A conical cup is made from a circular piece of paper with radius 6 cm by cutting out a sector and joining the edges as shown below. Suppose θ = 5π/3.
Answer:
(a) 10π cm
(b) r = 5 cm
(c) h = √11 cm
Step-by-step explanation:
(a) The surface of the opening the cup is circular in shape and a sector is cut from circle is calculate by formula,
C = r × θ
here, r = 6 cm
and θ = [tex]\frac{5\pi}{3}[/tex]
⇒ [tex]C = 6 \times \frac{5\pi}{3} = 10\pi[/tex]
(b) For finding the radius of the cup,
As the circumference of the circle is 10π
and we know that area of cone is calculate by formula, 2πr
⇒ 2πr = 10π
⇒ r = 5 cm
(c) In cone we know slant height(l) = 6 cm
Radius = 5 cm
Thus, using Pythagoras theorem,
l² = h² + r²
⇒ h² = l² - r²
⇒ h² = 36 - 25
⇒ h = √11 cm
Jim wants to build a rectangular parking lot along a busy street but only has 2,200 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.
The problem is an optimization problem in mathematics where one must use algebra and calculus to maximize the area of a rectangular parking lot with a given amount of fencing along three sides. By setting up a function for the area in terms of width and differentiating, the maximum area can be found.
Explanation:The problem presented involves finding the maximum area of a rectangular parking lot given a certain amount of fencing, when one side of the rectangle requires no fencing. This is a classic optimization problem in mathematics which involves the use of algebra and calculus. By setting up a function for the area of the rectangle in terms of one variable and differentiating to find the maximum value, we can determine the solution.
Lets assume that the length of the lot that is along the busy street doesn't require fencing, and let the width of the lot be w and the length be l. Since fencing is only required for three sides, and we have 2,200 feet of fencing, the perimeter equation is 2w + l = 2,200. Solving for l, we get l = 2,200 - 2w. The area A of the parking lot will be given by the equation A = w * l. Substituting the expression for l into the area equation, we get A = w(2,200 - 2w) or A = 2,200w - 2w^2. To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Once the width is found, we can find the length using the perimeter equation and thus calculate the maximum area of the lot.
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Frank can type a report in 4 hours and James takes 6 hours how long will it take the two of them typing together
Frank can type the report in 4 hours and James takes 6 hours. Together, it will take them 2.4 hours to type the report.
Explanation:To find out how long it will take for Frank and James to type a report together, we need to calculate their combined rate of typing. Frank can type the report in 4 hours, so his typing rate is 1/4 of the report per hour. James takes 6 hours to type the report, so his typing rate is 1/6 of the report per hour. To find their combined rate, we add their individual rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
Therefore, working together, Frank and James can type 5/12 of the report per hour. To find out how long it will take to type the entire report, we divide the total report (1 whole) by their combined rate (5/12 per hour): 1 / (5/12) = 1 * (12/5) = 12/5 = 2.4 hours. So, it will take them 2.4 hours to type the report together.
To determine how long it will take for Frank and James to type a report together, we add their individual typing rates and divide the total report by their combined rate.
Explanation:To determine how long it will take for Frank and James to type a report together, we need to calculate their combined typing rate. Frank can type the report in 4 hours, which means he types at a rate of 1/4 of the report per hour. Similarly, James can type the report in 6 hours, which means he types at a rate of 1/6 of the report per hour.
To find their combined rate, we add their individual rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12. This means that together, they can type 5/12 of the report per hour.
To find out how long it will take for them to complete the report, we can divide the total report by their combined rate: 1 / (5/12) = 12/5 = 2.4 hours. Therefore, it will take Frank and James approximately 2.4 hours to type the report together.
486 is 72% of what amount
A theater can seat 273 people. The number of rows is 8 less than the number of seats in each row. How many rows of seats are there?
What type of simple machine is the crescent wrench
The crescent wrench is a type of lever, a simple machine that amplifies force to provide greater torque on fasteners with less input effort.
The crescent wrench is a type of simple machine, specifically it is a form of a lever. When you use a crescent wrench, you apply force to the handle, which then applies force to the object you are turning. The pivot point, or fulcrum, is the adjustable jaw which grips the nut or bolt. This allows the user to exert a greater torque on the fastener with less force than would be needed if just using one's hands.
Like other levers, the crescent wrench allows for a mechanical advantage, which is the ratio of output to input forces for any simple machine. By lengthening the handle of the wrench (the effort arm), we achieve a greater mechanical advantage, and thus, can apply more torque to the bolt or nut we are trying to turn.
Pamela's age is two times Jiri's age. The sum of their ages is
33
. What is Jiri's age?
A hallway measuring 90 feet x 7 feet requires 1/2 a fluid ounce of cleaning solution per square foot. How much cleaning solution is required to clean the hallway
315 fluid ounces of cleaning solution are required to clean the hallway.
Finding the corridor's entire area and multiplying it by the cleaning solution needed per square foot can help us determine how much cleaning solution will be needed to thoroughly clean the hallway.
In order to determine a rectangle's area, multiply its length by its width. The hallway in this instance is 90 feet long and 7 feet wide. Consequently, the hallway's overall size is:
Area = Length x Width
= 90 feet x 7 feet
= 630 square feet
The total area must now be multiplied by the amount of cleaning agent required per square foot, which is 0.5 fluid ounce:
Amount of cleaning solution = Area x Amount per square foot
= 630 square feet x (1/2 fluid ounce/square foot)
= 315 fluid ounces
Therefore, 315 fluid ounces of cleaning solution are required to clean the hallway.
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What divided by 2 equals -12
a pail holds 2 3/4 gallons of water how much is this in cups
the perimeter of a rectangle is 32 centimeters. the width is 7 centimeters what is the area of the rectangle
A tree is 2 1/2 feet tall. How tall will it be in 3 years if it grows 1/4 foot each year? Which method will NOT give the correct number of feet?
The life span of a certain insect in days is uniformly distributed over the interval (20,36). What is the probability the insect will live 24 days or less? Possible Answers a) .24 b) .25 c) .20 d) .75
Answer:
b) 0.25
Step-by-step explanation:
The required probability is ...
(24 -20)/(36 -20) = 4/16 = 1/4 = 0.25
_____
Comment on the attached graph
The red line is the probability distribution function (pdf) for this uniform distribution. The green line is the cumulative distribution function (cdf) for this uniform distribution. It is the integral of the pdf.
The probability of interest is the value of the cdf at x=24. That value is 0.25, meaning the area under the pdf curve to the left of x=24 is 1/4 of the total area under the pdf curve. That proportion is what is calculated above.
a recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies directly with the amount of flours you use. find the direct variation equation for the relationship between the number of cups of flours and the number of muffins
One numer is 17 more than another number the sum of the two numbers is 25 find the numbers
a used car priced at$5000.00 . The salesperson then offered a discount of $250.00.
What is the percent discount?
the production line where you work can assemble 5 amplifiers every 30 minutes at this rate how long should it take the line to assemble 125 amplifiers
The time taken to assemble 125 amplifiers is required.
Time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.
Time taken to assemble 5 amplifiers is 30 minutes
[tex]5\ \text{amplifiers}=30\ \text{minutes}[/tex]
So,
[tex]1\ \text{amplifier}=\dfrac{30}{5}=6\ \text{minutes}[/tex]
[tex]125\ \text{amplifiers}=125\times 6=750\ \text{minutes}=\dfrac{750}{60}=12.5\ \text{hours}[/tex]
So, time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.
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the function f(x) varies directly with x and f(x)=250 when x=50
what is f(x) when x=5
10
15
25
50
The function f(x) varies directly with x and f(x) is 250 when x is 50, so
f(x) is 25 when x=5
What does the statement y varies directly as x describe?the function f(x) varies directly with x and
f(x)=250 when x=50
when x=5 f(x) = 5*5 = 25
Some textbooks will say "y varies directly as x," "y varies proportionally as x," or "y is directly proportional to x" to describe direct variation. This implies that the ratio between them always remains the same and that as x increases, y increases, and as x drops, y decreases.The direct variation equation can also be written as x = y / k. This indicates that the relationship between x and y is direct, with the constant of proportionality being equal to 1 / k.If x varies in direct proportion to y, the equation of variation is written as X times Y = K.To learn more about varies directly refer to:
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The area of a rectangle is 336 square inches. If the width of a rectangle is 6 inches. What is the length of the rectangle?
Answer:
56
Step-by-step explanation:
The product of two positive numbers is 120. One number is 7 more than the other. Determine the two numbers
hi there i could really use the help with this question please
John works two jobs. As a security guard he earns $8.75 per hour. As a landscaper he earns $14.00 per hour. One week John worked a total of 30 hours and earned $283.50. How many hours did he work at each job?
Explanation of how to find the number of hours John worked at each job given his total hours and earnings.
Explanation:The given problem: John worked a total of 30 hours and earned $283.50. He earns $8.75 per hour as a security guard and $14.00 per hour as a landscaper. We need to find out how many hours he worked at each job.
Step-by-step solution:
Let x be the hours worked as a security guard and y be the hours worked as a landscaper. Set up the equations: x + y = 30 and 8.75x + 14y = 283.50. Solve the system of equations to find x and y.Answer: John worked 15 hours as a security guard and 15 hours as a landscaper.
The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels over 200 is Normally distributed, with mean (in milligrams) μ and standard deviation σ = 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels over 200, but you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the hypotheses and you obtain a P-value of 0.052. Which of the following is true?
Answer:
some evidence against H0 can be seen, and a study using a larger sample size will be recommended
Step-by-step explanation:
The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels over 200 is Normally distributed, with mean (in milligrams) μ and standard deviation σ = 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels over 200, but you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the hypotheses and you obtain a P-value of
going by the parameters
standard deviation is 3
mean of the sample=μ
There is some evidence against H0, and a study using a larger sample size will be essential
what is the value of 4x to the second power +5x when x =1
Suppose that, from measurements in a microscope, you determine that a certain bacterium covers an area of 1.50μm2. Convert this to square meters.
Express your answer in square meters.
can you simplify 3/r + 7/r+3
Heights of men on a baseball team have a Bell shaped distribution with a mean of 172cm and a standard deviation of 8cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 156cm and 188cm b. 164cm and 180cm
jay simplified the expression 3 x (3 +12 / 3) -4. for his first step ,he added 3 + 12 to get 15. what was jay's error? find the correct answer
Jay's error was in the order of operations. The correct result is 17.
Jay's error lies in how he interpreted the expression. According to the order of operations (PEMDAS/BODMAS), multiplication and division should be performed before addition and subtraction.
So, the correct first step is to perform the division [tex]\( \frac{12}{3} = 4 \)[/tex]and then add 3 to the result, not add 3 and 12 together first.
The correct first step:
[tex]\[ 3 \times (3 + \frac{12}{3}) - 4 \][/tex]
[tex]\[ = 3 \times (3 + 4) - 4 \][/tex]
[tex]\[ = 3 \times 7 - 4 \][/tex]
= 21 - 4
= 17
Therefore, Jay's error was in the order of operations. The correct result is 17.
the iv has 500mg of antibiotics in 250 ml bag. The patient receives this antibiotic three times a day. how many mg of medication has the patient received in 24 hours and how many ml have been infused in 24 hour
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 9, x = 0, y = 9, y = 11
The volume of the solid obtained by rotating the region bounded by the curves about the x-axis is found using cylindrical shells, resulting in a total volume of 36π cubic units.
Explanation:To find the volume of the solid obtained by rotating the region bounded by the curves xy = 9, x = 0, y = 9, and y = 11 about the x-axis, we will utilize the method of cylindrical shells. The curves define a region in the xy-plane which, when rotated about the x-axis, forms a solid with varying radii. To apply the method, we first need to express the variable x in terms of y from xy = 9 to obtain x = 9/y.
Next, the volume of a representative cylindrical shell with thickness dy and height x = 9/y is given by the circumference of the shell (2πy) times the height (9/y) times the thickness (dy). This leads to the volume element dV = 2πy(9/y)dy = 18πdy. Integrating this volume element with respect to y between the limits 9 and 11 yields the total volume.
Using the integral calculus, the volume V is:
V = ∫911 18π dy = 18π [y]∫911 = 18π(11 - 9) = 36π cubic units.
Thus, the volume of the cylinder is 36π cubic units.