Answer:
-3x
Step-by-step explanation:
-3 is the coefficient and x is the variable.
Move the center of the circle horizontally to the left and then to the right of the y-axis. How does the equation of the circle change as the center crosses the y-axis?
Answer:
The equation of a circle centered in the point (a, b) and with a radius R.
(x - a)^2 + (y - b)^2 = R^2
Then, if you move the circle to the left, then you are decreasing the value of b.
Where b = 0 means that the center of the circle lies on the y-axis.
When you move the graph to the right you will be increasing the value of b.
Answer:
The variable h changes as the center of the circle moves horizontally. The sign of h is negative when the center is to the left of the y-axis and positive when it is to the right of the y-axis. The sign of the variable h flips when the center moves across the y-axis.
Step-by-step explanation:
plato answer from Equation of a Circle: Tutorial :)
This link will take you to a quizlet that is on this lesson with the other answers and test question answers!!
https://quizlet.com/519491317/geometry-b-unit-7-flash-cards/#:~:text=Move%20the%20center%20of%20the%20circle%20vertically%20so%20it%20lies,of%20the%20circle%20moves%20vertically.
Please help me as fast as you can. thanks
Answer:
<DEF = 40<EBF = <EDF = 56<DCF = <DEF =40<CAB = 84Step-by-step explanation:
In triangle DEF, we have:
Given:
<EDF=56
<EFD=84
So, <DEF =180 - 56 - 84 =40 (sum of triangle angles is 180)
____________
DE is a midsegment of triangle ACB
( since CD=DA(given)=>D is midpoint of [CD]
and BE = EA => E midpoint of [BA] )
According to midsegment Theorem,
(DE) // (CB) "//"means parallel
and DE = CB/2 = FB =CF
___________
DEBF is a parm /parallelogram.
Proof: (DE) // (FB) ( (DE) // (CB))
AND DE = FB
Then, <EBF = <EDF = 56
___________
DEFC is parm.
Proof: (DE) // (CF) ((DE) // (CB))
And DE = CF
Therefore, <DCF = <DEF =40
___________
In triangle ACB, we have:
<CAB =180 - <ACB - <ABC =180 - 40 - 56 =84(sum of triangle angles is 180)
[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK! [/tex]
The first term in a sequence of numbers is 1/2
Each term after the first term is 1 more than twice its previous term.
What is the 4th term?
OA. 4
B. 5
C. 11
OD. 23
Answer:
The correct answer is C. The 4th term is 11.
Step-by-step explanation:
Since the next term is one more than twice the previous, we can calculate it by the following expression:
[tex]a_{n} = 2*a_{n-1} + 1[/tex]
So the second term is:
[tex]a_2 = 2*\frac{1}{2} + 1\\a_2 = 2[/tex]
The third term:
[tex]a_3 = 2*2 + 1\\a_3 = 5[/tex]
And the fourth term:
[tex]a_4 = 2*5 + 1\\a_4 = 10 + 1 = 11[/tex]
The correct answer is C. The 4th term is 11.
please help me I’m struggling
Answer:
c
Step-by-step explanation:
the answer is c becuase i know this que
Answer:
All
Step-by-step explanation:
We can check it by using the Pythagorean theorem.
[tex]a {}^{2} + b {}^{2} = c {}^{2} = {3}^{2} + { \sqrt{27} }^{2} = 6 {}^{2} = 9 + 27 = 36 = 36 = 36 [/tex]
[tex] {a}^{2} + {b}^{2} = c {}^{2} = {8}^{2} + {15}^{2} = {17}^{2} = 64 + 225 = 289 = 289 = 289[/tex]
[tex]a {}^{2} + b {}^{2} = c {}^{2} = 5 {}^{2} + {5}^{2} = { \sqrt{50} }^{2} = 25 + 25 = 50 = 50 = 50 = [/tex]
Hope this helps ;) ❤❤❤
38. Convert 85 to a number in base eight.
O 95 (base eight)
O 105 (hase eight)
O 115 (base eight)
O 125 (base eight)
Answer:
divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125
Find the value of 2.7 ³ - 1.6 ³ - 1.1 ³ using a suitable identity.
Answer:
14.256
See details below
Step-by-step explanation:
2.7 ³ - 1.6 ³ - 1.1 ³
= (2.7 ³ - 1.1 ³) - 1.6 ³ expand difference of two cubes
= (2.7 - 1.1)*(2.7^2 + 2.7*1.1 + 1.1^2) - 1.6 ³
= 1.6*(2.7^2 + 2.7*1.1 + 1.1^2) - 1.6 ³ factor out 1.6
= 1.6*(2.7^2 - 1.6^2 + 2.7*1.1 + 1.1^2) expand difference of two squares
= 1.6*( (2.7 - 1.6)*(2.7 + 1.6) + 2.7*1.1 + 1.1^2)
= 1.6*( 1.1*4.3 + 2.7*1.1 + 1.1^2) factor out 1.1
= 1.6*1.1* ( 4.3 + 2.7 + 1.1)
= 1.6*1.1*8.1 rearrange
= 1.6 * 8.1 * 1.,1
= 16 * 0.81 * 1.1
= (4*0.9)^2 * 1.1
= 3.6^2 * 1.1
= 12.96 * 1.1 36*36=1296
= 14.256
(to multiply by 1.1, mentally start from the right, add the left digit, carry if necessary)
Simplify [tex]$\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$[/tex] $\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.$
Answer:
[tex]3 -\sqrt[2]3[/tex]
Step-by-step explanation:
Given
[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex]
Required
Simplify
Rewrite the given expression in index form
[tex]\frac{2 * 9 ^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 9^{\frac{1}{3}}}[/tex]
Express 9 as 3²
[tex]\frac{2 * 3^2^*^\frac{1}{3}}{1 + 3^{\frac{1}{3}} + 3^2^*^{\frac{1}{3}}}[/tex]
[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}}[/tex]
Multiply the numerator and denominator by [tex]1 - 3^{\frac{1}{3}}[/tex]
[tex]\frac{2 * 3^\frac{2}{3}}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}} * \frac{1 - 3^{\frac{1}{3}}}{1 - 3^{\frac{1}{3}}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) (1 - 3^{\frac{1}{3}})}{(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})(1 - 3^{\frac{1}{3}})}[/tex]
Open the bracket
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2}{3})(3^{\frac{1}{3}})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
Simplify the Numerator using Laws of Indices
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{2+1}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
Further Simplify
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^\frac{3}{3})}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3^1)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}}(1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}})}[/tex]
Simplify the denominator
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1}{3}})(3^{\frac{1}{3}}) - (3^{\frac{1}{3}})(3^{\frac{2}{3}})}[/tex]
Further Simplify Using Laws of Indices
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - (3^{\frac{1+1}{3}}) - (3^{\frac{1+2}{3}})}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^{\frac{3}{3}}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3^1}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}} - 3^{\frac{1}{3}} - 3^{\frac{2}{3}} - 3}}[/tex]
Collect Like Terms
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{1 - 3+ 3^{\frac{1}{3}} - 3^{\frac{1}{3}}+ 3^{\frac{2}{3}} - 3^{\frac{2}{3}} }}[/tex]
Group Like Terms for Clarity
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{(1 - 3) + (3^{\frac{1}{3}} - 3^{\frac{1}{3}}) + (3^{\frac{2}{3}} - 3^{\frac{2}{3}} )}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{(- 2)+ (0) + (0)}}[/tex]
[tex]\frac{2 (3^\frac{2}{3}) -2 (3)}{-2}}[/tex]
Divide the fraction
[tex]-(3^\frac{2}{3}) + (3)[/tex]
Reorder the above expression
[tex]3 -3^\frac{2}{3}[/tex]
The expression can be represented as
[tex]3 -\sqrt[2]3[/tex]
Hence;
[tex]\frac{2\sqrt[3]{9}}{1 + \sqrt[3]{3} + \sqrt[3]{9}}[/tex] when simplified is equivalent to [tex]3 -\sqrt[2]3[/tex]
In a survey conducted by the marketing agency 11mark, 241 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included texting and answering phone calls).
(a) What is the sample in this study? What is the population of interest?
(b) What is the variable of interest in this study? ls it qualitative or quantitative?
(c) Based on the results of this survey, obtain a point estimate for the proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom.
(d) Explain why the point estimate found in part (c) is a statistic. Explain why it is a random variable. What is the source of variability in the random variable?
(e) Construct and interpret a 95% confidence interval for the population proportion of adults 19 years of age or older who bring their cell phone every trip to the bathroom.
(f) What ensures that the results of this study are representative of all adults 19 years of age or older?
Answer: kindly check explanation
Step-by-step explanation:
A) The sample is a fraction of the total population used in the study.
The sample is 1000 19 years of age or older U.S adult.
The population : all U.S adults aged 19 or older.
B.) Confession about bringing cell phone to the bathroom and it is a qualitative variable
C.) point estimate (p) :
Total number of sample = 1000
Number who confessed to bring cellphone = 241
p = 241/ 1000
= 241/1000 = 0.241
D.) The point estimate was deduced from the sample information and not the population. Random selection because selection is unbiased.
E.) 95% confidence interval (CI)
95% CI = (1 - 0.95) = 0.05
For a two-tailed test : 0.05 / 2 = 0.025
Z - score = 1.96
Error : (√[p(1 - p) / n])*z
1.96 * √0.241(1-0.241)/1000
1.96* √0.000182919
1.96 * 0.0135247
= 0.0265085
Boundary :
(0.241 - 0.0265085), (0.241 + 0.0265085)
(0.2144915, 0.2675085)
F) The sample can be said to be representative of the total population since the sampling was performed and participants were chosen at random.
convert this number to scientific notation 1260000
Answer:
1.26 * 10 ^6
Step-by-step explanation:
1260000
Scientific notation is of the form a* 10 ^b
where a is a number between 1 and less than 10
Move the decimal 6 places to the left
1.26 ( dropping the extra zeros)
b = +6 since we moved the decimal 6 places)
1.26 * 10 ^6
The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].
We have,
1260000
Write the zeroes in powers of 10.
Write a number between 1 to 10 along with the power of 10.
Now,
126 x 10000
This can be written as,
126 x [tex]10^4[/tex]
Now,
126 can be written as 126/100 x 100.
i.e
1.26 x 100 or 1.26 x 10²
Now,
1.26 x 10² x [tex]10^4[/tex]
1.26 x [tex]10^{2 + 4}[/tex]
1.26 x [tex]10^6[/tex]
Thus,
The number 1260000 in scientific notation is 1.26 x [tex]10^6[/tex].
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Please I need help! Which of the following are true?
Answer:
choices A, B, and D are all true
choice C is false
Step-by-step explanation:
Choice A is true because both functions shown on the graph have exactly one asymptote at about y=1.
Choice B is true because well, the reason Choice C is not true. logarithmic graphs and exponential graphs look very similar. However, exponential graphs get very close to the x-axis but never actually touch it. In this graphing, the blue function crosses the x-axis, so it cannot be an exponential function. The only other function that has graphs that look like this is a logarithmic function, so Choice B is correct and Choice C is not correct.
Once again, Choice C is not correct because the blue graph crosses the x-axis and exponential functions never actually touch the x-axis no matter how close they get to it.
Choice D is correct because the red graph has been reflected over the x-axis and shifted upward, and the blue graph has been reflected across the y-axis and shifted to the right.
A game has an expected value to you of $1200. It costs $1200 to play, but if you win, you receive $100,000 (including your $1200 bet) for a net gain of $98 comma 800. What is the probability of winning? Would you play this game? Discuss the factors that would influence your decision.
Answer:
A) the probability of winning is 0.24%.
B) Yes i will play the game
C) Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.
Step-by-step explanation:
Expected value of X is denoted by;
E(X) = x1•p1 + x2•p2 +..... xn•pn
Where;
xi is the observation and pi is the probability of xi
Now, let's make p the probability of the winning bet and 1 - p be the probability of losing the game
If the bet is win, the net gain is $98,800 and if the bet is lose, the loss is -$1200.
Hence the probability distribution will be;
For xi = $98,800, pi = p
For xi = -$1,200, pi = 1 - p
So;
E(X) = Σxi.pi
Thus;
1200 = 98800p - 1200(1 - p)
1200 = 98800p - 1200 + 1200p
1200 + 1200 = 100000p
2400 = 100000p
p = 2400/100000
p = 0.024
Thus, the probability of winning is 0.24%.
Despite the fact that the probability of winning is very low, one should play the game because the expected value of the game is positive.
Which letter of the alphabet is next in the series?
JOTYD
(A) I (B) J (C) K (D) L
Answer:
(A) I
Step-by-step explanation:
With the numbers, I can correspond to a series of numbers to one of the 26 letters of the English language. Like the Roman numeral system, a number adds if the next one in the sequence is smaller, and vice versa if it is larger. Combining the structure of the Roman numerals with the numbers 1, 2, 5, 10, and 20 makes it so that you never have to use more than 3 numbers to express a letter.
Answer: it is (A)
Step-by-step explanation:
Which store has the lowest delivery charge?
Answer:
Igloo Ice has the lowest delivery charge.
Step-by-step explanation:
Igloo Ice when you plug in 120 for the y you get 25.714 as the x.
Freds freeze at 120 is 20.
And lastly Tasty treats at 120 is 24, so Igloo Ice has the lowest delivery charge per person (you pay $120 for 25.714 people.)
Answer:
Igloo Ice
Step-by-step explanation:
Igloo Ice C(n) = 1.75n + 75
Fred's Freeze C(n) = 2n + 80
Tasty Treats C(n) = 1.25n + 90
75 is the lowest delivery charge
C(n) is total charge including what they are delivering
PLEASE, I NEED HELP! I will not accept nonsense answers, but I will give the person a BRAINLIEST if you get it correct.
Answer: The last choice is correct. Edna can score 5 times as many points in the next level as in the level she has reached
Step-by-step explanation: chart of values for [tex]y= 5^{x}[/tex]
x is the level y, points possible)
x y
1 5
2 25
3 125
4 625
5 3125
You can see the exponential pattern
For what it's worth, two views of the graph of the equation are attached
The point values are astronomical!
If 1 meter = 1.093 yards, how many yards are in a kilometer? _____ yards
Answer: 1093 yards
Step-by-step explanation:
There are 1000 meters in a kilometer. Thus, there are 1.093*1000, or 1093 yards in a kilometer.
Hope it helps <3
Hey there! I'm happy to help!
There are 1,000 meters in a kilometer. If there are 1.093 yards in one meter, we can split this 1,000 meters into groups of 1.093 yards to see how many yards are in a kilometer.
1000÷1.093≈914.913
Therefore, there are about 914.913 yards in a kilometer.
Have a wonderful day! :D
Jonathan was laying on the ground and enjoying the shade but now the sun is shining
on him. He knows he is 10 yards away from the building that was shading the sun and
that the building is 8 yards high. At what angle does the sunlight hit the ground? Write
only the number rounded to the nearest degree.
Answer:
38.5°
Step-by-step explanation:
Given that the height of the building is 8 yard and the distance between Jonathan and the building is 10 yards.
The sun is at the top of the building, let the distance between Jonathan laying on the ground and the top of the building be x. Using Pythagoras:
x² = 10² + 8²
x² = 100 + 64
x² = 164
x = √164 = 12.86 yards
For a triangle with sides a, b, c and their respective opposite angles A, B, and C. The sine rule is given as:
[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]
Let the angle that the sunlight hit the ground be y°. The andle between the building and the ground is 90°. Therefore using sine rule:
[tex]\frac{8}{sin(y)}=\frac{12.86}{sin(90)}\\\\sin(y)=\frac{8*sin(90)}{12.86}\\\\sin(y)=0.622\\\\y=sin^{-1}0.622\\\\y = 38.5^0[/tex]
Please answer this question now
Answer:
44 degrees
Step-by-step explanation:
Since MN is a tangent, it forms a right angle wheng it intersects line MP since MP is the diameter. So, 90+46 is 136 and since there are 180 degrees in a traingle, 180-136 is 44.
Hope this is helpful! :)
The answer is 44 degrees.
:D
Need help ASAP please
CAN SOMEONE PLEASE HELP IT'S URGENT!
Answer:
D. y = f(x/-1)
Step-by-step explanation:
The function f(x) is reflected across the y-axis to make the red graph. Such a reflection is accomplished by a horizontal scale factor of -1.
For some horizontal scale factor k, the transformed function is ...
y = f(x/k)
Here, we have k = -1, so the transformed function is ...
y = f(x/-1)
Write the following phrase as an expression. "c less than 27"
Answer:
27 - c
Step-by-step explanation:
less than means it comes after and is subtraction
27 - c
Answer:
27-c
Step-by-step explanation:
It is 27-c because it says c less than 27. If it was subtract 27 from c, it would be c-27. but its not
can someone help me
Answer:
Step-by-step explanation:
The length of side length VY is 4z+2
The same as side length WX
A set of five integers has unique mode 7, median 9, and arithmetic mean 11. What is the greatest possible value in the set?
Answer:
22
Step-by-step explanation:
Since the mean of the set is 11, the sum of the integers in the set must be 11 * 5 = 55. The median must be the 3rd integer, therefore the 3rd integer is 9. Since 9 > 7 and there are only 2 integers less than the median, the 1st and 2nd integers must be 7 and 7 because 7 is the mode. This leaves the last two integers to have a sum of 55 - (9 + 7 + 7) = 32. In order for the last integer (the greatest one) to have the largest value, the fourth integer must be as small as possible. Therefore, the fourth integer is 10 (it can't be 9 because 7 is the only mode) which makes the answer 32 - 10 = 22.
Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
? = 23
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp/ adj
tan ? = 3/7
take the inverse tan of each side
tan ^-1 tan ? = tan ^-1 ( 3/7)
? = 23.19859051
To the nearest degree
? = 23
please solve i will give brainiest 100 point question ****** do the whole page please
Answer:
a) point (2, 1) is when the ball is on it's way down at 2 seconds
b) vertex (1, 2) is the highest the ball goes, which is 2 at 1 second.
c) y-intercept (0, 1) at time zero the ball is starting at a height of 1.
d) Points (0, 1) and (2, 1) are the points at which the ball starts and when it is in the same position from the ground as when it started, which is 1.
e) zero (x-int) is when the ball hits the ground at 2.5 seconds.
Step-by-step explanation:
Answer:
See below
step by step explanation
A. (2 , 1 ) is point on the parabola . It represents that the height of the ball after 2 second have passed.
b. The vertex is at ( 1 , 2 ) . It represent that the maximum height of the ball which is 2 units to at t = 1 second
c. The y - intercept is ( 0 , 1 ) . It represent that the initial height of ball at t = 0 second is 1 unit.
d. Point ( 0 , 1 ) and ( 2 , 1 )
This point represent the set of point having equal height at two different time. It represents how long before the ball reaches the same height from the starting point.
e. The zero or x - intercept is ( 2.5 , 0 )
It represent the time taken by ball before it reaches the ground.
Hope this helps...
Best regards!!
What is the gradient and y intercept of the following lines 1) y= 2X + 3 2) y = 5X + 1 3) y= 3X + 2
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope( gradient ) and y the y- intercept )
The 3 equations are in this form
(1)
y = 2x + 3
with gradient = 2 and y- intercept = 3
(2)
y = 5x + 1
with gradient = 5 and y- intercept = 1
(3)
y = 3x + 2
with gradient = 3 and y- intercept = 2
The marked price of
an electric fan is Rs.
1800-Iwhat is selling price with 13 % VAT ?
the VAT is equal to
1800 × 13/100
Rs. 234
selling price with VAT
1800 + 234
Rs. 2034
Can Someone help me with this question?
Brainliest to the correct answer/explanation ❤️
Thank you (:
Answer:
1.67years
Step-by-step explanation:
in one it increases by 1.1% of 7.1 billion
=7.81 million
dat is it increases 7.7181 billion in 1 year
it reaches 12 billion in x years
therefore x years = 12 billion/ 7.7181 billion
= 1.67 years
don't forget to tag me as brainliest answer
Which circle has a center angle that measures 40 degrees
Answer: B
Step-by-step explanation:
A center angle is an angle that has rays that originate from the center.
A particle moves along a straight line. The distance of the particle from the origin at time t is modeled by the equation below. s(t)equals2 sine t plus 3 cosine t Find a value of t between 0 and StartFraction pi Over 2 EndFraction that satisfies the equation s(t)equalsStartFraction 2 plus 3 StartRoot 3 EndRoot Over 2 EndFraction .
Answer:
The value of t that will satisfy the equation is π/6 (which is 30 degrees)
Step-by-step explanation:
The function that models the movement of the particle is given as;
S(t) = 2 sin(t) + 3 cos (t)
Now we want to the value of t between 0 and pi/2 that satisfies the equation;
s(t) = (2+ 3√3)/2 = 1 + 3√3/2
What we do here is simply find that value of t that would ensure that;
2sin(t) + 3cos(t) = 1 + 3√3/2
Without any need for rigorous calculations, this value of t can be gotten by inspection.
From our regular trigonometry, we know that the sin of angle 30 is 1/2 and its cos value is √3/2
We can make a substitution for it in this equation.
We obtain the following;
2 sin(30) + 3cos (30) and that is exactly equal to 1 + 3√3/2
Do not forget however that we have a range. And the range in question is between 0 and π/2
Kindly that π/2 in degrees is 90 degrees
So our range of values here is between 0 and 90 degrees.
So to follow the notation in the question, the value within the range that will satisfy the equation is π/6
Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$
Answer:
2√2
Step-by-step explanation:
By simplifying we get the value is [tex]2\sqrt{2}[/tex]
What is expression ?The combination in which numbers, variables, functions are present, is called expression.
Example : 6y-3x+2, 2y-3 etc.
What is the simplified form of the expression ?
The given expression is [tex]\frac{1}{\sqrt{2}+1 } +\frac{1}{\sqrt{2}-1 }[/tex]
Simplifying,
First we take the LCM of [tex]\sqrt{2}+1[/tex] & [tex]\sqrt{2}-1[/tex]
Then expression becomes, [tex]\frac{(\sqrt{2}-1)-(\sqrt{2}+1) }{(\sqrt{2}+1)(\sqrt{2}-1)}[/tex]
Now, using [tex](a+b)(a-b)=a^{2}- b^{2}[/tex] we get, [tex]\frac{\sqrt{2}-1+\sqrt{2}+1 }{(\sqrt{2}) ^{2} - 1^{2} }[/tex]
Now, simplifying, we get, [tex]\frac{2\sqrt{2} }{2-1}[/tex] = [tex]2\sqrt{2}[/tex]
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