a tank truck holds 33.8 kl of oil. How many gallons does it hold

To determine whether the given differential equation is exact, we need to check if it satisfies the condition:

∂M/∂y = ∂N/∂x

where M and N are the coefficients of dy and dx, respectively, in the differential equation:

(2sin(x)cos(y) − 2y^2)dy - (xsin^2(y) - 4x^2)dx = 0

Now, let's find the partial derivatives:

∂M/∂y = 2cos(x)cos(y) - 4y

∂N/∂x = -sin^2(y) - 8x

The equation is exact if ∂M/∂y = ∂N/∂x. Let's check:

2cos(x)cos(y) - 4y = -sin^2(y) - 8x

Rearranging the equation, we get:

sin^2(y) - 2cos(x)cos(y) - 8x + 4y = 0

Since ∂M/∂y = ∂N/∂x, the given differential equation is exact.

To solve the exact differential equation, we need to find a potential function φ(x, y) such that:

∂φ/∂x = M

∂φ/∂y = N

Integrating M with respect to x, we get:

φ(x, y) = ∫(2sin(x)cos(y) - 2y^2)dx

        = 2∫sin(x)cos(y)dx - 2∫y^2dx

        = -2cos(x)cos(y) - 2xy^2 + g(y)

Here, g(y) is the constant of integration with respect to x.

Next, we differentiate φ(x, y) partially with respect to y and equate it to N:

∂φ/∂y = N

-2sin(x)sin(y) - 4xy + g'(y) = -sin^2(y) - 8x

From this equation, we can equate the coefficients of the terms involving y:

-2sin(x)sin(y) - 4xy = -8x

-2sin(x)sin(y) - 4xy + 8x = 0

Comparing the coefficients, we have:

g'(y) = 0

Integrating g'(y), we obtain:

g(y) = c

Here, c is the constant of integration with respect to y.

Finally, the potential function φ(x, y) becomes:

φ(x, y) = -2cos(x)cos(y) - 2xy^2 + c

Therefore, the solution to the given exact differential equation is φ(x, y) = -2cos(x)cos(y) - 2xy^2 + c, where c is an arbitrary constant.

The measure of the angle m∠BEC is equal to 77° using the Angles of Intersecting Chords Theorem

The Angles of Intersecting Chords Theorem states that the angle formed by the intersection of the chords is equal to half the sum of the intercepted arcs, and conversely, that the measure of an intercepted arc is half the sum of the two angles that intercept it.

m∠BEC = (arc AD + arc BC)/2

m∠BEC = (45 + 109)/2

m∠BEC = 154/2

m∠BEC = 77°

Therefore, the measure of angle m∠BEC is equal to 77° using the Angles of Intersecting Chords Theorem

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Answer: Therefore, the price of a wrap is Rs 92.2 and the price of a milkshake is Rs (92.2 + 7) = 99.2.

Step-by-step explanation:

Let's assume the price of a wrap is x (in Rs).

According to the given information, a milkshake costs Rs 7 more than a wrap. So, the price of a milkshake would be x + 7 (in Rs).

The group buys 8 milkshakes and 2 wraps. Since they bought 8 milkshakes, the total cost of milkshakes would be 8 * (x + 7) = 8x + 56 (in Rs).

Similarly, the total cost of wraps would be 2x (in Rs).

The total cost for the lunch is given as Rs 978.

So, we can set up the equation:

Total cost of milkshakes + Total cost of wraps = Total cost of lunch

(8x + 56) + (2x) = 978

Combining like terms:

10x + 56 = 978

Subtracting 56 from both sides:

10x = 922

Dividing both sides by 10:

x = 92.2

Answer:

15 is 7 more than 8.

Step-by-step explanation:

The only plausible answer.

The logical fallacy in the provided statement is Ad Hominem.

The speaker in the statement is attacking the character and appearance of the other person ("dirty, longhaired hippie") instead of addressing the actual issue or argument at hand.

The speaker is making assumptions and judgments about the credibility and honesty of the other person based on their appearance and the type of car they drive, rather than presenting valid evidence or reasoning.

This fallacy diverts attention from the topic being discussed and focuses on personal characteristics or attributes of the individual.

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The area of the Shaded region, when the frame is 1 unit wide, is 20 square units.

The area of the shaded region when one rectangle is framed within another and the frame has a width of 1 unit, we need to calculate the difference between the areas of the outer rectangle and the inner rectangle.

the dimensions of the outer rectangle as length and width, and the dimensions of the inner rectangle as length' and width'. Based on the information provided, the length and width of the outer rectangle are 5 and 7 units, respectively.

The dimensions of the inner rectangle can be found by subtracting twice the width of the frame (1 unit) from the dimensions of the outer rectangle:

Length' = length - 2 * frame width = 5 - 2 * 1 = 3 units

Width' = width - 2 * frame width = 7 - 2 * 1 = 5 units

Now we can calculate the areas of the outer and inner rectangles:

Area of the outer rectangle = length * width = 5 * 7 = 35 square units

Area of the inner rectangle = length' * width' = 3 * 5 = 15 square units

Finally, to find the area of the shaded region, we subtract the area of the inner rectangle from the area of the outer rectangle:

Area of shaded region = Area of outer rectangle - Area of inner rectangle = 35 - 15 = 20 square units

Therefore, the area of the shaded region, when the frame is 1 unit wide, is 20 square units.

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The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer

a. The shape of the cross section is a rectangle.

b. To find the perimeter of the cross section, we need to determine the length of its sides.

In a cube with an edge length of 6 inches, when a plane intersects diagonally, it creates a rectangle with dimensions of the cube's diagonal and half of its edge length.

The diagonal of the cube can be found using the Pythagorean theorem:

diagonal = √(edge length^2 + edge length^2 + edge length^2) = √(6^2 + 6^2 + 6^2) = √(36 + 36 + 36) = √108 ≈ 10.39 inches

The length and width of the rectangle are half of the edge length, which is 6/2 = 3 inches.

Since the cross section is a rectangle, its perimeter is given by:

perimeter = 2 * (length + width) = 2 * (3 + 10.39) ≈ 26.78 inches

Therefore, the perimeter of the cross section, to the nearest hundredth, is approximately 26.78 inches.

c. To find the area of the cross section, we multiply the length and width of the rectangle:

area = length * width = 3 * 10.39 ≈ 31.17 square inches

Therefore, the area of the cross section, to the nearest hundredth, is approximately 31.17 square inches.

Step-by-step explanation:

The value of 7.682/0.072 using long division is 106 25/36

Division is a mathematical operation which involves the sharing of an amount into equal-sized groups.

By solving this, we need to make both the numerator and denominator a whole number by multiplying all by 1000

= (7.682×1000)/0.072 × 1000

= 7682/72

divide through by 2

= 3841/36

Now there is no common factor between the numerator and denominator,

We therefore find the number of 36 in 3841

= 106 remainder 25

therefore 7.682/0.072

= 106 25/36

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For the given graph of f(x), find the following values-

a. lim_x→4⁺  f(x) = ∞      b. lim_ x→-3 f(x) = -2      c. lim_x→6 f(x) = DNE

d. lim_ x→4⁻ f(x) = ∞     e. lim_ x→2⁺ = 2         f. f(-3) = -2  g. lim_x→2⁻ = 1

h. lim_x→-6 = 0.5

i. The type of discontinuity at x = 4 is an infinite discontinuity

j. There is no discontinuity at x=2 because the function is defined at x=2

For the discontinuities;

a. The limit as x approaches 4 from the right side is infinity. Given that  as x approaches 4 from the right side, the y-values of the function continue to increase without bound, while the x-value remains constant at 4.

b. The limit as x approaches -3 is -2

c. The limit as x approaches 6 does not exist given that 6 has a whole and a defined spot.\

d. The limit as x approaches 4 from the left side is infinity. Similar explanation as a.

e. The limit as x approaches 2 from the right side is 2

f. The value of f(x) at x = -3 is -2

g. The limit as x approaches 2 from the left side is 1

h. the limit of the function as x approaches -6 is 0.5

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Answer:

  see attached

Step-by-step explanation:

You want a series of functions and their transformations that will develop a graph of a block capital letter "M", using trig functions.

The block letter M consists mainly of straight lines. To approximate a straight line, we have elected to use the portion of the sine function in the interval [-π/3, π/3] where it is approximately straight, but shows a hint of the sine function.

First, we created a function that moves that segment of the sine function so it is defined between the points (0, 0) and (1, 1). This makes scaling relatively easy.

Then, we created a function that draws that segment between coordinates (a, b) and (c, d).

We used this second function to draw segments between the points we chose for the outline of the left half of the letter.

Finally, we created the right half of the letter by reflecting those functions over the vertical line of symmetry (at x = 4.7). The end result is shown in the first attachment. The function and segment definitions not shown in the first attachment are shown in the second attachment. The f( ) in the Reflection section fills in the horizontal segment between the two halves of the letter.

__

Additional comment

Appending this identifier to the Desmos URL will give you the graph and function definitions we show here. This should eliminate the need to type them, if the result here is suitable.

We have used 13 function definitions that need to be changed if you desire to move the letter to different coordinates or scale it. You could combine these into two piecewise functions (one for the top, one for the bottom), so that translation or scaling could be done more easily.

/calculator/mgh4fgvcge

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Answer:

45 tiles

Step-by-step explanation:

Nan has 30 tiles.

Sato has half the amount Nan does, so you would divide the amount Nan has by two.

30/2=15

Then, you add the two amounts up to find the total amount.

30+15=45 tiles

-1

We can solve in this way,

-3x-5x+8=16

-8x=16-8

-8x=8

x= -8/8

x= -1

Therefore for this equation, x= -1.

Answer:

AM=Dm=6

Step-by-step explanation:

this is a simple diameter....work on it by breaking it down

120.61 ft³ is the volume of the given cylinder.

Given that the diameter of the construction pipe is 3 ft, the radius (r) would be half of the diameter, which is 1.5 ft.

The length or height (h) of the pipe is given as 17 ft.

Plugging these values into the volume formula:

Volume = 3.14159 * (1.5 )² * 17

Calculating the expression:

Volume = 3.14159 * 2.25 * 17

Volume = 120.61 ft³

Therefore, the volume of the cylindrical construction pipe is approximately 120.645 cubic feet.

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h = hours till they're 58 miles apart

Check the picture below.

so they're travelling in opposite directions, however the combined distances is 58 miles at say "h" hours, by the time that happend Hopi has been walking "h" hours and Brittany has also being walking "h" hours too.

Since the combined distance is 58 miles than if Hopi has covered "m" miles then Brittany covered the slack of "58 - m".

[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Hopi&m&15&h\\ Brittany&58-m&14&h \end{array}\hspace{5em} \begin{cases} m=(15)(h)\\\\ 58-m=(14)(h) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{58-(\stackrel{m}{15h})=14h}\implies 58=29h\implies \cfrac{58}{29}=h\implies \boxed{2=h}[/tex]

The expression that will represent each side of the equilateral triangle shapes feild is 19x + 3.

An equilateral triangle is a shape that all the side lengths are of equal, given that the perimeter which is the total sum of the triangle boundary as 30x + 9, then each side is derived as follows:

30x + 9 = 3(10x + 3) {by factorization}

each side of the shape = 3(10x + 3)/3

each side of the shape = 10x + 3

Therefore, the expression that will represent each side of the equilateral triangle shapes feild is 19x + 3.

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The sentence can be completed thus: After 6 minutes, of cycling class, Tariq starts to burn more calories than Jim.

The sentence can be completed by stating that after 6 minutes of a cycling class, Tariq begins to burn more calories than Jim. In the tables, we see that Ji was burning 7 calories per minute while Tariq was burning calories at the rate of 5 per minute.

However, after the 6th minute, Triq burned 15 calories and continued at that rate while Jim maintained his rate. So, after 6 minutes Tariq exceeded Jim.

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Using substitution method, the solution to the simultaneous equations are;

1) x = 4, y = 2

2) x = 2, y = 4.

To solve the given simultaneous equations:

We can use substitution or elimination method. Let's use the substitution method:

From equation 2), we can express x in terms of y:

x = 6 - y

Substituting this value of x into equation 1):

[tex]2(6 - y)^2 - 5(6 - y)y + 2y^2 = 0[/tex]

Expanding and simplifying the equation:

[tex]2(36 - 12y + y^2) - 30y + 5y^2 + 2y^2 = 0\\72 - 24y + 2y^2 - 30y + 5y^2 + 2y^2 = 0\\9y^2 - 54y + 72 = 0[/tex]

Dividing the equation by 9 to simplify it further:

[tex]y^2 - 6y + 8 = 0[/tex]

Factoring the quadratic equation:

(y - 2)(y - 4) = 0

Setting each factor to zero:

y - 2 = 0 ;   y = 2

y - 4 = 0  ;   y = 4

Substituting these values of y back into equation 2) to find the corresponding values of x:

For y = 2:

x = 6 - y = 6 - 2 = 4

So, one solution is x = 4, y = 2.

For y = 4:

x = 6 - y = 6 - 4 = 2

So, another solution is x = 2, y = 4.

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Answer:

Step-by-step explanation:To find the diameter of a circular field given its circumference, we can use the formula:

Circumference = π * Diameter

In this case, the circumference is given as 132m. Plugging in the values into the formula, we have:

132m = π * Diameter

To solve for the diameter, we need to isolate it on one side of the equation. We can divide both sides of the equation by π:

132m / π = Diameter

Using a calculator, we can approximate the value of π as 3.14159. Plugging in this value, we have:

132m / 3.14159 ≈ Diameter

Simplifying the division, we get:

Diameter ≈ 42m

Therefore, the diameter of the circular field is approximately 42 meters

A time that an inequality was needed was when I was recently planning a trip to the beach with some friends. We wanted to make sure we had enough money to cover our expenses, so I used an equation to calculate our total cost.

The equation I used was:

Total cost > (number of people) x (cost per person)

In this case, the number of people was 4 and the cost per person was $100. So, our total cost was $400. I was able to use this equation to help me plan our trip and make sure we had enough money to cover our expenses.

I believe that by following these steps, my friend would be able to successfully plan their trip and avoid overspending.

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Answer:

The linear equation satisfying the given condition is,

[tex]x=t+15[/tex]

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

[tex]x = t + 15[/tex]

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

If Paul runs at the same pace, his rate will be 7 minutes per mile.

We know that, Paul runs 4miles in 28 minutes.

To find out his rate per mile, we need to divide 28 by 4.

Rate per mile,

27÷4

=7.

Therefore, Paul's rate is 7 minutes per mile.

Among the given options, the equation that matches this relationship is B. y = x + 5.

The table shows that as the value of x increases from 1 to 5, the corresponding values of y are 6, 7, 8, 9, and 10.

To determine the equation that represents the relationship between x and y, we can examine the patterns and relationships in the table.

Looking at the values, we can see that the y-values are always 5 more than the x-values.

Therefore, the equation that represents the relationship between x and y is:

y = x + 5

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The length of the arc is approximately 61.68 cm, and the area of the sector is approximately 1509.16 cm^2.

To find the length of the arc and the area of the sector, we can use the formulas related to circles and angles.

Length of the arc:

The formula to find the length of an arc in a circle is given by:

Arc Length = (angle / 360°) × (2πr)

In this case, the angle is 72°, and the radius is 49 cm. Substituting these values into the formula, we get:

Arc Length = (72° / 360°) × (2π × 49 cm)

Arc Length = (1/5) × (2π × 49 cm)

Arc Length = (2/5) × (π × 49 cm)

Arc Length = (2/5) × (π × 49 cm)

Arc Length ≈ 61.68 cm (rounded to the nearest hundredth)

Therefore, the length of the arc is approximately 61.68 cm.

Area of the sector:

To calculate the area of the sector, we need to use the formula:

Sector Area = (θ / 360°) × (π × r^2)

where θ is the central angle in degrees and r is the radius of the sector.

In this case, the central angle is 72° and the radius is 49 cm. Plugging these values into the formula, we have:

Sector Area = (72° / 360°) × (π × (49 cm)^2)

= (1/5) × (π × 2401 cm^2)

≈ (1/5) × (3.14159 × 2401 cm^2)

≈ (1/5) × 7545.8 cm^2

≈ 1509.16 cm^2

Therefore, the area of the sector is approximately 1509.16 cm^2.

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To sketch the graph of the function f(x) = 2cos^2(x) - 3x + 4 for the values of x between 0 and 2, we can follow these steps:

1. Determine key points: Find the critical points and important features of the function within the given range. This includes the x-intercepts, local maxima, and minima.

2. Plot the x-intercepts: To find the x-intercepts, set f(x) = 0 and solve for x. In this case, cos^2(x) = (0 + 3x - 4)/2. Find the values of x where this equation holds true.

3. Identify local maxima and minima: Use calculus or other methods to find the local maximum and minimum points of the function within the given range.

4. Sketch the graph: Once you have the key points, plot them on a graph and connect them smoothly. Pay attention to the shape and behavior of the function.

Since the process of sketching a graph is best done visually, I'm unable to provide an image here. However, by following the steps outlined above, you can plot the graph of f(x) within the range of x between 0 and 2. Remember to label the axes and indicate any important points you have found.

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When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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