Cual es la raíz cuadrada de 48?

It will take Thomas 40 months to empty the account if he continues to take out $400 each month of $16,000.

To find out how many months it will take for Thomas to empty the account, we need to set M to 0 and solve for t. This will give us the number of months it will take for Thomas to spend all of the $16,000 he won on the game show. The equation we need to solve is:
0 = 16000 - 400t

First, we'll isolate the variable t on one side of the equation by adding 400t to both sides:
400t = 1600

Next, we'll divide both sides of the equation by 400 to get the value of t:
t = 16000/400

Simplifying the right side of the equation gives us:
t = 40

So, it will take Thomas 40 months to empty the account if he continues to take out $400 each month for spending money.

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Answer:

x  = - y-12/5+4k

Step-by-step explanation:

Solve 12-5x-4kx=y for x

12-5x-4kx  =  y for x

substract 12 from both side

   -5x-4kx  =  y-12

Factor of -5x-4kx = -x(5+4k)

   -x(5+4k) =  y-12

Solve for x

             -x =  y-12/(5+4k)

Therefore x = - y-12/5+4k

The power series representation for the function is \(f(x) = \sum\limits^{\infty}_{0} {(-\frac x3)^n}\)

From the question, we have the following parameters that can be used in our computation:

f(x) = 1/(3 + x)

Rewrite the function as

\(f(x) = \frac{1}{3(1 + \frac x3)}\)

Expand

\(f(x) = \frac{1}{3(1 - - \frac x3)}\)

So, we have

\(f(x) = \frac{1}{3} * \frac{1}{(1 - (-\frac x3)}\)

The power series centered at x = 0 can be calculated using

\(f(x) = \sum\limits^{\infty}_{0} {r^n}\)

In this case

r = -x/3 i.e. the expression in bracket

So, we have

\(f(x) = \sum\limits^{\infty}_{0} {(-\frac x3)^n}\)

Hence, the power series for the function is \(f(x) = \sum\limits^{\infty}_{0} {(-\frac x3)^n}\)

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Question

Find a power series representation for the function. (give your power series representation centered at x = 0

f(x) = 1/(3 + x)

Answer:

C. y = 2x - 3

Step-by-step explanation:

Let's go through process of elimination!

First, we can see that the line intersects the y-axis at (0,-3), making the y-intercept -3. In the equation y = mx + b, b is the y-intercept. Therefore, we can easily take out A and D as the wrong answers because their b isn't -3.

Next, we should know that a line with a positive slope is going up, and this line, indeed, is going up. B can't be right because the slope is negative, meaning the line would go down. That leaves us with answer C as the correct choice.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Step-by-step explanation:

1A (3,-2)

1B

By substitution

\(4x - 3y = 18 \\ 2x + y = 4 \\ y = 4 - 2x \\ 4x - 3(4 - 2x) = 18 \\ 4x - 12 + 6x = 18 \\ 10x = 30 \\ x = 3 \\ y = 4 - 2(3) \\ y = 4 - 6 = - 2\)

1C

By elimination

\((4x - 3y = 18) -2 \times (2x + y = 4) \\( 4x - 3y = 18) - (4x + 2y = 8) \\ - 5y = 10 \\ y = - 2 \\ 4x - 3 \times ( - 2) = 18 \\ 4x + 6 = 18 \\ 4x = 12 \\ x = 3\)

Answer:

A = 72 B = 50% C = 40%

Step-by-step explanation:

Each space on the bottom is worth 10%.

Each space on the bottom is worth 36.

The values of the equations are solved and a = 72 , b = 50 % and c = 40 %

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

On the number line , the values above represents the numbers and the values below represents the percentage pf numbers

So , a = 20 % of the total value of the number line

b = ( 50 - 0 ) % = 50 % of the number line

And , c = 40 % of the number line which is 144

So , 40 % of the total value = 144

Substituting the values in the equation , we get

( 40 /100 ) A = 144

Multiply by 100 on both sides , we get

40A = 14400

Divide by 40 on both sides of the equation , we get

A = 360

So , the total value of the number line is 360

where a = 20 % of the number line

On simplifying the equation , we get

a = ( 20/100 ) 360

a = 20 x 3.6

a = 72

Therefore , a = 72 , b = 50 % and c = 40 %

Hence , the equations are solved

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For a. 10.2,

For b. 70,

For c. 0.15,

For d. 4,

For e. 13.02,

For f. 45.4

Answer:

I can't see the numbers well, but the graph is decreasing from (-inf, minimum) and increasing from (minimum, inf).  The minimum  is the vertex.  Hope this helps!

Step-by-step explanation:

The centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. option a.

When a car is driving around a curve, the centripetal force is provided by the frictional force between the tires and the road. This force acts inwards, towards the center of the circle, and is responsible for keeping the car moving in a circular path.

The centripetal force is always perpendicular to the direction of motion, so option (b) and (d) can be eliminated.

Additionally, there is no force that acts away from the center of the circle, so option (c) can also be eliminated. Option (e) is not applicable since the question is asking about the direction of the force, not its orientation.

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Running a 2⁵-1 central composite design instead of a full factorial design can be a reasonable approach to save experimental effort while still obtaining valuable information.

However, it is important to consider the specific requirements and goals of your study, as well as the potential limitations of the reduced design. The decision should be based on a trade-off between the resources available, the complexity of the system being studied, and the desired level of precision in estimating the quadratic model.

A central composite design is a type of experimental design that combines factorial points with additional center points to estimate a quadratic model with main effects, two-factor interactions, and quadratic terms.

In a full factorial design for 5 variables, there would be 2⁵ = 32 factorial points.

However, if you run a 2⁵-1 design, you would exclude one factorial point, reducing the number of experimental runs to 31.

By doing this, you can save some experimental effort while still obtaining a reasonable estimate of the quadratic model.

The decision to use a reduced design should be based on several factors. Firstly, consider the resources available, including time, cost, and available sample size.

Running a full factorial design may require a larger sample size and more resources, which may not be feasible or necessary in some cases. Secondly, evaluate the complexity of the system being studied.

If the system has many factors and interactions, a full factorial design might be more appropriate to capture the complexity accurately. However, if the system is relatively simple, a reduced design can still provide useful information about the quadratic model.

It is important to note that a reduced design will result in some loss of information compared to a full factorial design. The excluded factorial point represents a specific combination of factor levels that will not be investigated, potentially leading to some uncertainty in estimating the quadratic model parameters.

However, if the design is well-planned and carefully executed, the reduced design can still provide valuable insights and estimates of the quadratic model, especially if the excluded point is not expected to have a significant impact on the response variables of interest.

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Answer:

196

Step-by-step explanation:

diameter is 14. also side of square. so 14 x 14 is answer 14 x 14 is 196.

The distance from tire race to the rope climb is; 80 yards

The formula for the distance between two coordinates is;

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

We are given the coordinates of tire race and rope climb as;

Tire race = (-40, -30)

Rope climb = (40, -30)

Thus distance between tire race and the rope climb is;

D = √[(-30 - (-30))² + (40 - (-40))²]

D = √(80²)

D = 80 yards

Thus, we conclude that is the distance from tire race to the rope climb.

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Answer: The interest and amount to be paid at the end of 3 years is Rs.8700

Step-by-step explanation:

let P ,R, T be the Principle amount , Rate of interest and Time

             P= 6000rs

             R= 15%

             T=3 years

                      =6000rs×15r×3t÷100

                       =2700rs

                                                             = 8700rs

Answer:

x = –2

Step-by-step explanation:

– 6(1+4x) = –x +40

–6 – 24x = –x +40

24x –x = –6 –40

23x= – 46

x= – 46 / 23

x= – 2

I hope I helped you‌^_^

Answer:

$11654 approx

Step-by-step explanation:

Given data

Principal amount =  22300 dollars

Rate= 10.25%

time= 6 years

The expression for the decrease is given as

A=P(1-r)^t-----------Note the negative sign is because of the decrease

substitute

A= 22300(1-0.1025)^6

A=22300(0.8975)^6

A=22300*0.5226

A=$11653.98

Hence the new value is $11654 approx

Answer:

B

Step-by-step explanation:

since 5 is constant so you can take it out from the summation

By multiplying Equation 2 by 6, Yumiko ensures that the coefficient of "x" in both equations is 12, allowing her to add the equations and eliminate the "x" variable.

To eliminate a variable when adding the equations, Yumiko needs to multiply both sides of the other equation by a factor that will make the coefficients of one of the variables the same in both equations. Let's consider the system of equations:

Equation 1: 2x - 3y = 12

Equation 2: ax + by = c

Since Yumiko multiplied Equation 1 by 6, it becomes:

6(2x - 3y) = 6(12)

12x - 18y = 72

To eliminate the variable "x" when adding these equations, we need the coefficient of "x" in Equation 2 to be 12. Therefore, the factor by which Yumiko should multiply both sides of Equation 2 is 6.

6(ax + by) = 6(c)

6ax + 6by = 6c

Now, when we add Equation 1 and the modified Equation 2, the "x" terms will eliminate each other:

(12x - 18y) + (6ax + 6by) = 72 + 6c

(12x + 6ax) + (-18y + 6by) = 72 + 6c

(12 + 6a)x + (-18 + 6b)y = 72 + 6c

By multiplying Equation 2 by 6, Yumiko ensures that the coefficient of "x" in both equations is 12, allowing her to add the equations and eliminate the "x" variable.

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note the full question may be:

A carpenter is building a rectangular table with a length of 4 feet and a width of 3 feet. If the carpenter wants to increase the dimensions of the table by a factor of 2, what should be the new length and width of the table?

Answer:

48

Step-by-step explanation:

1) 9*8=72

2) 8*3=24

3)72-24=48

Answer:

60 cm^3

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Based on the given options, the displacement could be either 0 km or 6 km, depending on the specific details of Dr. Siva's route.

To determine the displacement, we need to consider the net change in position or the straight-line distance between the initial and final positions. Let's analyze the information given:

Dr. Siva walked from home to school, then from the school to the park, and finally walked back home.

The displacement is not determined by the total distance traveled but rather by the straight-line distance between the starting and ending points. We don't have specific information about the distances or directions between the locations, so we cannot calculate the exact displacement.

However, we can make some assumptions based on the given options:

If the distances from home to school and from the school to the park are the same, and Dr. Siva returns directly from the park back home, the displacement would be 0 km. This implies that the final position is the same as the initial position.

If Dr. Siva walks 10 km from home to school, then 10 km from the school to the park, and finally walks 10 km back home, the displacement would be 0 km. This is because the final position would be the same as the initial position.

If Dr. Siva walks 10 km from home to school, then 2 km from the school to the park, and finally walks 6 km back home, the displacement would be 6 km. This implies that the final position is 6 km away from the initial position in the direction of home.

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Answer:

Hello,

Step-by-step explanation:

n! + (n-1)!

=(n-1)! * n+ (n-1)!

=(n-1)! * (n+1)

Given:

The given equation is,

Required:

Solve for x.

Answer:

Let us solve the given equation for x.

Final Answer:

The value of x is,

Answer:

46 ≥ 2m + 4

m ≥ 21

Step-by-step explanation:

At least is ≥

Karen's age = 46 years old

Mary's age = m years old

Karen is at least 4 years more than twice mary's age (m).

46 ≥ 2m + 4

46 - 4 ≥ 2m

42 ≥ 2m

m ≥ 42/2

m ≥ 21

Cinematic layout lead, Technical Assistant, Game Artist, 2D Artist, and Game Producer are the best anime jobs that use geometry.

There are many opportunities for animators to get anime jobs that use geometry as well. In order to demonstrate how an object is rotated or shifted to be made larger or smaller—for the process of producing movement—animators must comprehend the geometrical characteristics of figures and apply linear algebra.

Due to their work with moving and changing objects, animators frequently use a number of mathematical techniques, including geometry, linear algebra, and others. The ability to utilize linear algebra to demonstrate how a certain figure or object is shifted or rotated with the intention of making it smaller or larger is crucial for animators. Movement is produced by this mechanism.

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.

Answer: hello frawn

Step-by-step explanation:

free point dootie head

Given \(y''+4y=g(t)\), and the initial values \(y(0) = 3, y'(0) = 0\), we have to obtain a formula for the solution using the convolution theorem using the variable v.

We first find the Laplace transforms of the given differential equation and the right-hand side using the initial values. \(L{y''} = s²Y(s) - s(0) - y'(0) = s²Y(s)L{y'} = sY(s) - y(0) = sY(s)L{g(t)} = G(s)\)

Now, substituting the Laplace transforms, we have: \(s²Y(s) - 3s + 0 + 4Y(s) = G(s)Y(s) = (1/4+s²)G(s) + 3/s\).

Now, the inverse Laplace transform of the product of F(s) and G(s) is given by:\(f(t) * g(t) = [L⁻¹{F(s)} * L⁻¹{G(s)}]\)

We have:  f(t) * g(t) = [L⁻¹{F(s)} * L⁻¹{G(s)}]\(f(t) * g(t) = [L⁻¹{F(s)} * L⁻¹{G(s)}]\)

Therefore, the solution to the given differential equation is given by :\(y(t) = (1/2)∫₀ᵗ g(τ)e^(-2(t-τ))sin(2(t-τ))dτ + 3/2sin(2t)\)

Hence, the formula for the solution using v as the convolution variable is: \(y(t) = (1/2)∫₀ᵗ g(τ)v(t-τ)sin(2v)dv + 3/2sin(2t)\)

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Answer:

the correct answer is SAS

Step-by-step explanation: