assume x and y are functions of t. evaluate dx/dt for 4xy-3x4y^3=-168, with the conditions dx/dt=-8, x=4, y=-3.

Total time for whole journey can be calculated by adding the three parts of the journey which would give answer as 2.5 hours.

What is a fraction?

The components of an entire or group of items are represented by fractions. A fraction consists of two components. The numerator is that the figure at the top of the line. It details the amount of equal portions that were taken from the total or collection. The denominator is that the figure that appears below the line.

Main Body:

total time = 20 minutes + 40 minutes + 1 hour 30 minutes

                = 2.5 hours or 5/2 hours.

Hence total time for journey is 2.5 hours.

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Answer:

The answer is 7 socks.

Step-by-step explanation:

To ensure one matching pair, you need to pull out 4 socks. If none of the first three match, the fourth one will guarantee a matching pair.

You will then need to pull out 3 more socks, for a total of 7 socks, to ensure two matching pairs.

Answer:

Q² (R³,S)

Step-by-step explanation:

Answer:

146 since the angle is a central that its measure is equal to the arc

Answer:  3.2 yd

Step-by-step explanation:

Notice that TWV is a right triangle.  

Segment TU is not needed to answer this question.

∠V = 32°, opposite side (TW) is unknown, hypotenuse (TV) = 6

\(\sin \theta=\dfrac{opposite}{hypotenuse}\\\\\\\sin 32=\dfrac{\overline{TW}}{6}\\\\\\6\sin 32=\overline{TW}\\\\\\\large\boxed{3.2=\overline{TW}}\)

Answer: Multiply 7 and 14

Step-by-step explanation: to find the answer you multiply 7 and 14 you get 98$ which is the total cost pls consider making me brainliest if im correct i really hope i am :)) make sure to tell me if im wrong

Answer:

Step-by-step explanation:

Step 1: Assume your variables

We can see that the money is being saved on a weekly basis.

So, let's assume the number of weeks for which the money is being saved to be the variable: \(x\)

And let's consider the total cost after \(x\) weeks to be: \(y\)

Step 2: Manipulate the variables according to the information given

$7 is being saved each week.

So, in one week, \(\$7\) is saved.

In two weeks, \(\$(7\times 2)\) is saved.

So, in \(x\) weeks, \(\$(7\times x)\) is saved.

Step 3: Create the equation

In words, the equation will be as such:

Total cost after \(x\) weeks = Amount saved in \(x\) weeks

Upon representing this mathematically, we get:

\(y=7\times x\\y=7x\)

The equation  \(y=7x\)  can be used to find the total cost.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold \mathbb {Z}.

Answer:x=2+2√3 OR x=2−2√3

Step-by-step explanation: The answer is too long to write down. For complete step-by-step, go to mathpapa algebra calculator and type in your question. It would be a bit too long and difficult to write down.

Hope this helps

BRAINLIEST please?

Answer:

195 m.

Step-by-step explanation:

The time for the  sound waves to reach the fish is 0.26/2 = 0.13 seconds.

Distance = speed * time

= 1500 * 0.13

= 195 m.

Answer:

x=20

Step-by-step explanation:

12.5/1.25=10

This means that to get from Figure B to A, you would need to divide by 1.25

So to get from Figure A to B, you would have to multiply by 1.25

16*1.25=20

Answer:

B

Step-by-step explanation:

m=n and C=D, as CD is an nxn matrix and In and Im have dimensions nxn and mxm, respectively.

To prove that m=n, let us consider the dimensions of the matrices involved. The matrix product CD has dimensions nxm times mxn, which gives an nxn matrix. On the other hand, the identity matrices In and Im have dimensions nxn and mxm, respectively. Therefore, for the products CA and AD to be well-defined, we must have m=n.

Now, let us show that C=D. We have:

CA = In (given)

AD = Im (given)

Multiplying both sides of the first equation by D on the right and both sides of the second equation by C on the left, we get:

CAD = D (from CA=In)

CAD = C (from AD=Im)

Since CAD is equal to both D and C, we have D=C. Therefore, the matrices C and D are equal, and we have proved that m=n and C=D.

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Answer:

7. m^21n^27

8. a^21b^28

Step-by-step explanation:

7. since m^7 raised to the 3rd power = m^( 7 * 3 ) = m^21

then  n^9 raised to the 3rd power = n^( 9 * 3 ) = n^27

your answer is m^21n^27

8. a^3 raised to the 7th power = a( 3 * 7 ) = a^21

b^4 raised to the 7th power = b( 4 * 7 ) = b^28

your answer is a^21b^28

hope this helps:)

Answer:

h = 0.139725

Step-by-step explanation:

Volume of a Cylinder Formula: V = πr²h

You are given V = 20 and r = 6.75.

20 = π(6.75)²h

20/45.5625π = h

h = 0.139725

I'm not sure if this is correct or not.

Answer:

≈1.4 m

Step-by-step explanation:

V= 20 l= 20 000 cm³

d= 13.5 cm ⇒ r= 13.5 cm / 2= 6.75 cm  (assume it is cm)

V= πr²h

h= V/πr²= 20000/3.14*6.75² ≈ 140 cm= 1.4 m

Answer:

\(a) \: 2. \sqrt{ - 4} = 2.2i = 4i = 0 + 4i \\ b) \: 3i.2i = 6 \sqrt{ - 1} \sqrt{ - 1} = - 6 + 0i \\c) \: {i}^{4} = \sqrt{ - 1} .\sqrt{ - 1} .\sqrt{ - 1} .\sqrt{ - 1} \\ = - 1 \times - 1 = 1 + 0i \\ d) \: 4 - 3 \sqrt{ - 1} = 4 - 3i\)

The complex form of the numbers will be,

a). 0+ 4i

b). -6 + 0i

c). 1 + 0i

d). 4-3i

A complex number is a number system that extends the real numbers by a specific element labelled I known as the imaginary unit, and satisfying the equation i²=-1; any complex number may be represented in the form a + bi, where a and b are real numbers.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The complex numbers will be solved as,

a). 2 x √-4 = 0+ 4i

b). 3i x 2i = -6 + 0i

c). i⁴ = 1 + 0i

d). 4 - 3√-1 = 4-3i

Therefore, the complex numbers are solved in this way.

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Answer:

A=9

C=9

B=18

\(d = 9 \sqrt{3 } \)

The numerical length of PQ is 20

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.

Given that the line segments are: -

OQ=11  O P = 9

The numerical value of PQ will be calculated as below.

OP+OQ=PQ

11+9=PQ=11+9=PQ

Therefore PQ=20=PQ

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The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

The given equation represents the motion of a mass connected to a spring with viscous friction. To plot the displacement, y(t), we need to solve the differential equation. With initial conditions y(0) = 0, we can find the solution using the Laplace transform. After solving the equation, we can plot y(t) for t < 0 and t ≥ 0 separately. For t < 0, the applied force, f(t), is zero, so the mass will not experience any external force and will remain at rest. For t ≥ 0, the applied force is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position.

To solve the given differential equation, we can start by finding the characteristic equation by setting the coefficients of y, its derivative, and its second derivative to zero:

s^2 + 18s + 102 = 0.

Solving this quadratic equation gives us the roots s1 = -3 + 3i and s2 = -3 - 3i. These complex roots indicate that the mass will undergo damped oscillations.

Using the Laplace transform, we can solve the differential equation and obtain the expression for Y(s), the Laplace transform of y(t):

(s^2 + 18s + 102)Y(s) = F(s),

where F(s) is the Laplace transform of f(t). Since f(t) = 10 for t ≥ 0, its Laplace transform is F(s) = 10/s.

Solving for Y(s) gives us:

Y(s) = 10 / [(s^2 + 18s + 102)].

To find y(t), we need to inverse Laplace transform Y(s). Using partial fraction decomposition, we can express Y(s) as:

Y(s) = A / (s - s1) + B / (s - s2),

where A and B are constants to be determined. After finding A and B, we can inverse Laplace transform Y(s) to obtain y(t).

With the given initial condition y(0) = 0, we can solve for A and B by setting up equations using the initial value theorem:

A / (s1 - s1) + B / (s1 - s2) = 0,

A / (s2 - s1) + B / (s2 - s2) = 0.

Solving these equations will give us the values of A and B. Finally, we can substitute these values back into the inverse Laplace transform of Y(s) to obtain y(t).

For t < 0, since the applied force f(t) is zero, the mass will not experience any external force. Therefore, y(t) will remain at its initial position, y(0) = 0.

For t ≥ 0, the applied force f(t) is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position. The displacement, y(t), will depend on the properties of the mass, the spring, and the viscous friction. The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

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The total number of ways or permutations of the letters of the word ANGUISHED be arranged in a row if A and N must remain next to each other are 80640.

According to the given question.

We have a word ANGUISHED.

Total number of letters in the word ANGUISHED is 9.

If we AN remains next to each other, then we will consider only 8 letters (considering AN as a single letter).

Now, "AN" can be arranged in 2 differents ways AN and NA.

And the remaining  8 letters can be arranged in 8!

Therefore, the total number of ways or permutations of the letters of the word ANGUISHED be arranged in a row if A and N must remain next to each other

= 8! × 2

= 80640

The total number of ways or permutations of the letters of the word ANGUISHED be arranged in a row if A and N must remain next to each other are 80640.

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Rationalizing the surd gives 4

From the information given, we have that;

\(\frac{5\sqrt{2} }{3\sqrt{2} } } - \frac{\sqrt{2} }{\sqrt{2} }\)

In order to simplify the surd form, we need to rationalize;

\(\frac{5\sqrt{2} * \sqrt{2} }{\sqrt{2}* \sqrt{2} } - \frac{\sqrt{2} * \sqrt{2} }{\sqrt{2}* \sqrt{2} }\)

Multiply through

\(\frac{5\sqrt{4} }{\sqrt{4} } - \frac{\sqrt{4} }{\sqrt{4} }\)

Find the squares

\(\frac{5(2)}{2} - \frac{2}{2}\)

\(\frac{10}{2} - \frac{1}{1}\)

5 - 1

= 4

Thus, rationalizing the surd gives 4

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The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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Answer:

radius = 8 ft

Step-by-step explanation:

area = 64π ft²

radius = 8 ft

Answer:

12

Step-by-step explanation:

average rate

\(=\frac{g(-1)-g(-7)}{-1-(-7)} \\=\frac{[12(-1)+1]-[12(-7)+1]}{-1+7} \\=\frac{[-12+1]-[-84+1]}{6} \\=\frac{-11+83}{6} \\=\frac{72}{6} \\=12\)

The solutions for 1 and 2 are given below.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

(1). Given:

LJ/JN = MK/KP

So,

9/JN = 18/6

JN = 3 unit.

(2). Polygon JKLM is similar to Polygon PQRS.

So,

(e). The proportionality ratio for sides,

JK/PQ = KL/QR = LM/RS = JM/PS

(a). The scale factor PQRS to JKLM,

= 4/5

(b). The value of x:

x/20 = 20/25

x = 16

The value of y:
y/10 = 25/20

y = 12.5

(c). The perimeter of JKLM = 58 units.

The perimeter of PQRS = 62.5 units.

(d). The ratio of the perimeter PQRS to JKLM = 62.5/58

(e). The proportionality ratio for sides,

JK/PQ = KL/QR = LM/RS = JM/PS

Therefore, all the required values are given above.

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Answer:

o.o326

Step-by-step explanation:

when dealing with negative exponents you move the decimal to the left

The time taken to reach the bottom when the person skies down will be 22.5 seconds.

It should be noted that the person is skiing down a 1,350 meter ski slope at 60 meters per second.

There, t represent your skiing time in seconds.

The appropriate expression to illustrate the scenario will be:

1350 - 60t = 0

Therefore, 60t = 1350

t = 1350/60

t = 22.5

The time taken to each the bottom will be 22.5 seconds.

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The correct answer is A. The statement is false. If λ+5 is a factor of the characteristic polynomial of A, then −5 is an eigenvalue of A. In order for 5 to be an eigenvalue of A, the characteristic polynomial would need to have a factor of λ−5. This is because the eigenvalues of a matrix A are the roots of its characteristic polynomial, which is given by det(A-λI) where I is the identity matrix.

If λ+5 is a factor of the characteristic polynomial, then det(A-(λ+5)I)=0. This implies that A has an eigenvector corresponding to eigenvalue -(λ+5), which is -5 in this case. Therefore, 5 is not necessarily an eigenvalue of A. Moreover, the diagonal of A-λI contains the eigenvalues of A, not λ+5 as mentioned in option B. Option C is also incorrect because having λ+5 as a factor of the characteristic polynomial does not necessarily mean that λ=5 is a root of the polynomial. Option D is also incorrect because the factors of the characteristic polynomial are used to determine both the eigenvalues and eigenvectors of a matrix.

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The statement is false. If λ+5 is a factor of the characteristic polynomial of A, then it means that λ=-5 is an eigenvalue of A, not 5. This is because the characteristic polynomial is defined as det(A-λI), where I is the identity matrix and det is the determinant function. Setting λ+5 as a factor means that det(A-(-5)I) = 0, which implies that -5 is an eigenvalue of A.

Therefore, in order for 5 to be an eigenvalue of A, the characteristic polynomial would need to have a factor of λ-5, not λ+5. It is also important to note that while the characteristic polynomial is useful for determining both the eigenvalues and eigenvectors of a matrix, the factors of the polynomial only determine the eigenvalues, not the eigenvectors.

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The solution of the differential equation y - 3y' + 2y" = e³x is: y = c₁eˣ + c₂e²ˣ + 1/8 e³x

The given differential equation is:y - 3y + 2y" = e³xWe are to solve the above differential equation using undetermined coefficient method. The characteristic equation is given as:r² - 3r + 2 = 0Simplifying the above equation, we get:(r - 1)(r - 2) = 0

Hence, the roots of the above equation are:r₁ = 1 and r₂ = 2.The general solution of the differential equation y" - 3y' + 2y = 0 is given as:y = c₁eᵣ₁ˣ + c₂eᵣ₂ˣ Where, c₁ and c₂ are the constants of integration. Substituting the values of r₁ and r₂ in the above general solution, we get:y = c₁eˣ + c₂e²ˣ...........(1)

Now, we need to find a particular solution of the differential equation:y - 3y' + 2y" = e³xAssuming a particular solution as: yₚ = Ae³xwhere, A is the constant of proportionality.Differentiating yₚ w.r.t x, we get:y'ₚ = 3Ae³xDifferentiating y'ₚ w.r.t x, we get:y"ₚ = 9Ae³xSubstituting the values of yₚ, y'ₚ and y"ₚ in the given differential equation, we get:Ae³x - 9Ae³x + 18Ae³x = e³x

Simplifying the above equation, we get:8Ae³x = e³xHence, A = 1/8Thus, the particular solution of the differential equation y - 3y' + 2y" = e³x is:yₚ = 1/8 e³xSubstituting the values of yₚ in the general solution (1), we get: the solution of the differential equation y - 3y' + 2y" = e³x is:y = c₁eˣ + c₂e²ˣ + 1/8 e³x

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