LINEARIZATION AND LAPLACE TRANSFORMS Question 1: Linearize the following differential equations dy +zy = dr a. d? dq = y2 + 2+ + = dt? dt b. dy dt ay +By? + y In y A, B, y: constants C. Q: constant dy

One way to compare quantities is with fractional numbers that represent quantities using divided numbers.

Fractional number is a mathematical concept that refers to a quantity divided by another quantity. Common fractions are made up of: numerator, denominator and dividing line between them (horizontal or oblique bar).

Some examples of fractional numbers are:

Note: This question is incomplete because there is some information missing. However I can answer it based on my general prior knowledge.

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Answer:

The word is RATIO.

Step-by-step explanation:

Your problem is incomplete. However, I came across the same problem and solved it (Lesson 23, question 220c). Use the coordinates ONLY from the previous question and compare from there.

sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

To find sin(t), cos(t), and tan(t) we need to use the coordinates of the terminal point p(x,y) determined by the real number t.
Given that the terminal point is (1/5, -2/6), we can find the values of sin(t), cos(t), and tan(t) using the following formulas:
sin(t) = y / r
cos(t) = x / r
tan(t) = y / x
where r is the distance from the origin to the point p(x,y), which can be calculated using the Pythagorean theorem:
r = sqrt(x^2 + y^2)
Plugging in the values for the coordinates of p(x,y), we get:
r = sqrt((1/5)^2 + (-2/6)^2) = sqrt(1/25 + 4/36) = sqrt(36/900 + 25/900) = sqrt(61/900)
sin(t) = (-2/6) / (sqrt(61/900)) = -sqrt(61) / 30
cos(t) = (1/5) / (sqrt(61/900)) = sqrt(61) / 15
tan(t) = (-2/6) / (1/5) = -5/3
Therefore, sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

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A. The minimum value is 18 (Round to the nearest tenth as needed.)

B. There is no minimum value.

A. To solve this problem, we can graph the feasible region formed by the intersection of the given constraints. The feasible region represents the set of points that satisfy all the constraints simultaneously.

Upon graphing the given constraints, we find that the feasible region is a triangle with vertices at (0, 3), (4, 1), and (5, 0).

Next, we evaluate the objective function z = 5x + 6y at each vertex of the feasible region.

z(0, 3) = 5(0) + 6(3) = 18
z(4, 1) = 5(4) + 6(1) = 26
z(5, 0) = 5(5) + 6(0) = 25

Thus, the minimum value of z is 18, which occurs at the vertex (0, 3) within the feasible region.

B. To solve this problem, we can graph the feasible region formed by the intersection of the given constraints. The feasible region represents the set of points that satisfy all the constraints simultaneously.

Upon graphing the given constraints, we find that the feasible region is unbounded and extends indefinitely in certain directions.

Since the feasible region is unbounded, there is no finite minimum value for the objective function z = 5x + 6y. The value of z can be arbitrarily large or small as we move towards the unbounded regions.

Therefore, in this case, there is no minimum value for z.

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Answer:

x=43

Step-by-step explanation:

supplementary angles add up to 180. Therefore 89+2x+5=180.2x=180-94

2x=86 and x is therefore 43.

Answer:

x=43

Step-by-step explanation:

supplementary angles add up to 180. Therefore 89+2x+5=180.2x=180-94

2x=86 and x is therefore 43.

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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To find two unit vectors that are orthogonal to both j 2k and i -2j 3k, we can use the cross product and normalization techniques. The two unit vectors that satisfy the condition are (2/3)i + (2/3)j + (1/3)k and (2/3)i - (2/3)j - (1/3)k.

First, we need to calculate the cross product of j 2k and i -2j 3k, which is given by:

j 2k × i -2j 3k = (-6) i -3k - (-4)j -6k = (-6) i + 4j -9k

This cross product vector is orthogonal to both j 2k and i -2j 3k, but it is not a unit vector. To find two unit vectors that are orthogonal to both j 2k and i -2j 3k, we need to normalize this cross product vector. We can do this by dividing the cross product vector by its magnitude:

\(||(-6) i + 4j -9k|| = \sqrt{(-6)^2 + 4^2 + (-9)^2) } = 11\\\)

Therefore, the first unit vector that is orthogonal to both j 2k and i -2j 3k is:

\(u1 = (1/11)(-6)i + (4/11)j - (9/11)k\)

To find the second unit vector, we can take the cross product of the first unit vector and either j 2k or i -2j 3k. Let's take the cross product of u1 and j 2k:

\(u1 × j 2k = (-8/11) i - (6/11)j - (2/11)k\)

This vector is also orthogonal to both j 2k and i -2j 3k, but it is not a unit vector. To find the second unit vector, we need to normalize this vector:

\(||(-8/11) i - (6/11)j - (2/11)k|| = \sqrt{(-8/11)^2 + (-6/11)^2 + (-2/11)^2} \\= 2/3\)

Therefore, the second unit vector that is orthogonal to both j 2k and i -2j 3k is:

\(u2 = (2/3)(-8/11)i - (2/3)(6/11)j - (2/3)(-2/11)k \\ = (2/3)i - (2/3)j - (1/3)k\)

Thus, the two unit vectors that are orthogonal to both j 2k and i -2j 3k are (2/3)i + (2/3)j + (1/3)k and (2/3)i - (2/3)j - (1/3)k.

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Answer:

1.77×10^6 is the answer ig :)

Answer:

Evaluate.

Scientific Notation:

1.77

⋅

10

6

Expanded Form:

1770000

Step-by-step explanation:

thas what i got

The probability of drawing one black ball and one white ball in two consecutive draws from the urn is approximately 0.42.

To calculate the probability of drawing one black ball and one white ball in two consecutive draws, we need to consider the outcomes of each draw.

In the first draw, there are 10 balls in total (3 black and 7 white). The probability of drawing a black ball on the first draw is 3/10, and the probability of drawing a white ball is 7/10.

For the second draw, after removing one ball from the urn, there are now 9 balls left. The probability of drawing a black ball on the second draw, given that a black ball was drawn on the first draw, is 2/9. Similarly, the probability of drawing a white ball on the second draw, given that a white ball was drawn on the first draw, is 6/9.

To calculate the overall probability, we multiply the probabilities of the individual events. The probability of drawing one black ball and one white ball in two consecutive draws is (3/10) * (6/9) + (7/10) * (2/9) ≈ 0.42.

Therefore, the probability of getting one black ball and one white ball in two consecutive draws from the urn is approximately 0.42.

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Answer:

Step-by-step explanation:

Given,

Let's assume,

We know that,

On substituting the values we get,

→ 2(6x × 5x) + (5x × 4x) + (4x × 6x) = 1332

→ 2 ( 30x² + 20x2 + 24x²) = 1332

→ 2 × 74x² = 1332

→ 74x² = 1332/2

→ 74x² = 666

→ x² = 666/74

→ x² = 9

→ x = √9

→ x = 3

Hence,

Length of cuboid :

→ 6x

→ 6 × 3

→ 18 cm

Therefore, length of the cuboid is 18 cm.

\( \huge \bold \: \bf \: Solution \)

Let ,

\( \sf \: Formula \)

\( \displaystyle \large \sf \mapsto \: 2(lb \: + \: bh \: + hl) = 1332\)

\(\displaystyle \large \sf \mapsto \: 2(6x \times 5x + 5x \times 4x + 4x \times 6x )= 1332\)

\(\displaystyle \large \sf \mapsto2(30 {x}^{2} + {20x}^{2} + {24x}^{2} ) = 1332\)

\(\displaystyle \large \sf \mapsto \: 2(74 {x}^{2} ) = 1332\)

\(\displaystyle \large \sf \mapsto148 {x}^{2} = 1332\)

\(\displaystyle \large \sf \mapsto \: x {}^{2} = 9\)

x = √9

x = 3

Now,

Putting the value of

Length

Breadth

Height

Thus, Length of cuboid = 18 cm.

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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Answer:

value of property multiply by the tax rate

Step-by-step explanation: value of the property x the tax rate of the country

it doesn't represent a proportional relationship because it doesn't cross the origin, instead it has a y-int of (0,5)

Answer:

the numbers are drecreasing and increasing

Answer: To find the inverse of a function f(x), we need to switch the x and y variables and then solve for y.

So, the inverse function f^-1(x) of f(x) = 2x - 3 is:

f^-1(x) = (x+3)/2

This is the inverse of the function, and it can be denoted by f^-1(x) = (x+3)/2

Step-by-step explanation:

Answer:

.033

Step-by-step explanation:

6th term = 8(1/3)^7

If 8x ≤ g(x) ≤ 4x4 − 4x2 + 8 for all x,  x will be evaluated as lim x→1 g(x), 1 is 8.

To evaluate the limit of g(x) as x approaches 1, we must first examine the given inequality. It states that if 8x is less than or equal to g(x), and g(x) is less than or equal to 4x4 - 4x2 + 8, then this is true for all x.

Calculating the limit of g(x) as x approaches 1, we start by substituting x = 1 into the given inequality. This gives us 8(1) ≤ g(1) ≤ 4(1)4 - 4(1)2 + 8. Simplifying, this gives us 8 ≤ g(1) ≤ 8, so g(1) must be equal to 8.

Therefore, the limit of g(x) as x approaches 1 is 8.

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Answer

Step-by-step explanation:

U have to know what y is other wise its impossible

Answer:

tht hard

Step-by-step explanation:

so i need points

The fraction is 1/6. Option D

First, we need to know the conversion factor the parameters.

Then, we have that';

1 liter = 1000 milliliter

10 milliliters (ml) = 1 centiliter (cl)

10 centiliters =  1 deciliter (dl) = 100 milliliters

1 liter =  1000 milliliters

1 milliliter =  1 cubic centimeter

1 liter =  1000 cubic centimeters

Then, we can say that;

If 1 liter = 1000ml

Then 2 4/8 = 400ml

2.4 liters is equal to 2.4 x 1000= 2400 milliliters.

400/2400

Simplify the fraction;

4/24

Divide the values, we get;

1/6

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Answer:

see explanation

Step-by-step explanation:

Using the chain rule

Given

y = f(g(x)), then

\(\frac{dy}{dx}\) = f'(g(x))  × g'(x) ← chain rule

and the standard derivatives

\(\frac{d}{dx}\) (\(log_{a}\) x ) = \(\frac{1}{xlna}\) , \(\frac{d}{dx}\)(lnx) = \(\frac{1}{x}\)

(a)

Given

y = \(log_{a}\)\(\sqrt{(1+x)}\)

\(\frac{dy}{dx}\) = \(\frac{1}{lna\sqrt{(1+x)} }\) × \(\frac{d}{dx}\) (\((1+x)^{\frac{1}{2} }\)

   = \(\frac{1}{lna\sqrt{(1+x)} }\) × \(\frac{1}{2}\) \((1+x)^{-\frac{1}{2} }\) × \(\frac{d}{dx}\) (1 + x)

   = \(\frac{1}{lna\sqrt{(1+x)} }\) × \(\frac{1}{2\sqrt{(1+x)} }\) × 1

   = \(\frac{1}{2lna(1+x)}\)

   = \(\frac{1}{(1+x)lna^2}\)

(b)

Given

y = ln sinx

\(\frac{dy}{dx}\) = \(\frac{1}{sinx}\) × \(\frac{d}{dx}\)(sinx)

   = \(\frac{1}{sinx}\) × cosx

   = \(\frac{cosx}{sinx}\)

   = cotx

Answer:

first statement

Step-by-step explanation:

The graph opens up and the vertex is a maximum

Answer:

The answer is simple

Step-by-step explanation:

The answer is B, on a line graph the order goes from 0, 1, 2, 3 and so on without this order you can't use negative terms without a equation  

A personality test may probably be given to assess,

a. individual behavior patterns

We have to given that,

To find A personality test may be given to assess.

Since, We know that.,

Acquiring certain skills or solving problem rarely has to do with personality, while testing actual skills is not a part of one's personality.

Hence, A personality test may probably be given to assess,

a. individual behavior patterns

Thus, The correct option is,

a. individual behavior patterns

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i. cos 0 =  \(\sqrt{3}\)

ii. tan 0 = 1/ \(\sqrt{3}\)

Trigonometric functions are a set of given functions which are required in determining the value(s) of the sides or internal angle(s) of a given right angled triangle; when the value of one none right angle is given.

In the given question, we have;

sin 0 = 1/2

This implies that;

sin 0 = opposite/ hypotenuse = 1/2

So that;

opposite = 1

hypotenuse = 2

Apply the Pythagorean's theorem so as to determine its adjacent, we have;

adjacent = \(\sqrt{3}\)

Then,

cos 0 = adjacent/ hypotenuse

         =  \(\sqrt{3}\) / 1

cos 0 =  \(\sqrt{3}\)

ii. tan 0 = opposite/ adjacent

            = 1/  \(\sqrt{3}\)

tan 0 = 1/ \(\sqrt{3}\)

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Answer:

14

Step-by-step explanation:

10 questions = 4 correct + 6 incorrect

4 correct = 4* 5 = 20

6 incorrect = 6* (-1) = -6

His score is 20 -6 = 14 points