Answer:
130
Step-by-step explanation:
Angle 1 and 13 are supplementary.
So 13 is 180- angle 1
180-50 = 130
Answer:
130
Step-by-step explanation:
theyre supplementary angles I believe so 180-50=130
pls answers asap!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
i know that the first one is correct because its infinite but I'm sorry i don't know the second one. : ( (try the increasing -&,&) tho im not sure
Step-by-step explanation:
If jill has 6 different sweaters and 4 different pairs of pants, how many different combinations could she wear?.
Using the fundamental counting principle, it is found that there are 24 different combinations she can wear.
The sweaters and the pants are independent, and this is why the fundamental counting principle is used.
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
6 sweaters 4 pairs of pants.Thus:
T = 6 * 4 = 24
There are 24 different combinations.
A combination in mathematics is a selection of items from a fixed that have amazing members, making the order of selection irrelevant (not like permutations). For instance, given a set of three fruits—say let's an apple, an orange, and a pear—one can choose between three combinations: an apple and a pear, an apple.
A hard and fast S's ok aggregate is, more precisely, a subset of S's ok amazing components. As a result, two combinations are equal if and best if each contains the same players. (The ties between the people in each group are not considered.)
(n/k) ={ n(n - 1) . . . (n – k + 1)}/{k(k - 1) . . . 1}
n!/{k!(n - k)!}
k > n.
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Maria brought home a delicious, mouth watering Italian submarine sandwich, dripping with delicious dressing, that was 6 1/8 feet long. She was going to share it with 6 of her friends. if Maria and her friends were able to share the sub equally, how much of the sub each person get?
Using division, the length of the sandwich each friends got was 1.02083ft
What is DivisionDivision is a mathematical operation that divides one number (the dividend) by another (the divisor) to find the answer (the quotient). It is one of the four basic operations in mathematics, along with addition, subtraction, and multiplication.
To determine the size each one got, we have to divide the total length of the sandwich by the number of friends.
We need to convert the mixed fraction into improper fraction or decimal
6 1/8 = 49/8 = 6.125
Now, let's divide this by 6
6.125 / 6 = 49/48 = 1.02083
The length each of her friends will get is 1.02083ft
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15. The expression √x is equivalent to 14i√3. What is the value of x?
a.-588
b. -588i
c.588
d. 588i
16. An expression is shown below.
x^5 + 6x^3 +8x
Which value of x makes the expression equal to 0?
a. -2i²
b. -2i
c. 4i
d. 4i²
(15) The value of x is -588 (option A).
(16) The value of x makes the expression equal to 0 is -2i. (option B).
What is the value of x?The value of x is calculated by solving the equation as follows;
(15) We have the equation:
√x = 14i√3
Squaring both sides, we get:
x = (14i√3)^2
x = -588
(16) Factoring the expression, we get:
x(x⁴ + 6x² + 8)
Setting each factor equal to 0, we get:
x = 0 or x⁴ + 6x² + 8 = 0
Let's solve for the second equation:
Let y = x²
Then we have:
y² + 6y + 8 = 0
Factorizing, we get:
(y + 2)(y + 4) = 0
So y = -2 or y = -4
Since y = x², this means:
x² = -2 or x² = -4
Taking the square root of both sides, we get:
x = ±√(-2) or x = ±√(-4)
Simplifying using imaginary numbers, we get:
x = ±i√(2) or x = ±2i
Thus, for the expression √x is equivalent to 14i√3, the value of x is -588. And for the expression x⁵ + 6x³ + 8x, x = -2i.
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determine the domain and the range of the function .f = {(10,1 ),(17,-6),(45,1 ),(51,5 )}
The given function f, with the provided set of ordered pairs, has a domain of {10, 17, 45, 51} and a range of {-6, 1, 5}.
The domain of a function refers to the set of all possible input values or x-values for which the function is defined. In this case, the given set of ordered pairs determines the domain. Looking at the x-values in the set {10, 17, 45, 51}, these are the unique inputs for which the function f is defined. Hence, the domain of f is {10, 17, 45, 51}.
On the other hand, the range of a function refers to the set of all possible output values or y-values that the function can take. By examining the y-values in the set {-6, 1, 5}, we can observe the distinct outputs generated by the function f. Thus, the range of f is {-6, 1, 5}.
In summary, the domain of the function f is {10, 17, 45, 51}, and the range of f is {-6, 1, 5}.
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The ticket price to a concert is $65 plus an additional (d) dollars service fee per ticket. The total cost for four people to attend the concert is $308. Calculate the cost of the service fee charged for each ticket.
SHOW HOW YOU DID IT PLEASE!!!
Answer: d=12
Step-by-step explanation:
4(65)+ 4d=308
multiply 65 by 4
260+4d=308
move the constant to the right
4d=308-260
calculate
4d=48
divide both sides
d=12
12.5% of a number is 25, find the number
Answer:
200
Step-by-step explanation:
Let's call the number x :
12.5% of x = 25
Changing 12.5% into decimal would be 0.125
Now we have the equation :
0.125x = 25
Divide both sides by 0.125 to make x the subject :
x = 25 ÷ 0.125
x = 200
To check we can substitute this value into the question :
12.5% of 200 = 25
Hope this helped and have a good day
The mat around the picture shown measures x inches
across. Which one of the following equations says that
the area of the picture itself is 800 square inches?
32 in.
40 in.
x in.
.x in.
The equation that says the area of the picture itself is 800 square inches is option C: (40 - 2x)(32 - 2x) = 800.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The length of the bigger rectangle is = 32 inches
The width of the bigger rectangle is = 40 inches
The distance between bigger and smaller rectangle is x inches.
In terms of bigger rectangle -
The length of smaller rectangle = 32 - (x + x)
The length of smaller rectangle = (32 - 2x) inches
The width of the smaller rectangle = 40 - (x + x)
The width of the smaller rectangle = (40 - 2x) inches
The area of the smaller rectangle is 800 in².
The formula for the area of rectangle is -
Area = length × width
800 = (32 - 2x)(40 - 2x)
Therefore, the equation is obtained as 800 = (32 - 2x)(40 - 2x).
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PKS HELP
find the slope of : a(-2,-4) B(2,4)
Answer: undefined
Step-by-step explanation:
Gary makes $7.48 an hour. He grossed $310.42 last week. How many hours did he work?
Answer:
Gary worked 41 and a half hours
Step-by-step explanation:
$310.42 divided by $7.48 per hour = 41.5 hours
What would the number of sides be on a polygon with an interior angle of 176 degrees
The number of sides on a polygon with an interior angle of 176 degrees would be 10.
Here's how you can solve it:
To find the number of sides in a polygon, we need to use the formula below:
(n - 2) × 180° / n = Interior
Angle where n is the number of sides in a polygon and Interior
Angle is the angle in the polygon.
To solve for n in this formula, we need to use the given angle.
So, we can rearrange the formula as shown below:
n = (Interior Angle × n) / (n - 2)
We know that the given Interior Angle is 176 degrees.
Substituting this value in the above formula, we get:
n = (176 × n) / (n - 2)
Multiplying both sides by n - 2, we get:n(n - 2) = 176n
Expanding the left-hand side of the equation:n² - 2n = 176n
Rearranging the equation to solve for n:n² - 178n = 0n(n - 178) = 0
So, n = 0 or n = 178.
But we can discard n = 0
because the number of sides of a polygon can't be zero.
Hence, n = 178 is the extraneous solution that we can discard.
The correct solution is:n = 10
Therefore, the number of sides on a polygon with an interior angle of 176 degrees is 10.
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Solve the following quadratic equation by factoring:
x^2 + 2x - 8 = 0
Answer: x = -4 and x = 2.
To factor a quadratic equation in the form of x^2 + bx + c = 0, we need to find two numbers that when multiplied together, give us c, and when added or subtracted, give us b.
We need to find two numbers whose product is -8 and whose sum is 2. These numbers are 4 and -2, so we can write:
x^2 + 2x - 8 = (x + 4)(x - 2) = 0
Setting each factor to zero, we get:
x + 4 = 0 or x - 2 = 0
Solving for x in each equation, we get:
x = -4 or x = 2
So, the solutions to the equation x^2 + 2x - 8 = 0 are x = -4 and x = 2.
Let X have a Poisson distribution with parameter λ > 0. Suppose λ itself is random, following an exponential density with parameter θ.
(a) What is the marginal distribution of X?
(b) Determine the conditional density for λ given X = k.
(a) The marginal distribution of X is Poisson with parameter θ.
(b) The conditional density for λ given X = k is Gamma with shape parameter k+1 and scale parameter θ.
(a) What is the Poisson distribution's parameter for X?The marginal distribution of X refers to the distribution of the random variable X on its own,without considering any other variables. In this case, X follows a Poisson distribution with parameter θ.The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the events happen independently and at a constant rate. The parameter θ represents the average rate of events occurring in the given interval.In summary, the marginal distribution of X is a Poisson distribution with parameter θ, representing the average rate of events.
(b) What is the conditional density for λ given X=k?The conditional density for λ given X = k is a way to describe the distribution of the parameter λ when we know that the random variable X takes on a specific value, k. In this scenario, the conditional density follows a Gamma distribution with a shape parameter of k+1 and a scale parameter of θ. The Gamma distribution is often used to model continuous positive-valued variables and is particularly useful for modeling waiting times or durations.In summary the conditional density for λ given X = k is a Gamma distribution with a shape parameter of k+1 and a scale parameter of θ, providing information about the parameter λ when X takes on a specific value, k.
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what phrase describes the shape of the data
The phrase "shape of the data" refers to the overall pattern or distribution exhibited by a set of data points. It describes the visual representation of the data points when plotted on a graph or chart. The shape of the data can vary depending on the characteristics and distribution of the data points.
Common shapes include:
Symmetrical: The data points are evenly distributed around a central point, creating a bell-shaped curve.
Skewed: The data points are concentrated on one side of the graph, resulting in an asymmetrical distribution.
Bimodal: The data points exhibit two distinct peaks or modes, indicating the presence of two separate groups or categories.
Uniform: The data points are evenly distributed across the entire range, creating a flat and constant pattern.
Outliers: The presence of extreme data points that deviate significantly from the general shape or pattern of the data.
The shape of the data provides insights into its characteristics and helps in understanding the underlying trends and relationships.
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How to solve a equation using elemination method
Answer:
Below.
Step-by-step explanation:
I assume you are referring to a system of equations.
Example:
2x - y = 4
x + y = 5
If we add these 2 equations then the y is eliminated because -y + y = 0:-
3x + 0 = 9
x = 3
Now we plug x = 3 into the first equation to find y:
2(3) - y = 4
-y = 4 - 6 = -2
y = 2.
If we cannot eliminate one of the variables we multiply one of the equations so that one of the variables so that it can be eliminated.
For example:
2x - 3y = 5 A
x + y = 6 B
We multiply the second equation B by 3 so that when we add -3y + 3y gets eliminated:
3x + 3y = 18
- so adding this to equation A
5x + 0 = 23.
In some cases we may have to multiply both equations by different values to get terms that can be eliminated.
10pts
Cierra had $18 to spend on 6 pencils for school. After
buying the pencils she had $7.50 left. How much did
she spend on each pencil? Write an equation to represent your problem
Answer:
Step-by-step explanation:
$18-$7.50= $10.50
Answer:
f(x)=3x
f(x)=x+2
f(x)=3√3+x2
Step-by-step explanation:
A roll of carpet will cover an area the size of a 12-foot by 14-foot room. How many rolls must be bought to cover a 50-foot by 70-foot restaurant dining room?
we will need about 21 rolls of carpet to cover the 50-foot by 70-foot restaurant dining room.
How many rolls must be bought to cover a 50-foot by 70-foot restaurant dining room?
We know that a roll of carpet covers an area of 12ft by 14ft, then each roll covers an area of:
a = 12ft*14ft = 168ft^2
And we want to cover an area of 50ft by 70ft, that area gives:
A = 50ft*70ft = 3,500ft^2
The number of rolls that we need is given by the quotient between the areas, we will get:
number of rolls = A/a = (3,500ft^2)/(168ft^2) = 20.83
Rounding to the next whole number, we get 21.
So we will need about 21 rolls of carpet to cover the 50-foot by 70-foot restaurant dining room.
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Help please............
Answer:
\( \tan(J) =\frac{5\sqrt{66}}{66} \)
Step-by-step explanation:
\( \tan(J) =\frac{5}{\sqrt{66}} \)
\( \tan(J) =\frac{5}{\sqrt{66}} \times \frac{\sqrt{66}}{\sqrt{66}} \)
\( \tan(J) =\frac{5\sqrt{66}}{\sqrt{66}\times\sqrt{66} } \)
\( \tan(J) =\frac{5\sqrt{66}}{66} \)
Question 1
Merlion LuxBus Pte Ltd provides point-to-point coach services between Singapore and various Cities in Malaysia. It competes based on differentiated luxury and on-time services. It owns a fleet of 12 buses, each with a capacity of only 24 passengers in a 2 is to 1 seating arrangement per row and up to 8 rows. This allows the seats to be nearly fully reclined with good leg room for passengers. Singapore is the hub of Merlion's operations. Point-to-point travel service means that buses will depart in the morning for a Malaysian city. The same buses will return to Singapore with Malaysian passengers in the evening. The COVID19 pandemic in 2020 and 2021 closed land travel between Singapore and Malaysia. This severely affected the business of Merlion. To cope with the downturn, they pivoted towards local tour services. With both countries now moving towards the endemic phase of COVID19 and opening up quarantine-free cross border travel, Merlion is now planning to revert to its core business of luxury point-to-point services between the 2 countries.
(a) State three (3) practical assumptions applicable to this particular linear programming (LP) problem.
(b) Develop an LP model to maximise daily profit for Merlion. Your model must be in the form of algebraic equations and inequalities all of which must be annotated. Define your Decision Variables, Objective Function and Constraints clearly.
(c) Solve the LP model using the Excel Solver software and present your Answer and Sensitivity Reports in their original formats generated by Solver. Show, also, the underlying Excel matrix model used to run Solver. You may screenshot this part of your answer. State explicitly how the buses will be deployed and the maximum profit achievable.
(d) Determine what the profit per passenger has to be for buses to be deployed to Malacca. Explain how you derive your answer. (e) How will Merlion’s profit be impacted if 2 buses were to break down on a given day. Explain your analysis.
A. Three practical assumptions applicable to this particular linear programming (LP) problem could be: Constant demand, Fixed costs and prices, Full utilization of capacity.
B. LP Model: Decision Variables, Objective Function, Constraints.
C. set up the LP model in Excel and run Solver to obtain the answer and sensitivity reports.
D. it would not be feasible to deploy buses to Malacca.
E. The revenue would decrease due to the lower number of passengers, while the cost may remain relatively fixed (assuming the breakdowns do not incur additional repair costs).
(a) Three practical assumptions applicable to this particular linear programming (LP) problem could be: Constant demand, Fixed costs and prices, Full utilization of capacity.
Constant demand: The LP model assumes that the demand for Merlion's point-to-point coach services remains constant throughout the planning period. This means that the number of passengers traveling between Singapore and Malaysia is assumed to be consistent.
Fixed costs and prices: The LP model assumes that the costs associated with operating the buses, such as fuel, maintenance, and driver salaries, remain fixed. It also assumes that the ticket prices charged to passengers are constant and do not change based on factors like demand or competition.
Full utilization of capacity: The LP model assumes that all available seats on each bus will be filled by passengers. It does not account for scenarios where there might be empty seats due to insufficient demand or other factors.
(b) LP Model: Decision Variables, Objective Function, Constraints.
Decision Variables:
Let X i represent the number of buses deployed to city i, where i can take values 1 to n (n being the total number of cities in Malaysia).
Objective Function:
Maximize daily profit:
Maximize Profit = ∑(Revenue - Cost)
Constraints:
Capacity constraint for each city:
∑(X i * Seats per Bus) ≤ Total Available Seats
Demand constraint for each city:
X i ≥ Minimum Demand i
Non-negativity constraint:
X i ≥ 0 for all i
(c) Solution using Excel Solver:
Please provide the following information:
Total available seats
Seats per bus
Minimum demand for each city
Revenue and cost data
With the given input, I can help you set up the LP model in Excel and run Solver to obtain the answer and sensitivity reports.
(d) To determine the profit per passenger required for buses to be deployed to Malacca, we need to consider the revenue and cost associated with each passenger. Let's assume the revenue per passenger is R and the cost per passenger is C.
The profit per passenger can be calculated as follows:
Profit per Passenger = Revenue per Passenger - Cost per Passenger
To deploy buses to Malacca, the profit per passenger should be at least equal to zero or positive. If the profit per passenger is negative, it means that the cost per passenger is higher than the revenue per passenger, resulting in a loss for each passenger. In such a case, it would not be feasible to deploy buses to Malacca.
(e) If two buses were to break down on a given day, it would impact Merlion's profit because there would be a reduction in the number of available buses to transport passengers. This could result in a lower revenue as fewer passengers can be accommodated.
To analyze the impact on profit, you would need to consider the revenue and cost implications of operating with reduced capacity. The revenue would decrease due to the lower number of passengers, while the cost may remain relatively fixed (assuming the breakdowns do not incur additional repair costs).
By estimating the revenue and cost changes based on the reduced capacity, you can compare the new profit with the original profit to determine the impact.
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A researcher's results should be considered fraudulent if Group of answer choices animals were used while conducting experiments. the researcher used any form of survey to collect the data. participants were not debriefed after completion of the study. data were changed in order to support the hypothesis
A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.
Explanation:
A researcher's results should be considered fraudulent if data were changed in order to support the hypothesis. This is a serious ethical violation and goes against the scientific method. Additionally, if animals were used while conducting experiments, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. If a survey was used to collect data, the researcher should have ensured the survey was properly designed and administered to avoid any biases or errors. Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Overall, it is important for researchers to adhere to ethical standards and maintain the integrity of their research.
The scientific method requires researchers to conduct experiments in a transparent and objective manner. This means that the researcher should design experiments to test hypotheses, collect data systematically, and analyze data objectively. Any manipulation of data to support a hypothesis undermines the scientific method and is considered unethical. Researchers who intentionally manipulate data can be considered fraudulent and may face disciplinary action.
If animals were used in the experiment, the researcher should have followed ethical guidelines and obtained proper approval and care for the animals. Ethical guidelines ensure that animals are treated humanely, minimize their pain and discomfort, and maximize their welfare. Researchers who violate these guidelines can be considered fraudulent and may face disciplinary action.
If a survey was used to collect data, the researcher should have ensured that the survey was properly designed and administered to avoid any biases or errors. Surveys can be susceptible to various sources of error, including sampling errors, measurement errors, and non-response bias. Researchers who fail to address these sources of error can produce biased or invalid results, which can be considered fraudulent.
Finally, if participants were not debriefed after completion of the study, this could be seen as unethical and potentially harmful to their well-being. Debriefing allows participants to understand the purpose of the study, ask questions, and voice any concerns they may have. Participants who are not debriefed may feel deceived or harmed by the study, which can damage their trust in research and researchers.
In summary, researchers must adhere to ethical standards and maintain the integrity of their research. This includes avoiding data manipulation, following ethical guidelines for animal welfare, ensuring that surveys are properly designed and administered, and debriefing participants after completion of the study. Failure to do so can result in fraudulent research and harm to participants, animals, and the scientific community as a whole.
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Question 4
Evaluate the expression if a =2, b = -3, c = 4, h = 6, y = 4, and z =
- 1.
5-|c+1|
Answer:
0 is the answer.
Step-by-step explanation:
5 - |4 + 1|
5-5
0
Write an equation of the graph shown in terms of cosine:
Answer:
Step-by-step explanation:
A squiggly line can refer to a variety of different shapes or patterns. To create an equation using cosine that resembles a squiggly line, you can use a combination of sine and cosine functions with different frequencies and amplitudes. Here's an example equation that produces a squiggly pattern:
y = A * cos(B * x) + C * sin(D * x)
In this equation, A, B, C, and D are constants that you can adjust to modify the shape and characteristics of the squiggly line. By experimenting with different values for these constants, you can create various squiggly patterns. Keep in mind that the specific equation may vary depending on the exact shape and features you have in mind for the squiggly line.
The area of a trapezoid is 128 square feet. If the height of the trapezoid is increased by a factor of 5, what is the area of the new trapezoid?
7/6 * 16/6 in simplest form
Answer:
3.83333333333
Step-by-step explanation:
employees in a large company are entitled to 15-minute coffee breaks. a random sample of the duration of coffee breaks for 10 employees was taken with the times shown below. assuming that the times are normally distributed, is there enough evidence at the 1% significance level to indicate that on average employees are taking longer coffee breaks than they are entitled to? the null hypothesis is?
There is enough evidence to indicate that on average employees are taking longer coffee breaks than they are entitled to.
What is the null hypothesis?
The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.
Here, we have
Given: Employees in a large company are entitled to 15-minute coffee breaks. a random sample of the duration of coffee breaks for 10 employees was taken with the times.
The sample mean = x = ΣX/n = 16.8000
The population mean = µ = 15
The alpha error = 0.01
The confidence coefficient = 99%
Sample Size = n = 10
Sample Variance = 3.0667
The alternative hypothesis is µ > 15
The calculated test statistics (four decimals)
t-test statistic = (16.8-15)/0.5538 = 3.2504
Hence, there is enough evidence to indicate that on average employees are taking longer coffee breaks than they are entitled to.
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a formula for 6 gallons of light green paint uses 3/8 gallon of white paint. Liam has 9/16 gallon does Liam have enough white paint to make 8 gallons of light green paint?
Given:
6 gallons of light green paint uses \(\dfrac{3}{8}\) gallon of white paint.
Liam has \(\dfrac{9}{16}\) gallon of white paint.
To find:
Whether Liam have enough white paint to make 8 gallons of light green paint.
Solution:
Here, 6 gallons of light green uses \(\dfrac{3}{8}\) gallon of white paint.
So, the white paint for 1 gallon of light green \(=\dfrac{\dfrac{3}{8}}{6}\)
\(=dfrac{3}{8\times 6}\)
\(=\dfrac{3}{48}\)
\(=\dfrac{1}{16}\)
It means, 1 gallons of light green uses \(\dfrac{1}{16}\) gallon of white paint.
White paint for 8 gallon of light green \(=8\times \dfrac{1}{16}\)
\(=\dfrac{8}{16}\)
She has \(\dfrac{9}{16}\) gallon of white paint, which is greater than \(=\dfrac{8}{16}\) gallons.
Therefore, Liam have enough white paint to make 8 gallons of light green paint.
If Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint
Given that 6 gallons of light green paint use 3/8 gallon of white paint, this can be expressed as:
3/8 gallons of white paint = 6 gallons of light green
We are to determine if 9/16 gallons will be enough to make 8 gallons of light green paint. This can be expressed as
9/16 gallons of white paint = x
Divide both expressions
3/8 * 16/9 = 6/x
2/3 = 6/x
Cross multiply
2x = 3 * 6
2x = 18
x = 18/2
x = 9
This shows that if Liam has 9/16 gallon, he has enough white paint to make 8 gallons of light green paint
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Gravel is being dumped from a conveyor belt at a rate of 30 ft 3ymin, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high
The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.
Given the following data: Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min.
Its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.
The pile is 10 ft high.
To determine how fast the height of the pile is increasing, we need to differentiate the formula for the volume of a cone with respect to time.
We know that the volume of a cone is given by: \(V = (1/3)πr²h\)
We are given that the base diameter and the height of the cone are always equal, so we can write: r = (d/2)and h = d
where d is the diameter of the base of the cone.
The volume of the cone is given by: V = (1/3)π(d/2)²d
Simplifying, we get:\(V = (1/12)πd³\)
Differentiating both sides with respect to time, we get:
dV/dt = (1/4)πd² (dd/dt)
We are given that dV/dt = 30 ft³/min, and we want to find dd/dt when h = 10 ft.
Substituting V = (1/3)π(10/2)²(10)
= (1/3)π(25)(10)
= (250/3)π and d = 10,
we get:
30 = (1/4)π(10²)(dd/dt)
Simplifying, we get:
dd/dt = 12/π
The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.
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Use integers that are that are closest to the number in the middle. < - v119
Answer:
-11 and -10
Step-by-step explanation:
-11² = -121
-(√119)² = -119
-10² = -100
_____
-√119 is between -11 and -10
f(x) = 2x + 6
g(x) = x^2 - 2x + 6
Find: f(x) • g(x)
Answer: x2 . f(x) - 2x . f (x) + 6 . f(x)
Step-by-step explanation:
what is the answer for this question (5+×)²
\((5+x)^2\\\\=5^2 +2\cdot5\cdot x +x^2\\\\=25+10x +x^2 \\\\=x^2 +10x +25\)