The area of the shaded region - [tex]\int\limits^\frac{5\pi }{4} _\frac{3\pi }{4}[/tex] [tex]cos^{2}[/tex] 2θ dθ
Determine α, β and f(θ).
To determine α and β, imagine a clock dial that turns counter-clockwise around the origin. The shaded area must be passed over by the dial. Place the dial in its starting position, and find the angle it makes with the horizontal axis, this angle is α. Do the same for the dial's end position, this angle [tex]\beta[/tex] .
To find f(θ), this equals r.
α= [tex]\frac{3\pi }{4}[/tex]
β= [tex]\frac{5\pi }{4}[/tex]
f(θ)=r=cos2θ
we know the integration formula,
A = [tex]\int\limits^\alpha _\beta[/tex] f (θ )² dθ
Hence, the area of the shaded region:
A = [tex]\int\limits^\frac{5\pi }{4} _\frac{3\pi} {4} \,[/tex] [tex]cos^{2}[/tex] 2θ dθ
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if you were to add 25 to y what would you get in all?
Answer:
25 + y
Step-by-step explanation:
It looks like you might be missing some information.
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. They are considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers.
Develop hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.
The null hypothesis set up for the hypothesis test of the population parameter is given by H₀: p ≥ 0.1 .
We would set up the hypothesis test.
For the null hypothesis,
H₀: p ≥ 0.1
For the alternative hypothesis,
Hₐ: p < 0.1
This is a two-tailed test.
Taking into account the population proportion, p = 0.1 q = likelihood of failure = 1 - p
q = 1 - 0.1 = 0.9
b) In light of the sample,
P = x/n = sample proportion
Where x = the number of successes, n = the number of samples, and p = 13/100 = 0.13
The test statistic, the z score, would be calculated as z = (P - p)/pq/n z = (0.13 - 0.1)/(0.1 0.9)/100 = 1.
The determined test statistic is 1 for the right tail and - 1 for the left tail.
Since α = 0.05, the critical value is calculated using the normal distribution table.
α₂ = 0.51/2 = 0.025 on the left
The z score for an area to the left of 0.025 is - 1.96
α₂ = 1 - 0.025 = 0.975 for the right
1.96 is the z score for an area to the right of 0.975.
The test statistic must be less than - 1.96 or larger than 1.96 in order to reject the null hypothesis.
We cannot reject the null hypothesis since - 1 > - 1.96 and 1 1.96.
As a result of the hypothesis test results, Eagle Outfitter should take the promotion national.
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How do I solve this problem. Please explain step by step if u could
0.25 + (-3) =
Answer:
0.25 − 3
=0.25 + −3
= −2.75
( a number line to help to)
Step-by-step explanation:
David says that a triangle with side measures 9 cm, 12 cm, and 17 cm is a right triangle. Susie says it is not. Who is correct? Explain
your reasoning.
12 cm
17 cm
9 cm
Answer: Susie is correct.
Step-by-step explanation:
Susie is correct, because the Pythagorean theorem does not work on this triangle. Since the Pythagorean theorem only works on right triangles, we can conclude that Susie is correct, and that this triangle is NOT a right triangle.
a²+b² = c²
a = 9
b = 12
c = 17
9² + 12² = 17²
==> 81 + 144 = 289
==> 225 = 289, This is not true
Therefore this triangle is not a right triangle.
Write a quadratic function in standard form whose graph has a vertex of (2, 6) and passes through the point (4, 10) .
Using the above graphic, it takes about _____ years to transition from using no oil to consuming 100 million barrels per day whereas it takes about______ years to transition from using 100 million to 200 million barrels per day.
A. 60, 10
B. 10, 60
C. 120, 50
D. 50, 120
It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.
As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.
The right axis indicates the global consumption rate of oil in millions of barrels per day.
To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.
The bottom axis is time in years.
The graph attached at the end of the solution.
Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.
Let the number of years of transition from using 100 million to 200 million barrels per day be b.
From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.
But it takes 50 years to go from 100 million to 200 million.
This is known as exponential growth.
Therefore, the value of a is 120 and the value of b is 50.
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Need Awnser asap
Right Awnser gets branliest
Answer:
x1,y16 is the rate of change
Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1
You brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
what is equivalent to (32−−√5)13
Answer:
Your answer is 416 + 13 [tex]\sqrt{5}[/tex].
Step-by-step explanation:
In the last 24 days, it rained 18 days. What is the ratio of rainy days to total days written as a percent?
The ratio of rainy days to total days written as a percent will be 75%.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.
Since in the last 24 days, it rained 18 days.
Number of rainy days = 18.
Number of total days = 24
The ratio of rainy days to total days written as a percent will be:
= Number of rainy days / Total days × 100
= 18/24 × 100
= 3/4 × 100
= 75%
Therefore, the ratio is 3:4 which is 75%.
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Is 5x-8+7y=y-6 linear or nonlinear
Answer:
Step-by-step explanation:
The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.
After a snowstorm in the town of Golden Glen, the morning temperature was
–
10°F. But by the afternoon, the temperature had risen by 17°F.
The change in temperature based on the information is 27°F.
How to illustrate the relationship?It should be noted that temperature simply means the degree of coldness and hotness in a body. In this case, after a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F.
Let the change in temperature be represented by x.
Therefore, -10 + x = -17
x = 17 + 10
x = 27
The Temperature is 27°F.
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After a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F. What was the change in temperature?
Answers fast please I need them fast
The answers to find are 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
What are similar triangles?When two triangles having congruent corresponding angles and the corresponding sides are in equal ratio, then the triangles are said to be similar triangles.
Given are the similar triangles,
1) Δ HJG ~ Δ CAB
Scale factor = 3:1
2) Δ NPM ~ Δ ABC
Scale factor = 1:2
3) KJML ~ CDAB
Scale factor = 1:2
4) 40/x = 20/5
x = 10
5) 18/x = 21/7
x = 6
6) 6/3 = x/15
x = 30
Hence, the answers are: 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
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use the data above to test the claim that marble color preference and club membership are related, as follows: (2 pts) carefully state the hypotheses. Hypothesis is
H0: marble color preference and income class are independent
H1: marble color preference and income class are dependent
The Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".
The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample. Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.
We can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypotheses. However, the hypotheses can also be phrased in a general way that applies to any test.
We are given that to test the claim that marble color preference and club membership are related.
Thus, the Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".
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A bag contains 3 red, 6 blue, and 7 yellow marbles. What is
the probability of drawing 2 marbles of different colors out of
the bag?
The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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The length of a rectangular poster is 8 more inches than three times its width. The area of the poster is 256 square inches. Solve for the dimensions (length and width) of the poster
The dimensions are
inches ___ by ____ inches.
When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
let length be l and width be w.
l=3w+8
l*w=256
(3w+8)*w=256
3w²+8w=256
3w²+32w-24w-256=0
3w(w-8)+32(w-8)=0
(3w+32)(w-8)=0
w=-32/3, 8
w=8 inch
l=3*8+8
l=32 inch
The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.
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Let the discrete random variable X have the geometric distribution with parameter p. (a) Give a real-life example in which the geometric distribution can be applied. (b) Use the definition of the expected value to show that: E[X] = 1/p. (c) Explain why it makes sense that the expected value of X is inversely proportional to p.
a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.
b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.
c) E(x) = 1/p
Discrete Random Variable:
A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.
Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...
Geometric Distribution :
The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.
The Geometric Random Variable can be written as X ~ G(p).
The probability mass function is P(X = x) = (1 - p)ˣ⁻¹ p
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Find the Probability of, A King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.
As per the given data,
we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
We know that,
Probability(Event) =Number of Favorable Outcomes/Total number of
Outcomes = x/n.
Total number of Outcomes is 52 (given)
So, we will calculate Number of Favorable Outcomes as follows:
The total no. of King in deck of card is 4
The total no. of queen in deck of card is 4.
The total no. of ace in deck of card is 4.
The total no. of jack in deck of card is 4.
Therefore, the number of favorable outcomes is 4+4+4+4= 16
Now, putting values in the above stated formula of probability, we get:
Probability= 16/52=4/13
Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.
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A recent study Indicated that 27% of the 142 women over age 55 in the study were widows
A sample size of [214] to be within 5 % of the true proportion of women over age 55 who are widows and be 900 % confident.
What is standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
We are given that recent study Indicated that 27% of the 142 women over age 55 in the study were widows
Margin of error = 0.05 = E
z-score = z/2 = 1.645
n = 0.27 x 0.73 (1.645/ 0.05)²
n = 213.343
n=214
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Which of the following equations have only one solution? Select all correct answers. x 2 - x - 6 = 0 5 x 2 + 20 x + 20 = 0 9 x 2 - 25 = 0 4 x 2 + 4 x = 0 x 2 + 6 x + 9 = 0
Answer: wutttttttttt
Step-by-step explanation: i jus need points
A building has a height of 125 meters and a length of 80 meters. On a scale drawing of the building, the height is 25 centimeters. What is the length of the building on the scale drawing in centimeters?
The length of the building on the scale drawing is found as 16 centimeters.
Describe the term scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a specific widths is known as a scale factor (bigger or smaller).Scale factor ratios can be written as a colon, 1:2, or as a fraction, 12. A ratio calculates the difference between two values.However, that ratio isn't a scale factor, thus you could not build a ratio for left-handed pupils to all students.For the given data in the question-
Dimensions of the building;
Height of 125 meter length of 80 meters.Dimensions of the drawing of the building;
height is 25 centimetersLet the length be 'x'.Thus, taking ratios of Height to length
125/80 = 25/x
On simplification;
x = 80 x 25 / 125
x = 16
Thus, the length of building on the scale drawing is found as 16 centimeters.
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The enrollment at MSU is described by the function
f(x) = 250x + 6000, where x is the number of years since 2010.
I. Find the enrollment in 2016.
II. In what year will the enrollment reach
10,000?
1) The enrollment in 2016 will be 7500.
2) In 2026 year the enrollment reach 10,000.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function f(x) represents the number of enrollment.
Defined as;
⇒ F(x) = 250x + 6000
Where x represents year since 2010.
(1) Now for finding the enrollment in 2016;
Put x = 2016 - 2010 = 6 in the function
⇒ F(6) = 250x6 + 6000
= 7500
Thus, The required number of enrollment = 7500
(2) Now we have to find the year in which enrollment reach 10,000;
i.e f(x) = 10,000
=> 250x + 6000 = 10000
=> 250x = 4000
=> x = 16
Thus, The required year = 2010 + 16
= 2026 answer.
1) The enrollment in 2016 will be 7500.
2) In 2026 year the enrollment reach 10,000.
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One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.) dy dt = ky 1-y. (b) Solve the differential equation. Assume y(0) = C. y = 1-ce-kt +1 (c) A small town has 1300 inhabitants. At 8 AM, 100 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round the final answer to one decimal place.) hours after the beginning
(a) The differential Equation that is satisfied by y is dy/dt = k × y × (1 - y) ,
(b) Solution of the differential equation assuming y(0) = c is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
In the question ,
Part (a)
let the fraction of people who heard the rumor is = y
So , the fraction who have not heard the rumor is = 1 - y .
the rate of rumor spread is ⇒ dy/dt = k×y(1 - y)
dy/y(1-y) = k.dt ...where k is the constant of proportionality .
So , the differential equation is ..
dy/dt = k × y × (1 - y)
Part (b)
So , 1/y(1-y) = 1/y + 1/(1 - y) ....equation(1)
integrating equation(1) , we get
∫dx/(1 + ax) = ㏑(1 + ax)/a ,....where a is the constant
㏑y + ㏑(1-y)/(-1) = kt + d ,.....where d is the constant
By using , ㏑a - ㏑b = ㏑(a/b) and taking exponential . we get ,
y/(1 - y) = c₁[tex]e^{k\times t}[/tex]
for t = 0 and y(0) = c
solving further , we get
c₁ = c/(1 - c)
So , y = (1-y)c₁[tex]e^{k\times t}[/tex]
y(1 + c₁[tex]e^{k\times t}[/tex]) = c₁[tex]e^{k\times t}[/tex]
y = c₁[tex]e^{k\times t}[/tex]/(1 + c₁[tex]e^{k\times t}[/tex])
taking c₁[tex]e^{k\times t}[/tex] common , and substituting the value of c₁ we get ,
the solution as , y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
Therefore , (a) the differential equation is dy/dt = k × y × (1 - y) and
(b) the solution is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
The given question is incomplete , the complete question is
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.
(a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.)
(b) Solve the differential equation. Assume y(0) = C.
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a) Determine the series of the given function. In the first box after the summation symbol, type in -1 or 1 indicating whether the series is alternating or not.
b) Write out the sum of the first four nonzero terms of the series representing this function.
c) Determine the interval of convergence. The outside boxes require the endpoints and the inside boxes
a) The given function is [tex]$\frac{x^2-2x+2}{(x-1)^2(x+2)}$[/tex]. The series of this function is [tex]$\sum_{n=0}^{\infty}(-1)^n(n+1)x^n$[/tex]. Therefore, the series is alternating (-1).
b) The sum of the first four nonzero terms of the series is [tex]$-1x^1+2x^2-3x^3+4x^4$.[/tex]
c) The interval of convergence is [tex](-2, 1)[/tex]. This is because the denominator [tex]$(x-1)^2(x+2)$[/tex] has a zero at [tex]$x=-2$[/tex] and a zero at [tex]$x=1$[/tex], and the function is undefined at these two points. Therefore, the interval of convergence is the open interval [tex]$(-2, 1)$[/tex].
Convergence is the process of two or more different entities coming together and becoming one. In mathematics, it can refer to a sequence converging to a limit, or the process of a function approaching a finite value as the number of trials approaches infinity. In technology, convergence can refer to the combining of different media types into a single medium, such as the combination of audio, video, and text into a multimedia presentation.
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sketch the region enclosed by the given curves (within the given bounds, if provided) and find its area.
The area enclosed by the curves f(x) and g(x) is 1/12
Integral calculus can be used to compute the area between two curves, which is the region between two intersecting curves.
When we are aware of the equation for two curves and the locations of their intersections, integration can be utilized to determine the area under the curves.
Let our given curves be :
f(x) = x² and g(x) = x³ within the interval [0,1]
Formula to calculate area under these curves is
=> A = [tex]\int\limits^{c}_{a} {|f(x) - g(x)| \, dx[/tex]
Interval is given from 0 to 1
Therefore ,
=> A = [tex]\int\limits^{1}_{0} {[x^2 - x^3]} \, dx[/tex]
Integrating,
=> [tex][\frac{x^3}{3} - \frac{x^4}{4}]^{1}_{0}[/tex]
=> 1/3 - 1/4
=> 1/12 is required area
The given question is incomplete So, I've answered the question in general
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find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius r.
The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
Now, According to the question:
The given sphere is of radius R.
Let h be the height and r be the radius of the cylinder inscribed in the sphere.
We know that:
Volume of cylinder
V = [tex]\pi R^2h[/tex] .....(1)
In right Triangle OBA
[tex]AB^2 + OB^2 = OA^2[/tex]
[tex]R^2 + \frac{h^2}{4} = r^2[/tex]
So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]
Putting the value of [tex]R^2[/tex] in equation (1), We get
V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]
V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex] ....(2)
dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)
For, Stationary point, dV/dh = 0
[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0
[tex](r^2 - \frac{3h}{4} )[/tex] => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]
Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]
[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex] = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0
Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]
Maximum volume is :
[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]
[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
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an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answer: x = 9/10 - 7/10
Step-by-step explanation:
which properties of equality do you use to solve the
equation 15 =x/3 + 18?
The adding property of equality should be used to satisfy the given equation.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
-15 + x/3 = 18
Add 15 on both sides of the equation
So, we have
45 + x = 18 × 3
x = 54 + 45
x = 99
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In AUVW, m/U = (3x - 10)°, m/V = (6x + 5)°, and m/W = (4x - 10)°. What is the value of x?
Answer:
x = 15
Step-by-step explanation:
You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
U +V +W = 180°
(3x -10)° +(6x +5)° +(4x -10)° = 180°
13x -15 = 180 . . . . . . . divide by °, collect terms
13x = 195 . . . . . . . add 15
x = 15 . . . . . . . divide by 13
The value of x is 15.
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
70
Step-by-step explanation:
