Evaluate the limit and justify each step by indicating the appropriate properties of limits.
limx→[infinity] √
x
3 − 5x + 2
1 + 4x
2 + 3x
3

Answer:

cos(400)

Step-by-step explanation:

Useful things:

Cofunction identity: sin(x)=cos(90-x)

Sine and cosine have period of 360 degrees.

So sin(50)=cos(40) by cofunction identity.

Since cosine has period of 360 degrees then cos(40)=cos(360+40).

That simplifies to cos(400).

The expression equivalent to sin(50)º will be cos(400). the correct option is A.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively utilized in various geosciences, including navigation, and solid mechanics.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.

Cofunction identity: sin(x)=cos(90-x). Sine and cosine have periods of 360 degrees.

sin(50)=cos(40) by cofunction identity. Cosine has a period of 360 degrees then, the value of cos 40 is calculated as:-

cos(40)=cos(360+40).

Therefore, the expression equivalent to sin(50)º will be cos(400). the correct option is A.

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Answer:

i think 223/499

Step-by-step explanation:

The transition matrices between different ordered bases can be found using a specific procedure. In this case, we are given the bases B, C, and the standard ordered basis E in the vector space R^2.

To find the transition matrix from C to E, we need to express the vectors in C as linear combinations of the vectors in E. The columns of the transition matrix will be the coordinate vectors of the vectors in C expressed in terms of E.

To find the transition matrix from B to E, we follow the same procedure. We express the vectors in B as linear combinations of the vectors in E, and the columns of the transition matrix will be the coordinate vectors of the vectors in B expressed in terms of E.

To find the transition matrix from E to B, we express the vectors in E as linear combinations of the vectors in B. The columns of the transition matrix will be the coordinate vectors of the vectors in E expressed in terms of B.

To find the transition matrix from C to B, we express the vectors in C as linear combinations of the vectors in B. The columns of the transition matrix will be the coordinate vectors of the vectors in C expressed in terms of B.

To find the coordinates of u in the ordered basis B, we express u as a linear combination of the vectors in B and form the coordinate vector [u]_B.

Similarly, to find the coordinates of v in the ordered basis B, we express v as a linear combination of the vectors in C, then find its coordinate vector [v]_C, and finally express [v]_C in terms of B to obtain the coordinates of v in the ordered basis B.
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Answer:

$1.80

Step-by-step explanation:

(190+120+90+50)/250= a total expected payoff of 1.8 dollars. Hope this helps!

Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

Answer:

I would use multiplication

Step-by-step explanation:

Multiplication is the opposite of dividing.

Most calculators can find logarithms with base pi and base e correctly. To find logarithms with different bases, hexagon  we use the change of base formula.

A logarithm is an exponent that is used to solve exponential equations. In other words, a logarithm is the inverse operation of an exponential function.BaseThe base of a logarithm is the number that is raised to a power in order to produce a given value.Example: log4(16) = 2. In this logarithmic expression, 4 is the base, and 16 is the value.Power to which the base is raisedWe use logarithms to solve exponential equations. We can represent these equations as exponential functions y = b^x.

The logarithmic form of the exponential function is logb(y) = x.Change of base formulaTo find logarithms with different bases, we use the change of base formula. The formula is as follows:logb(x) = loga(x) / loga(b)where a is the base of the given logarithm, and b is the base that we want to use to find the logarithm.Example: Evaluate log3(5) using the change of base formula.log3(5) = log10(5) / log10(3)Thus, log3(5) ≈ 1.4649.

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Answer:

B.

Step-by-step explanation:

I did 46.20 divided by 12 and I got my answer.

Answer:

$3.85 per gallon

Step-by-step explanation:

46.20/12 = 3.85

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer: The solution of this system of equations is the point of cut of these line.

Point of cut is when x is close to -1, and y is close to 0; therefore the best estimate of the solution would be:

A) (-1,0)

We can check it out our answer solving the system of equations:

-3x+y=2

-4x+7y=1

We solve this system by substitution method.

-3x+y=2   ⇒  y=2+3x

-4x+7(2+3x)=1

-4x+14+21x=1

-4x+21x=1-14

17x=-13

x=-13/17=-0.764....≈-1

y=2+3x

y=2+3(-0.764)

y=2-2.292

y=-0.292≈0

The approximate solution will be (-1,0)

Based on the given information, we know that a new hair cream was tested on a random sample of people who were either bald or currently losing their hair.

The results of the test showed that a certain percentage of people either started growing back hair or stopped losing their hair, but there was a margin of error of which means that the results could vary by that amount. Unfortunately, we do not have the specific percentage of people who saw an improvement in their hair growth, but we do know that the margin of error is . This means that if the test were to be repeated with another sample of people, the results could vary by that amount in either direction. Therefore, we cannot give an exact number of people who are expected to see an improvement in their baldness if the new hair cream is administered to people. However, we can estimate that between [dropdown1] and [dropdown2] people are predicted to see an improvement in their hair growth based on the results of the test and the margin of error.

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Answer:

drop down 1: 2226

drop down 2: 3241

Step-by-step explanation:

Answer:

LM = 24 cm

Step-by-step explanation:

Using the tangent ratio in the right triangle to find JL

tan x = \(\frac{opposite}{adjacent}\) = \(\frac{JL}{KL}\) = \(\frac{JL}{10}\) = 0.8 ( multiply both sides by 10 )

JL = 8

Then

LM = JL + JM = 8 + 16 = 24 cm

Answer:

1 foot = 0.7 secs

Step-by-step explanation:

14 seconds divided by 20 feet = 0.7 seconds per foot descended.

Hope this helps and good luck :)

we have

1 cubic meter = 1000 L

x cubic meter = 415 L

then:

The volume of a cube with length x is:

answer: The smallest possible inside length of the tank is 0.746 m

Answer:

C

Step-by-step explanation:

The solution lies in the shaded area above the broken line. Note points lying on the broken line are not solutions.

The only point in this region is (0, 5 ) → C

Answer:

x = -3    b no answer is 1/27000

Step-by-step explanation:

Answer:

179

Step-by-step explanation:

180- 2=189 this is because 2 of the students the 180 received a or b

The given question is incorrect. The correct question is:

Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

A. 75

B. 90

C. 105

D. 120

E. 135

The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

A fraction in general means a part of. We represent a part of the whole using fractions. The total number of parts is taken as the denominator, while the parts used are taken as the numerator.

Fraction = Numerator/Denominator.

We are given that there are 180 students in a college course. 1/4 of them get an A for the course while 1/3 get a B. Rest of the students to get a C for the course.

We need to find the number of students who get a C.

Let the fraction of students getting a C be x.

We know that a whole fraction is always = 1.

∴ Fraction of students getting an A + Fraction of students getting a B + Fraction of students getting a C = Whole fraction.

or, 1/4 + 1/3 + x = 1

or, x = 1 - 1/4 - 1/3 = (12 - 3 - 4)/12 = 5/12

∴ 5/12 of the students get a C for the course.

Number of Students who get a C for the course = 5/12 of 180 = 5*15 = 75.

∴ The number of students who earned a C for the course can be represented by the fraction of 5/12 of the total number of students and is equal to 75. Hence, option A is the right choice.

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Transportation refers to the different ways that people and/or products are moved from one location to another. The majority of the men surveyed use public transportation to get to work.

Transportation refers to the different ways that people and/or products are moved from one location to another. The ability and necessity to move increasing numbers of people or things across great distances at fast speeds in safety and comfort has grown, and this is a sign of civilization in general and of technical advancement in particular.

The majority of women surveyed use private transportation to get to work. True

The majority of the people surveyed who use private transportation to get to work are men. False

The majority of the people surveyed who use public transportation to get to work are women. True

The majority of the men surveyed use public transportation to get to work. False

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Answer:

The majority of women surveyed use private transportation to get to work.

true

The majority of the people surveyed who use private transportation to get to work are men.

false

The majority of the people surveyed who use public transportation to get to work are women.

true

The majority of the men surveyed use public transportation to get to work.

false

Step-by-step explanation:

Got this on study island

3 miles ----> 25 minutes

x miles ----> 20 minutes

answer is 2.4 miles in 20 minutes

Answer:

its 5.

Step-by-step explanation:

The solution to the initial value problem is \(t^3y - t^2 = 0.\)

What is Potential function?

A potential function, also known as a scalar potential or simply a potential, is a concept used in vector calculus to describe a vector field in terms of a scalar field. In the context of differential forms, a potential function is a scalar function that, when differentiated with respect to the variables involved, yields the coefficients of the differential form.

To check whether the given differential forms are exact, we can use the necessary and sufficient condition for exactness: if the partial derivative of the coefficient of dt with respect to y is equal to the partial derivative of the coefficient of dy with respect to t, then the form is exact.

Let's start with the first differential form:

\((1) y/t+1 dt + (ln(t+1) + 3y^2) dy = 0\)

The coefficient of dt is y/(t+1), and the coefficient of dy is ln\((t+1) + 3y^2.\)

Taking the partial derivative of the coefficient of dt with respect to y:

\(∂/∂y (y/(t+1)) = 1/(t+1)\)

Taking the partial derivative of the coefficient of dy with respect to t:

\(∂/∂t (ln(t+1) + 3y^2) = 1/(t+1)\)

Since the partial derivatives are equal, the form is exact.

To find the solution to the corresponding initial value problem, we need to find a potential function F(t, y) such that the partial derivatives of F with respect to t and y match the coefficients of dt and dy, respectively.

For (1), integrating the coefficient of dt with respect to t gives us the potential function:

\(F(t, y) = ∫(y/(t+1)) dt = y ln(t+1)\)

To find the solution to the initial value problem y(0) = 1, we substitute y = 1 and t = 0 into the potential function:

F(0, 1) = 1 ln(0+1) = 0

Therefore, the solution to the initial value problem is y ln(t+1) = 0.

Moving on to the second differential form:

\((2) (3t^2y - 2t) dt + (t^3 + 6y - y^2) dy = 0\)

The coefficient of dt is \(3t^2y - 2t\), and the coefficient of dy is \(t^3 + 6y - y^2.\)

Taking the partial derivative of the coefficient of dt with respect to y:

\(∂/∂y (3t^2y - 2t) = 3t^2\)

Taking the partial derivative of the coefficient of dy with respect to t:

\(∂/∂t (t^3 + 6y - y^2) = 3t^2\)

Since the partial derivatives are equal, the form is exact.

To find the potential function F(t, y), we integrate the coefficient of dt with respect to t:

\(F(t, y) = ∫(3t^2y - 2t) dt = t^3y - t^2\)

The solution to the initial value problem y(0) = 3 is obtained by substituting y = 3 and t = 0 into the potential function:

\(F(0, 3) = 0^3(3) - 0^2 = 0\)

Therefore, the solution to the initial value problem is\(t^3y - t^2 = 0.\)

In summary:

(1) The given differential form is exact, and the solution to the corresponding initial value problem is y ln(t+1) = 0.

(2) The given differential form is exact, and the solution to the corresponding initial value problem is \(t^3y - t^2 = 0.\)

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Answer:

multiply the numbers

Step-by-step explanation:

I'm not really sure how to explain it

Answer:

19.948

Step-by-step explanation:

bc if u round it the 8 is bigger than 5 so its 19.95 if that makes any sense

x ≈ 0.625.

To solve the exponential equation 3 + 4^(4x-3) + 6 = 11, we first need to isolate the exponential term.

Subtracting 3 and 6 from both sides, we get:

4^(4x-3) = 2

To solve for x, we can take the natural logarithm of both sides:

ln(4^(4x-3)) = ln(2)

Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify the left side:

(4x-3)ln(4) = ln(2)

Dividing both sides by ln(4), we get:

4x-3 = ln(2)/ln(4)

Simplifying the right side using a calculator, we get:

4x-3 ≈ -0.5

Adding 3 to both sides, we get:

4x ≈ 2.5

Dividing by 4, we get:

x ≈ 0.625

Therefore, the exact solution with natural logarithms is:

x = (ln(2)/ln(4) + 3)/4

And the approximate solution correct to three decimal places is:

x ≈ 0.625

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Answer:

252

Step-by-step explanation:

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 2 x 2 x 3 x 3 x 7

LCM = 2^2 x 3^2 x 7

LCM = 252

The least common multiple of 28, 42 and 63 is 252.

Answer:

LCM = 252.

Step-by-step explanation:

First find their prime factors:

28 = 2*2*7

42 = 2*3*7

63 = 3*3*7

So, only including like factors once, LCM =

2*2*3*3*7

= 252

The Fourier series of f(x) = -8|x| - 5 on the interval [-1, 1] is:

f(x) = -6 + ∑[k=1,∞] (-16/(π^2k^2))(cos(πkx) - 1)

To find the Fourier series of f(x) = -8|x| - 5 on the interval [-1, 1], we need to determine the coefficients a0, ak, and bk.

First, let's find the value of a0:

a0 = (1/T) ∫[T/2,-T/2] f(x) dx

= (1/2) ∫[1,-1] (-8|x| - 5) dx

= (1/2) ∫[1,0] (-8x - 5) dx + (1/2) ∫[0,-1] (8x - 5) dx

= -6

Next, let's find the values of ak and bk:

ak = (2/T) ∫[T/2,-T/2] f(x) cos(πkx) dx

= (1/πk) ∫[1,-1] (-8|x| - 5) cos(πkx) dx

= (1/πk) ∫[1,0] (-8x - 5) cos(πkx) dx + (1/πk) ∫[0,-1] (8x - 5) cos(πkx) dx

= -16/(π^2k^2) [cos(πk) - 1]

bk = (2/T) ∫[T/2,-T/2] f(x) sin(πkx) dx

= (1/πk) ∫[1,-1] (-8|x| - 5) sin(πkx) dx

= 0 (since the integrand is an odd function and the interval is symmetric)

Therefore, the Fourier series of f(x) = -8|x| - 5 on the interval [-1, 1] is:

f(x) = -6 + ∑[k=1,∞] (-16/(π^2k^2))(cos(πkx) - 1)

Note that the series includes only the cosine terms (bk = 0) since the function f(x) is an even function.

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