Find the maximum volume of a cylindrical soda can such that the sum of its height and its circumference is 150 cm.

In table 9.1, the marginal cost of producing the seventh unit of output is equal to $8.
Marginal cost refers to the additional cost incurred when producing one more unit of output. To find the marginal cost of producing the seventh unit of output, follow these steps:

1. Locate the total cost column in table 9.1.
2. Identify the total cost of producing 6 units of output.
3. Identify the total cost of producing 7 units of output.
4. Subtract the total cost of producing 6 units from the total cost of producing 7 units.

The difference you get from step 4 is the marginal cost of producing the seventh unit of output.

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Answer:

4.020

4.030

4.021

4.006

Step-by-step explanation:

Answer:

5 1/4 mph

Step-by-step explanation:

21 divided by 4= 5 1/4

Answer:

Average Speed = 5.25 mph

Step-by-step explanation:

Given:

Distance = 21 miles

Time = 4 hours

Required:

Average Speed

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

Average Speed = 21/4

Average Speed = 5.25 mph

Answer:

a₁ = - 256 , r = - \(\frac{1}{4}\)

Step-by-step explanation:

The nth term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

Given

\(a_{n}\) = - 256 \((-\frac{1}{4}) ^{n-1}\) , then by comparison

a₁ = - 256 and r = - \(\frac{1}{4}\)

Equivalent expressions are expressions that have equal values

The value of x is 25/6

From the question, the values of ac and ec are equivalent

So, we have:

8x - 14 = 2x + 11

Collect like terms

8x - 2x = 14 + 11

Evaluate the like terms

6x = 25

Divide both sides by 6

x = 25/6

Hence, the value of x is 25/6

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Answer:

(6, 97) is the outlier.

Step-by-step explanation:

When we have a data set:

x: x₁, x₂, x₃, ..., xₙ

y: y₁, y₂, y₃, ..., yₙ

Each one of the pairs (x₁, y₁), (x₂, y₂), etc, is an ordered pair that belongs to the data set.

Usually, these values are distributed in some way that, we assume, is normalized. So if one of these ordered pairs is really different from the others, then that pair is called an "outlier".

In the data set, we have:

Number of homework completed vs Score assigned.

You can see that, as the number of homework completed increases, also does the score

For example, for the smaller number of homework completed, (5) the score is 67, the minimum score.

And as the number of homework completed reaches to 10, the score increases to 90 or 98.

But there is an outlier there, you can see that a student that only completed 6 times the homework, has a score of 97 (one of the largest scores) (this score is more than all the scores for the students with 6, 7, 8 and 9 completed homeworks) so we can conclude that this one is the outlier.

(6, 97) is the outlier.

Answer:

By the vertical Angles Theorem , < 1 = <2 and < 4 = <3.  <1 = <4 is given , so <2 = <3 by the transitive property of Congruence.

Step-by-step explanation:

By the vertical Angles Theorem , < 1 = <2 and < 4 = <3.  <1 = <4 is given , so <2 = <3 by the transitive property of Congruence.

The transitive property of congruence states that two objects that are congruent to a third object are also congruent to each other

1 =4

and 4=3

and 1=2

so 2=3

Answer:

no tengo idea

Step-by-step explanation:

The first derivative of the given function is f'(x)=2x-3 and the value is -1. Therefore, the correct answer is option C.

The given function is f(x)=x²-3x+5.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Here, first derivative of the given function is as follows

f'(x)=2x-3

Now, x increases from 1 to 1.

f'(1))=2(1)-3

= -1

Therefore, the correct answer is option C.

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Answer:

\(a = \frac{49}{2}\)

\(b = 18\)

Step-by-step explanation:

Lets focus on the third equation to find a:

50 - 2a = 1

Add 2a to both sides of the equation:

50 - 2a + 2a = 1 + 2a

50 = 1 + 2a

Subtract 1 from both sides of the equation:

50 - 1 = 1 + 2a - 1

49 = 2a

Divide both sides by 2:

\(\frac{2a}{2} = \frac{49}{2}\)

\(a = \frac{49}{2}\)

Now substitute in the know a variable into the first equation:

\(2a - 3b = -5\)

\(49 - 3b = -5\)

Add 3b to both sides:

\(49 - 3b + 3b = -5 + 3b\\49 = -5 + 3b\)

Add 5 to both sides:

\(49 + 5 = -5 + 3b + 5\)

54 = 3b

Divide both sides by 3:

\(\frac{53}{3} = \frac{3b}{3}\)

\(b = 18\)

c cannot be solved as there is no c variable.

Hope this helps!

As per the angle of elevation, the plane’s height above ground level at the time of the bird strike is 880 meters

To find the value of d, we can use the cosine function, which relates the adjacent side of a right triangle to its hypotenuse. We can write:

cos(7.7°) = d/6.44

To solve for d, we can rearrange this equation as follows:

d = 6.44 * cos(7.7°)

Now we have all the information we need to calculate the height of the plane above the ground at the time of the bird strike. We can substitute the value of d into our equation for h:

h = (6.44 x cos(7.7°)) * tan(7.7°)

Using a calculator, we find that h is approximately 0.88 kilometers, or 880 meters. Therefore, the plane was about 880 meters above the ground at the time of the bird strike.

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Complete Question:

On January 15, 2009 at approximately 3:30 PM (ET), US Airways flight 1549 made an emergency water landing as a result of a bird strike (a large flock of Canadian geese) in the Hudson River in New York. There were 150 passengers on board and five crew members. There were no fatalities and only minor injuries. Passengers were assisted by emergency first responders from the New York/New Jersey area as well as by ferry companies.

The plane left LaGuardia airport at 3:25pm and about 2 minutes later struck a flock of birds (3:27.11pm). The plane was 4 miles from LaGuardia airport and was ascending at an angle of 7.7° degrees.

Calculate the plane’s height above ground level at the time of the bird strike.

To solve x² + 6x - 8 < 0 using a table, by graphing, and algebraically:Using a tableTo solve x² + 6x - 8 < 0 using a table, we make a table with the expression on one side and zero on the other side. Then we factorize the quadratic and solve for the values of x such that the inequality holds.x² + 6x - 8 < 0x² + 6x - 8 = 0(x + 4)(x - 2) < 0When the expression on the left side of the inequality is zero, then (x + 4)(x - 2) = 0.

Thus, x = -4 or 2. We now insert these values in the table.We can therefore say that the solution of x² + 6x - 8 < 0 is (-4, 2).Using graphingTo solve x² + 6x - 8 < 0 using graphing, we begin by sketching the parabola of x² + 6x - 8 = 0. Next, we draw a horizontal line at y = 0 (x-axis) and examine where the curve is below the x-axis. We find the range of x where the inequality holds by observing the part of the curve below the x-axis.

The range is the set of values of x where the inequality is true.Graphical SolutionAlgebraicallyTo solve x² + 6x - 8 < 0 algebraically, we make use of the quadratic formula x = -b ± √(b² - 4ac)/2a. We then plug in the values of a, b, and c into the formula and solve for the values of x that satisfies the inequality.x² + 6x - 8 < 0a = 1, b = 6, c = -8x = (-6 ± √(6² - 4(1)(-8)))/2(1)x = (-6 ± √(60))/2x = (-6 ± 2√(15))/2x = -3 ± √(15)We can therefore say that the solution of x² + 6x - 8 < 0 is (-4, 2). This is true for all the methods used above.

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Answer:

x = 32

Step-by-step explanation:

(41)² - (40)² = 1681 - 1600

= 81

\( \sqrt{81} = 9\)

|EC| = 9

x = 41 - 9

x = 32

The 2 triangles share 2 sides of common lengths and a common angle between these sides, therefore they are congruent.

Answer:

880 feet per hour.

Step-by-step explanation:

26 inches to foot = 2.2

9 seconds to hour =  0.0025

2.2/0.0025 = 880 feet per hour.

If you need any more help please let me know and i will make a video for you.

Answer:

The oceans – the largest CO2-reservoir

Step-by-step explanation:

The oceans absorb substantial amounts of carbon dioxide, and thereby consume a large portion of this greenhouse gas, which is released by human activity.

The ocean is a natural 'reservoir' for dissolved carbon dioxide.

We have,

The _____________  is a natural 'reservoir' for dissolved carbon dioxide.

Oceans absorb large amounts of carbon dioxide consuming a large portion of greenhouse gas such as carbon dioxide which is released by human activity.

Oceans are the largest carbon dioxide reservoir.

Thus,

The ocean is the answer.

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The amount Brayden will have after 1 year is $30 and 99 cents by Simple Interest .

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. 

Simple interest is calculated by multiplying the principal by the time, interest rate, and time period. "Simple Interest = Principal x Interest Rate x Time" is the written formula. The simplest formula for calculating interest is this one.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.

Principal amount = $30

interest rate = 3.3%

Time = 1 year

Simple Interest = (principal * rate * time )/100 = 30 * 3.3 /100 = $.99

So the amount Brayden will have after 1 year is $30 and 99 cents by Simple Interest .

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Answer:

c

Step-by-step explanation:

edg 21 ^u^

Answer:

The person above me is correct. :D

Step-by-step explanation:

Answer:

80 = x

Step-by-step explanation:

The base angles are the same if the side lengths are the same

The unmarked angle is 50 degrees

The sum of the angles is a triangle is 180 degrees

180= 50+50+x

180 = 100 +x

180 -100 = 100+x-100

80 = x

Answer:

80°

Step-by-step explanation:

In an isosceles triangle, if the two sides are the same length, then the two angles formed on the base line are equal.

The other angle on the base line is also equal to 50°.

Angles in a triangle add up to 180°.

x° + 50° + 50° = 180°

x° + 100° = 180°

x° = 180° - 100°

x° = 80°

Answer:

B

Step-by-step explanation:

2.5 is smaller than 2.25 because 2.5 = 2.50

15 8/9 less than the product of 5 and a number b​:

Answer:

Step-by-step explanation:

At the flower store they told her that the vase should be filled 2/3 for the flowers to last the longest. Her cylinder vase has a radius of 3in and a height of 8in. How much water should Mary pour into the vase? Follow • ... Get the right answer, fast. ... No packages or subscriptions, pay only for the time you need.

Green's theorem can be used to evaluate the line integral along the triangular path from (0, 0) to (2, 0) to (2, 1) to (0, 0) of the function xy dx + y^3 dy.

Green's theorem relates a line integral around a closed curve to a double integral over the region enclosed by the curve. The theorem states that the line integral of a vector field F along a simple closed curve C is equal to the double integral of the curl of F over the region D enclosed by C. In this case, we are given the line integral of the function xy dx + y^3 dy along the triangular path.

To evaluate the line integral using Green's theorem, we first need to find the curl of the vector field associated with the function. The curl of F = (P, Q) is given by ∂Q/∂x - ∂P/∂y, where P and Q are the components of the vector field.

In this case, P = xy and Q = y^3. Taking the partial derivatives, we get ∂Q/∂x = 0 and ∂P/∂y = x. Therefore, the curl of F is 0 - x = -x.

Now, we can evaluate the double integral of the curl of F over the region D enclosed by the triangular path. The region D is a triangle with vertices (0, 0), (2, 0), and (2, 1). By integrating -x over this region, we can find the value of the line integral.

Performing the double integral and simplifying the result will give us the final answer for the line integral along the given path using Green's theorem.

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Answer:

Point form: (5,-3)

Equation form: x=5, y=-3

Step-by-step explanation:

Hope this helps <3

The sum of the given series ∑ \((cos(n) / 2^n)\)  from n=1 to infinity converges absolutely.

To determine whether the series converges absolutely, conditionally, or not at all, we will analyze the given series:
∑ \((cos(n) / 2^n)\) from n=1 to infinity.

Step 1: Test for absolute convergence: We can test for absolute convergence by applying the Ratio Test to the absolute value of the terms in the series. We first consider the series: ∑ \(|cos(n) / 2^n|\) from n=1 to infinity.

Step 2: Apply the Ratio Test: For the Ratio Test, we compute the limit as n approaches infinity of the ratio of consecutive absolute terms: lim (n→∞) \((|cos(n+1) / 2^(n+1)|) / (|cos(n) / 2^n|)\)
= lim (n→∞) \((|cos(n+1)| / |cos(n)|) * (2^n / 2^(n+1))\) = lim (n→∞) \((|cos(n+1)| / |cos(n)|) * (1/2)\)

Since the cosine function has values between -1 and 1, the limit of the ratio of consecutive cosine terms exists but does not have a specific value. However, since we're multiplying the limit by 1/2, which is less than 1, the Ratio Test concludes that the series converges absolutely.

So, the given series ∑ \((cos(n) / 2^n)\) from n=1 to infinity converges absolutely.

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The difference between the height (h) and the slant height (L) of the pyramid is that the height measures the vertical distance from the apex to the base, while the slant height measures the length along the surface of the pyramid from the apex to any point on the base's edge.

The height (h) of a pyramid refers to the perpendicular distance between its base and its apex. It is the vertical measurement from the highest point of the pyramid to the base. In the given context, the specific value of the height (h) is not provided, so we cannot determine its exact value.

On the other hand, the slant height (L) of a pyramid refers to the length of the line segment that connects the apex of the pyramid to any point on the edge of its base. The slant height is measured along the surface of the pyramid, forming an inclined line from the apex to the base. In this case, the slant height is given as 10.50 units.

Therefore, the difference between the height (h) and the slant height (L) of the pyramid is that the height measures the vertical distance from the apex to the base, while the slant height measures the length along the surface of the pyramid from the apex to any point on the base's edge.

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Two consecutive odd numbers are:

n and n+2

The sum of two consecutive odd numbers

the sum of two consecutive odd numbers is 72:

Use this equation to find the value of n:

n=35

n+2=35+2=37

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)