[tex]\large\underline{\sf{Solution-}}[/tex]
We have to prove that:
[tex]\rm\longmapsto \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) } = \tan(x) [/tex]
Taking LHS, we get:
[tex]\rm = \dfrac{ \sin(x) - 2 \sin^{3} (x) }{2 \cos^{3} (x) - \cos(x) }[/tex]
We can take sin(x) as common from numerator part. We get:
[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{2 \cos^{3} (x) - \cos(x) }[/tex]
Similarly, we can take cos(x) as common from first two terms. We get:
[tex]\rm = \dfrac{ \sin(x) \{1- 2 \sin^{2} (x) \}}{ \cos(x) \{ 2 \cos^{2} (x) -1\}}[/tex]
[tex]\rm = \dfrac{ \sin(x) }{ \cos(x) } \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]
As we know that:
[tex]\rm\longmapsto \dfrac{ \sin(x) }{ \cos(x) } = \tan(x) [/tex]
We get:
[tex]\rm = \tan(x) \cdot \dfrac{\{1- 2 \sin^{2} (x) \}}{\{ 2 \cos^{2} (x) -1\}}[/tex]
Now, we will expand the terms in fraction:
[tex]\rm = \tan(x) \cdot \dfrac{\{1- \sin^{2} (x) - { \sin }^{2}(x) \}}{\{\cos^{2} (x) + \cos^{x}(x) -1\}}[/tex]
As we know that:
[tex]\rm \longmapsto \sin^{2}(x)+cos^{2}(x)=1[/tex]
[tex]\rm \longmapsto\cos^{2}(x)=1-sin^{2}(x)[/tex]
[tex]\rm \longmapsto\cos^{2}(x) - 1=-sin^{2}(x)[/tex]
Now substitute the values in the expression, we get:
[tex]\rm = \tan(x)\cdot \dfrac{ \cos^{2} (x)-{ \sin }^{2}(x)}{\cos^{2} (x) - \sin^{2} (x) }[/tex]
[tex]\rm = \tan(x)\cdot1[/tex]
[tex]\rm = \tan(x)[/tex]
Here, we notice that LHS = RHS
Proved.
[tex]\sqrt{72x^{7} q^{8} }[/tex]
Convert the 144 km/h into meters per second
Answer:
144 Kilometers per Hour = 40 Meters per Second
Step-by-step explanation:
multiply the value in kilometers per hour by the conversion factor '0.27777777777778'.
So, 144 kilometers per hour = 144 × 0.27777777777778 = 40 meters per second.
please mark 4 brainliests.
Answer: 40 m/s
Step-by-step explanation: you can multiplied by 5/18 to convert km/h to m/s ,and you can multiplied by 18/5 to convert m/s to km/h.
gloria rode her bicycle 11.75 miles in the morning and 2.3 miles in the afternoon how many miles did gloria ride altogether.
Answer:
13.05
Step-by-step explanation:
1
11.75
+ 2.3
13.05
Answer:
14.05 miles
Step-by-step explanation:
To find the total amount of miles, we have to add 11.75 and 2.3, or 2.30. First, we add our hundredths:
0.05 + 0.00 = 0.05
Then, we add our tenths:
0.7 + 0.3 = 1
Then, we add our ones:
1 + 2 = 3
Finally, we add our tens:
10 + 0 = 10
Now, let's add all those numbers together. 10 + 3 + 1 + 0.05 = 14.05.
Suppose two trains leave a certain station, at the same time, traveling in opposite directions. One train travels 30 mph faster than the other. In 2.5 hours, the trains are 205 miles apart. Find the speed of each train
9514 1404 393
Answer:
56 mph, 26 mph
Step-by-step explanation:
The trains are separating at the rate of (205 mi)/(2.5 h) = 82 mi/h. If we let s represent the speed of the slower train, then that sum of their speeds is ...
s + (s+30) = 82
2s = 52 . . . . . . . . . . subtract 30
s = 26 . . . . . . . . . divide by 2
s +30 = 56 . . . the speed of the other train
The speeds of the two trains are 56 mph and 26 mph.
Hunter has a quarters and y dimes, having at least 18 coins worth at most
combined. A minimum of 4 of the coins are quarters and a minimum of 12
coins are dimes. Solve this system of inequalities graphically and determint
possible solution.
Answer:The number of nickles is 6
The number of dims is 12 .
Step-by-step explanation:
Given as :
Sum of total number of dims and nickels coins = 18
The value of total combination = $1.50
Let The total number of dims = d
Let The total number of nickels = n
1 nickles = $0.05
1 dims = $0.1
According to question
Total number of dims and nickels coins = number of dims + number of nickels
Or, d + n = 18 .........1
And
$0.1 ×d + $0.05 ×n = $1.50
Or, 0.1 d + 0.05 n = 1.50 .........2
Now, Solving eq 1 an eq 2
0.1 × (d + n) - (0.1 d + 0.05 n) = 0.1 × 18 - 1.50
Or, (0.1 d - 0.1 d) + (0.1 n - 0.05 n) = 1.8 - 1.50
Or, 0 + 0.05 n = 0.3
Or, 0.05 n = 0.3
∴ n =
i.e n = 6
So, The number of nickles = n = 6
Put the value of n int eq 1
∵ d + n = 18
Or, d = 18 - n
Or, d = 18 - 6
i.e d = 12
So, The number of dims = d = 12
Hence, The number of nickles is 6 and the number of dims is 12 .
Step-by-step explanation:
SHOW WORK. Algebra question. 100 POINTS. Easy
Answer:
D. -1 < x < 3Step-by-step explanation:
The given function is negative between the x - intercepts -1 and 3.Your choice is correct.Answer:
D. -1 < x < 3
Step-by-step explanation:
The given function is negative between the x - intercepts -1 and 3.
Your choice is correct.
If Kamina can do a job in 43 hours and Simon and Kamina working together can do the same job in 15 hours, find how
long it takes Simon to do the job alone.
hours
Answer:
Answer:
645/28 hours
Step-by-step explanation:
In 1 hour, Kamina does 1/43 of the job.
Simon takes x hour to do the job alone.
In 1 hour, Simon does 1/x of the job.
Together, they do the job is 15 hours, so in 1 hour, they do 1/15 of the job.
1/43 + 1/x = 1/15
15x/(645x) + 645/(645x) = 43x/(645x)
15x + 645 = 43x
28x = 645
x = 645/28
i need help with this question
Answer:
below
Step-by-step explanation:
I'm not absolutely know what are you asking for the answer, but this graph shows ...
The first 20 minutes he has a constant speed of 1.8/20=0.09 km/min progress to 1.8 km away from home, then has 10 minutes (from 20-30) stop at the spot.
Then he drive home with speed of 0.045 km/min (1.8/40=0.045) for 40 minutes to return to the start point.
Find the difference.
678-595.8
Answer:
82.2
Step-by-step explanation:
The difference is subtracting:
678 - 595.8 = 82.2
Answer:
82.2
Step-by-step explanation:
Check the image below.
help pls don't get it wrong I have an election tmr to see if I have good grades pls help
BTW,,
[tex]join \: bunny \: squad[/tex]
[tex]just \: comment \: if \: you \: want[/tex]
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Answer:
pls mark my brainliest because you didn't wriitten coorect question
Step-by-step explanation:
Jake has a wooden board that measures 8.25 feet long. He cuts the board into pieces that each measure 0.75 foot so he can make signs. If Jake earns $15.95 for each sign he sells, how much money can he earn from the signs he makes with this board?
Step-by-step explanation:
Answer:
Jake cuts the board into pieces that measure .75 feet each. Before cutting the board, it is 8.25 feet long. So, we must divide 8.25/.75 to find out how many pieces of board jake cut.
8.25/.75= 11 pieces
Since he makes $15.95 per sign, and there are 11 signs, we must multiply 15.95 by 11. This is equal to 175.45.
Therefore, jake can earn $175.45
Step-by-step explanation:
Can you give me brainliest?
Need help with this...pronto..please
SHOW THE GRAPH AS WELL PLEASE
Plot the x- and y-intercepts to graph the equation. y=−12x−3
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x To find the y-intercept, substitute in 0 for x and solve for y .
x-intercept(s): ( − 6 , 0 )
y-intercept(s): ( 0 , − 3 )
Use the slope-intercept form y = m x + b to find the slope m .
Slope: [tex]m = -\frac{1}{2}[/tex]
Graph in pic
(Credits: Symbolab)
Answer:
pls help
Step-by-step explanation:
y"+y'-6y = 12e^3t+12e^-2t
Answer
yc(T)=y"+y'-6y=0
Step-by-step explanation:
Kiran has 27 nickels and quarters in his pocket, worth a total of $2.75.
a. Write a system of equations to represent the relationships between the
number of nickels n, the number of dimes d, and the dollar amount in
this situation.
Answer:
[tex]\begin{cases}n+d = 27\\0.05n+0.10d = 2.75\\\end{cases}[/tex]
====================================================
Explanation:
n = number of nickels
d = number of dimes
The n and d are placeholders for positive whole numbers.
Since we have 27 coins, we know that n+d = 27. The two subcounts must add to the grand total of 27. That explains how the first equation is set up.
The second equation is set up by looking at the dollar amount each group of coin brings in.
0.05n = amount of money in dollars the nickels bring in
0.10d = amount of money in dollars the dimes bring in
0.05n+0.10d = total amount of money in dollars = 2.75
The single curly brace to the left of the equations tells the reader we're dealing with a system of equations. The equations are tied together.
A receptionist setting up tables for an event used 5 round tables and 2 rectangular tables.
Write a ratio that compares the number of round tables to the number of rectangular tables.
I
Answer:
5:2
or
5 to 2
or
5/2
Step-by-step explanation:
=
Find the slope of the graph of — 4x + 2y = 10 by
rewriting the equation in slope-intercept form.
Answer:
multiply by -1
Step-by-step explanation:
Slope intercept form : y = mx + b
-4x + 2y = 10 Solve the equation for y
+4x = +4x
2y = 4x + 10
y = 4x/2 + 10/2 Divide all terms by 2
multiply by -1 Simply
Can someone please show me their working on these on how to work out?
To rationalize essentially means to get rid of the radical.
The trick to all of these it to multiply the top and bottom by a radical that will turn the radical you have into the square root of a perfect square.
Part a: [tex]\dfrac{1}{2\sqrt{5}}[/tex]
One approach that will always work, but not be the smallest radical, is to just multiply by the radical that is already there.
In the case of [tex]\dfrac{1}{2\sqrt{5}}[/tex], you can multiply the top and bottom by [tex]\sqrt{5}[/tex], so you'll really do this:
[tex]\dfrac{1}{2\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}}[/tex]
But in the bottom, [tex]\sqrt{5}\cdot\sqrt{5} = \sqrt{25}=5[/tex], so your work finishes out like this:
[tex]\dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}} = \dfrac{\sqrt{5}}{2\sqrt{25}} = \dfrac{\sqrt{5}}{2\cdot5} = \dfrac{\sqrt{5}}{10}[/tex]
Part b: [tex]\dfrac{4}{5\sqrt{2}}[/tex]
In the case of [tex]\dfrac{4}{5\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], so you'll really do this:
[tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:
[tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{4\sqrt{2}}{5\sqrt{4}}=\dfrac{4\sqrt{2}}{5\cdot{2}}=\dfrac{4\sqrt{2}}{10}[/tex]
Sometimes the fraction can be reduced, so this should be reduced to [tex]\dfrac{2\sqrt{2}}{5}[/tex].
Looking at all the others, they'll follow this same approach and they will all reduce at the end.
Here's part c, for one more example.
Part c: [tex]\dfrac{3}{3\sqrt{2}}[/tex]
In the case of [tex]\dfrac{3}{3\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], but you should also reduce the initial fraction first.
[tex]\dfrac{3}{3\sqrt{2}} = \dfrac{1}{1\cdot\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]
And now proceed with rationalizing:
[tex]\dfrac{1}{\sqrt{2}} \cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:
[tex]\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{1\cdot\sqrt{2}}{\sqrt{4}}=\dfrac{\sqrt{2}}{{2}}[/tex]
And you're done.
Hopefully that helps you finish the rest of those.
To check your answers, here is the answer key for the rest:
part d:[tex]\dfrac{2\sqrt{6}}{5}[/tex]
part e:[tex]\dfrac{4\sqrt{2}}{3}[/tex]
part f:[tex]\dfrac{4\sqrt{5}}{7}[/tex]
part g:[tex]\dfrac{5\sqrt{10}}{3}[/tex]
part d:[tex]\dfrac{5\sqrt{2}}{3}[/tex]
Answer:
Step-by-step explanation:
(a) 1/(2 sqrt5) x (sqrt 5)/(sqrt5) = (sqrt 5)/10
(b) 4/(5bsqrt2) x (sqrt2)/(sqrt2) = (4sqrt2)/10 = (2sqrt2)/5
(c) 3/(3 sqrt2) x (sqrt2)/(sqrt2) =(sqrt2)/2
(d) 12 /(5 sqrt6) x (sqrt6)/(sqrt6) = (12sqrt6)/30 = (2sqrt6)5
(e) 8/(3 sqrt2) x (sqrt2)/(sqrt2) = (8 sqrt2)/6 = (4 sqrt2)/3
(f) 20/(7 sqrt5) x (sqrt5)/(sqrt5) = (20 sqrt5)/35 = (4 sqrt5)/7
(g) 50/(3 sqrt10) x (sqrt10)(sqrt10) = (50 sqrt10)/30 = (5sqrt10)/3
(h) 10/(3 sqrt2) x (sqrt2)/(sqrt2) = (10 sqrt2)6 = (5 sqrt2)/3
Write the recurring decimal 0.05 as a fraction in its simplest form
Answer:
1/20
Step-by-step explanation:
Step 1: Write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly.
In this case, 0.05 has two numbers after the decimal, so, we place 100 in the denominator and remove the decimal point. This will make it 5/100
Step 2: Then, this fraction can be simplified. 5/100 = 1/20
Thus, 0.05 as a fraction is written as 1/20
Answer:
Step-by-step explanation:
let the fraction be a
a*100.....=0.05*100
100a......=05.00
99a....=0.05
100a= 5.00
99a= 0.05
a= 4.95/99
6. Find the missing lengths of the sides.
Answer: D
30 60 90 trinagle rules
a=8
b=a sqaure root of 3 or 8square root of 3
c=2a or 2*8 or c=16
Step-by-step explanation:
Step-by-step explanation:
sin30°=8/c
1/2=8/c
8×2=c
16=c
tan30°=8/b
[tex] \frac{1}{ \sqrt{3} } = \frac{8}{b} \\ 8 \sqrt{3} = b[/tex]
option. d
How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
5/28
Step-by-step explanation:
[tex] \frac{1}{4} + \frac{4}{7} = \frac{7 + 16}{28} = \frac{23}{28} \\ 1 - \frac{23}{28} = \frac{5}{28} [/tex]
NEEDS HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation:
I have no idea how to draw the last one … any help plz
Answer:
The intersection of the x and y axis is one point one the line, another one is (1, 1). The range of y<x is below the line I just described.
Step-by-step explanation:
there are 9 acorns in each pile. there are 8 piles. how many acorns are there in all? write an equation that can be used to solve this problem
Answer:
72 acorns.
Step-by-step explanation:
9 (acorns per pile)
*
8 (piles)
Answer:
9x8=72 making the answer 72 acorns in total.
0.35 x 9 = 3.15
Is this an overstatement understatement
[tex]over \: \: statement \: \\ \\ 0.35 \times 9 = 3.15 \\ \\ multiply \: 0.35 \times 9 \\ 3.15 = 3.15 \\ \\ so \: the \: answer \: is \: \: overstatemnt \\ \\ hope \: \: it \: \: helps[/tex]
fill in the blank (Geometry B)
Step-by-step explanation:
ratio
to
sind = d/e
sinf = f/e
Okay very important question.
When your doing pemdas , will you get a different answer then just calculating the problem on a calculator.
For example,
11x10-12 divided by 3
Calculated is 106
What’s the answer using pemdas?
Answer: It depends on how you put it in the calculator
Step-by-step explanation:
11x10=110
110-12=98
93/3 = 32.66
hurry help!!!!! im doing a math portfolio and i dont remeber what is 15.33 rounded to the nearest whole is!!! please HELP ME ITS WORTH 30 POINTS OF MY GRADE!!
Answer:
15
Step-by-step explanation:
Cause 15.33 is closer to 15 than 16.
Answer:
15 is the answer I know I already told you but here it is again
Step-by-step explanation:
Maybe brainliest if I helped???
Its 15 because if the decimal after the whole number is less than 0.5 you go to the closest whole number down. Meaning whatever the whole number is attached to your decimal lower than 0.5 is your answer. If it's higher than 0.5 or IS 0.5 you round the nearest whole number, so one bigger than the number attached to your decimal. So if it was say:
15.67
The nearest whole would be 16
I hope I helped!
find the value of 3x^3y-2xy^2 when x=3 and y=-2
Answer:
sorry I don't remember bye I will try to remember
g(n) = 2n + 3
h(n)=n-1
Find (g•h)(n)
Answer:
Step-by-step explanation:
g(n) = 2n + 3
h(n) = n − 1
(g * h)(n) = g(h(n))
= g(n − 1)
= 2(n − 1) + 3
= 2n − 2 + 3
= 2n + 1