Looks like the claim is
(2 tan(x) - sin(2x)) / (2 sin²(x)) = tan(x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
as well as the definition of tangent:
tan(x) = sin(x) / cos(x)
Then on the left side, we can cancel factors of 2 sin(x) to get
(2 sin(x) / cos(x) - 2 sin(x) cos(x)) / (2 sin²(x))
= (1/cos(x) - cos(x)) / sin(x)
Multiply this by cos(x)/cos(x) :
(1/cos(x) - cos(x)) / sin(x) = (1 - cos²(x)) / (sin(x) cos(x))
Recall that for all x,
sin²(x) + cos²(x) = 1
so that
(1 - cos²(x)) / (sin(x) cos(x)) = sin²(x) / (sin(x) cos(x))
= sin(x) / cos(x)
= tan(x)
as required.
find the mean, variance, and standard deviation of sampling distribution of the sample population p=.2 and n=107
Answer:
2923 is your p is equal to 2 and n
Find nth term of the sequence: 11, 15, 19, 23
The term
tn=a+(n−1)d
Where a= first term and d= common difference
hope it helps...!!!
PLS HELP MARK AS BRAINLIEST
Suppose that the relation S is defined as follows.
S= {(4, p), (p, 0), (3, 3), (7, m)}
Give the domain and range of S.
Write your answers using set notation.
Answer:
Domain= {4,p,3,7}
Range= {p,0,3,m}
Step-by-step explanation:
⇒Domain: is the set of the first number in every pair.
⇒Range: is the set of the second number in every pair
TO FIND THE DOMAIN: S= {(4,p),(p,0),(3,3),(7,m)}
so Domain= {4,p,3,7}
TO FIND THE RANGE: S= {(4,p),(p,0),(3,3),(7,m)}
so Range= {p,0,3,m}
Hope this helps :)
4x+11y=7
4x+3y=-1
what are the steps
Answer:
x = -1, y = 1
Step-by-step explanation:
Given that:
[tex]\begin{bmatrix}4x+11y=7\\ 4x+3y=-1\end{bmatrix}[/tex]
Isolate x for 4x + 11y = 7 which ⇒ [tex]x=\frac{7-11y}{4}[/tex]
Substitute [tex]x=\frac{7-11y}{4}[/tex] into the equation: which is:
[tex]\begin{bmatrix}4\cdot \frac{7-11y}{4}+3y=-1\end{bmatrix}[/tex]
Drop Down to:
[tex]\begin{bmatrix}7-8y=-1\end{bmatrix}[/tex]
Isolate y for 7-8y = -1: y = 1
Thus, [tex]x=\frac{7-11y}{4}[/tex]
Substitute y = 1
Hence,
[tex]x=\frac{7-11\cdot \:1}{4}=-1[/tex]
Solution ⇒ x = -1 and y = 1
~learn with lenvy~
Answer:
x = -1 , y = 1
Step-by-step explanation:
Starting with x
x = 7 - 11y/4
4 × 7-11y/4 + 3y = -1
7 - 8y = -1
Now for y
7-8y = -1 ⇒ y = 1
Hence, x = -1 and y = 1
[RevyBreeze]
Number of Handshakes If eight people greet each other at a meeting by shaking hands with one another, how many handshakes take place?
The number of handshake that took place is 28.
In any situation where order of an outcome does not matter, mathematical combination (C) are use calculate the total outcomes of an event.
8 people are to shake each other once. The concept to be use to derive the number of hands that took place is Combination.
The formulae of Combination for this Scenario is n(n-1)/2n(n−1)/2 .
The number of people (n) is 8.
\begin{gathered}Total handshake = n(n-1)/2\\Total handshake = 8 * (8-1)/2\\Total handshake = 8 * 7/2\\Total handshake = 56/2\\Total handshake = 28\end{gathered}Totalhandshake=n(n−1)/2Totalhandshake=8∗(8−1)/2Totalhandshake=8∗7/2Totalhandshake=56/2Totalhandshake=28
In conclusion, the number of handshake that took place is 28.
Answer:
28
Step-by-step explanation:
3 people
A B C
AB
AC
BC
3 total
4 people
A B C D
AB
AC
AD
BC
BD
CD
6 total
this can be modeled with
n*(n - 1)/2
8*(8 - 1)/2
8*3.5
28
What is the equation of the trend line in the scatter plot?
Answer:
y=(x-1)
Step-by-step explanation:
What is the vertex of this quadratic function? y=6(x+1)2-9 Please Help!
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y = 6(x+1)^2-9\implies y = 6[x-(\stackrel{h}{-1})]^2\stackrel{k}{-9}\qquad \qquad \stackrel{vertex}{(-1~~,~~-9)}[/tex]
Among all rectangles that have a perimeter of 172, find the dimensions of the one whose area is largest. Write your answers as fractions reduced lowest terms.
Answer:
43 x 43 units 1849 units^2
Step-by-step explanation:
The largest area will be a square (equla sides)
172 / 4 = 43
a square IS a rectangle
43 x 43
You deposit $2000 in an account earning 8% interest compounded monthly. How much will you
have in the account in 15 years?
Round to the nearest penny.
$
Answer:
Answer:
\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149
Step-by-step explanation:
Standard equation of a circle: \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2
(where (a, b) is the center and r is the radius of the circle)
Substitute the given center (-14, -5) into the equation:
\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2
\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2
Now substitute the point (-7, 5) into the equation to find r²:
\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2
\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2
\sf \implies 149=r^2⟹149=r2
Final equation:
\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149
A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 8 flags will be flown. Find the number of different signals consisting of 8, if the first flag must be blue.
If the first flag is blue then the number of different signals consisting of 8 flags is ??
Using the permutation formula, it is found that there are 17,297,280 different signals consisting of 8 flags.
In this problem, the order in which the flags are visited is important, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
The first flag is blue, then the remaining 7 are taken from a set of 14, hence:
[tex]P_{(14,7)} = \frac{14!}{7!} = 17,297,280[/tex]
There are 17,297,280 different signals consisting of 8 flags.
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If the odds against an event are 5:8, then the probability that the event will fail to occur is
Answer:
Step-by-step explanation:
5/8
Odds against event are 5:8
Means ration of not happening of work =
5/8
Sample space has 8+5=13 possibilities
Probability it being to work=
8/13
How to sketch this graph?
Answer:
get a book from shop and draw with ruler and write the numbers too
Using the illustrations below, determine the relationship between the volumes of
the two given solid figures. Put a check ( / ) on the blank if the sentence states
the correct relationship
Answer:
I don't see the illustrations
Admission to the county fair is $15, and each ride ticket costs $1.75. Write an expression to describe the total cost of 8 rides.
If f (x)=
(3 + x)/
(x-3)
what is f(a + 2)?
[tex]f(x) = \frac{3 + x}{x - 3} [/tex]
[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} = \frac{a + 5}{a - 1} [/tex]
You estimate that a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P500 stock index that represents the stock market, yields an expected rate of return of 13% with a standard deviation of 25%. You manage an active portfolio with expected return 18% and standard deviation 28%. The risk-free rate is 8%.
a. Draw the CML (Capital Market Line) and your funds’ CAL (Capital Allocation Line) on an expected return-standard deviation diagram. Indicate their slopes.
b. Suppose your client ponders whether to switch the 70% that is invested in your fund to the passive portfolio. Explain to your client the disadvantage of the switch.
c.In the context of part b, Show him the maximum fee you could charge (as a percentage of the investment in your fund, deducted at the end of the year) that would leave him at least as well of investing in your fund as in the passive one.)
(Hint: The fee will lower the slope of his CAL by reducing the expected return net of the fee.)
The capital market line with fee will be 0.3771 and the capital allocation line will be 0.24.
How to calculate the slope?The slope of the capital market line will be:
= (17% - 7% - f)/27
= (10% - f)/27
f = 0.3771
The slope of the capital allocation line will be:
= (13% - 7%) / 25%
= 0.24
The reward to variability ratio will be:
= (17 -7)/27
= 0.3771
The client's reward to variability ratio will be:
= (13 - 7)/25
= 0.25
This shows that the client will be disadvantaged of the switch since it's lower.
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What is the value of h?
21 + h = 345
Answer:
324
Step-by-step explanation:
21 + h = 345
group like terms
h = 345 - 21
h = 324
Answer:
h=324
Step-by-step explanation:
21+h = 345
(Substituting the equation)
h=345 - 21
h= 324
!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!
Write an equation of the line with a slope of 0 and y -intercept of 5 .
y=
Answer:
y=-5
Step-by-step explanation:
The function f(t) = 3 cos(pi over 6t) + 5 represents the tide in Blastic Sea. It has a maximum of 8 feet when time (t) is 0 and a minimum of 2 feet. The sea repeats this cycle every 12 hours. After nine hours, how high is the tide? 12 feet 5 feet 4.5 feet 2.5 feet
Answer:
5 feet
Step-by-step explanation:
[tex]f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}[/tex]
Find the quotient of 3/5 and 2/3
Give your answer as a fraction in its simplest form.
A. 28/12
B. 12/28
C. 7/3
D. 3/7
Answer:
28/12 Samsung felo tee Samsung felo tee Samsung felo tee
The hanger image below represents a balanced equation, write an equation to represent the image.
Samantha collected 352 books to give to her students. If she gives 4 books to her students each day, how many days will it take her to give all of her books away?
Answer: 88
Step-by-step explanation:since we know 4 books are given each day and the total is 352 . 352 divided by 4 is 88
Answer:
the answer is 88
Step-by-step explanation:
352÷4=88
exg(x), where g(0) = 6 and g'(0) = 1, find f '(0).
The revenue generated by a company manufacturing lawn mowers is
R=−0.9x2+90.2x , where x represents the number of mowers produced. The cost to produce the mowers is C=29x+500 , where x is the number of mowers produced.
The profit generated in terms of x is −0.9x²+61.2x - 500
How to calculate profit functionsGiven the following parameters
Revenue generated by a company = R=−0.9x²+90.2x
The cost to produce the mowers C(x) = 29x + 500
Determine the profit function
p(x) = R(x) - C(x)
P(x) = −0.9x²+90.2x - (29x + 500)
P(x) = −0.9x²+90.2x - 29x - 500
P(x) = −0.9x²+61.2x - 500
Hence the profit generated in terms of x is −0.9x²+61.2x - 500
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4. Jorge has a mass of 45 kilograms and
is skateboarding with a velocity of
3 meters/second north. What is Jorge's
momentum? The units for momentum are
kg-m/s north.
Jorge's momentum given his mass and the velocity while skateboarding is 135kg-m/s north.
What is momentum?Momentum can be described as the impetus that is gained by an object that is motion. Momentum is velocity multiplied by mass. When put simply, momentum can be described as mass in motion. Thus, when an object is moving, it has momentum.
Momentum velocity x mass
45 x 3 = 135kg-m/s north.
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7
Perez Company is considering an investment of $29,480 that provides net cash flows of $8,900 annually for four years.
(a) What is the internal rate of return of this investment? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from
the tables provided. Round your present value factor to 4 decimals.)
(b) The hurdle rate is 7%. Should the company invest in this project on the basis of internal rate of return?
Complete this question by entering your answers in the tabs below.
Book
Required A
Required B
Hint
What is the internal rate of return of this investment?
Present value factor
Internal rate of return
%
Esk
< Retired A
Required B
Print
erences
The internal rate of return of this investment is 8%.
If the hurdle rate is 7%, the investment should be invested in.
What is internal rate of return?Internal rate of return is a capital budgeting method that determines the the discount rate that equates the after-tax cash flows from an investment to the amount invested
If the internal rate of return is greater than the hurdle rate, the investment should be undertaken. If this is not the case, the investment should not be invested in.
IRR can be calculated with a financial calculator
Cash flow in year 0 = $-29,480
Cash flow each year from year 1 to 4 = 8900
IRR = 8%
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Evaluate the triple integral
Answer:
Wow thats hard
Step-by-step explanation:
though luck
if the scale of a map is 1 in = 62.5 mi, how long is the distance on the map if the actual distance between the two cities is 218.75 miles
Answer:
3.5in
Step-by-step explanation:
so what i would do is i would divide 218.75 by 62.5
218.75/62.5= 3.5
3.5 in= 218.75 mi
hope that hepls :)
HELP ME PLEASE 30 points, HELP
Answer:A
Step-by-step explanation:
When you translate you are simply moving the shape up, down, left right. You are not rotating it or chanding it's orientation.
Answer: the answer is B
Step-by-step explanation: B because it would’ve reflected off of the 1st quadrant on a grid so it would be facing the opposite direction.
