Answer:
The answer is "[tex]8\pi[/tex]"
Step-by-step explanation:
[tex]\to r(v,u) =(4 \cos v, 4 \sin v,u) \\\\0\leq v \leq 2\pi, \ \ 4\leq u\leq 5\\\\\to r_v= (-4 \sin v, 4 \cos v, 0)\\\\\to r_u=(0,0,1)[/tex]
[tex]\to r_v\times r_u = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4 \sin v& 4 \cos v& 0\\0&0&1\end{array}\right| \\\\[/tex]
[tex]= (4 \cos v, -4 \sin v, 0)[/tex]
[tex]|r_v \times r_u| = \sqrt{16 \cos^2 v +16 \sin^2 v}\\\\[/tex]
[tex]= \sqrt{16( \cos^2 v + \sin^2 v)}\\\\= \sqrt{16(1)}\\\\= \sqrt{4^2}\\\\=4[/tex]
Calculating the surface area:
[tex]=\int^{2\pi}_{0} \int^{5}_{4} 4 \ du \ dv \\\\=\int^{2\pi}_{0} 4[4]^{5}_{4} \ dv \\\\=\int^{2\pi}_{0} 4[5-4] \ dv \\\\=\int^{2\pi}_{0} 4 \ dv \\\\=4 [v]^{2\pi}_{0}\\\\= 4 \times 2\pi\\\\= 8\pi[/tex]
This question is based on the parametrization. Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.
Given:
The portion of the cylinder [tex]x^{2} +y^{2} = 16[/tex] between the planes z=4 and z=5.
Let u=z and v=θ and use cylindrical coordinates to parameterize the surface.
We need to express the area of the surface as a double integral.by using parametrization.
According to the question,
It is given that u=z and v=[tex]\theta[/tex],
Therefore, r(v,u) = (4 Cos v,4 Sin v, u)
Range of v : 0 [tex]\leq[/tex] v [tex]\leq[/tex] 2[tex]\pi[/tex]
Range of u : 4 [tex]\leq[/tex] u [tex]\leq[/tex] 5
[tex]\rightarrow r_v= (-4 \;sin\; v,4\;cos\; v,0)\\\rightarrow r_u=(0,0,1)[/tex]
[tex]\rightarrow r_u \times r_v =\begin{bmatrix} \hat{i}& \hat{j} & \hat{k}\\ -4\; sin\;v & 4\; cos\; v & 0 \\ 0 & 0 & 1\end{bmatrix}\\\\=(4 cos v,\;-4 sin v ,0)\\\\\left | r_v \times r_u \right | = \sqrt{16cos^{2}v+16sin^2v } \\\\= \sqrt{16(cos^{2}v+sin^2v) }\\\\=\sqrt{16}\\\\=4[/tex]
Now calculating the surface area,
[tex]=\int\limits^{2\pi}_0\int\limits^5_4 4 du\; dv\\\\=\int\limits^{2\pi}_0 4[u]^5_4 dv\\\\=\int\limits^{2\pi}_0 4[5-4] dv\\\\\\=\int\limits^{2\pi}_0 4dv\\\\\\=4[v]^{2\pi}_0 = 4(2\pi-0)= 8\pi[/tex]
Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.
For more details, please refer this link:
https://brainly.com/question/15585522
An object dropped from rest from the top of a tall building on Planet X falls a distance feet in the first t seconds. Find the average rate of change of distance with respect to time as t changes from to . This rate is known as the average velocity, or speed. The average velocity as t changes from to seconds is:________
Complete Question:
An object dropped from rest from the top of a tall building on Planet X falls a distance d(t)=13t^2 feet in the first t seconds. Find the average rate of change of distance with respect to time as t changes from t1=2 to t2=10. This rate is known as the average velocity, or speed.
The average velocity as t changes from 2 to 10 seconds is _______ feet/sec?
Answer:
[tex]v = 156[/tex]
Step-by-step explanation:
Given
[tex]d(t)=13t^2[/tex]
Time Interval: (a,b)
[tex]a = 2[/tex]
[tex]b = 10[/tex]
Required
Determine the average rate of change (v)
This is calculated as thus:
[tex]v = \frac{d(b) - d(a)}{b - a}[/tex]
Substitute values for b and a
[tex]v = \frac{d(10) - d(2)}{10 - 2}[/tex]
[tex]v = \frac{d(10) - d(2)}{8}[/tex]
Calculate d(10): Substitute 10 for t
[tex]d(t)=13t^2[/tex]
[tex]d(10) = 13 * 10^2[/tex]
[tex]d(10) = 13 * 100[/tex]
[tex]d(10) = 1300[/tex]
Calculate d(2): Substitute 2 for t
[tex]d(t)=13t^2[/tex]
[tex]d(2) = 13 * 2^2[/tex]
[tex]d(2) = 13 * 4[/tex]
[tex]d(2) = 52[/tex]
The equation [tex]v = \frac{d(10) - d(2)}{8}[/tex] becomes
[tex]v = \frac{1300 - 52}{8}[/tex]
[tex]v = \frac{1248}{8}[/tex]
[tex]v = 156[/tex]
Hence, the average rate of change is 156ft/s
Some History teachers at Riverside High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Levin bought 27 student tickets and 25 adult tickets, which cost a total of $614. Mr. Lawson spent $733, getting 27 student tickets and 32 adult tickets. What is the price for each type of ticket?
Answer:
Cost of student ticket = $7
Cost of Adult ticket = $17
Step-by-step explanation:
Let cost of student ticket = x
Cost of Adult ticket = y
Making expressions from statements
Mrs. Levin bought 27 student tickets and 25 adult tickets, which cost a total of $614. [tex]27x+25y=614[/tex]
Mr. Lawson spent $733, getting 27 student tickets and 32 adult tickets. [tex]27x+32y=733[/tex]
Now solving these equations to find values of x and y
Let
[tex]27x+25y=614--eq(1)\\27x+32y=733--eq(2)[/tex]
Subtracting both equations
[tex]27x+25y=614\\27x+32y=733\\-\:\:\:-\:\:\:\:\:\:\:\:\:\:\:\:-\\-------\\-7y=-119\\y=\frac{-119}{-7}\\y=17[/tex]
So, we get value of y = 17
Now, finding value of x, by putting value of y in eq(1)
[tex]27x+25y=614\\Put\:y=17\\27x+25(17)=614\\27x+425=614\\27x=614-425\\27x=189\\x=\frac{189}{27}\\x=7[/tex]
So, we get value of x = 7
Cost of student ticket = x = $7
Cost of Adult ticket = y = $17
I BEG u pls answer this question.. im using my remaining points for these and i will give u brainliest if they are correct
Answer:
Step-by-step explanation:
1. Alternate interior angles. Inside the transversal and opposing sides
8. Set all three angles equal to 180, since they're supplementary
34+41+x = 180
180 = 75+x
105 = x
Hurry please!!!!!!!!! It’s a timed test!!!!!!!
The function /(x) is shown on the graph.
What is f(0)?
A.12 only
B. 2 and 3 only
C. -2, -1, -1, and 2 only
D. -2,-1, 1, 2 and 12
Answer:
c
Step-by-step explanation:
HEY YOU!! PLEASE I NEED HELPPP
find angle BAC and angle FAB
Answer:
m∠BAC = 105°
m∠FAB = 75°
Step-by-step explanation:
By using the property of an exterior angle of a triangle,
Measure of an exterior angle is equal to the sum of opposite two angles of a triangle.
From the triangle given in the picture,
m∠ABC + m∠BCA + m∠CAB = 180°
(13x - 3)° = (3x + 2)° + 55°
13x - 3 = 3x + 57
13x - 3x = 57 + 3
10x = 60
x = 6
m∠FAB = (13x - 3)° = 75°
m∠ABC = (3x + 2)° = 20°
Since, ∠BAC and ∠FAB are the linear pair of angles,
m∠BAC + m∠FAB = 180°
m∠BAC + 75° = 180°
m∠BAC = 180° - 75° = 105°
What is the system of equations represented by the graph?
{y≥1
y−x>0
{y≥1
y−x<0
{y≤1
y−x<0
{y≤1
y−x>0
Answer:
c is the answer
Step-by-step explanation:
{ y≤1
y-x<0
Original: $100, Discount: 13%
Answer:
Step-by-step explanation:
$87
IM THE COOL KID 121212
Mrs. Cousins works in a pool store and earns a 9.5% commission on every swimming pool she sells. How much commission would she earn for selling a pool that costs $5,600?
Answer:
$532
Step-by-step explanation:
19/200 * 5600/1
Cross cancellation makes this:
19/1 * 28/1
19 * 28
(19 * 20) + (19 * 8)
380 + 152
$532 in commission
The average selling price is $0.60 per unit, the average variable cost is $0.36 per unit, and the total fixed costs are $1,500. If operating profits of $900 are desired, a sales volume of 2,500 units is necessary. True False
The statement is False.
Given that the SP is $0.60 per unit and the CP is $0.36 per unit.
So, profit per unit = $(0.60-0.36)
= $ 0.24
So, now we have to check whether 2500 units sales is required if we want a profit of $900.
To check we have to multiply the profit per unit with the sales,
⇒ 0.24 × 2500
⇒ $ 600
We can see clearly that we get a profit of $600 if we sale 2500 units. So, to make a profit of $900 we have to sale = [tex]\frac{900}{0.24}[/tex]
= 3750 units
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Hello please help with this math. Some one rush.
Answer:
the experiment is mine is my favorite but us and I can you too I don't revel in a bit if ok to come to
PLEASE answer i’ll do anything please
Answer:
25
Step-by-step explanation:
[tex]f(x) = {3}^{x} - 2 \\ \\ plug \: x = 3 \\ \\ f(3) = {3}^{3} - 2 \\ \\ f(3) = 27 - 2 \\ \\ f(3) = 25[/tex]
Explain how you can tell by looking at a graph if there is a
proportional
You can tell if a graph represents a proportional relationship by identifying the y-intercept, or the point of the line that crosses the y-axis.
If the y-intercept is 0, then the relationship is proportional. This is called a direct relationship.
If the y-intercept is anything other than 0, then the relationship is not proportional. This is called an indirect relationship.
I hope this helps!
A line passes through the points (5,21) and (6,22).
Hey there!
The formula is: y₂ - y₁ / x₂ - x₁
y₂ = 22
y₁ = 21
x₂ = 6
x₁ = 5
Your equation: 22 - 21 / 6 - 5
22 - 21 = 1 ← numerator (TOP number)
6 - 5 = 1 ← denominator (BOTTOM number)
We can say that the line that passes through lines (5 , 21) (6 , 22): 1/1
(or you can simply 1 because 1 ÷ 1 gives you 1)
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
The circumference of the base of a cone is 10π cm. The circumference of the base of a second similar cone is 20π cm. What is the ratio of the surface area of the first cone to that of the second cone?
Given:
The circumference of the base of a cone is 10π cm.
The circumference of the base of a second similar cone is 20π.
To find:
The ratio of the surface area of the first cone to that of the second cone.
Solution:
Let the radii of base of two cones are [tex]r_1[/tex] and [tex]r_2[/tex] respectively.
Circumference of the circular base is [tex]2\pi r[/tex], where, r is radius.
We have,
[tex]2\pi r_1=10\pi\text{ cm}[/tex]
[tex]r_1=\dfrac{10\pi}{2\pi}\text{ cm}[/tex]
[tex]r_1=5\text{ cm}[/tex]
And,
[tex]2\pi r_2=20\pi\text{ cm}[/tex]
[tex]r_2=\dfrac{20\pi}{2\pi}\text{ cm}[/tex]
[tex]r_2=10\text{ cm}[/tex]
It two cons are similar, then ratio of there areas is equal to square of the ratio of there corresponding dimensions, i.e., radius or heights.
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{r_1}{r_2}\right)^2[/tex]
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{5}{10}\right)^2[/tex]
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{1}{2}\right)^2[/tex]
[tex]\dfrac{A_1}{A_2}=\dfrac{1}{4}[/tex]
The ratio form is
[tex]V_1:V_2=1:4[/tex]
Therefore, the ratio of the surface area of the first cone to that of the second cone is 1:4.
The ratio of the surface area of first cone to that of the second cone is; 1:4
Surface AreaFormula for the circumference of the base of a cone is;
C = 2πr
Where;
C is circumference
r is radius
Thus;
For the first cone;10π = 2πr
r = 10π/2π
r = 5
For the second cone;20π = 2πr
r = 20π/π
r = 10
Now, formula for surface area of the base is;
A = πr²
Thus, ratio of both area of first cone to second cone is;
A1/A2 = 5²/10²
A1/A2 = 25/100
A1/A2 = 1/4
Thus, ratio of first cone to that of the second cone is; 1:4
Read more on surface area of cone at; https://brainly.com/question/6613758
If four loaves of bread costs $8, a loaf of bread and a bag of oranges costs $5, and a loaf of bread, two bags of oranges and a basket of apples costs $12, what is the cost of a basket of apples?
Answer:
$6
Step-by-step explanation:
4 loaves of bread ---- $8
1 loaf of bread ---- $8 ÷ 4 = $2
one bag of oranges --- $5 - $2 = $3
two bags of oranges --- $3 × 2 = $6
one basket of apples --- $12 - $6 = $6
The cost of a basket of apples is $6.
What is the slope of y = log(x) when x=20 ?
The formula for the slope is _________ for h close to 0 (but not equal )
The best estimate for the slope is____
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The formula for slope according to first principle is :
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{f(x + h) - f(x)}{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log(x + h) - log(x)}{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log( \frac{x + h}{x} ) }{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log( \frac{ h}{x} + 1 ) }{h} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{ log( \frac{ h}{x} + 1 ) }{ \frac{h}{x} \times x} \][/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \displaystyle\lim_{x\to0} \: \: \sf \frac{1}{x} \bigg(\frac{ log_{e} ( \frac{ h}{x} + 1 ) }{ \frac{h}{x} \times log_{e}(10) } \] \bigg)[/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{x \: log_{e}(10) } \displaystyle\lim_{x\to0} \: \: \sf \bigg(\frac{ log_{e} ( \frac{ h}{x} + 1 ) }{ \frac{h}{x} } \] \bigg)[/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{x \: log_{e}(10) } [/tex]
Now, the best estimate of slope is at x = 20 :
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{20\times 2.303} [/tex]
[tex] \qquad \sf \dashrightarrow \: \[ \dfrac{1}{46.06} [/tex]
[tex] \qquad \sf \dashrightarrow \: \approx0.0217[/tex]
Add. 25+14 Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:
25 + 14 = 39 and the fraction form can be [tex]\frac{39}{100}[/tex]
Step-by-step explanation:
Simplify The Equation
–9(–8p + 12) – 6p
Answer:
9/8
Step-by-step explanation:
389. A racquetball court is 40 ft by 20 ft. What is the area of the court?
a. 60 ft2
b. 80 ft2
c. 800 ft2
d. 120 ft2
Answer: 800 ft^2 ==> c
Step-by-step explanation:
A=Area, l=length, w=width
A=l*w
A=40*20
A=800 ft^2 ==> c
tan 3( ) tan 3 lim
h
xh x
® h
Answer:
27
Step-by-step explanation:
know that
h = 3
h × h × h
3 × 3 × 3
= 27
which equation represents a linear function?
Answer:
Equation 3
Step-by-step explanation:
Answer:Equation 3
linear functions dont have exponents
Step-by-step explanation:
What is the reciprocal of 3/7 ?
A) 3/7
B) 2 1/3
C) 7/3
D) 7
Answer:
c ) 7/3
Step-by-step explanation:
The speed, s, of an ant (in centimeters per second) is related to the temperature, t (in degrees Celsius), by the formula
s = 0.167t - 0.67
If the temperature is 40 degrees Celsius, how fast is the ant moving?
Answer:
binod
Step-by-step explanation:
binod is binod and is binod
If sales tax is 7%, how much tax will Miguel pay for a TV that costs $150?
Answer:
$10.50
Step-by-step explanation:
To find how much tax is added on to the $150 we have to multiply .07 by 150.
(150)(.07) = 10.5
Therefore, Miguel will have to pay $10.50 in tax.
I hope this helps!
- Kay :)
630 people went a McDonald's yesterday. If 60% of them ordered fries, how many ordered fries?
Answer:
total no. of people =630
let the no. of people who ordered fries be x
Then,
60%of 630=x(since 60% of them ordered fries)
60/100×630=x=378
Therefore,the no of people who ordered fries are 378.
Thankyou
# 3 A cellular phone company offers several different service options. If the total cost per month is given by the
formula C = 0.42 m+ 7.81, how much will you pay in a month when you did not use the phone?
Answer:7.81
Step-by-step explanation:
7.81=0.42*0 +7.81
Write the equation of the line in slope-intercept form that has a slope of -2 and passes through (3, 3)
Answer:
y = -2x + 9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Slope m = -2
Point (3, 3)
Step 2: Find equation
Substitute in slope [Form]: y = -2x + bSubstitute in point: 3 = -2(3) + bMultiply: 3 = -6 + bIsolate b: 9 = bWrite equation: y = -2x + 9Solve the formula for the specified variable
Q=R + Rst for s
[tex]Q=R+Rst \\ \\ Q=R(1+st) \\ \\ \frac{Q}{R}=1+st \\ \\ \frac{Q}{R}-1=\frac{Q-R}{R}=st \\ \\ \boxed{s=\frac{Q-R}{Rt}}[/tex]
A company is looking to cover a floor in their office with wood. How many square yards of wood does the company need to cover the floor?
Answer:
[tex]Area = 72[/tex]
Step-by-step explanation:
From the attachment, we can see that the floor has a trapezium shape with the following dimensions.
[tex]Height = 6yd[/tex]
The parallel sides (P1 and P2) are:
[tex]P_1 = 10 + 4 = 14[/tex]
[tex]P_2 = 10[/tex]
The square yard needed to cover the floor is the area of the trapezium surface and this is calculated as follows:
[tex]Area =\frac{1}{2} * (Sum\ of\ parallel\ sides) * Height[/tex]
[tex]Area =\frac{1}{2} * (P_1 + P_2) * Height[/tex]
[tex]Area = \frac{1}{2} * (10 + 14) * 6[/tex]
[tex]Area = \frac{1}{2} * (24) * 6[/tex]
[tex]Area = 12 * 6[/tex]
[tex]Area = 72[/tex]
Hence, 72 square yards is needed to cover the floor