What is the volume of this figure? Round your answer to the nearest tenth

The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.

What is a differential equation?

A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.

The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Given,

    [tex]\frac{dy}{dx} = xy^{4}[/tex]

a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]

In quadrant II, the values of x < 0 and the values of y >0.

So  [tex]\frac{d^{2} y}{dx^{2} }[/tex] =  [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.

Therefore the concavity is up for of all solution curves of the given differential equation.

b)

         [tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]

      Now it is given that initial condition is f(4) = -1

   So substituting x =4 and y = -1 is the above equation to find c, we get

        [tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]

Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.

  [tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]

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Step-by-step explanation:

y varies inversely as x=

y= k/xz

-5= k(-5)/6

k= 6

y=6/xz

y=6/5×-8

y= -3/20

Answer:

[tex] \frac{7}{8} \times \frac{4}{5} = \frac{7 \times 1}{2 \times 5} \\ = \frac{7}{10} [/tex]

Answer: 0.15%

Step-by-step explanation: edmentum

Answer:

Step-by-step explanation:

the answer is 0.15

The average rate of change is equivalent to 2.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is the table as shown below -

[x] :  0  1  2  3  4

[y] :  -2 -3 1  3  6

The rate of change in the interval 0 < x < 4 is -

AROC = (6 + 2)/(4 - 0)

AROC = 8/4

AROC = 2

Therefore, the average rate of change is equivalent to 2.

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Answer:

g(x) - f(x) = 3^x - 9 - (5x - 1) = 3^x -5x - 8

Answer:

Understand Given kite ABCD and isosceles trapezoid WXYZ, complete a two-​column proof to show that ... 9. △ADW ≅ △CDZ. 9. SAS. 9. Apply In Bhutanese architecture, the faces of buildings are trapezoids. If the row of decorative brick shown is 28.5 feet wide, what is the width of the base of the building? 25 ft. 16 ft. 16 ft.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

4 i think

Step-by-step explanation:

i think 2 but i dont know for sure ahahahaha

Answer:

not directly proportional

Step-by-step explanation:

if the cost is directly proportional to number of rolls , then the unit cost for both will be equal.

first

one roll costs $1.99 ÷ 6 = $0.33 ( to 2 decimal places )

second

one roll costs $2.69 ÷ 9 = $0.30 ( to 2 decimal places )

since the unit costs are different there is not a directly proportional relationship.

Answer:

No because to buy nine rolls would be $2.69 but to buy six and then three to make nine then it would be $2.985 which is more expensive.

Step-by-step explanation:

$1.99 divided by 2 = 0.995

$1.99 + 0.995 = $2.985

$2.985 > $2.69

Two-way table showing meal pairings with frequency of salad, soup, chicken and fish.

Meal Pairing Salad Soup Chicken Fish

Frequency  46.          32.           ?. 35

To calculate the frequency of chicken, subtract the frequency of salad and fish from the total of 78 meals.

Frequency of chicken

= 78 - 46 - 35

= 27.

Meal Pairing Salad Soup Chicken Fish

Frequency 46.           32.            27. 35

The total number of meals served is 78. Of the 46 meals that included salads, 21 also included fish. This means that the frequency of fish is 35. The frequency of chicken can be calculated by subtracting the frequency of salad and fish from the total number of meals. The frequency of chicken is 27. The two-way frequency table representing this situation is as follows: Meal Pairing, Salad, Soup, Chicken, Fish; Frequency, 46, 32, 27, 35. This table shows that there were 46 meals with salad, 32 meals with soup, 27 meals with chicken, and 35 meals with fish.

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The table that is a justification for the given solution to the system of equations is table 1

The two linear equations are

y=4x-9 and

y=2x-5

We that the following points for x : -1, 0, 1, 2, 3

When we substitute the values in the two equations we will have

x           y₁              y₂

-1         -13             -9

0           -9             -5

1             -5            -3

2            -1              - 1

3            3                1

Conclusively the values of y₁, and y₂ are shown in the table above

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Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.

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Answer:

42000

Step-by-step explanation:

Original price (before VAT) is 100% of price.

VAT is 13%, of the original price so final price is 113% of original price.

113% = 1.13

original price = 47460/1.13 = 42000

Answer:

3:1 or 3

Step-by-step explanation:

the left triangle is scaling up to the right triangle. 5/15 is 1/3

7/21 is 1/3

4/14 is 1/3

since it is scaling UP, the scale factor is 3:1

The measure of the angle ∠C in the triangle ABC can be gotten using tan m∠C = 2

An equation shows how two or more numbers and variables are related to each other.

On the other hand, trigonometric ratios are used to show the relationship between the sides and angles of a right angled triangle.

The basic equations of the trigonometry ratios are

Using the above as a guide, and the given triangle:

We have:

tan m∠C = opposite/adjacent

Substitute the known values in the above equation, so, we have the following representation

tan m∠C = 6/3

Evaluate

tan m∠C = 2

Hence, the true equation is (d) tan m∠C = 2

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Answer:

38 bows

Step-by-step explanation:

50 ÷ 1.3 ≡ 38 6/13

38 × 1.3 = 49.4

Since you cant make 6/13 of a ribbon, Elizabeth would be able to make 38 bows.

Answer:e5

Step-by-step explanation:

Here you go

Answer:

10^14

Step-by-step explanation:

The expression (10^2)^7 uses an exponent rule known as power raised to a power.

The rule states that when you multiply a base and its exponent to a power, you multiply the inner exponent and the outer exponent:

[tex](a^m)^n\\a^m^n[/tex]

Thus, we have

[tex](10^2)^7\\10^2^*^7\\10^1^4[/tex]

Answer:

4.88

Step-by-step explanation:

Hops This Helps!

To convert 4 7/8 into a decimal, we first need to turn the mixed number into an improper fraction.

In order to turn the mixed number into an improper fraction, we need to multiply the whole number by the denominator and add it up with the numerator.

[tex]4\dfrac{7}{8}[/tex]

[tex]4\times8=32+7=39[/tex]

Now, put that sum over the denominator:

[tex]\dfrac{39}{8}[/tex] (improper)

Now, to turn the improper fraction into a decimal, we need to divide the numerator by the denominator:

[tex]39\div8[/tex]

[tex]=\fbox{4.875}[/tex]  (final answer)

Answer:

Step-by-step explanation:

Here's the complete question:

It cost Nike $55.00 to make the Kyrie 5, but it is selling for $130.19. Calculate the markup/percent Increase for the shoe. On Amazon, you found the same shoe for $108. What is the percent difference between the price of the original shoe and the price of the amazon shoe

The percentage Increase of the shoe will be:

= Selling price - Cost/ Cost × 100

= (130.19 - 55.00) / 55.00 × 100

= 75.19 / 55.00 × 100

= 136.71%

The percent difference between the price of the original shoe and the price of the amazon shoe will be:

= (130.19 - 108)/130.19 × 100

= (22.19 / 130.19) × 100

= 17%

Answer:

(2) y = -2x² + 6x - 6

Step-by-step explanation:

Notice that the only leading coefficient that is negative is in the 2nd equation. Hence, the shape of the parabola will be upside down, making it have a maximum.

Answer:

It is best it you guess. What grade are you in

Step-by-step explanation:

Answer:

I think <BCH would also be 108 since its corresponding angles

and with <MNJ would also be 97 since its alternate exterior angles

Answer:

912 cm²

Step-by-step explanation:

Formula for area of triangle: 1/2bh

So you'll first multiply the base by the height of the triangle

48 x 38 = 1,824

Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)

1,824 ÷ 2 = 912

Answer:

240

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

5x-3=-15

Step-by-step explanation:

Answer:

SW =XW and ST=XU and UW=TW

Step-by-step explanation:

All are true and correct since the two triangles are congruent

Answer:

Explanation is^{}

in a file

bit.^{}

ly/3gVQKw3

Answer:

22cm  

the ans is in the picture with the steps  

(hope it helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

21.98 rounded = 22

Step-by-step explanation:

There are two formulas to find circumference either C=2πr or C=πd.

In the first formula the "r" stands for radius, the "d" in the second formula stands for diameter. Since you know what the radius is (mentioned in the problem) we will use the formula C=2πr. You will substitute "r" for 3.5, it will look like this C=2π3.5. Now you will multiply 3.5x2=7. Now you are left with C=7π. Now you would multiply 7 times π (you could use 3.14 as a substitution for π) 7x3.14=21.98. Since you need to round to the nearest tenth, your answer would be 22.