Show that 12 cos 30degrees + 2 tan 60degrees can be written in form roots where k is an integer
Answers
The square root of k is 192 which is an integer.
Define Trigonometric functions
A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.
Given expression is,
12 cos 30° + 2 tan 60°
We know,
cos 30° = √3/2
tan 60° = √3
Now, plug in the values
⇒12 * √3/2 + 2 * √3
⇒6√3 + 2√3
⇒8√3
We know, 8 * 8 = 64
The above value in square root form,
⇒√8*8*3
⇒√192
⇒√k (where, k is 192 an integer)
Hence, the square root of k is 192 which is an integer.
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Related Questions
10. The function f defined above; has derivatives of all orders. Let g be the function defined by g(+)=1+ f ()dt _ Write the first three nonzero tcrms and the general term of the Taylor series for cos x about * Use this series to write the first three nonzero terms and the general term of the Taylor series for aboul * Use the Taylor series for 'about x =0 found in part (&) t0 determinc whether f relative minimum; or neither at * =0 Give reason for has relative maximum_ your answer: Write the fifth-degree Taylor polynomial for g about x=0.
Answers
The fifth-degree Taylor polynomial for g(x) about x=0. is\(g(x) = 1 + x - x^{3}/3! + x^{5}/5! - x^{7}/7! + x^9/9!\)
We are given the function f(x) and the function g(x) defined by:
g(x) = 1 + ∫[0, x] f(t) dt
We need to find the first three nonzero terms and the general term of the Taylor series for cos(x) about x=0, and then use this series to write the first three nonzero terms and the general term of the Taylor series for g(x) about x=0. Finally, we will use the Taylor series for g(x) to determine whether f(x) has a relative minimum, maximum, or neither at x=0.
The Taylor series for cos(x) about x=0 is given by:
\(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)
The first three nonzero terms are:
\(cos(x) = 1 - x^2/2! + x^4/4!\)
The general term of the series is:
\((-1)^n x^{(2n)} / (2n)!\)
Now, we can use this series to write the Taylor series for g(x) about x=0. We have:
g(x) = 1 + ∫[0, x] f(t) dt
Taking the derivative of g(x), we get:
g'(x) = f(x)
Taking the derivative of g'(x), we get:
g''(x) = f'(x)
And so on, we can take the nth derivative of g(x) to get:
\(g^{(n)(x)} = f^{(n)(x)\)
Using the Taylor series for cos(x), we can write:
g(x) = 1 + ∫[0, x] f(t) dt
\(= 1 + x - x^3/3! + x^5/5! - x^7/7! + .\)..
= cos(x) + ∫[0, x] (f(t) - cos(t)) dt
The first three nonzero terms are:
\(g(x) = 1 + x - x^3/3!\)
The general term of the series is:
(-1)^n ∫[0, x] (f(t) - cos(t)) dt * x^(2n) / (2n)!
To determine whether f(x) has a relative minimum, maximum, or neither at x=0, we need to look at the sign of the second derivative of g(x) at x=0. We have:
g''(x) = f''(x)
Therefore, g''(0) = f''(0). Since we don't have any information about the sign of f''(0), we cannot determine whether f(x) has a relative minimum, maximum, or neither at x=0.
Finally, to write the fifth-degree Taylor polynomial for g(x) about x=0, we need to include the first five nonzero terms of the series:
\(g(x) =1 + x - x^3/3! + x^5/5! - x^7/7! + x^9/9!\)
This is the fifth-degree Taylor polynomial for g(x) about x=0.
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please help due soon
Answers
Answer:
5z^2-8z+3
-5×-3=15
-5+-3=-8
so...
5z^2-5z-3z+3
5z(z-1)-3(z-1)
therefore the answer is...
(5z-3) (z-1)
2 mi equal how many ft?
Answers
Answer:
10560Feet
Step-by-step explanation:
Answer: 10560 ft
Step-by-step explanation: 2 mi conversion. a mile is a unit of distance equal to 5,280 feet or exactly 1.609344 kilometers. it is commonly used to measure the distance between places in the United States and kingdom. so you convert 2 mi to ft.
Javier wants to go to the movies. He has some money saved but does not want to use all his savings on a movie
ticket. Javier’s mother offers to pay some of the cost of the ticket for every pound of potatoes he peels for her.
The graph shows the cost to Javier for the purchase of the movie ticket after peeling x pounds of potatoes for
his mother.
Answers
Answer:
1. true 2. false 3. true 4. false 5. false
Step-by-step explanation:
yurr
A shoemaker sold a pair of for $245.99 if the buyer a $300.00 bill, how much will the buyer receive in change?
*two decimal places don't forget your $ sign. Example: $50.00 NOT 50*
Answers
Answer:
$54.01
Step-by-step explanation:
All you have to do is $300.00-$245.99 .
the ____ format specifier is used to denote a signed decimal integer.
Answers
The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.
When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.
For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.
Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.
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Which expression is equivalent to (4.3x + 4)(−1.8x)?
Answers
The expression which is equivalent to the given expression is -7.74x² - 7.2x.
The given expression is (4.3x + 4)(−1.8x).
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Now, the given expression can be solved as follows:
(4.3x + 4)(−1.8x)
Using distributive property
4.3x × (−1.8x) + 4 × (−1.8x)
= -7.74x² - 7.2x
Therefore, the expression which is equivalent to the given expression is -7.74x² - 7.2x.
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The sides of a right-angled triangle are in the ratio 8:15:17. If the perimeter of the triangle is 160 cm, find the area.
Answers
Let us consider ratio values as 8x,15x,17x
Now let’s add these values 8x+15x+17x=40x
Here8x is the height,15xis the base
Perimeter =160cm
So x=160/40
=4cm
Now the measurements are 40cm,60cm,68cm
Here 40 is height,60is base
Area of triangle is 1/2 x base x height
=1/2 x 40 x 60
=1200 cm square
HOPE THIS HELPS
X^4 + x^2 - 90 = 0
Help solve please
Answers
Answer:
The answer to your question is x= −3 or it can be x=3
Steps of solving
The first step we have to do to solve this equation is to Factor left side of our equation
(x+3)(x−3)(x^2+10)=0
The second step that we would have to do would be Setting the factors that equal to 0.
You can go with any of these
x+3=0, x−3=0 or you can lastly go with x^2+10=0
And that's how you would get your answer : x= −3 or x=3
A normal population has a mean of $75 and standard deviation of $5. You select random samples of 40. a Apply the central limit theorem to describe the sampling distribution of the sample mean with » = 40. What condition is necessary to apply the central limit theorem?
Answers
The Central Limit Theorem states that for a random sample of n observations drawn from any population with a finite mean μ and a finite standard deviation σ, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
To apply the Central Limit Theorem, the following condition is necessary:
1. The random sample should be selected from a population that has a finite mean (μ) and a finite standard deviation (σ).
In this case, the population mean is given as $75 and the population standard deviation is given as $5. Since both the mean and standard deviation are finite, the condition for applying the Central Limit Theorem is satisfied.
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2(3x-2)+2(2x+7)=30 x=?
Answers
Answer:
x=2
Step-by-step explanation:
2(3x-2)+2(2x+7)=30
6x-4+4x+14=30
10x+10=30
10x=20
x=2
Using the data below, Use the 2 period moving average to create the forecast calculate the absolute error for the 3rd week. Week Actuals 17.00 20.00 10.00 11.00 Submit Answer format: Number: Round to: 1 decimal places. Using the data below, calculate the squared error for the 4th week. Use the 2 period moving average to create the forecast. Week Time Series Value 16.00 5.00 25.00 9.00 Submit Answer format: Number: Round to: 1 decimal places.
Answers
The absolute error for the 3rd week is 5.0.
To calculate the 2-period moving average, we take the average of the current and previous periods.
Given data:
Week 1: Actuals = 17.00
Week 2: Actuals = 20.00
Week 3: Actuals = 10.00
To calculate the forecast for Week 3 using the 2-period moving average, we average the values of Week 2 and Week 3:
Forecast Week 3 = (Week 2 + Week 3) / 2
= (20.00 + 10.00) / 2
= 15.00
The forecast for Week 3 is 15.00.
To calculate the absolute error for Week 3, we subtract the actual value from the forecast:
Absolute Error Week 3 = |Forecast Week 3 - Actuals Week 3|
= |15.00 - 10.00|
= 5.00
The absolute error for the 3rd week is 5.0.
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Using the data below, Use the 2 period moving average to create the forecast calculate the absolute error for the 3rd week. Week Actuals 17.00 20.00 10.00 11.00 Submit Answer format: Number: Round to: 1 decimal places.
You find 13,406,190 pennies which is $134,061.90 and weighs 118,222.45 lbs. Now assume a movie ticket costs $9.00, how many movie tickets could you buy with the pennies?
Answers
Answer:
14895.6
Step-by-step explanation:
Craig sells cabinets at a 600% percent markup from the cost of materials. He spent $2000.00 on the materials for cabinets he just built. What will be the price he sells those cabinets for?
Answers
Answer:
3781
Step-by-step explanation:
80 hours × $18=$1440 for labor. 1440+15%(1440×.15)=$216.00 + material cost=$2125
(2125.00+1440.00+216=3781)
Your gross pay is $1,957 and your federal tax witholding rate is 16%. What is your net pay?
Answers
What are the three main types of tectonic plate boundaries? a. Convergent, divergent, and transform b. Continental, oceanic, and convergent c. Oceanic, convergent, and divergent d. Transform, continental, and divergent.
Answers
The three main types of tectonic plate boundaries are convergent, divergent, and transform.
Tectonic plate boundaries refer to the edges of the Earth's tectonic plates where they come into contact with one another.
The three main types of tectonic plate boundaries are:1. Divergent boundaries: At divergent boundaries, tectonic plates move away from each other, forming new crust as magma rises to the surface and solidifies. This process is responsible for the formation of mid-oceanic ridges and rift valleys.
2. Convergent boundaries: At convergent boundaries, tectonic plates move towards each other. When two continental plates collide, they form mountains. When an oceanic plate collides with a continental plate, the oceanic plate is subducted beneath the continental plate and can form volcanic island arcs.
3. Transform boundaries: At transform boundaries, tectonic plates slide past each other horizontally. This type of boundary is responsible for the formation of strike-slip faults, such as the San Andreas Fault in California.
It's important to notice that these three types of boundaries are not mutually exclusive, there are areas where multiple types of boundaries are interacting, such as subduction zones where two plates are converging and one plate is being subducted beneath the other.
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49
george plays cricket and scores a run every time he runs the length of the cricket
pitch. his average score after 4 garnes is 23 runs. after the fifth game, his average
score is 21 runs.
how many runs did he score in the fifth game?
Answers
Answer:
George gets 13 runs in the fifth game
Step-by-step explanation:
He gets x in the fifth game so, ( 23 · 4 + x ) + 5 = 21
So 92 + x = 105
-92 -92
x = 13
( will give brainlyest)
Write an expression equivalent to the following problems using the fewest number of terms. ( number 1)
Answers
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s)
The map below is being reduced by a scale factor of 2/3 and printed at
the subway station. How many square inches will the map take up? *
length 21 in
width 15 in
Answers
To find the area of the reduced map, we need to calculate the area of the original map and then scale it down using the given scale factor of 2/3.
The reduced map will take up approximately 8.75 square inches.
The original map has a length of 21 inches and a width of 15 inches. To find the area of the original map, we multiply the length by the width:
Area of the original map = 21 inches * 15 inches = 315 square inches.
Next, we need to scale down the area using the scale factor of 2/3. To scale down an area, we square the scale factor:
Scaled down area = \((2/3)^2\) * 315 square inches = 4/9 * 315 square inches = 140 square inches/3 ≈ 8.75 square inches.
Therefore, the reduced map will take up approximately 8.75 square inches.
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Find the equation of the line that passes through (3,-4) and is parallel to 3x+y+2=0 Leave your answer in the form y=mx+c
Answers
Answer:
2x+y
Step-by-step explanation:
Simply remove the +2
Answer:
y = - 3x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x + y + 2 = 0 ( subtract 3x + 2 from both sides )
y = - 3x - 2 ← in slope- intercept form
with slope m = - 3
Parallel lines have equal slopes, thus
y = - 3x + c ← is the partial equation
To find c substitute (3, - 4) into the partial equation
- 4 = - 9 + c ⇒ c = - 4 + 9 = 5
y = - 3x + 5 ← equation of line in form y = mx + c
A man leaves home at 22:15 hours and reaches his destination at 04:00 hours on the following day. how many hours did the journey take?
Answers
Answer,
Leaves from home=22:15hour
get to destination=4:00hour
time taken on a journey,
from time 22:15hour to 24:00hour=2:45hour and,
time is taken form 22:00hour to 4:00hour=4:00hour
So, the total time taken to reach the destination is 2:45+4:00=6:45hour
You have developed the technology to use gold to produce high capacity fiber optic switches. The technology has cost $ 5 million to develop. You need $50 million of initial capital investment to start production. Sales of the switch sales will be $20 million per year for the next 5 years and then drop to zero. The main cost of production is gold. Each year, you need 20,000 ounces of gold. Gold is currently selling for $250 per ounce. Your supplier thinks that the gold price will appreciated at 5% per year for the next 5 years. The cost of capital is 10% for the fiber-optics business. The tax rate is 35%. The capital investment can be depreciated linearly over the next 5 years.
1. Calculate the after-tax cash flows of the project
2. Should you take the project?
Answers
1. After-tax cash flows of the project are shown below. Since the net present value (NPV) of the project is negative, it should not be pursued, which means that you should not take the project.
To determine if the project should be taken, we will calculate the project's net present value (NPV) using a 10% discount rate and comparing it to the initial capital investment of $50,000,000.Net present value (NPV) = Sum of discounted cash flows - Initial investment= $6,811,041 - $50,000,000= -$43,188,958Since the net present value of the project is negative, it should not be pursued, which means that you should not take the project.
Calculating the after-tax cash flows of the project are shown below:Year 1Year 2Year 3Year 4Year Net cash flows12,880,00012,796,00012,729,38712,680,50612,648,036The net present value (NPV) of the project will be calculated using a 10% discount rate and compared to the initial investment of $50,000,000. If the net present value (NPV) of the project is positive, the project should be pursued, but if it is negative, the project should not be pursued.Net present value (NPV) = Sum of discounted cash flows - Initial investment= $6,811,041 - $50,000,000= -$43,188,958. Since the net present value (NPV) of the project is negative, it should not be pursued, which means that you should not take the project.
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A children's wind-up car toy travels a distance, d inches, as modeled by the function d=12 +8t where t is the number of seconds after the car has been wound up and released. If the car is released at 12 feet, to the nearest second, how many seconds would it take to rcach 21 feet?
0 10
O 11
O 12
O 13
O 14
Answers
Answer 14
Step-by-step explanation:
Hello guys
can u please help me ?
THANKS YOU MUCH
9. Give the answer in simplest form.
A. 7/8 ×1 1/4 ÷(3/16- 1/8) =
B. 9/8 ×(2/5+ 3/7 × 1/3+ 3/5)×4=
Answers
Answer:
a is 17 1/2 i dont know b sorry
Answer:
A.7/2
alternate form: 3 1/2
B.36/7
alternate form: 5 1/7
i hope it help
PLEASE HELP
x = ___ units
Answers
Answer:
x = 16 units
Step-by-step explanation:
∆ABC is a 45-45-90 triangle, and ∆BCD is a 30-60-90 triangle.
If side opposite of 90° [∆] = x, side opposite of 45° [∆] = x / √2 = x √ 2 / 2.
Given side AC is opposite of 90° [∆ABC] = 32 √ 2, side opposite of 45° [∆ABC] = 32 √ 2 / √ 2 = 32 which is AB or BC.
Since side BC is part of BCD.
Side opposite of 90° [∆BCD] = BC = 32.
Since x is opposite of 30° [∆BCD].
x = Side opposite of 90° [∆BCD] / 2 = 32 / 2 = 16.
can you please answer this for me
Answers
Answer:
you are on the right track
Step-by-step explanation:
the second ones right so you are right :)
Classify angle D in the figure as right, straight, acute, or obtuse.
Choose the correct classification for angle D.
A. Right
B. Straight
C.Acute
D.Obtuse
Answers
Answer:
C.
Step-by-step explanation:
The angle D. is acute
Rewrite the fraction in the sentence below as a percentage.
At a certain wedding 11/20, of the guests were over 25 years old.
What is the Percent notation: %?
Answers
The percent notation is 55%.
What is the percent notation?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentage is %. In order to convert a fraction to percentage notation, multiply by 100.
Percent notation = fraction that attended the wedding x 100
= 11/20 x 100 = 55%
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Use the net to compute the surface area of the three dimensional figure.
130?
152?
166?
182?
Answers
Answer:
166
Step-by-step explanation:
Answer:
I think ur answer luv would be c.)166
Step-by-step explanation:
hope this helps
Need help with this his one!
Answers
Answer:
a) 6(6x-5)
=(6×6x) - (6×5)
=36x-30
b)11y+4y+10y
=y(11+4+10)
=y(25)
=25y