Answer:
The area of surface is [tex]\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]
Step-by-step explanation:
Given that,
The equation of cylinder is
[tex]x^2+y^2=9[/tex]
The part of the surface z = xy
The coordinates is,
[tex]z_{x}=y[/tex]
[tex]z_{y}=x[/tex]
We need to calculate the value of ds
Using formula of ds
[tex]ds=\sqrt{1+z_{x}^2+z_{y}^2}dA[/tex]
Put the value in to the formula
[tex]ds=\sqrt{1+y^2+x^2}dA[/tex]....(I)
We know that.
The polar coordinates,
[tex]x=r\cos\theta[/tex]
[tex]y=r\sin\theta[/tex]
The general equation of cylinder is
[tex]x^2+y^2=r^2[/tex]
compare from given equation
[tex]x^2+y^2=3^2[/tex]
0<=θ<=2π, 0<=r<=3
Area element in polar coordinates is,
[tex]dA=r dr d\theta[/tex]
Put the value of dA in equation (I)
[tex]ds=\sqrt{1+r^2}r dr d\theta[/tex]....(II)
We need to calculate the area of surface
Using equation (II)
[tex]s=\int_{0}^{2\pi}\int_{0}^{3}\sqrt{1+r^2}r dr d\theta[/tex]
[tex]s=\int_{0}^{2\pi}\dfrac{1}{3}((1+r^2)^{\frac{3}{2}})_{0}^{3}d\theta[/tex]
[tex]s=\int_{0}^{2\pi}\dfrac{1}{3}((1+3^2)^{\frac{3}{2}}-(1+0^2)^{\frac{3}{2}})d\theta[/tex]
[tex]s=(\dfrac{1}{3}((10)^{\frac{3}{2}}-1)\theta)_{0}^{2\pi}[/tex]
[tex]s=\dfrac{1}{3}(10^{\frac{3}{2}}-1)(2\pi-0)[/tex]
[tex]s=\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]
Hence, The area of surface is [tex]\dfrac{2}{3}(10^{\frac{3}{2}}-1)\pi[/tex]
Complete the sentences to make true statements 6 is 100 times 0.06 is 10 times 60 is 1/100 of
Answer:
6 is 100 times 0.06
0.06 is 10 times 0.006
60 is 1/100 of 6,000
Step-by-step explanation:
Since 6/100 is equal to 0.06, we can say that 6 is the result of multiplying 0.06 by one hundred (0.06 x 100 = 6).
On the other hand, since 0.06 / 10 is equal to 0.006, it is correct to say that 0.006 x 10 is equal to 0.06 (0.006 x 10 = 0.06).
Finally, 60 is one hundredth of 6000, since multiplying 60 x 100 the result is 6,000 (6,000 / 100 = 60).
Somebody please help me make some sense out of this:
“One morning a certain number of passengers got on an elevator at the main floor of an office building. Four got off at the second floor, of the remainder at the third floor, 75% of the remainder at the fourth floor and 3 at the 5th floor. If the elevator was empty at this point, how many got on the elevator at the main floor?”
perform the indicated operation (-2i+3i)+(-1-4i)
Answer:
-1 -3i
Step-by-step explanation:
It is unusual to have two imaginary terms grouped together like this. Taking the question at face value, we treat i as though it were a variable, and collect terms in the usual way.
(-2i +3i) +(-1 -4i) = i(-2+3-4) -1 = -1 -3i
Beyoncé drove 6 miles in 18 minutes and Kelly drove 4 miles in 16 minutes. Who
traveled at a greater average speed? Define an appropriate unit of speed and provide
mathematical justification for your answer.
Beyoncé 18 min = 18/60= = .3 per hour
Kelly = 16 min. 16/60 = 2.6 per hour
So your answer is Beyoncé
The number of hot dogs needed for the
picnic is two for each student
How many hot dogs do we need for 150
students?
Ava is 23cm taller then Olivia, and Olivia is half the height of Lucas. If Lucas is 1.78m tall, how tall are Ava and Olivia
Answer:
Ava = 1.12 m tall
Olivia = 0.89 m tall
Step-by-step explanation:
given;
Ava is 23cm taller then Olivia,
Olivia is half the height of Lucas.
If Lucas is 1.78m tall
find:
how tall are Ava and Olivia
-------------------------------------
Ava = Olivia + 0.23
Olivia = Lucas / 2
Lucas = 1.78
plugin values into the equation above
Olivia = 1.78 / 2 =
Olivia = 0.89 m tall
Ava = 0.89 + 0.23
Ava = 1.12 m tall
Malik is planning a 6-day summer vacation trip. He has $840 in savings, and he earns $45 per hour for tutoring. The trip will
cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel. How many hours must he tutor to
have enough money to pay for the trip?
Answer:
23
Step-by-step explanation:
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of hours required to tutor to have enough money to pay for the trip is 23 hours.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of days for the summer vacation = 6
Savings = $840
Earnings per hour = $45
Airfare cost = $525
Food and sightseeing = $780
Hotel cost per night = $95
Number of hours = x
We can make an expression.
525 + 780 + 6 x 95 = 840 + 95x
525 + 780 + 570 = 840 + 45x
1875 = 840 + 45x
1875 - 840 = 45x
1035 = 45x
1035/45 = x
x = 23
This means 23 hours.
Thus,
The number of hours required to tutor to have enough money to pay for the trip is 23 hours.
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Round 35,124 nearest ten thousands
Answer:
40,000
Step-by-step explanation:
because of the 5 in the thousands place means were rounding up
A government agency has 6000 employees. As an alternative to the traditional five day work week, employees were asked whether they preferred a four day work week (10 hours per day) or flexible hours. The employee data provides the results by age category. What is the probability that a randomly selected employee at this government agency prefers a four day work week or is under 30
The table showing the data is missing, so i have attached it.
Answer:
0.8
Step-by-step explanation:
We want to find the probability that a randomly selected employee at this government agency prefers a four day work week or is under 30.
Now, we are told that the government agency has 6000 employees. Also, from the attached table, we see that the number of people who prefer a 4 day work week are a total of:
600 + 1200 + 2100 = 3900
Thus, probability of people who prefer a 4 day work week = 3900/6000 = 39/60
Also, we see that total number of people aged under 30 = 600 + 300 = 900
Thus, probability of people aged under 30 is;
900/6000 = 3/20
Thus;
probability that a randomly selected employee at this government agency prefers a four day work week or is under 30 = 39/60 + 3/20 = 48/60 = 4/5 = 0.8
Point S is on line segment RT.Given ST = 2x, and RT = 4x, and RS = 4x – 4,
determine the numerical length of RS
Answer:
2
Step-by-step explanation:
The required measure of the numerical length of RS is 4.
Given that,
Point S is on line segment RT.
ST = 2x, and RT = 4x, and RS = 4x – 4,
To determine the numerical length of RS.
A line is a curve showing the shortest distance between 2 points.
Standard equation of the line, y = mx + c, where m is slope of the equation and c is y-intercept of the equation.
Here,
Point S is on line segment RT
The total length of RT,
RT = RS + ST
4x = 4x - 4 + 2x
4x = 6x - 4
2x = 4
x = 2
RS = 4 x - 4
RS = 4 * 2 - 4
RS = 4
Thus, the required measure of the numerical length of RS is 4.
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Rewrite the quality 827,000,000,000,000 pico second to show :
1sig. Fig.
2sig. Fig.
3sig. Fig.
4 dig. Fig.
5sig. Fig.
Answer:
a. 1 sig. fig. _800,000,000,000,000 picoseconds (8 x 10^14 picoseconds)
b. 2 sig. figs. 830,000,000,000,000 picoseconds (8.3 x 10^14 picoseconds)
c. 3 sig. figs. 827,000,000,000,000 picoseconds (8.27 x 10^14 picoseconds)
d. 4 sig. figs. 827,000,000,000,000 picoseconds (8.270 x 10^14 picoseconds)
e. 5 sig. figs. 827,000,000,000,000 picoseconds (8.2700 x 10^14 picoseconds)
Step-by-step explanation:
S=c+g for g (help)!!!!!
Answer:
g = S - c
Step-by-step explanation:
Isolate the variable, g. Note the equal sign, what you do to one side, you do to the other. Simply subtract c from both sides:
S = g + c
S (-c) = g + c (-c)
S - c = g
g = S - c is your answer.
~
I need help with this question
Answer:
188 miles or 188.5 miles
Step-by-step explanation:50-17.95/17
solve the equation x to the power of 2=10
Answer:
√10,−√10
Step-by-step explanation:
award brainliest
Will give brainliest answer
Answer:
-105°Step-by-step explanation:
Rotation is counterclockwise
It means the angle is negative
We can see point C of the original figure is making a vertical line with point P
If we connect P to C' it is going to make more than 90 degree angle as it is above the horizontal line passing through the point P
Therefore we can estimate the angle as -105°
HELP PRECALC DO NOT UNDERSTAND WILL GIVE BRAINLIEST
Answer:
the lower right matrix is the third correct choice
Step-by-step explanation:
Your problem statement shows that you have correctly selected the matrices representing the initial problem setup (middle left) and the problem solution (middle right).
Of the remaining matrices, the upper left is an incorrect setup, and the lower left is an incorrect solution matrix.
__
We notice that in the remaining matrices on the right that the (2,3) term is 0, and the (3,2) and (3,3) terms are both 1.
The easiest way to get a 0 in the 3rd column of row 2 is to add the first row to the second. When you do that, you get ...
[tex]\left[\begin{array}{ccc|c}1&1&1&29000\\1+2&1-3&1-1&1000(29+1)\\0&0.15&0.15&2100\end{array}\right] =\left[\begin{array}{ccc|c}1&1&1&29000\\3&-2&0&30000\\0&0.15&0.15&2100\end{array}\right][/tex]
Already, we see that the second row matches that in the lower right matrix.
The easiest way to get 1's in the last row is to divide that row by 0.15. When we do that, the (3,4) entry becomes 2100/0.15 = 14000, matching exactly the lower right matrix.
The correct choices here are the two you have selected, and the lower right matrix.
Solve for x. 9x=288
Answer:
x = 32
Step-by-step explanation:
9x=288
divde both side by 9
6th grade math please help thx!!
Describe the error in the work shown below.
Find an expression equivalent to 18 + 30.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1,2,3,5, 6, 10, 15, 30
18 + 30 = 6(3 + 10)
Pls help fast
one millon divide by 473.8
Answer:23(22.95684113865932)
Step-by-step explanation:
Match each situation to the simulation that represents it.
Answer: rolling aa six sided die- fiona is deciding which forest
selecting a playing card- Athena has to select 1 student
spinning a spinner - Jenny isa picking a marble
Step-by-step explanation:
Answer:
Fiona- Rolling A Six-Sided Die.
Althea- Selecting A Playing Card From
The Hearts Suit.
Jenny-Spinning A Spinner Divided Into
Five Equal Sections
3. A company makes a profit of $60 per software program and $45 per video game. The company can produce at most 300 software programs and at most 200 video games per week. Total production cannot exceed 400 items per week. How many items of each kind should be produced per week in order to maximize the profit? Use linear programming to solve. Show all your work. Answer:
Answer:
Step-by-step explanation:
This problem is a maximization problem
the objective is to maximize profit
let software program be x
and video program be y
the objective function is
60x+45y>P-------1
constrains
300x+200y<400------2
we can further reduce the expressions
3x+2y<4-----2
Ann invested $61,000 into two accounts. The first account pays an annual interest rate of 5% and the second account pays an annual interest rate of 7%. After one year, Ann earned $3430 in interest. How much was invested in each account? Round your answer to the nearest cent, if necessary. [For full credit, set a system of linear equations and solve the system]
Answer:
2nd Account has $19,000
1st Account has $42,000
Step-by-step explanation:
First let's split the money invested.
x is money in account 1
y is money in account 2
1st equation
$61,000=x+y
5%=0.05
7%=0.07
2nd equation
0.05*x+0.07*y=$3,430
x=61,000-y
substitute into 2nd equation
0.05(61,000-y)+0.07y=3430
Solve.
3050-0.05y+0.07y=3430
0.02y=3430-3050
0.02y=380
y=380/0.02
y=$19,000
There are 2(two) ways to solve for the 1st account, but I will do it the long way.
y=61,000-x
substitute into 2nd equation
0.07(61,000-x)+0.05x=3430
Solve.
4270-0.07x+0.05x=3430
-0.02x=3430-4270
-0.02x=-840
x=-840/-0.02
x=$42,000
The short way...
x=61,000-y
x=61,000-19,000
x=$42,000
4.88 + 1.6*
What is the answer
Answer:
6.48 is the answer.
number 27 please.. i can not figure it out.
Answer: x=-12
Step-by-step explanation:
To solve for x, you want to use algebraic properties to isolate x.
[tex]\frac{x}{4}=2+\frac{x-3}{3}[/tex] [subtract both sides by [tex]\frac{x-3}{3}[/tex]]
[tex]\frac{x}{4}-\frac{x-3}{3}=2[/tex] [get common denominator]
[tex]\frac{3x}{12} -\frac{4x-12}{12} =2[/tex] [subtract]
[tex]\frac{-x+12}{12} =2[/tex] [multiply both sides by 12]
[tex]-x+12=24[/tex] [subtract both sides by 12]
[tex]-x=12[/tex] [divide both sides by -1]
[tex]x=-12[/tex]
Now, we know that x=-12.
Help pls I will mark you brainliest
Answer:
no#2
Step-by-step explanation:
Billy walks 2.5 miles every day to soccer practice and catches a ride home from his Grandma. Billy had 5 practices last week. How many miles did Billy walk last week to practice? 10 points please help
Answer:12.5 mike he walked to practice last week
Step-by-step explanation:
2.5 miles everyday
5 practices last week
2.5 miles x 5 practices
Find the midpoint of segment AB A(-7,6) B(4,-2)
Answer:4,05
Step-by-step explanation:
In the figure shown, suppose m angle ABC=n and m angle ABD=2(m angle DBC). The angle bisector of angle DBC is BE. What is m angle EBC
Answer:
n/6
Step-by-step explanation:
If angle bisector of angle DBC is BE. What is m angle EBC, then <DBE = <EBC
Since <ABC = <ABD+<DBC
n = 2<DBC+<DBC
n = 3<DBC
<DBC = n/3
Since <DBC = 2EBC
n/3 = 2<EBC
n/6 = <EBC
Hence <EBC = n/6
The school athletic director had a budget of $500 to purchase 164 items
for the soccer team. She purchased vests for $2.50 each, soccer balls for
$9.25 each, and cones for $0.75 each. She purchased 40 more cones than
balls. How many of each item can purchase?
Answer: She purchased 72 cones, 32 balls, and 60 vests.
Step-by-step explanation:
The total number of items is 164.
The price of the vests is $2.50 each.
The price of the soccer balls is $9.25 each.
The price of the cones is $0.75 each.
The total budget was $500.
If V is the number of vests, B the number of balls, and C the number of cones, we have that:
V + B + C = 164.
V*$2.50 + B*$9.25 + C*$0.75 = $500.
and:
"She purchased 40 more cones than balls."
C = B + 40.
Then we have a system of 3 equations and 3 variables:
V + B + C = 164.
V*$2.50 + B*$9.25 + C*$0.75 = $500.
C = B + 40.
Here the first step is to replace the third equation into the other two, in this way we eliminate one variable and one equation:
V + B + (B + 40) = 164
V*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500.
Now we want to isolate one variable in one of the equations, i will isolate V in the first equation:
V = 164 - 2*B - 40 = 124 - 2*B
Now i can replace this into the other equation:
(124 - 2*B)*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500
Now let's solve this for B.
$310 - $5*B + B*$9.25 + B*$0.75 + $30 = $500
B*( $9.25 - $5 + $0.75) = $500 - $310 - $30
B*$5 = $160
B = 160/5 = 32
Now we know the value of B.
And by the equations above:
V = 124 -2*B = 124 - 2*32 = 60
C = B + 40 = 32 + 40 = 72.
Then:
She purchased 72 cones, 32 balls and 60 vests.