Answers
Answer:
[tex] \frac{1}{1 + \cos(x) } [/tex]
Step-by-step explanation:
[tex]y = \frac{ \sin(x) }{1 + \cos(x) } [/tex]
differentiating numerator wrt x :-
(sinx)' = cos x
differentiating denominator wrt x :-
(1 + cos x)' = (cosx)' = - sinx
Let's say the denominator was "v" and the numerator was "u"[tex] (\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} } [/tex]
here,
since u is the numerator u= sinx and u = cos x v(denominator) = 1 + cos x; v' = - sinx[tex] = \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} } [/tex]
[tex] = \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} } [/tex]
since cos²x + sin²x = 1
[tex] = \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} } [/tex]
diving numerator and denominator by 1 + cos x
[tex] = \frac{1}{1 + \cos(x) } [/tex]
Related Questions
In a nationwide survey conducted by a reputable research center, a sample of adults in a certain country were asked whether they favor a plan to break up a small collection of megabanks, which controlled about % of the banking industry; % of those sampled responded in the affirmative. According to the report, "the margin of sampling error is / percentage points with a % level of confidence." Find and interpret a % confidence interval for the percentage of all adults in the country who favor a plan to break up the megabanks.
Answers
Answer:
(42% ; 48%)
We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%
Step-by-step explanation:
The confidence interval is used to estimate the range of values for which the population value may lie at a certain level of confidence.
Given that :
Phat = 45%
Margin of error = ±3%
The confidence interval is defined as :
C. I = Phat ± margin of error
C. I = 45% ± 3%
Lower boundary :
45% - 3% = 42%
Upper boundary :
45% + 3% = 48%
C.I = (42% ; 48%)
We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%
find the surface area of the prism HURRY HURRY
Answers
Answer:
should be 192
Step-by-step explanation:
If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse?
Answers
Answer:
13
Step-by-step explanation:
If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + 12^2 = c^2
25+144= c^2
169 = c^2
Take the square root of each side
sqrt(169) = sqrt(c^2)
13= c
Answer:
The length of the hypotenuse is 13.
Step-by-step explanation:
[tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex]
[tex]a^2 = 12^2 + 5^2[/tex]
[tex]a^2 = 144 + 25[/tex]
[tex]a^2 = 169[/tex]
a=[tex]\sqrt{169}[/tex]
a= 13
Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.
HOPE THIS HELPED
Mr Makgato sells his car for R42 000.00. The total commission is 7.2% of the selling price of which the broker receives 2 thirds and the salesperson receives the rest. How much does the broker receive?
Answers
Answer:
2016
Step-by-step explanation:
using USA dollars:
$42000 x .072 (7.2%) = 3024 total commission
3024 x 2/3 = 2016 brokers amount
What is 24/9 in simplest form
Answers
Answer:
2 2/3
Step-by-step explanation:
hope this helps :)
don't be afraid to ask questions
A ball is thrown from an initial height of
1 meter with an initial upward velocity of
1 m/s. The ball's height h
(in meters) after t
seconds is given by the following. h=1+30t-5t^2
Find all values of t
for which the ball's height is 11
meters.
Round your answer(s) to the nearest hundredth.
Answers
Answer:
Step-by-step explanation:
If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:
[tex]11=-5t^2+30t+1[/tex] and
[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get
t = .35 seconds and t = 5.6 seconds
Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.
PLEASEE HELP ME ASAPPP (geometry)
Answers
Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC
=> EF // và bằng 1/2 AB
=> AB = 16
Step-by-step explanation:
Answer:
AB=16
Step-by-step explanation:
Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.
AD=DB
AD+DB=AB=2EF
AB=2×8=16
Y= 3x-1
2x+6=y substitution method
Answers
Answer: (7, 20)
Concept:
There are three general ways to solve systems of equations:
EliminationSubstitutionGraphingSince the question has specific requirements, we are going to use substitution to solve the equations.
Solve:
Given equations
y = 3x - 1
2x + 6 = y
Substitute the y value since both equations has isolated [y]
2x + 6 = 3x - 1
Add 1 on both sides
2x + 6 + 1 = 3x - 1 + 1
2x + 7 = 3x
Subtract 2x on both sides
2x + 7 - 2x = 3x - 2x
[tex]\boxed{x=7}[/tex]
Find the value of y
y = 3x - 1
y = 3(7) - 1
y = 21 - 1
[tex]\boxed{y=20}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A toddler is allowed to dress himself on Mondays, Wednesdays, and Fridays. For each of his shirt, pants, and shoes, he is equally likely to put it on correctly as incorrectly. Getting these articles of clothing on correctly are independent of each other. On the other days, the mother dresses the toddler with 100% accuracy. Given that the toddler is correctly dressed, what is the probability that today is Monday
Answers
Answer:
0.0286 = 2.86% probability that today is Monday.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Dressed correctly
Event B: Monday
Probability of being dressed correctly:
100% = 1 out of 4/7(mom dresses).
(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So
[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]
Probability of being dressed correctly and being Monday:
The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:
[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]
What is the probability that today is Monday?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]
0.0286 = 2.86% probability that today is Monday.
Find the value of x.
Answers
the tic marks show that all sides are congruent, same with the angles. 60+60+60=180 also.
Complete the Similarity statement below only if the triangles are similar.
Answers
(4m-n-3). 12n13
8m 20
Answers
Answer:
24n^7/m^16
Step-by-step explanation:
Just simplify and rewrite what ever you get simplify again 2 times and now make the calculation as you see every big number is a whole number and is a pair.
The product of two positive integer numbers is 70 and the sum of the same two numbers is 17. Find the
numbers.
Answers
Answer:
7 and 10
Step-by-step explanation:
7 * 10 = 70
7 + 10 = 17
Answer:
10 and 7
Step-by-step explanation:
call them a and b, respectively
so a*b=70 -> b=70/a
a+b=17 ->a+70/a=17 ->a=10 b =7
A line passes through the point (-2,4) and has a slope of 7. Write an equation for this line
Answers
Answer: y = 7x + 18
Step-by-step explanation:
y = mx + b, (-2,4), m = 7
4 = 7(-2) + b
4 = -14 + b
b = 18
y = 7x + 18
I will give brainliest if you answer properly.
Answers
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
please help! Here are the shopping times(in minuts) of nine shoppers at a local grocery store. complete the grouped frequency distribution for the data. in the distribution, the frequency of a class is the number of shopping times in that class.( Note that we are using a class width of 6.)
Answers
Answer:
The shopping time (in minutes) of the nine shoppers are:
15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged everything from least to greatest.)
We can see, that 3 shoppers shopped for 15-20 minutes.
And, 3 shoppers shopped for 21-26 minutes.
And finally, 3 shoppers shopped for 27-32 minutes.
So the answer for all 3 of the boxes is 3.
Let me know if this helps.
GIVING 25 POINTS AND BRAINIER IF ANSWERED!
What is one thing you would not do when finding the question in a word problem?
A. Look for a problem similar to the word problem you are trying to solve.
B. The question may not be directly stated.
C. So you can understand what the facts are in the word problem.
D. To define your strategy or game plan to solve the word problem.
Answers
Answer:
B. The question may not be directly stated.
simplify the following without using calculator
√50 + √98
Answers
Answer:
The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8
Step-by-step explanation:
√50 + √98 = √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2
please help !!!!
i would really appreciate it
Answers
Answer: A
Step-by-step explanation: x=-2, y=3, z=-3
Answer:
A. -2, 3, -3
Step-by-step explanation:
x = 7 - 2y + z
y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =
= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z
13y = 63 + 8z
y = (63 + 8z)/13
2x + 2y - 3z = 11
2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11
2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11
14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11
-2×(63 + 8z)/13 - z = -3
-2×(63 + 8z) - 13z = -39
-126 - 16z - 13z = -39
-29z = 87
z = -3
y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3
x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2
At a sale this week, a desk is being sold for $312. This is a 35% discount from the original price.
What is the original price?
Answers
Answer:
$480
Step-by-step explanation:
Let original price be x
{Original price - discount amount = sale price}
So, x - (x * 35/100) = 312
x - 35x/100 = 312
100x - 35x / 100 = 312
65x/100 = 312
65x = 31200
x = 31200/65
x = $480
So I think the original price of desk was $480
The original price of the desk is $480.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, a desk is being sold for $312.
Let the original price of the desk be x.
Here, x-35% of x =312
x- 35/100 ×x=312
x-0.35x=312
0.65x=312
x=312/0.65
x=480
Therefore, the original price of the desk is $480.
To learn more about the discount visit:
https://brainly.com/question/3541148.
#SPJ2
[tex]\sqrt{25}[/tex]
Answers
Answer:
5
Step-by-step explanation:
Calculate the square root of 25 and get 5.
Thank you for all the help guys
Answers
Answer:
a is the right answer thanksTwo cards are drawn without replacement from a standard deck of 5252 playing cards. What is the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a club
Answers
Answer:
The probability is 0.51
Step-by-step explanation:
We want to find the of choosing a red card for the second card drawn, given that the first card drawn without replacement, was a club.
Then we need to assume that the first card drawn was a club, so now we have a deck of 51 cards with:
13 hearts
13 diamonds
13 spades
12 clubs.
Now with this deck, the probability of drawing a red card is equal to the quotient between the number of red cards and the total number of cards in the deck.
We have 26 red cards (13 hearts + 13 diamonds)
And there is a total of 51 cards in the deck, then the probability of drawing a red card now is:
P = 26/51 =0.51
The probability is 0.51
Carmen Abdul and David sent a total of 78 text messages over their cell phones during the weekend . Abdul sent 10 fewer messages then Carmen . David sent two times as many messages as Abdul how many messages did they each send?
Answers
Answer:
Carmen:27
Abdul:17
David=34
Step-by-step explanation:
Carmen+Abdul+David = 78
Carmen-Abdul=10
David=2Abdul
Carmen=Abdul+10
Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78
4Abdul=68
Abdul = 68/4=17
Carmen = 17+10=27
David = 2 * 17 = 34
27+17+34=78
14feet 23feet round each measurement to the nearest ten
Answers
20ft
I hope that’s correct ☺️
14 feet and 23
Step-by-step explanation:
It’s already rounded to the nearest tenth
Is -8 an irrational number?
yes or no
Answers
no bc it is not no no no no no no no
The height of a triangle is 4 yards greater than the base. The area of the triangle is 70 square yards. Find the length of the base and the height of the triangle.
Answers
9514 1404 393
Answer:
base: 10 yardsheight: 14 yardsStep-by-step explanation:
Let b represent the length of the base. Then (b+4) is the height and the area of the triangle is ...
A = 1/2bh
70 = 1/2(b)(b+4)
b² +4b -140 = 0 . . . . . multiply by 2, put in standard form
(b +14)(b -10) = 0 . . . . factor
b = 10 . . . . the positive solution
The base of the triangle is 10 yards; the height is 14 yards.
Desde cierto paradero se transportan 300 pasajeros en
4 microbuses. ¿Cuántos micros se deben aumentar para
que por cada 3 micros se transporten 90 pasajeros?
Answers
Se necesitan 10 micros si queremos que cada 3 micros transporten 90 pasajeros.
En principio, sabemos que 300 pasajeros pueden transportarse en 4 microbuses.
Entonces, el numero de pasajeros que va por cada micro será el cociente entre el numero de pasajeros y el numero de micros:
N = 300/4 = 75
Queremos responder:
¿Cuántos micros se deben aumentar para que por cada 3 micros se transporten 90 pasajeros?
Definamos X como el numero de grupos de 3 micros que tendriamos en esta situación.
Entonces 300 sobre X, debe ser igual a 90 (el numero de pasajeros que va en cada grupo de 3 micros)
300/X = 90
300 = 90*X
300/90 = X = 3.33...
Notar que el número total de micros sera 3 veces X:
3*X = 3*3.33.... = 10
Se necesitan 10 micros.
Si queres leer más sobre el tema, podes ver.
https://brainly.com/question/23854869
father of economics
Answers
Answer: Adam Smith
For an avid bird watcher, the probability of spotting a California Condor while birdwatching in the Grand Canyon area is 0.3. The probability of being able to take a clear picture of the bird suppose one is able to spot it is 0.8. What is the probability that the bird watcher is able to take a clear picture of a California Condor
Answers
Answer:
the probability of taking a clear picture of a California candor is .24
