Answers
Answer:
y=-x+pi/3+sqrt(3)/2
Step-by-step explanation:
*I assume you are asking for help on part a because the other question is a calculator question.*
We want to find tangent line to y=2sin(x)cos(x) at x=pi/3.
First I prefer to use y=sin(2x). (Double angle identity: sin(2x)=2sin(x)cos(x) .)
Differentiate using chain rule:
y'=2cos(2x)
y' gives us the slope for any tangent along our curve.
So at x=pi/3, the slope is 2cos(2×pi/3)=2cos(2pi/3)=2(-1/2)=-1.
We also need to know a point our line to find the equation of our line.
At x=pi/3, y=sin(2×pi/3)=sin(2pi/3)=sqrt(3)/2.
So a point on our line is (pi/3, sqrt(3)/2).
So by point-slope form of a line we have
y-y1=m(x-x1)
y-sqrt(3)/2=-1(x-pi/3)
Distribute:
y-sqrt(3)/2=-x+pi/3
Add sqrt(3)/2 on both sides:
y=-x+pi/3+sqrt(3)/2
Answer:
y= -x+(pi/3)+(sqrt3)/2
Step-by-step explanation:
The given is y=2sin(x)*cos(x)
to take the derivative we will need to use the constant rule (which says when taking the derivative of any constant multiplied by an expression you take the derivative of the function and multiply it by the constant) and the multiplication rule to get
y'=2(sin(x)*-sin(x)+cos(x)*cos(x))
this would simplify to be
y'=-2sin^2(x)+2cos^2(x)
We then substitute in the given x value to find the slope of the tangent line at that point and get
-2sin^2(pi/3)+2cos^2(pi/3)
which simplifies to
-2*3/4+2*1/4
which is -1
Since we have the slope we need to find the y value to go with the original x so that we have a point to use in point slope form. When we substitute pi/3 into the given equation we get (sqrt 3)/2 and have the point (pi/3, sqrt3/2)
now we write the point slope form equation
y-(sqrt3)/2= -(x-pi/3)
y-(sqrt 3)/2 = -x+pi/3
y= -x+pi/3+(sqrt3)/2
you could simplify the last two terms, but I think it is simplest to understand this way.
For b, enter both equations into graphing software or a calculator
Related Questions
Whats 10 Divided by 4 with a Remainder?
Answers
Answer:
Step-by-step explanation:
10/4= 2 r 2
Answer: it’s 2.5, with a remainder it’s 2 r2
Step-by-step explanation:
Roy collected 30 Avenger stickers. He gave 3/5 of them to her friends. How many stickers did he give to his friends
Answers
Answer:
29.4
Step-by-step explanation:
then convert to whole number
A video game system costs $350. The sales tax rate is 796, what
is the final cost
Your answer
Answers
Answer:
$377.86
Step-by-step explanation:
Given: Video game system costs $350, sales tax rate is 796.
To find: Final cost
Solve: Calculating Total Cost. Multiply the cost of an item or service by the sales tax to find out the total cost.
3.5 × 7.96 = 27.86
Add the total sales tax to the Item or service cost to get your total cost.
27.86 + 350 = 377.86
The final cost is $377.86
Mr. Wilson invested money in two accounts. His total investment was $20,000. If one account pays 3% in interest and the other pays 6% in interest, how much does he have in each account if he earned a total of $960 in interest in 1 year?
He invested $__ in the 3% account and $__ in the 6% account.
Answers
Answer:
8000 and 12,000
Step-by-step explanation:
Let the amount of money deposited in the 3% account be known as "x"
The amount of money deposited in the 6% account would be "20,000 - x" (aka the remaining amount of money not put into the first account)
3% Interest -> 0.03 *
6% Interest -> 0.06 *
0.03 * x + 0.06 * (20,000 - x) = 960
0.03x + 1200 - 0.06x = 960
-0.03x = -240
x = 8000
20,000 - x
20,000 - 8000 = 12000
which statement best describes the product of 240 and 1/3
the product is less than 99 the product is between 100 and 150 the product is between 200 and 250 the product is greater than 400
Answers
Answer:
Step-by-step explanation:
240 x 1/3 = 240/3 = 80
so the answer is: the product is less than 99
Driving instructors Mr. Adams and Mr. Bateman teach class independently of each other. Among Mr. Adams’s students, 68% pass the driving test on the first try, while 74% of Mr. Bateman’s students pass the driving test on the first try. Suppose there are 40 students in Mr. Adams’s class and 50 students in Mr. Bateman’s class. Let A = the proportion of students who pass the driving test on the first try from Mr. Adams’s class and B = the proportion of students who pass the driving test on the first try from Mr. Bateman’s class. What is the probability that Mr. Bateman’s class has more students who pass on the first try?
Find the z-table here.
0.266
0.547
0.734
0.765
Answers
Answer:
0.989 = 98.9% probability that Mr. Bateman’s class has more students who pass on the first try
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution, the binomial approximation to the normal and subtraction of normal distributions.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Subtraction of normal distributions:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
Among Mr. Adams’s students, 68% pass the driving test on the first try. Sample of 40.
This means that [tex]p = 0.68, n = 40[/tex].
[tex]\mu_A = np = 40*0.64 = 27.2[/tex]
[tex]s_A = \sqrt{40*0.68*0.32} = 2.95[/tex]
74% of Mr. Bateman’s students pass the driving test on the first try. Sample of 50:
[tex]p = 0.74, n = 50[/tex]
[tex]\mu_B = np = 50*0.74 = 37[/tex]
[tex]s_B = \sqrt{50*0.74*0.26} = 3.1016[/tex]
What is the probability that Mr. Bateman’s class has more students who pass on the first try?
This is the probability that B - A is greater than 0.
Distribution B - A:
Mean:
[tex]\mu = \mu_B - \mu_A = 37 - 27.2 = 9.8[/tex]
Standard deviation:
[tex]\sigma = \sqrt{s_A^2 + s_B^2} = \sqrt{2.95^2 + 3.1016^2} = 4.28[/tex]
Probability of being larger than 0:
1 subtracted by the pvalue of Z when X = 0. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 9.8}{4.28}[/tex]
[tex]Z = -2.29[/tex]
[tex]Z = -2.29[/tex] has a pvalue of 0.011
1 - 0.011 = 0.989
0.989 = 98.9% probability that Mr. Bateman’s class has more students who pass on the first try
Answer:
0.734, c
Step-by-step explanation:
1/4-1/20 in simplest form
Answers
Answer:
1/5
Step-by-step explanation:
Answer: 1/5
Step-by-step explanation:
For his long distance phone service, Tom pays an 8 monthly fee plus 6 cents per minute. Last month, Tom's long distance bill was $16.34. For how many minutes was Tom billed?
Answers
8 + 0.06x = 16.34
0.06x = 8.34
x = 139
Please lmk if you have any questions
The Roger's applied for a $70,000 mortgage for 30 years at 9%. Since they had a good credit history,
they actually qualified for a 25 year mortgage at 7%. What were the payments on the 9% loan, and the
7% loan? What do they save monthly? What is the total repayment on the 9% loan and the 7% loan, and
what do they save over the life of the loan?
Answers
9514 1404 393
Answer:
9% payments: $563.247% payments: $494.75monthly savings: $68.499% total repaid: $202,764.907% total repaid: $148,423.63savings: $54,341.27Step-by-step explanation:
It works nicely to let a calculator or spreadsheet figure the payment and loan values. The graphing calculator work is attached.
Answer:
9% payments: $563.24
7% payments: $494.75
monthly savings: $68.49
9% total repaid: $202,764.90
7% total repaid: $148,423.63
savings: $54,341.27
Step-by-step explanation:
Find the perimeter and area of the polygon shown below.
P= 72 feet, A = 300 square feet
O P = 56 feet, A = 308 square feet
P= 87 feet, A = 360 square feet
P = 72 feet, A = 308 square feet
Answers
Answer:
A. P = 72 feet, A = 300 square feet
Step-by-step explanation:
✔️Perimeter = sum of all sides of the polygon = 15 + 16 + 17 + 8 + 16 = 72 ft
✔️Area of the polygon = area of a trapezoid = ½(a + b)h
Where,
a = 16 ft
b = 16 + 8 = 24 ft
h = 15 ft
Substitute
Area = ½(16 + 24)15
Area = ½(40)15
Area = 300 ft²
Find the height of the cone plsss
Answers
Answer: the last one, 31.6
Answer:
the answer is about 31.6
Step-by-step explanation:
the formula for the height of a cone is 3(V/πr^2), so if you plug in the number, you'll get about 31.6.
Brainliest for correct answer, asap please.
Answers
Answer:
Not a function
Not a function
Function
Step-by-step explanation:
The 1st one isn't as clear in the picture, but it looks like the ends of each line overlap the each other.
Find the volume of a cone that has a height of 15 centimeters and a radius of 6 centimeters.
WILL MARK BRAINLEST!!!
Answers
Answer:
565.2
Step-by-step explanation:
Cone=1/3bh
B is pir^2
so that means b=pi36 (6*6 =36)
36*15/3 is 565.2
1. The perimeter of a square box is 12x+32. Write an equivalent expression that shows the perimeter as four times the side length of the box.
Answers
Answer:
4(3x+8)
Step-by-step explanation:
Tools -
Question 10
Steven fosses a fair coin 100 times. The coin lands on heads 57 times and tails 43 times.
What is the probability and relative frequency of the coin landing on heads?
A
The probability is 50% and the relative frequency 43%
B
The probability is 50% and the relative frequency 57%
The probability is 43% and the relative frequency 50%.
D
The probability is 57% and the relative frequency 50%.
Answers
Answer: D
Step-by-step explanation:
The probability of the coin landing on heads is 50% and the relative frequency of the coin landing on heads is 57%
The probability of the coin landing on headsThe sample space of a coin is:
S = {Head, Tail}
The sample size is:
n(S) = 2
The probability of the coin landing on heads is calculated as:
P(Head) = n(Head)/n(S)
So, we have:
P(Head) = 1/2
Express as percentage
P(Head) = 50%
Hence, the probability of the coin landing on heads is 50%
The relative frequency of the coin landing on headsFrom the question, we have:
Toss = 100
Head = 57
The relative frequency of the coin landing on heads is calculated as:
Frequency = 57/100
Express as percentage
Frequency = 57%
Hence, the relative frequency of the coin landing on heads is 57%
Read more about probability at:
https://brainly.com/question/251701
A circular patio has a radius of 4 yards. The patio is expanded so that the
radius increases by 2 yards. By how many square yards does the area of the
patio increase?
Answers
Answer:
20pi or 62.83
Step-by-step explanation:
when r=4
pi r^2
16pi
when r=6
pi r^2
36pi
36pi-16pi=20pi or 62.83
A plane descends 1000 ft while flying
2.7 mi. What is the angle of descent?
Answers
Answer:
4.02°
Step-by-step explanation:
The angle of descent can be obtained using trigonometry ;
Since we have a right angled triangle ;
Let's use the relation:
Sin θ = opposite / hypotenus
Hypotenus = 2.7 miles
1 mile = 5280 feets
2.7 miles = (2.7 * 5280) = 14256 feets
Sin θ = 1000 / 14256
Sin θ = 0.0701459
θ = sin^-1(0.0701459)
θ = 4.0223674
The order is for 500 mL D5 1/2 NaCl to run in 6 hours. Set calibration is 15 gtt/mL calculate the flow rate in mL/hrs
Answers
Answer:
16 is correct
Step-by-step explanation:
can some help me plz I will give the brainlist
Answers
Answer:
A-0.125
B-15%
C- I think .15 would
Step-by-step explanation:
Sorry if i am incorrect
Answer:
A=.125
B=.14
Step-by-step explanation:
C=.15 would give him more candy.
A rectangular prism has a length of 12 inches, a height of 16 inches, and a with of 20 inches. What's the volume, in cubic inches
Answers
Answer:
3840in²
Step-by-step explanation:
Formula:
V = whl
Insert the values:
V = 20 * 16 * 12
Multiply the values:
V = 3840in²
pls I need assistance with this I promise brainiest
1. (-4)*(-3)*(+2)/(-6)*(-4)
2. -8*(-11)*9*(-5)/2*(-33)*(-3)
Answers
Answer:
1) 16
2) -196020
Step-by-step explanation:
simple answer using DMAS rule
D = Division
M = Multiplication
A = Addition
S = Subtraction
here's the question
Answers
Lamont has 30 book pack in boxes. Each box holds 7 books. If he fills each box,how many books are left over?
Answers
Answer:
2 are left over
since 7 goes into 30 4 times which makes 28 books. Meaning 2 are going to be left over
in the triangle shown determine a to the nearest degree
Answers
Answer:
43
Step-by-step explanation:
Cos A= 8/11
Cos A= 43.34
A=43.34
rectangle has area 80 square centimeters. the rectangle is dilated using A as a center and a scale factor of 1/2 what is the area of the image
Answers
9514 1404 393
Answer:
20 square centimeters
Step-by-step explanation:
The area of the dilated figure is the original area multiplied by the square of the dilation factor. The center of dilation is irrelevant.
dilated area = (1/2)² × original area
dilated area = 1/4 × 80 cm²
dilated area = 20 cm²
what is the greatest common factor (GCF) of the following monomials?
Answers
Answer:
2x is the greatest common factor.
Step-by-step explanation:
Looking for what they have in common and what is the highest number they can both go into.
An artist makes triangular -shaped sculptures using steel long. There are several rods are 12,13,14,15 or 16 feet long .there are several rods of each length?
Answers
Answer:
You are having a stroke.
Step-by-step explanation:
1. Go to the hospital.
3.4x=8.5
on a text plz answer
Answers
Answer:
x=.4
Step-by-step explanation:
Answer:
2.5
Step-by-step explanation:
PLZ HELP
Which is the sum of 3.15 × 10^7 +9.3 × 10^6 ? Write your answer in
scientific notation.
A. 4.08 × 10^7
B. 4.08 × 10^6
C. 0.408 × 10^8
D. 40.8 × 10^6
Answers
Answer: A 4.08x10^7
Step-by-step explanation:
Expanded form: 40800000
Mort bought his house in 2004 for $279,000. it was recently appraised at $186,000. What is the approximate percent of decrease in value
Answers
Answer:
33.3%
Step-by-step explanation:
(279,000 - 186,000) / 279,000 = 0.33333333333
0.33333333333*100= 33.3333333333
Formula used:
[tex]V_{2} -V_{1}[/tex] / [tex]V_{2}[/tex] × 100
V2= 279,000
V1= 186,000
The approximate percentage of the decrease in value of the house is 33.33%.
Purchase price of the house = $279,000
Appraisal cost of the house = $186,000
What is a percentage?The percentage is the value per hundred.
The percent of the decrease in value = (279000-186000)/279000 *100
The percent of the decrease in value =(93000/279000) *100
The percent of the decrease in value =33.33%
Hence, the approximate percentage of the decrease in value of the house is 33.33%.
To get more about percentages visit:
https://brainly.com/question/24304697