i have been trying to solve this compound and double angle question please help me find the answer to these question guys
Answers
Answer:
These type of questions are super tricky b/c you have to remember all the different versions of the identities, and then they put the question in some odd form, I feel like this should land math professors in jail , for dishonesty , b/c it's really a form of "how tricky can I make a question and still have a way to solve it" anyway,
Step-by-step explanation:
a)
next the question asks 1-cos 2A and this is total abuse of notation. the way this should be written is 1- cos( 2A) so we know that the A is part of the cosine functions input... btw.. in any computer program, it would never ever let you get away with that top form of the expression. :/ anyway... I keep ranting.. huh... sorry :P
1-cos(2A) is an odd form of the identity 1/2(1-cos(2A) = [tex]sin^{2}[/tex](A) the 1/2 is missing but we can add that pretty easy, we just have to remember to take it out too. I usually forget to do that. and my professor marks me off completely, totally wrong, but I just miss one small thing :/ anyway....
our 1-cos(2A) needs the 1/2 added to it. or if we move that 1/2 to the other side it looks like 2*[tex]sin^{2}[/tex](A) = 1-cos(2A) and this is that "odd" from of the identity that I was talking about.
next let's deal with sin(2A) it has an identity of 2 sin(A)cos(A) which is really nice for us b/c it will cancel out the 2 in then numerator for us, nice !
now our fraction looks like [2* [tex]sin^{2}[/tex](A)] / 2 sin(A)cos(A)
so cancel out one of the sines
2*sin(A) / 2 cos(A)
cancel the 2s
Sin(A) / Cos(A) = Tan(A)
nice it worked out :P
b)
by the above that we just worked out, then
Tan(15) = Sin(15) / Cos(15)
I had to look up what sin of 15 is b/c it's not one of those special angles but it does have an exact form of
Sin(15) = (√3 - 1) / 2√2
Cos(A) = (√3 + 1) / 2√2
you can use rule of Cos(A-B) = Cos(A)Cos(B)+Sin(A)Sin(B) to get the above and a similar rule for Sin(A-B)
back to our problem, the 2√2 will cancel out
then we have
Tan(15) = (√3 - 1) /(√3 + 1)
in the form that is above that's exact, the roots could be approximated but i'll just leave that in the form that is exact. Most math professors like that form.
Related Questions
If a gold ring has a sale price of $21, what was the original price?
There was a sale that was 30% off.
Answers
Answer:
27.30
Step-by-step explanation:
what is the length of the hypotenuse of the triangle when x=7?
Answers
Answer:
c=57.8
Step-by-step explanation:
6*7+4=46
5*7=35
c= 46^2+35^2=57.80138
The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, each cross section perpendicular to the x -axis is a semicircle. What is the volume of the solid?
Answers
Answer:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
Please refer to the graph below.
Recall that the area of a semi-circle is given by:
[tex]\displaystyle A=\frac{1}{2}\pi r^2[/tex]
The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:
[tex]\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx[/tex]
Substitute:
[tex]\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx[/tex]
Simplify:
[tex]\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx[/tex]
Integrate:
[tex]\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right][/tex]
Evaluate:
[tex]\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3[/tex]
The volume of the solid is π/40 cubic units.
Volume of a solid is the measure of the 3 dimensional space it occupies. The volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
How to find the volume of a three dimensional region bounded by curves?For that, we can try to find infinitesimally small 3-d region's volume, and then integrate that region over the dimensions available to get the total volume of the specified region.
We can also use the fact that continuous curves are almost linear and non-changing in infinitely zoomed region.
The given solid has base bounded by x-axis, [tex]y=x^2[/tex] and 0≤x≤1
Its three dimensional region is along the z axis, for each x, there is a semicircle perpendicular with radius being 'y'.
If we take [tex]dx[/tex]x-axis, then the curve [tex]y=x^2[/tex]cylinder(split from height because of semicircle)) with diameter y, and height [tex]dx[/tex]volume is : [tex]V_{dx} = \dfrac{1}{2} \times \pi (\dfrac{y}{2})^2 \times dx = \dfrac{\pi (x^2)^2}{8}dx = \dfrac{\pi x^4}{8} dx[/tex]
Integrating this for 0≤x≤1, we will get the volume of the three dimensional region needed as:
[tex]V = \int_0^4V_{dx} = \int_0^1 \dfrac{\pi x^4}{8} dx = \dfrac{\pi}{8} [\dfrac{x^5}{5}]^1_0 = \dfrac{\pi 1^4}{40} = \dfrac{\pi}{40}[/tex] (in cubic units).
Thus, the volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
Learn more about volume of three dimensional region here:
https://brainly.com/question/338504
Need help ASAP now plz now z now now now
Answers
X = 2
What is the area of the circle with the radius of 5? Round to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
area of circle=π(5)²=25 π≈25×3.14≈78.5
Answer:
A≈78.54
Step-by-step explanation:
A=πr2=π·52≈78.53982
Also i left this out but the radius of the circle is 5.
Chill im only a 7th grade nerd studying in Real Estate and Finances
Also hopes this helps ;0
Easy problem just look at the photo
Answers
Answer:
55
Step-by-step explanation:
a triangle adds up to 180°
25+30+x= 180
55+x=180
x=180-55
x=125
x and y is a straight line so it adds up to 180°
x=125 y=?
x+y=180
125+y=180
y=180-125
y=55°
y= 55°
A carnival game involves drawing a card from a deck of 40 cards, replacing it, shuffling the deck, and drawing another
card. Thirty of the cards are blank and ten are labeled 8 tokens. Your prize is the sum of the cards you draw. What is the
expected payoff for this game?
4 tokens
2 tokens
8 tokens
O tokens
Answers
Answer:
4 tokens.
Step-by-step explanation:
The expected value of a given event is calculated as:
EV = (x₁*p₁ + x₂*p2 + ... + xₙ*pₙ)
Where xₙ is the n-th outcome, and pₙ is its probability.
In this case, our experiment is:
You draw two times.
We have 30 cards with no prize
We have 10 cards with a prize.
A total of 40 cards.
As we draw two times (and the first time we draw a card we put it back in the deck) we can consider the events as independent, so we can find the expected value per draw.
Now we can define:
x₁ = drawing a blank card = 0 tokens
The probability will be equal to the quotient between the number of blank cards and the total number of cards
p₁ = 30/40 = 3/4
x₂ = drawing a prized card = 8 tokens.
The probability will be equal to the quotient between the number of prized cards and the total number of cards:
p₂ = 10/40 = 1/4
Then the expected value per draw is:
EV = ( (3/4)*0 tokens + (1/4)* 8 tokens) = 2 tokens.
And we have two draws, then the expected value of two draws is two times the expected value per draw, this means that the expected value in our case is:
expected value = 2*(2 tokens) = 4 tokens.
The correct option is the first one, counting from the top.
evaluate y-x when y= -9 and x = -5
Answers
Answer:
-5
Step-by-step explanation:
If 2^2x = 2^3, what is the value of x?
Answers
Answer:
x = 2
Step-by-step explanation:
Brie needs cups of flour for her recipe. Which amount is enough for Brie's recipe?
Answers
Answer:
2[tex]\frac{1}{2}[/tex] cups
Step-by-step explanation:
Hi there,
When dealing with these types of problems, it is highly recommended to set the same denominators for the fractions you are dealing with. In this problem, we can see that 2[tex]\frac{1}{2}[/tex] is equivalent to [tex]\frac{5}{2}[/tex]; making this the correct answer choice.
Hope this explanation helps.
Cheers.
At a peace summit, seven Hatfield and nine McCoy family
members sit down for a meeting. If the Sheriff orders two
randomly selected participants to shake hands at the end of
the meeting, what is the probability that the two are from
different families?
Answers
Answer:
0.525 = 52.5% probability that the two are from different families.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, the order in which the two participants are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
1 from the Harfield family(from a set of 7).
1 from the McCoy family(from a set of 9). So
[tex]D = C_{7,1}*C_{9,1} = \frac{7!}{1!6!}*\frac{9!}{1!8!} = 7*9 = 63[/tex]
Total outcomes:
2 from a set of 16. So
[tex]T = C_{16,2} = \frac{16!}{2!14!} = 120[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{63}{120} = 0.525[/tex]
0.525 = 52.5% probability that the two are from different families.
In the image below, the length of the arc defined by the sector is
Answers
Answer:
10pi feet
Step-by-step explanation:
The formula for arc length (degrees) is: 2pi x radius x angle/360
2pi x 30 x 60/360
60pi x 1/6
10pi
simplify:(-5/8x3/7x4/-15)+(4/7x-21/8)
Answers
Answer:
4x/7 - 143/56
Step-by-step explanation:
In a sample of 800 people, 420 are in favor of a proposed scoring system. A golf course wants to implement an electronic scoring system where shots are counted by satellites to reduce human error and to show real-time scores at the clubhouse. Is there enough evidence to conclude that the majority of the golfing community is a proponent of the new system at an alpha level of .05. Determine the number of tails for this problem, the critical value and the test statistic.
Answers
Answer:
We accept H₀ with 95 % of Confidence Interval we have enough evidence to conclude that the majority of members agree with the new system
Step-by-step explanation:
Sample size 800
Sample x₁ = 420 ( number of people in favor of a proposed scoring system), then
p₁ = 420/800 p₁ = 0,525 p₁ = 52,5 % then
q₁ = 1 - p₁ q₁ = 1 - 0,525 q₁ = 0,475
Sample size enought to use the approximation of the binomial didtribution to normal distribution
If significance level is 0,05 α = 0,05
and from z-table we look for z(c) ( z critical value)
z (c) = 1,64
Hypothesis Test:
Null Hypothesis H₀ p₁ = 0,5
Alternative Hypothesis Hₐ p₁ > 0,5
Alternative hypothesis tells us about a one tail-test to the right
To calculate
z(s) = ( p₁ - 0,5) / √ (p₁*q₁) / n
z(s) = 0,025 / √ 0,525*0,475/800
z(s) = 0,025 / √0,000311
z(s) = 0,025/0,01765
z(s) = 1,416
Comparing z(c) and z(s)
z(s) < z(c) 1,416 < 1,64
z(s) is in the acceptance region we accep H₀.
Escribe en forma de potencia y encuentra el valor
a) 2⁴ . 2² =
b) (-5)⁸/(-5)³=
c) ((-9)² )3³
Answers
Answer:
a) =2^(4+2)
=2^6
=64
b) =(-5)^(8-3)
=(-5)^5
= - 3125
c) =(81)(27)
=2187
pls help me i suck at math and i really need this done.
Answers
Answer:
1.x²+x-2
=x²+2x-x-2
=x(x+2)-1(x+2)
=(x+2)(x-1)
2.
(x²+x-2)/(x-1)
={x²+2x-x-2}/(x-1)
={x(x+2)-1(x+2)}/(x-1)
={(x+2)(x-1)}/(x-1)
=(x+2) true
What is m<1? Help please
Answers
Answer:
139
Step-by-step explanation:
Inside angles of a triangle = 180 degrees
61 + 78 = 139
180 - 139 = 41
unknown interior angle = 41 degrees
So m<1 = 139
(Or just add the two interior angles together)
A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground?
Answers
Answer:
t = 9.58 s
Step-by-step explanation:
Given that,
The height from where the cell phone is dropped, h = 450 feet
We need to find the time for the cell phone to reach the ground. Let the time be t. Using second equation of kinematics to find it.
[tex]h=ut+\dfrac{1}{2}at^2[/tex]
u is initial velocity, u = 0
a = g
So,
[tex]h=\dfrac{1}{2}at^2\\\\t=\sqrt{\dfrac{2h}{g}} \\\\t=\sqrt{\dfrac{2\times 450}{9.8}} \\\\t=9.58\ s[/tex]
So, it will take 9.58 seconds to reach the ground.
a) 2x – 7x +3y if x= 3, y= -4
b) y + 3xy if x= 7, y= 5
c) 5x3 + 2y2 if x= 2, y =3
Answers
=6 - 21 + (-12)
=-27
b) (5) + 3(7)(5)
=5 + 105
=110
c) is 3 and 2 an exponent? if so
5(2)^3 + 2(3)^2
=40 + 36
=76
A rectangular swimming pool has a width of 42 ft and a diagonal of 70 ft. Find the length of the pool.
Answers
Answer:
56 feet.
Step-by-step explanation:
The formula for finding the length of a rectangle, given the diagonal and the width is [tex]\sqrt{d^2 -{w^{2}[/tex]. So, [tex]\sqrt{4900 - 1764[/tex]. If you put this thing in the calculator you get 56.
The amount of water that fits in a fish tank represents the _______________ of the fish tank.
Answers
Answer:
Volume
Step-by-step explanation:
The amount of water that fits in a fish tank represents the Volume of the fish tank.
When you pour water, it occupies the space and the weight of the tank increases. So, it represent the volume
if the nth term of a number sequence is n squared-3 if the first 3 terms and the 10th term
Answers
Answer:
First three terms: -2, 1, 6
Tenth term: 97
Step-by-step explanation:
Given
[tex]T_n =n^2 -3[/tex]
Required
The first three terms and the tenth
So, we have:
First term: n =1
[tex]T_1 = 1^2 - 3 = 1 - 3 = -2[/tex]
Second term: n = 2
[tex]T_2 = 2^2 - 3 = 4 - 3 = 1[/tex]
Third term: n = 3
[tex]T_3 = 3^2 - 3 = 9 - 3 = 6[/tex]
Tenth term: n = 10
[tex]T_{10} = 10^2 - 3 = 100 - 3 = 97[/tex]
If n12=1536
then n=
Hellllllllllllllppppp
Answers
Answer:
this should help you understand...
Step-by-step explanation:
What is the greatest common factor of 10x^2 and 15x ?
Answers
Answer:
5
Step-by-step explanation:
because 5 is used for both numbers and that's why
Answer:
5x
Step-by-step explanation:
Both 10 and 15 have a HCF of 5
And both values have x in common
Please help. We are stuck on this one question. Thank you
Answers
Answer:
D
Step-by-step explanation:
All the x and y values have a proportion of 5:1
Answer:
D
Step-by-step explanation:
Proportional relationship means there is a common difference between X and Y. That is only present in D, where x/5 = y.
X Y
5/5 = 1
10/5 = 2
15/5 = 3
20/5 = 4
25/5 = 5
A cube with a surface area of 54 square centimeters is shown.
Twelve cubes like the one shown are combined to create a larger cube. What is the volume, in cubic centimeters of the new cube?
Answers
Answer:
54 cm
Step-by-step explanation:
they are the same i think
is 2+2=4 or is it 2+2=22
Answers
Answer:
[tex]2+2=4[/tex] obviously...
Pls mark brainliest!Answer:
well it depends
Step-by-step explanation:
if you wanna be hallarius then 22 but the real mathmatics is 4
PLS GIVE BRAINLIEST
PLEASE HELP URGENT ILL GIBE BRANLIEST
Answers
Answer:
A 1.85
Step-by-step explanation:
cos 72 = 6/x
x cos 72 = 6
x = cos 72/6 = 1.84
Answer:
A
Step-by-step explanation:
1.84
Suppose you have a right triangle with congruent legs and a hypotenuse that measure (12√5)/5. What is the length of the smaller leg? Round to the nearest hundredth
Answers
Answer:
5.4 is the length
Step-by-step explanation:
5.333 - (12√5)/5 - round to nearest hundreth (5.4)
length total 5.4
Thanks and Rate my Answer Please!
The length of the smaller leg is 3.8 unit.
What is Pythagoras theorem?Pythagoras theorem states that "the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c)" i.e.
[tex]c^{2} = a^{2} + b^{2}[/tex]
Let the length of the leg be b and a.
According to the given question.
We have a rigth triangle which have congruent legs.
And hypotenuse, c = [tex]\frac{12\sqrt{5} }{5}[/tex]
Since, the legs are congruent.
Therefore,
a = b
Now, according to the Pythagoras theorem.
[tex]c^{2} = a^{2} + b^{2}[/tex]
[tex]\implies c^{2} = a^{2} + a^{2}[/tex]
[tex]\implies c^{2} = 2a^{2}[/tex]
[tex]\implies (\frac{12\sqrt{5} }{5} )^{2} = 2a^{2}[/tex]
[tex]\implies \frac{144\times 5}{25} = 2a^{2}[/tex]
[tex]\implies \frac{144}{5} = 2a^{2}[/tex]
[tex]\implies \frac{72}{5} = a^{2}[/tex]
[tex]\implies a = \sqrt{\frac{74}{5} }[/tex]
[tex]\implies a = \sqrt{14.8}[/tex]
[tex]\implies a = 3.84[/tex]
[tex]\implies a = 3.8[/tex] unit
Hence, the length of the smaller leg is 3.8 unit.
Find out more information about Pythagoras theorem here:
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Find the slope and y-intercept from the following graph of a linear equation.