12/37
Step-by-step explanation:
What is a complementary angle versus a supplementary angle?
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
Step-by-step explanation:
90
∘
then the two angles are said to be complementary.
If sum of two angles equals
180
∘
then the two angles are said to be supplementary.
Verticall Angles are the angles opposite each other when two lines cross. They are always equal. "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.
____________ prove that the people traded over long distances. a. Ancient tree stumps, discovered by scientists, b. Written records c. Buildings that were built with logs from mountains about 50 miles away d. Oral traditions
Answers
Answer:
It’s c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Chris can be paid in one of two ways. Plan A is a salary of $400 per month, plus
a commission of 7% of sales. Plan B is a salary of $692 per month, plus a
commission of 3% of sales. For what amount of sales is Chris better off selecting
plan A?
Answers
Answer:
$7300
Step-by-step explanation:
For Chris to select plan A, Plan A salary should be greater than that of plan B. Let the amount of sales be x
[tex]400 + \frac{7}{100} x > 692 + \frac{3}{100} x \\ \frac{7}{100} x - \frac{3}{100} x > 692 - 400 \\ \frac{4}{100} x > 292 \\ x > 7300[/tex]
32(2 + 3) + 5 what is the operation
Answers
Answer: first add everything in the (parentheses) then multiply that by 32 then add 5 = 165
Step-by-step explanation:
Perform the operation (7x3)+(- 2x3/8x2)
Answers
21 + (-6) (16)
21+96
117
Twice the sum of a number and 7 is more than 6 or at most -3. Which compound inequality can represent this relationship
Answers
Answer:
C
Step-by-step explanation:
The inequality 2(x + 7) > 6 and 2(x + 7) ≤ -3 will represents the given situation so option (C) will be correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
Let's say that number is x
Then,
sum of a number and 7 = x +7
Twice the sum of a number and 7 is more than 6
So,
2(x + 7) > 6
And
Twice the sum of a number and 7 is at most -3, it means it can go up to -3 not more than.
So,
2(x + 7) ≤ -3
Hence "The inequality 2(x + 7) > 6 and 2(x + 7) ≤ -3 will represents the given situation".
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