find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t3i 8t2j, t = 5

The value that is added on the left-hand side to make the equation equal is -1/100.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows: multiplication, division, addition, and subtraction.

Given [1/-2  - 3/4  of -8/15],

to add a number so the sum equals the product of -7/50 and 11/14

let the number be x

according to the question,

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

taking LHS

[1/-2  - 3/4  of -8/15] = -1/2 - (3(-8)/60)

[1/-2  - 3/4  of -8/15] = -1/2 + 24/60

[1/-2  - 3/4  of -8/15] = (-30 + 24)/60

[1/-2  - 3/4  of -8/15] =-6/60 = -1/10

RHS

-7/50*11/14 = -77/700 = -11/100

substitute the values

[1/-2  - 3/4  of -8/15] + x = -7/50*11/14

-1/10 + x = -11/100

x = -11/100 + 1/10

x = (-11 + 10)/100

x = -1/100

Hence -1/100 is added to make the equation equal.

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The true statements are Sample space S = {1, 2, 3, 4, 5, 6.

If A is a subset of S, A could be {5, 6}.

If a subset A represents the complement of rolling a 5, then

A = {1, 2, 3, 4, 6}.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Given, A number cube has faces numbered 1 to 6.

∴ The three statements are,

Sample space S = {1, 2, 3, 4, 5, 6} as sample space is all the elements in the given set.

If A is a subset of S, A could be {5, 6} as 5 and 6 contains in the set.

If a subset A represents the complement of rolling a 5, then

A = {1, 2, 3, 4, 6} as a complement of 5 means, not 5.

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Answer:

C, D

Step-by-step explanation:

A number cube has faces numbered 1 to 6.

What is true about rolling the number cube one time? Select three options.

S = {1, 2, 3, 4, 5, 6}

If A is a subset of S, A could be {0, 1, 2}.

If A is a subset of S, A could be {5, 6}.

If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}.

If a subset A represents the complement of rolling an even number, then A = {1, 3}

The Equilibrium Points are: (0,0).

Stability of Equilibrium Points: Inconclusive.

Outcome from Various Initial Points:

Equilibrium Points: The equilibrium points are the points where the system comes to rest, indicated by dx/dt = 0 and dy/dt = 0. Solving the equations dx/dt = 5x and dy/dt = -5y, we find x = 0 and y = 0. Therefore, the equilibrium points are (0,0).

Stability of Equilibrium Points: The stability of the equilibrium points can be determined using linearization. The Jacobian matrix J(x,y) is given as J(x,y) = [5 0; 0 -5]. For the equilibrium point (0,0), we have J(0,0) = [0 0; 0 0]. The eigenvalues of the Jacobian matrix are both zero, indicating that they lie on the imaginary axis. From this analysis, we cannot conclude anything about the stability of the equilibrium point (0,0).

Outcome of the System from Various Initial Points:

Case 1: When x(0) > 0 and y(0) > 0:

Both dx/dt and dy/dt are positive, causing the solution curve to move upwards and to the right. The trajectory approaches the equilibrium point (0,0) as t approaches infinity.

Case 2: When x(0) < 0 and y(0) < 0:

Both dx/dt and dy/dt are negative, causing the solution curve to move downwards and to the left. The trajectory approaches the equilibrium point (0,0) as t approaches infinity.

Case 3: When x(0) > 0 and y(0) < 0:

dx/dt is positive and dy/dt is negative. The solution curve moves upwards and to the left. The trajectory does not approach the equilibrium point (0,0) as t approaches infinity.

Case 4: When x(0) < 0 and y(0) > 0:

dx/dt is negative and dy/dt is positive. The solution curve moves downwards and to the right. The trajectory does not approach the equilibrium point (0,0) as t approaches infinity.

Please note that the stability analysis for the equilibrium point (0,0) is inconclusive, as the eigenvalues are both zero.

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Answer:

no

Step-by-step explanation:

Answer:

Yes they are equivalent

Step-by-step explanation:

8 ÷ 2 = 4

\(8*\dfrac{1}{2}=\dfrac{8}{2}=4\)

Answer: $113.55

Step-by-step explanation:

add up the cost of the lesson, boots, board, and ticket

the lesson costs $33.80 and the ticket costs $25, these cover the whole day so no need to be multiplied. the boots cost $2 and the board costs $8.95 each hour, jim will need to pay the cost of both 5 times for 5 hours.

here is the equation to solve

33.80 + 5(8.95 + 2.00) + 25 =

33.80 + 5(10.95) + 25 =

33.80 + 54.75 + 25 =

33.80 + 79.75 = 113.55

the total cost is $113.55

Answer:

where is the question

Step-by-step explanation:

u do not have a question so there us nothing to answer

In the given point (2,1/4), 2 is on the x axis and 1/4 represent the y axis. The point (2,1/4) on the coordinate plane is given below;

In the given question we have to represent the given point in the coordinate plane.

The given coordinate is (2, 1/4).

Firstly we learn about the coordinate.

The coordinate are the points that shows the position of point on the x axis and y axis.

The first point shows the x axis and second point shows the y axis.

So in the given point 2 is on the x axis and 1/4 represent the y axis.

We can write 1/4 as 0.25.

The point (2,1/4) on the coordinate plane is given below;

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Answer:

1 x 106

Step-by-step explanation:

Therefore, the components of vector E⃗ are Ex = 1 and Ey = -11. Thus, E⃗ = (1, -11).

To solve this equation, let's break it down component-wise. Given:

E⃗ = 2A⃗ + 3B⃗

We can write the equation in terms of its components:

Ex = 2Ax + 3Bx

Ey = 2Ay + 3By

We are also given the components of vectors A⃗ and B⃗:

Ax = 5

Ay = 2

Bx = -3

By = -5

Substituting these values into the equation, we have:

Ex = 2(5) + 3(-3)

Ey = 2(2) + 3(-5)

Simplifying:

Ex = 10 - 9

Ey = 4 - 15

Ex = 1

Ey = -11

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Answer:

40*8.5=340

6*90=540

total=880/2.5=352bags

Answer:

35.5 cm

Step-by-step explanation:

The perimeter (P) is calculated as

P = (2 × 6.75 ) + (2 × \(\sqrt{121}\) )

  = 13.5 + (2 × 11) = 13.5 + 22 = 35.5 cm

Answer:

35.5cm

Step-by-step explanation:

The perimeter (P) is calculated as

P = (2 × 6.75 ) + (2 × \sqrt{121}121 )

  = 13.5 + (2 × 11) = 13.5 + 22 = 35.5 cm

An experiment consists of tossing a fair coin 10 times in succession and the expected number of heads is 5. Hence option 4 is correct.

To find the expected number of heads when tossing a fair coin 10 times in succession, we can use the concept of linearity of expectation. Since each coin toss is independent and has a 50% chance of landing on heads, the expected number of heads in a single toss is 0.5.

Since the expected value is a linear operator, we can add the expected number of heads for each toss to find the expected number of heads in 10 tosses.

Therefore, the expected number of heads in 10 tosses is:

E(#heads) = 10 × E(#heads in a single toss) = 10 × 0.5 = 5.

Therefore, the correct answer is option 4: E(#heads) = 5.

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Step-by-step explanation:

These two angles are same side corresponding interior angles so they are equal to each other

\(5x + 20 = 120\)

\(5x = 100\)

\(x = 20\)

Answer:

$91.55

Step-by-step explanation:

The money belen pay in state taxes in 3 years is $91.84.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =P(1+r/n)^rt

We are given that;

Belen pays= $76.00

Rate= 6.4%

Now,

Plugging these values into the formula, we get:

A=76(1+0.064)3

A=76(1.064)3

A≈91.84

Therefore, by the interest the answer will be $91.84.

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When two straight lines or rays intersect at a single point, an angle is created and in the illustration, line BC is opposite to angle ∠BAC.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex.

The name "angle" comes from the Latin "angulus", which means "corner".

Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.

So, in the given situation observe the given diagram:

We can easily conclude that ∠BAC is opposite to line BC.

Therefore, when two straight lines or rays intersect at a single point, an angle is created and in the illustration, line BC is opposite to angle ∠BAC.

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The derivatives are as follows:

1. The derivative of  \(\(Y = \ln(x^2(x^3 + 10))\)\) with respect to x is

\(\(\frac{{5x^4 + 20x}}{{x^2(x^3 + 10)}}\)\).

2. The derivative of \(\(Z = e^{(x^2 + 10x)}\)\) with respect to x is

\(\((2x + 10) \cdot e^{(x^2 + 10x)}\)\).

To find the derivatives of the given functions, let's consider each function separately.

1. For function \(\(Y = \ln(x^2(x^3 + 10))\):\)

The derivative of Y with respect to x is given by:

\(\[\frac{{dY}}{{dx}} = \frac{{d}}{{dx}} \left[\ln(x^2(x^3 + 10))\right]\]\)

Using the chain rule, the derivative can be calculated step by step:

\(\[\frac{{dY}}{{dx}} = \frac{{1}}{{x^2(x^3 + 10)}} \cdot \frac{{d}}{{dx}} \left[x^2(x^3 + 10)\right]\]$\\\\\[\frac{{dY}}{{dx}} = \frac{{1}}{{x^2(x^3 + 10)}} \cdot \left[2x(x^3 + 10) + x^2(3x^2)\right]\]\)

\(\[\frac{{dY}}{{dx}} = \frac{{1}}{{x^2(x^3 + 10)}} \cdot \left[2x^4 + 20x + 3x^4\right]\]\)

\(\[\frac{{dY}}{{dx}} = \frac{{1}}{{x^2(x^3 + 10)}} \cdot (5x^4 + 20x)\]\)

Therefore, the derivative of Y with respect to x is:

\(\[\frac{{dY}}{{dx}} = \frac{{5x^4 + 20x}}{{x^2(x^3 + 10)}}\]\)

2. For function \(\(Z = e^{(x^2 + 10x)}\):\)

The derivative of Z with respect to x is given by:

\(\[\frac{{dZ}}{{dx}} = \frac{{d}}{{dx}} \left[e^{(x^2 + 10x)}\right]\]\)

Using the chain rule, the derivative can be calculated step by step:

\(\[\frac{{dZ}}{{dx}} = e^{(x^2 + 10x)} \cdot \frac{{d}}{{dx}} \left[(x^2 + 10x)\right]\]\\\\$\\\[\frac{{dZ}}{{dx}} = e^{(x^2 + 10x)} \cdot (2x + 10)\]\)

Therefore, the derivative of Z with respect to x is:

\(\[\frac{{dZ}}{{dx}} = (2x + 10) \cdot e^{(x^2 + 10x)}\]\)

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Answer:

Step-by-step explanation:

Answer: Undefined

Step-by-step explanation:

because the X values are the same making it Undefined

Answer:

8:5. 16:10

Step-by-step explanation:

5 was doubled so you would double 8 aswell

Answer: "3 + x".

Step-by-step explanation:

Diameter = 17 cm

Radius = r = Diameter /2 = 17/2 =8.5 cm

Surface area of a sphere: 4 π r^2

Replacing with the values given:

SA = 4 π (8.5) ^2 = 907.92 cm^2

The values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

The concept of the integral is a fundamental part of calculus and it is used to calculate the area under a curve or the volume of a 3-dimensional object. In this context, we will be exploring the integral of a two-dimensional set in the R^2 plane.

For every two-dimensional set C contained in R^2 for which the integral exists, the function Q(C) is defined as the double integral of the function (x^2 + y^2) over the set C. The double integral is a mathematical tool for finding the total volume under a surface.

Let's consider the three sets C1, C2, and C3 and find Q(C1), Q(C2), and Q(C3).

C1={(x,y) : −1 ≤ x ≤ 1, −1 ≤ y ≤ 1}

Q(C1) = ∬C1 (x^2 + y^2) dxdy = ∫^1_{-1}∫^1_{-1} (x^2 + y^2) dxdy = ∫^1_{-1} [(x^2 + y^2)/2]^1_{-1} dx = 4.

C2 ={(x,y):−1≤x≤1,−1≤y≤1}

Q(C2) = Q(C1) = 4.

C3 = {(x,y):x^2 + y^2 ≤1}

Q(C3) = ∬C3 (x^2 + y^2) dxdy = π.

In conclusion, the values of Q(C1), Q(C2), and Q(C3) are 4, 4, and π, respectively.

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The type of polyhedron that can be assembled from this net is a triangular prism because if you assemble this net you get a figure like this

90 cubic feet  is the volume of the rectangular prism.

A polyhedron with two congruent and parallel bases is a rectangular prism.

It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.

It is referred to as a prism because of the length of its cross-section. The study of shapes and the arrangement of objects is known as geometry.

The surface area and volume of a rectangular prism are similar to those of other three-dimensional forms.

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces).

The prism's faces are all rectangular in shape. There are three sets of identical faces as a result.

According to our question-

V = Base x Height is the formula for a rectangle prism.

V = 18 x 5 square feet.

V = 90 cubic feet

Hence, 90 cubic feet  is the volume of the rectangular prism.

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π/3 = 60° so we will find the trigonometric function for 60°.

Given that θ = π/3, we need to evaluate each trigonometric function,

π/3 = 60°

The trigonometric functions can be evaluated as follows when is equal to π/3:

Sine: The sine of three is three and a half.

Cosine (cos): 1/2 is the cosine of /3.

Tangent: The tangent of /3 is equal to (3/2) / (1/2), which is written as 3.

Cosecant (csc): The sine's reciprocal, or 2/3, is the cosecant of /3.

Secant (sec): The reciprocal of the cosine, which is 2, is the secant of /3.

Cotangent (cot): The reciprocal of the tangent, which is 1/3 or 3/3, is the cotangent of /3.

These are the values of the trigonometric functions at θ = π/3.

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Answer:

$53.88

Step-by-step explanation:

27.38+5.3*5

5.3 x 5 = 26.5

27.38 + 26.5 = 53.88

The first six terms of the Maclaurin series for the function f(x) = 5 ln(1 + x²) - ln 5 can be obtained by expanding the function using the Maclaurin series expansion for ln(1 + x).

The expansion involves finding the derivatives of the function at x = 0 and evaluating them at x = 0.

The Maclaurin series expansion for ln(1 + x) is given by:

ln(1 + x) = x - (x²)/2 + (x³)/3 - (x⁴)/4 + (x⁵)/5 - ...

To find the Maclaurin series for the function f(x) = 5 ln(1 + x²) - ln 5, we substitute x² for x in the expansion:

f(x) = 5 ln(1 + x²) - ln 5

= 5 (x² - (x⁴)/2 + (x⁶)/3 - ...) - ln 5

Taking the first six terms of the expansion, we have:

f(x) ≈ 5x² - (5/2)x⁴ + (5/3)x⁶ - ln 5

Therefore, the first six terms of the Maclaurin series for the function f(x) = 5 ln(1 + x²) - ln 5 are: 5x² - (5/2)x⁴ + (5/3)x⁶ - ln 5.

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In this equation x=18

Work Shown:

5x-12=3x+24

Add 12 to both sides

5x-12+12=3x+24+12

Simplify

5x=3x+36

Subtract 3x from both sides

5x-3x=3x+36-3x

Simplify

2x=36

Divide both sides by two

2x/2 = 36/2

Simplify

x=18

Answer:

x=18

Step-by-step explanation:

1. Add 12 to both sides

5x-12 +12 = 3x+24 +12

2. Simplify

5x=3x+36

3. Subtract -3x from both sides

5x-3x=3x+36-3x

4. Simplify

2x=36

5. Divide both sides by same factor (2)

2x/2=36/2

6. Simplify

ANSWER: x=18

Answer:

b

Step-by-step explanation:

Using the trigonometric identity

secx = \(\frac{1}{cosx}\) and cos60° = \(\frac{1}{2}\)

Given

sec [ \(sin^{-1}\) \(\frac{\sqrt{3} }{2}\) ] ← evaluate bracket

= sec60°

= \(\frac{1}{cos60}\)

= \(\frac{1}{\frac{1}{2} }\)

= 2 → b