Answer:
6
because a dozen is 12 and a half dozen is 6.
The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 4 − x2, 0 ≤ x ≤ 3
Answer:
The area of the surface is 2.72 units
Step-by-step explanation:
The area of a curve y = (x) a ≤x ≤ b rotated about the y axis is given by:
[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]
y = 4 - x²
dy / dx = -2x
(dy/dx)² = (-2x)² = 4x²
Hence:
[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\\\s=\int\limits^0_3 {2\pi x\sqrt{1+4x^2} } \, dx\\\\Let\ u = 1+4x^2\ \\\frac{du}{dx}=8x\\\frac{du}{8x}=dx\\\\Substituting\ value\ of\ u \ and\ dx:\\ \\s=\int\limits^0_3 {2\pi x\sqrt{u} } \, \frac{du}{8x} \\\\s=\frac{\pi }{4} \int\limits^0_3 {\sqrt{u} } \, du\\\\s=\frac{\pi }{4}|\frac{2}{3}u^{3/2}|_0^3\\\\s=\frac{\pi }{4}*\frac{2}{3}(5.196)\\\\s=2.72\ units[/tex]
The area of the surface is 2.72 units
The area of the resulting surface is [tex]37.3437\pi[/tex].
Curve:
A curve is an object that is similar to a line, but that does not have to be a straight line. A curve may be regarded as a trace left by a moving point.
Given:
[tex]y=4-x^{2}[/tex] , [tex]0 \leq x\leq 3[/tex]
Surface area[tex]=2\pi \int_{a}^{b}x\sqrt{1+\left ( \frac{dx}{dy} \right )^{2}dy}[/tex]
[tex]x=\sqrt{4-y} \ , \ \frac{dx}{dy}=-\frac{1}{2\sqrt{4-y}}[/tex]
when [tex]x=0 \ , \ y=4[/tex]
[tex]x=3 \ , \ y=-5[/tex]
Area of surface[tex]=2\pi \int_{-5}^{4}\sqrt{4-y}\sqrt{1+\frac{1}{4\left ( y-4 \right )}dy}[/tex]
[tex]=2\pi \int_{-5}^{4}\sqrt{4-y+\frac{4-y}{4\left ( y-4 \right )}dy} \\ =2\pi \int_{-5}^{4}\sqrt{4-y+\frac{1}{4}dy} \\ =\frac{2\pi }{2}\int_{-5}^{4}\sqrt{17-y} \ dy \\ =\pi \int_{-5}^{4}\sqrt{17-y} \ dy[/tex]
Solving with calculator:
[tex]\Rightarrow \pi\left [ \frac{1}{6}\left ( 37\sqrt{37}-1 \right ) \right ][/tex]
[tex]=37.3437\pi[/tex]
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the peak of Mt. johnson is 19,360 feet above sea level. The top of Mt. Harrison is 23,350 feet above sea level. round each height to the nearest thousand to estimate the difference in elevation of these two peaks.
-5(x-2) - 2x + 6 help me answer this!
Answer:
x=2.2 this is nice question
Two cars traveling toward each are 200 miles apart. Car A is traveling 20 miles per hour faster than car B. The cars pass after 2 hours. How fast is each car traveling?
Answer:
Step-by-step explanation:
d = 200 miles
B rate = x
A Rate = x + 20
Each has traveled two hours
The total distance each travels after two hours is 200 miles (they pass each other).
d = r * t
2*x + 2*(x + 20) = 200 Remove the brackets
2x + 2x + 40 = 200 Combine like terms
4x + 40 = 200 Subtract 40 from each side
4x = 200 - 40
4x = 160 Divide by 4
x = 160/4
x = 40
There B's rate is 40 miles / hour
A's rate is 40 + 20 = 60 miles / hour
9 less than one-fifth of c
Answer: The equation in math form is [tex]\frac{1}{5}c[/tex] - 9.
Step-by-step explanation:
So the givens are:
9 less than one-fifth of c
Let's put this equation in math form:
[tex]\frac{1}{5}c[/tex] - 9
Hence your answer!
Let α ∈ S n α∈Sn for n ≥ 3 . n≥3. If α β = β α αβ=βα for all β ∈ S n , β∈Sn, prove that α α must be the identity permutation; hence, the center of S n Sn is the trivial subgroup.
Answer:
Sn is the trivial subgroup
Step-by-step explanation:
To prove that α must be the identity permutation and also Sn is the trivial subgroup we have to make assumptions :
when we assume α is not an identity permutation
α(i) = -j but since n ≥ 3 we will make another assumption of a number k
hence we will choose : β = ( i k )
from these assumptions we can deduce that
αβ (i) = α(k) ≠ -j since α(i) = -j
also βα (i) = β(-j) = -j
from the equations above we can conclude that
αβ ≠ βα which is in contradiction to the expression : αβ=βα . this simply shows that α must be the identity permutation, and the number of permutations of Sn is true for every number of permutation of Sn provided it is other than the identity
hence the center Sn is the trivial subgroup
The height of a house is 52 ft. A tree beside the house is 7 ft more than twice as tall. What is the height of the tree?
Answer:
111 ft
Step-by-step explanation:
52 x 2 then just add 7
Percy spent money on new shirts for the summer each shirt cost $7 he spent $42 all together how many shirts did Percy buy
According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass mmm that moves in an acceleration aaa is equal to m\cdot am⋅am, dot, a. An object whose mass in 808080 grams has an acceleration of 202020 meters per seconds square. What calculation will give us the sum of the forces that act on the object, in Newtons (which are \dfrac{\text{kg}\cdot\text{m}}{\text{s}^2} s 2 kg⋅m start fraction, start text, k, g, end text, dot, start text, m, end text, divided by, start text, s, end text, squared, end fraction)?
What calculation will give us the sum of the forces that act on the object, in Newtons (which are \dfrac{\text{kg}\cdot\text{m}}{\text{s}^2}
[tex]kg . m \ S^{2}[/tex]
Answer:
If you are on Khan Academy doing this, then the answer is 80/100 X 20
Step-by-step explanation:
If the mass of object is 808080 grams and acceleration is 202020 meter per seconds square then the force will be 1632483216 kg [tex]m^{2}[/tex].
What is force?A force is an effect that can change the motion of an object. A force can change the position of an object.
Force=mass*acceleration
How to calculate force?We have been given mass of the object=808080 grams and acceleration =202020 meters per second.
We have to calculate force in kg per meters square so firstly we have to change mass which is in grams into kilogram=808080/1000=808.080 kg
Force =808.080*202020
=163248321
Force=163248321 kg [tex]m^{2}[/tex]
Hence is mass is 808080 grams and acceleration is 202020 meters per second then force will be 163248321 kg meters square.
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Please help me out!!!!
Answer:
You should multiply the exponents "-3" and "-6"
Then your answer is:
4^18Hope this helps..
Best of luck!
Answer:
4^18Step-by-step explanation:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(4^{-3}\right)^{-6}=4^{-3\left(-6\right)}\\\\-3\left(-6\right)=18\\\\=4^{18}[/tex]
Any system of government based on rule by the people is called
Answer:
a democracy
I hope this helps!
The West Edmonton Mall in Canada is the largest mall in the world. 20,000,000 people visit the mall each year. If the mall is opened every day, what is the average number of people per day at the mall? (1 yr. – 365 days)
Answer:
54,795
Step-by-step explanation:
Consider the following. (Round your answers to four decimal places.)f(x, y) = yex(a) Evaluate f(2, 1) and f(2.5, 1.65) and calculate Δz(b) Use the total differential dz to approximate Δz.
Answer:
Step-by-step explanation:
Given the function f(x,y) = ye^x
To evaluate f(2,1), we will substitute x = 2 and y = 1 into the given function to have;
f(2,1) = 1×e^2
f(2,1) = e^2
f(2,1) = 7.3891(to 4dp)
For f(2.5, 1.65), x = 2.5 and y =1.65
f(2.5, 1.65) = 1.65e^2.5
f(2.5, 1.65) = 1.65×12.1825
f(2.5, 1.65) = 15.2281 (to 4dp).
∆z = f(2.5, 1.65) - f(2, 1)
∆z = 15.2281-7.3891
∆z = 7.8390
dz = fxdx + fydy
fx is the differential of the function with respect to x keeping y constant.
Since f(x,y) = ye^x
fx = ye^x + 0e^x
fx = ye^x
dx = x2-x1 = 2.5-2
dx = 0.5
fy = e^x
dy = (y2-y1) = 1.65-1
dy = 0.65
Using the point (2, 1) for x and y and substituting the values gotten into dz function:
dz =ye^x(0.5) + e^x(0.65)
If x = 2 and y = 1
dz = 1e^2(0.5) + e^2(0.65)
dz = 7.3891(0.5)+7.3891(0.65)
dz = 7.3891(0.5+0.65)
dz = 7.3891(1.15)
dz = 8.4975
Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $300. The store allows the coupons to be combined. Which coupon should be applied first, and what is the final purchase price?
Answer:
Apply the 15% discount first, and the final purchase price is $332.50.
Step-by-step explanation:
The 15% discount of the two coupons should be applied first so that the final price is cheaper.
The final purchase price at the department store is $332.5.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Cost = $450
Two coupons.
Offer = 15% discount
off = $50
Now,
15% discount first and then $50 off.
(450 - 15/100 x 450) - 50
= (450 - 67.5) - 50
= $332.5
Now,
$50 off first and then the 15% discount.
(450 - 50) = 400
400 - 15/100 x 400
= 400 - 60
= $340
We see that,
When the 15% discount is applied first the final price is cheaper.
Thus,
15% discount should be applied first.
The final purchase price is $332.5.
Learn more about percentages here:
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calculate the area of area of a rectangular with a base of 10cm and a height of 6cm
Answer:
60cm²
Step-by-step explanation:
Length = 6cm
Breadth = 10cm
Area of rectangle = l×b
=( 10 ×6)cm
= 60cm²
Hope it helps.
Answer:
[tex]\Huge \boxed{\mathrm{60 \ cm^2 }}[/tex]
Step-by-step explanation:
Area of a rectangle is length × width.
The length of the rectangle is 10 cm.
The width of the rectangle is 6 cm.
[tex]\Rightarrow 10 \cdot 6 \\\\\\ \Rightarrow 60[/tex]
The area of the rectangle is 60 cm².
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.
x = 5t − 2, y = 2t + 1.
Please find attached
Answer:
equation : 2x+9-5y=0
Step-by-step explanation:
x and y cut axes at -4.5 and 1.4 respectively
given
when x=0
9-5y=0
y=1.4
When y=0
2x+9=0
x=-4.5
40 points! Find the distance UV between the points U(2,−2) and V(−5,−3). Round your answer to the nearest tenth, if necessary.
Answer:
7.1
Step-by-step explanation:
Using the distance formula
d = sqrt ( (x2-x1)^2 + ( y2-y1)^2)
sqrt ( (-5-2)^2 + ( -3- -2)^2)
sqrt( ( -7)^2 + ( -3 +2)^2)
sqrt( ( 49 + 1)
sqrt( 50)
7.071067812
To the nearest tenth
7.1
Answer:
7.1 units
Step-by-step explanation:
We can use the distance formula to find the distance between these two points.
The distance formula is:
[tex]\sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex].
x1 is 2, x2 is -5, y1 is -2, and y2 is -3, so we can plug these values into the equation.
[tex]\sqrt {\left( {2 - (-5) } \right)^2 + \left( {-2 - (-3) } \right)^2 }\\\\\sqrt {7^2 + 1^2}\\\\\sqrt{49+1}\\\\\sqrt{50}\approx7.1[/tex]
Hope this helped!
Hank invested a total of $20,000, part at 7% and part at 10%. How much did he invest at each rate if the total interest earned in one year was $1640?
Answer:
We have a total investment of $20,000 in two different amounts A and B.
Then:
A + B = $20,000.
And we know that the interest of the amount A is 7%, and the interest of the amount B is 10%. (i will assume that both interests are yearly interest)
And after one year, Hank earns $1,640 thanks to those interests, then we have that:
(7%/100%)*A + (10%/100%)*B = $1,640
And we can write this as:
0.07*A + 0.1*B = $1,640
Then we have a system of equations:
A + B = $20,000
0.07*A + 0.1*B = $1,640
To solve this, the first step is isolating one of the variables in one of the equations.
Let's isolate A in the first equation:
A + B = $20,000
A = $20,000 - B.
Now we can replace this in the other equation:
0.07*A + 0.1*B = $1,640
0.07*($20,000 - B) + 0.1*B = $1,640
$1,400 - 0.07*B + 0.1*B = $1,640
0.03*B = $1,640 - $1,400 = $240
B = $240/0.03 = $12,000
Then we have:
A = $20,000 - $12,000 = $8,000
Hank invests $12,000 in the 10% account and $8,000 in the 7% one.
You want to buy a car. The loan amount will be $18,000. The company is offering a 5% interest rate for 48 months (4 years). What will your monthly payments be?
Answer:
393.5$
Step-by-step explanation:
$18,000 -- car price
Total sum (105%) = [tex]\frac{18000}{100}[/tex]* 105%
Hence
[tex]\frac{18000/100*105}{48}[/tex] = 393.5$
19 - 5 (2m - 3) + 9m = 36
Answer:
m = -2
Step-by-step explanation:
For this problem, we will simply solve the equation for m.
19 - 5 ( 2m - 3 ) + 9m = 36
19 - 10m + 15 + 9m = 36
34 - m = 36
-m = 2
m = -2
Hence, for this equation to be true, m must equal negative 2.
Cheers.
The radius of the wheel on a bike is 21 inches. If the wheel is revolving at 154 revolutions per minute, what is the linear speed of the bike, in miles per hour
Answer:
The linear speed of the bike is 19.242 miles per hour.
Step-by-step explanation:
If sliding between the bottom of the wheel and ground can be neglected, the motion of the wheel can be well described by rolling, which is a superposition of coplanar pure rotation and translation, The speed of the bike occurs at the center of the wheel, where resulting instantaneous motion is pure translation parallel to ground orientation. The magnitude of the speed of bike ([tex]v_{B}[/tex]), measured in inches per second, is:
[tex]v_{B} = R\cdot \omega[/tex]
Where:
[tex]R[/tex] - Radius, measured in inches.
[tex]\omega[/tex] - Angular speed, measured in radians per second.
Now, the angular speed must be converted from revolutions per minute into radians per second:
[tex]\omega = \left(154\,\frac{rev}{min} \right)\cdot \left(2\pi\,\frac{rad}{rev} \right)\cdot \left(\frac{1}{60}\,\frac{min}{s} \right)[/tex]
[tex]\omega \approx 16.127\,\frac{rad}{s}[/tex]
The speed of the bike is: ([tex]R = 21\,in[/tex] and [tex]\omega \approx 16.127\,\frac{rad}{s}[/tex])
[tex]v_{B} = (21\,in)\cdot \left(16.127\,\frac{rad}{s} \right)[/tex]
[tex]v_{B} = 338.667\,\frac{in}{s}[/tex]
Lastly, the outcome is converted into miles per hour:
[tex]v_{B} = (338.667\,\frac{in}{s} )\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(\frac{1}{63360}\,\frac{mi}{in} \right)[/tex]
[tex]v_{B} = 19.242\,\frac{mi}{h}[/tex]
The linear speed of the bike is 19.242 miles per hour.
: What is the volume of this triangular right prism?
6.5 ft
6 ft-
11 ft
5 ft
Answer:
[tex] Volume_{Prism} = 165 ft^3 [/tex]
Step-by-step explanation:
Volume of triangular prism is given as base area * height of prism
Base area = area of triangle = ½*base of the traingle*height of the traingle
Base area = 5 ft * 6 ft = 30 ft²
Height of prism = 11 ft
Volume of the prism = [tex] \frac{1}{2}*30*11 [/tex]
[tex] Volume_{Prism} = 15*11 [/tex]
[tex] Volume_{Prism} = 165 ft^3 [/tex]
dwight can drive 60 miles for each gallon of gas on his motorcycle how far can dwight go if he has 3 gallons of gas
Answer:
180
Step-by-step explanation: 60+60 =120 120+6
n(n+p)-n; use n=5, and p=3
Answer:
45
Step-by-step explanation:
We can first expand the expression:
n(n+p) - n
= n^2 + np + n
Then, we can plug in values of n and p into the expression:
n^2 + np + n = (5)^2 + (5)(3) + 5 = 25 + 15 + 5 = 45
Answer:
35
Step-by-step explanation:
Substitute the value of the variable into the expression and simplify
Mrs. Phillips ordered 56 sub sandwiches for a team meal, and 2/7 of them were ham. how many of the sandwiches were ham?
Answer:
16
Step-by-step explanation:
Take the total number of sandwiches and multiply the fraction that were ham
56 * 2/7
56/7 *2
8 *2
16
16 sandwiches were ham
What is the area of rectangle whose
height is 2.5 in and base is 12 in?
Step-by-step explanation:
Area of a rectangle is base times height.
A = bh
A = (12 in) (2.5 in)
A = 30 in²
Solve:
A rectangular garden has length of 24m and width of 17.2m. Use the correct number of
significant digits to write the perimeter of the garden.
meters
Answer:
82.4
Step-by-step explanation:
Graph the parabola y=x^2+3 by plotting any three points on the parabola. Move the key points on the graph to create the parabola.
Answer:
Use a graphing calc.
Step-by-step explanation:
If graphing by hand, use the vertex as one of the main points and then find other points by plugging in x-values.
Answer:
See be'ow
Step-by-step explanation:
We can use a graphing calculator to plot the points of the parabola.
See the attached file!
How is a coefficient different than a constant... please give me an example as well thank you.. I’m giving max points
Answer:
A coefficient is a number that is in front of a variable. A number that is multiplied by a variable in a variable expression; in an expression such as 3ab, the numerical coefficient of ab is 3. The word constant means unchanging. Since a number’s value never changes, a number with no variable factors is a constant. A constant is a numerical term in an expression. a term that has no variables
Example: 5a+4 The coefficient is 5 and the constant is 4 because it does not have a variable in front of it.
Hope this helps
HELP WOULD BE GREATLY APPRECIATED GURANTED BRAINLIEST
Answer: Choice A) 9
=================================================
Explanation:
We have some variable r that we divide over 3, and then we add on 5. Note the order of operations PEMDAS says to divide first and then add (since D comes before A in PEMDAS).
When we isolate r, we follow PEMDAS in reverse and undo everything. We undo addition by subtracting 5 from both sides
[tex]\frac{r}{3} + 5 \le 8\\\\\frac{r}{3} + 5-5 \le 8-5\\\\\frac{r}{3} \le 3\\\\[/tex]
Then we undo the division happening to r. So we multiply both sides by 3
[tex]\frac{r}{3} \le 3\\\\3*\frac{r}{3} \le 3*3\\\\r \le 9\\\\[/tex]
Since r is less than or equal to 9, this means that r could be 9 or smaller
Only choice A applies.