Answers
Answer:
[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex]
Step-by-step explanation:
We are given the graph of r = cos( θ ) + sin( 2θ ) so that we are being asked to determine the integral. Remember that [tex]\:r=cos\left(\theta \right)+sin\left(2\theta \right)[/tex] can also be rewritten as [tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex].
Let's apply the functional rule [tex]\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex],
[tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex] = [tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex]
At the same time [tex]\int \cos \left(\theta \right)d\theta \right=\sin \left(\theta \right)[/tex] = [tex]sin( \theta \right ))[/tex], and [tex]\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]-\frac{1}{2}\cos \left(2\theta \right)[/tex]. Let's substitute,
[tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \right)[/tex]
And adding a constant C, we receive our final solution.
[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex] - this is our integral
Related Questions
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answers
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
Try to get to every number from 1 to 10 using four 4's and any number of arithmetic operations (+, −, ×, ÷). You may also you parentheses.
Answers
Answer:
Step-by-step explanation:
1. 4/4+4-4=1
2. 4/4+4/4=2
3. 4+4/4-4=3
4. 4 × (4 − 4) + 4=4
5. (4 × 4 + 4) / 4=5
6. 44 / 4 − 4=6
7. 4+4-4/4=7
8. 4+4+4-4=8
9. 4+4+4/9=9
10. 44 / 4.4=10
Answer:
1 = (4 x 4)/(4 x 4) or (4 + 4)/(4 + 4) or (4 / 4) x (4 / 4) or (4 / 4)/(4 / 4)
2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)
3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4
4 = 4 - (4 - 4)/4
5 = (4 x 4 + 4)/4
6 = 4 + (4 + 4)/4
7 = 4 - (4/4) + 4
8 = 4 + (4 x 4)/4
9 = 4 + 4 + (4/4)
10 - I tried the best. You might need ! or sqrt operator to get 4.
Updated:
I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:
10 = (44 - 4)/4
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answers
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
What is the solution to X+9 = 24?
A. x = 33
B. x= 15
C. x= 18
D. x= 9
Answers
Answer:
X+9=24
Or,x=24-9
:.x=15
Step-by-step explanation:
Answer:
B. x=15
Step-by-step explanation:
To find the solution to the equation, we must get x by itself on one side of the equation.
[tex]x+9=24[/tex]
9 is being added to x. The inverse of addition is subtraction. Subtract 9 from both sides of the equation.
[tex]x+9-9=24-9[/tex]
[tex]x=24-9[/tex]
[tex]x=15[/tex]
Let's check our solution. Plug 15 in for x.
[tex]x+9=24 (x=15)[/tex]
[tex]15+9=24[/tex]
[tex]24=24[/tex]
This checks out, so we know our solution is correct. The answer is B. x=15
Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)
Answers
Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have yet to attend?
Answers
Answer:
320
Step-by-step explanation:
Total no of employees = 1600
% of employees attended the training = 80%
no. of employee who attended the training = 80/100* 1600 = 1280
No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training = 1600-1280 = 320
Thus, 320 employees have yet to attend the training
Last Sunday, the average temperature was 8\%8%8, percent higher than the average temperature two Sundays ago. The average temperature two Sundays ago was TTT degrees Celsius. Which of the following expressions could represent the average temperature last Sunday?
Answers
Work Shown:
T = average Celsius temperature two Sundays ago
8% = 8/100 = 0.08
8% of T = 0.08T
L = average Celsius temperature last sunday
L = 8% higher than T
L = T + (8% of T)
L = T + 0.08T
L = 1.00T + 0.08T
L = (1.00 + 0.08)T
L = 1.08T
The 1.08 refers to the idea that L is 108% of T
Answer:
b and d
Step-by-step explanation:
khan
The function fix) = (x - 4)(x - 2) is shown.
What is the range of the function?
8
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1
6
2
16
2
14
COL
40
8
G D
Answers
Answer:
The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1
Step-by-step explanation:
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
Answers
the product of two consecutive positive integer is 306
Answers
Answer:
[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]
Step-by-step explanation:
The product means multiplication.
There are two positive consecutive integers.
Let the first positive consecutive integer be x.
Let the second positive consecutive integer be x+1.
[tex](x) \times (x+1) =306[/tex]
Solve for x.
Expand brackets.
[tex]x^2 +x =306[/tex]
Subtract 306 from both sides.
[tex]x^2 +x -306=306-306[/tex]
[tex]x^2 +x -306=0[/tex]
Factor left side of the equation.
[tex](x-17)(x+18)=0[/tex]
Set factors equal to 0.
[tex]x-17=0[/tex]
[tex]x=17[/tex]
[tex]x+18=0[/tex]
[tex]x=-18[/tex]
The value of x cannot be negative.
Substitute x=17 for the second consecutive positive integer.
[tex](17)+1[/tex]
[tex]18[/tex]
The two integers are 17 and 18.
The product of two consecutive positive integers is 306.
We need to find the integers
solution : Let two consecutive numbers are x and (x + 1)
A/C to question,
product of x and (x + 1) = 306
⇒x(x + 1) = 306
⇒x² + x - 306 = 0
⇒ x² + 18x - 17x - 306 = 0
⇒x(x + 18) - 17(x + 18) = 0
⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18
so x = 17 and (x +1) = 18
Therefore the numbers are 17 and 18.
Hope it helped u if yes mark me BRAINLIEST
TYSM!
Find the area of the shape shown below.
3.5
2
2
Answers
Answer:
26.75 units²
Step-by-step explanation:
Cube Area: A = l²
Triangle Area: A = 1/2bh
Step 1: Find area of biggest triangle
A = 1/2(3.5)(2 + 2 + 5)
A = 1.75(9)
A = 15.75
Step 2: Find area of 2nd biggest triangle
A = 1/2(5)(2)
A = 1/2(10)
A = 5
Step 3: Find area of smallest triangle
A = 1/2(2)(2)
A = 1/2(4)
A = 2
Step 4: Find area of cube
A = 2²
A = 4
Step 5: Add all the values together
A = 15.75 + 5 + 2 + 4
A = 20.75 + 2 + 4
A = 22.75 + 4
A = 26.75
Please help with this
Answers
Answer:
A
Step-by-step explanation:
● first one:
The diagonals of a rhombus are perpendicular to each others wich means that they form four right angles.
STP is one of them so this statement is true.
● second one:
If ST and PT were equal this would be a square not a rhombus.
● third one:
If SPQ was a right angle, this woukd be a square.
● fourth one:
Again if the diagonals SQ and PR were equal, this would be a square.
Which expression is equal to 7 times the sum of a number and 4
Answers
Answer:
7(n + 4)
Step-by-step explanation:
Represent the number by n. Then the verbal expression becomes
7(n + 4).
Identify whether the sampling method is simple random, systematic, stratified, cluster, or convenience. Explain.
In a nationwide study of registered voters conducted by The New York Times, 390 people are randomly selected out of those registered as Republicans, 430 people are randomly selected out of those registered as Democrats, and 180 people are randomly selected out of those registered as Independents.
Answers
Answer: stratified
Step-by-step explanation:
In stratified sampling, you divide the population into subgroups, or strata, with similar characteristics, like here we have divided the population into subgroups that depend on their political alignment. This is used when you can expect that the results have a noticeable variation between the different subgroups. Usually, you want to have the same number of population for eac subgroup, but sometimes it is hard for different reasons (not enough people in one subgroup, for example)
In cluster sampling we also use subgroups, but the subgroup itself is the unit of the sampling, while in this case, we are randomly selecting individuals of the given subgroups.
So this would be a "stratified sampling".
Find the area of the surface generated by revolving x=t + sqrt 2, y= (t^2)/2 + sqrt 2t+1, -sqrt 2 <= t <= sqrt about the y axis
Answers
The area is given by the integral
[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]
where C is the curve and [tex]dS[/tex] is the line element,
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
We have
[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]
[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]
[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]
So the area is
[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]
Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:
[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]
What is the solution to this system of linear equations?
y-x = 6
y + x = -10
(-2,-8)
(-8.-2)
(6.-10)
(-10.6)
Answers
Answer:
The correct answer is A
Step-by-step explanation:
Answer:
(-8, -2)
Step-by-step explanation:
y-x = 6
y + x = -10
Add the two equations together to eliminate x
y-x = 6
y + x = -10
--------------------
2y = -4
Divide by 2
2y/2 = -4/2
y = -2
Now find x
y+x = -10
-2+x = -10
x = -8
A speedboat moves at a rate of 25 km/hr in still water. How long will it take
someone to ride the boat 87 km downstream if the river's current moves at a rate of
4 km/hr?
Answers
Answer:
3 hours
Step-by-step explanation:
Downstream, the speeds add up:
25 + 4 = 29 km/hIt will take:
87/29= 3 hrsTo ride 87 km.
Tessa’s employee benefits include family health care coverage. She contributes 18% of the cost. Tessa gets paid biweekly and $108.00 is taken out of each paycheck for family health care coverage. How much does her employer contribute annually for the family coverage? Clearly show your work.
Answers
The answer is $12792
Explanation:
It is known Tessa pays $108.00 to contribute to family coverage every two weeks and this represents 18% of the total payment. This implies the employer pays the 82% missing (100% - 18% = 82%). Additionally, with this information, it is possible to know the amount the employer has to pay every two weeks that represents 82%. The process is shown below:
1. Write the values you know and use x to represent the value you need to find
108 = 18
x = 82
3. Cross multiply
x 18 = 8856
4. Find the value of x by solving this simple equation
x = 8856 ÷ 18
x = 492 - Amount the employer pays every two weeks for Tessa's family coverage
Now that we know the money the employer pays every two weeks, it is possible to calculate the annual amount of money. Follow the process below.
1. Consider one year has a total of 52 weeks and divide this number of weeks by 2 because the payment for the family coverage occurs every 2 weeks
52 ÷ 2 = 26
2. Finally, multiply the money paid by the employer every two weeks by 26
26 weeks x $492 = $12792- This is the total the employer pays annually
Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answers
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?
Answers
Answer:
Step-by-step explanation:
positive integer divisible by 3 includes
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...
less than highest possible value is 42
point estimate A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean
Answers
Answer:
The 95 percent Confidence Interval is for the population is (38.911 , 41.089)
Step-by-step explanation:
To solve the above question, we would be making use of the confidence interval formula:
Confidence Interval = Mean ± z score × σ/√n
In the above question,
Mean = 40
σ = Standard deviation = 5
n = number of samples = 81
Confidence Interval = 95%
The z score for a 95% confidence interval = 1.96
Therefore, the confidence interval =
= 40 ± 1.96 (5/√81)
= 40 ± 1.96(5/9)
= 40 ± 1.0888888889
Confidence Interval
a)40 + 1.0888888889
= 41.0888888889
Approximately = 41.089
b ) 40 - 1.0888888889
= 38.911111111
Approximately = 38.911
Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)
Quick! Andrew has to play 15 games in a chess tournament. At some point during the tournament he has won half of the games he has played, he has lost one-third of the games he has played and two have ended in a draw. How many games has Andrew still to play?
Answers
[tex]x[/tex] - the number of the games he played
[tex]\dfrac{x}{2}[/tex] - the number of the games he won
[tex]\dfrac{x}{3}[/tex] - the number of the games he lost
[tex]x=\dfrac{x}{2}+\dfrac{x}{3}+2\Big|\cdot6\\6x=3x+2x+12\\x=12[/tex]
[tex]15-12=3[/tex]
so, he has still 3 games to play
What is the value of x to the nearest tenth?
Answers
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
Two charged particles, Q1, and Q2, are a distance r apart with Q2 = 5Q1 Compare the forces they exert on one another when F1 is the force Q2 exerts on Q1and F2 is the force Q1 exerts on Q2.
a) F2 = 5F1.
b) F2 =-5F1.
c) F2 = F1.
d) F2 = -F1.
e) 5F2 = F1.
Answers
Answer:
d) F2 = -F1.
Step-by-step explanation:
According to Coulomb's law of forces on electrostatic charges, the force of attraction is proportional to the product of their charges, and inversely proportional to the square of their distance apart.
What this law means is that both particles will experience an equal amount of force on them, due to the presence of the other particle. This force is not just as a result of their individual charges, but as a result of the product of their charges. Also, the force is a vector quantity that must have a direction alongside its magnitude, and the force on the two particles will always act in opposite direction, be it repulsive or attractive.
Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)
Answers
The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80How to graph the line y=4/3x
Answers
Answer:
make a table of values
Step-by-step explanation:
then plot using those values
The required graph has been attached which represents the line y = 4/3x
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
We have been given the equation of a line below as:
y = 4/3x
Rewrite in slope-intercept form.
y = (4/3)x
Use the slope-intercept form to discover the slope and y-intercept.
Here the slope is 4/3 and y-intercept = (0, 0)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
When substitute the value of x = 0, then the value of y = 0, and When substitute the value of x = 3, then the value of y = -4,
Hence, the graph represents the line y = 4/3x
Therefore, the required graph of the line y=4/3x will be shown in the as attached file.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ2
Find the volume of the cylinder. Round your answer to the nearest tenth.
Answers
Answer:
716.75 m^3
Step-by-step explanation:
Volume of a cylinder:
=> PI x R^2 x H
H = Height
R = Radius
=> PI x 3.9^2 x 15
=> PI x 15.21 x 15
=> PI x 228.15
=> 228.15 PI
or
=> 228.15 x 3.14159
=> 716.75 m^3
On a coordinate plane, a line goes through (negative 3, 3) and (negative 2, 1). A point is at (4, 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = Negative one-half(x – 4) y – 1 = One-half(x – 4) y − 1 = 2(x − 4)
Answers
Answer:
y - 1 = -2(x - 4).
Step-by-step explanation:
First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).
(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.
The line will be parallel to the given line, so the slope is the same.
Now that we have a point and the slope, we can construct an equation in point-slope form.
y1 = 1, x1 = 4, and m = -2.
y - 1 = -2(x - 4).
Hope this helps!
The slope of the line passing parallel to the given line and passes through the point (4, 1) is y = -2x + 9
The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The slope of the line passing through the points (-3,3) and (-2,1) is:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]
Since both lines are parallel, hence they have the same slope (-2). The line passes through (4,1). The equation is:
[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]
Find out more at: https://brainly.com/question/18880408
The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.
Answers
Answer:
[tex]\approx \bold{6544\ in^3/sec}[/tex]
Step-by-step explanation:
Given:
Rate of change of radius of cylinder:
[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]
(This is increasing rate so positive)
Rate of change of height of cylinder:
[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]
(This is decreasing rate so negative)
To find:
Rate of change of volume when r = 20 inches and h = 16 inches.
Solution:
First of all, let us have a look at the formula for Volume:
[tex]V = \pi r^2h[/tex]
Differentiating it w.r.to 't':
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]
Let us have a look at the formula:
[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]
[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]
Applying the two formula for the above differentiation:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]
Now, putting the values:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]
So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]
The base of a triangle is 4 cm greater than the
height. The area is 30 cm. Find the height and
the length of the base
h
The height of the triangle is
The base of the triangle is
Answers
Answer:
Step-by-step explanation:
Formula for area of a triangle:
Height x Base /2
Base (b) = h +4
Height = h
h + 4 x h /2 = 30cm
=> h +4 x h = 60
=> h+4h =60
=> 5h = 60
=> h = 12
Height = 12
Base = 12 +4 = 16
