Find dy/dx for the indicated function y

The recurrence relation an = an-1 + an-3 counts the number of ways to climb n stairs if you can take either 1 stair or 3 stairs at a time.

What is a recurrence relation?

A recurrence relation is an equation that defines a sequence of values in terms of the preceding terms of the sequence. It is a mathematical tool used to define a sequence of numbers, functions, or other mathematical objects in a recursive manner.

To find a recurrence relation that counts the number of ways to climb n stairs if you can take either 1 star or 3 stairs at a time, we can use the following steps:

Identify the base cases. In this case, the base cases are the number of ways to climb 0 stairs (an = 1) and the number of ways to climb 1 stair (an = 1).

Determine the recurrence relation. For n > 1, the number of ways to climb n stairs is equal to the number of ways to climb n-1 stairs (taking 1 stair at a time) plus the number of ways to climb n-3 stairs (taking 3 stairs at a time). Therefore, the recurrence relation is:

an = an-1 + an-3

Use the base cases and the recurrence relation to determine the values of an for the desired range of n.

For example, to determine the values of an for n = 0, 1, 2, 3, 4, and 5, we can use the following table:

n | an

0 | 1

1 | 1

2 | an-1 + an-3 = 1 + 1 = 2

3 | an-1 + an-3 = 2 + 1 = 3

4 | an-1 + an-3 = 3 + 2 = 5

5 | an-1 + an-3 = 5 + 3 = 8

Hence, the recurrence relation an = an-1 + an-3 counts the number of ways to climb n stairs if you can take either 1 stair or 3 stairs at a time.

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To take 10% of something, move the decimal point one spot to the left

Examples:

Answer:

The solution to the system of equations is x = 28, y = -40.

Step-by-step explanation:

3x + 2y = 4

-2x + 2y = 24

---------

x = 28

3x + 2y = 4

3(28) + 2y = 4

84 + 2y = 4

2y = -80

y = -40

the solution to the system of equations is x = 28, y = -40.

The linearization of the given function near x = -0.9 is approximated by the linear equation -x - 7, with the center of the linearization at x = -1. This equation is obtained by evaluating the function and its derivative at x = -1, then using them to approximate the value of the function at x = -0.9.

The linearization of the given function f(x) = 3x^2 + 2x - 3 near the point x = -0.9 is a linear equation that approximates the value of the function at the point. To obtain the linearization, we must first choose a suitable integer near -0.9 at which the function and its derivative are easy to evaluate. In this case, we choose x = -1 as the center of the linearization. To obtain the linearization equation, we evaluate the function and its derivative at x = -1, then use them to approximate the value of the function at x = -0.9. This results in the linear equation -x - 7. This equation allows us to approximate the value of the function at x = -0.9 without having to calculate the value of the function directly.

f(-1) = 6

f'(-1) = -1

Linearization: f(x) ≈ f(-1) + f'(-1)(x + 1)

= 6 - 1(x + 1)

= -x - 7

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Put the value where the variable is, read the graph, and do the arithmetic.

 g(2) = 3f(2) -2 = 3(-1) -2

 g(2) = -5

In a mathematics problem or experiment, a variable is a quantity that can change. To indicate a variable, we often use a single letter. Generic symbols used frequently for variables include the letters x, y, and z.

A trait that is measurable and capable of taking on several values is known as a variable. There are many variables, including height, age, wealth, province of birth, academic standing, and kind of dwelling. Two categories—categorical and numeric—can be used to categorize variables.

Here,

Given : f(x)=√x+1-3

for odd ,

f(-x) = √-x+1-3

f(-x) ≠ -f(x)

Thus it is not odd function.

f(x) is an even function.

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The function t(t) can be expressed as t(t) = xt where x refers the number of stocks and t refers the number of days.

In math, the term function refers an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here we have given that a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week, t(t).

And we need to find the function t(t) can be expressed.

While we looking into the given question, we have identified the that the function that represents the situation is written as t(t).

In this one t refers the number of days in the week they spend on the tesla stocks.

And here let us consider x be the number of stocks did the a brokerage firm keeps track.

So, the resulting function is written as,

=> t(t) = xt.

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As per the condition for defining the function with name shiftdiagonal , we need to define the function with two parameter (x,y,z). Then the function ultimately increments the values in x and y by z and returns the updated  values of x, y.

Simply said, a function is a "block" of code that you may reuse again rather than having to write it out several times. Programmers can divide an issue into smaller, more manageable parts, each of which can carry out a specific job, using functions. The specifics of how a function operates can virtually be forgotten once it has been built. By abstracting the specifics, the programmer may concentrate on the broad picture.

In Python 'def' keyword is used to define functions.

for example:-  def function_name( ):

The code for a function definition to fulfill the conditions put by the question(using python) is given below:

def shiftdiagonal(x , y, z):

   x = x + z

   y = y + z

   return x,y

In the above code z is supposed to be the amount to shift x and y by.

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Answer:

1. 2 pounds of beans and 1 pound of rice

2. 0.6 pounds of beans and 9 pounds of rice

3. b pounds of beans and (12-b)/2 pounds of rice

Step-by-step explanation:

1. You know that 2 pounds of beans costs 2*5 so $10. Then you subtract 12-10 to get 2.

2 pounds of rice

2. You multiply 0.6 by 5, and then you subtract that from 12, getting 9. then you divide by 2 (cost of rice per pound) getting 4.5 pounds of rice

Answer:

Triangle RST rises 4 units and runs 8 units.

Triangle XYZ rises 3 units and runs 6 units.

The slope of line b is 1/2.

Step-by-step explanation:

Triangle RST rises 4 units and runs 8 units.

Triangle XYZ rises 3 units and runs 6 units.

The slope of line b is 1/2.

(2, 0) and (8, 3)

m = 3-0/8-2

m = 3/6

m = 1/2

Answer:

(x+17)°=25° <---Smallest Angle

(7x-16)°=40°

115°=115°

Step-by-step explanation:

Because the angles in a triangle add up to 180°, 115°+(x+17)°+(7x-16)°=180°

Now we can solve algebraically.

115°+(x+17)°+(7x-16)°=180°

115+x+17+7x-16=180

Rearrange:

115+17-16+7x+x=180

Solve:

115+1+8x=180

116+8x=180

8x=180-116

8x=64

x=8

Now we can fill x in to find the measure of the angles.

(x+17)°

(8+17)°

=25°

(7x-16)°

56-16

=40°

Check:

40+25+115

65+115

5+175

=180°, so our angles add up.

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something noteworthy is that, the y-coordinate for Line 1 is the same, well that simply means that Line 1 is a horizontal line, anything perpendicular to a horizontal line is simply a vertical line, Check the picture below.

Answer:

[tex]r = \frac{3}{4}[/tex]

Step-by-step explanation:

Geometric sequence formula: [tex]a_n = a_1 r^{n-1}[/tex]

From the provided sequence, we know that the first term is -4

The second term is -3

Inserting to value to the formula

( n = 2, since we are using the value of the second term)

[tex]a_2 = -4 * r^{2-1}\\[/tex]

[tex]-3 = -4 * r[/tex]

[tex]r = \frac{-3}{-4}[/tex]

[tex]r = \frac{3}{4}[/tex]

The result of derivative by evaluating the integral and differentiating is 2sinx.

The function itself is the derivative of a function's integral. But only in the case of indefinite integrals is this always the case. Only when the lower limit of the integral is a constant and the higher limit is the variable we are differentiating with, is the derivative of a defined integral of a function the function itself.

The function itself is the derivative of an indefinite integral of a function. Specifically, d/dx f(x) dx = f (x)

d/dx ∫x -x (sin t) dt

⇒ d/dx [- cos t] x -x

⇒ - d/dx [cos x - cos (-x)]

⇒ - d/dx [ 2 cos x]

⇒ -2 d/dx [cos x]

⇒ -2 [- sin x]

⇒ 2 sin x

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Answer:

g = 18 - 2t

Step-by-step explanation:

They start with 18 gal.

To find how much gas they use while driving:

(2 gal/hr)(t hr)

Subtract that amount from the 18 gal they had in the tank to start with.

g = 18 gal - (2 gal/hr)(t hr)

The value of the brand new Ford F-150 after five years is approximately 32,435 dollars. Rounded to the nearest dollar, the value of the Ford F-150 after five years is 32,000 dollars.

The value of a new vehicle after the first 12 months of ownership is given by the equation:

value after 12 months = value at time of purchase × (1 - depreciation rate)

In this case, the value of the vehicle at the time of purchase is 63,580, and the depreciation rate is 20%. Plugging these values into the equation gives us:

value after 12 months = 63,580 × (1 - 0.20) = 50,864

The value of the vehicle after five years is given by the equation:

value after 5 years = value after 12 months × [tex](1 - depreciation rate)^n[/tex]

where n is the number of years after the first 12 months of ownership. In this case, n is 4 (5 years - 1 year).

Plugging the values for the value after 12 months, the depreciation rate, and n into the equation gives us the following:

value after 5 years = 50,864 × [tex](1 - 0.10)^4[/tex] = 32,435

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y-6=-1/2(x+1)

1. the point-slope form is y-y1=m(x-x1)

x1 and y1 are the coordinates of the point (-1,6) because the line we are looking for its equation passes through it. "m" is the slope.

2. plug in the point (-1,6) in the form from step 1

y-6=m(x+1)

3. to find the slope of this line, the question tells us that this line is parallel to another line that passes through two given points. Any parallel lines, their slopes are the same. That means we have to find the slope of the 2nd line and use it for the 1st line.

The slope formula is m=(y2-y1)/(x2-x1)

plug in the two points m=(4-2)/(2-6), which is equal to -1/2

4. plug in "m" value in the equation from step 2.

Done

The number as a product of two fractions is 4/2 * 1/5

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

Fractions = 2/5

To express it as a product of two fractions, we start with the following equation (first split)

Fractions = 2/1 * 1/5

Express 2 as 4/2

So, we have the following representation

Fractions = 4/2 * 1/5

Hence, the fraction products is 4/2 * 1/5

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The value of c in the triangle is 14.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

In the triangle LMN, m ∠L = (3c + 66)°. The exterior  angle to ∠L measures 72 degrees.

Therefore, let's find c.

Hence, the sum of the exterior angle and the interior angle is 180 degrees.

Therefore,

72 + 3c + 66 = 180

3c = 180 - 66 - 72

3c = 42

divide both sides by 3

c = 42 / 3

Therefore,

c = 14

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The percentage of students graduating from engineering or business

is ~50%

as per given in the questions

An university is divided into 6 colleges

with which the most of the students graduating from the four of the colleges given in the graph below

the percentage of students who are interested in biological science colleges are  20%

the percentage of students who are interested in mathematics  colleges are 10%

the percentage of students who are interested in Engineering colleges are  20%

the percentage of students who are interested in business colleges

are 30%

from the graph, graduating from either Engineering or Business

is = 20% + 30% = 50%

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The required area of the regular 12-gon is obtained as 3 square units.

A regular polygon can be defined as a polygon having all of its sides and angles equal to one another. The expression for each angle of a regular polygon is 180(n - 2)/n.

The angle between two sides of regular 12-gon is given as below,

180(12 - 2)/12 = 150°.

Now, the area of regular 12-gon is equivalent to the area of sum of 12 triangles.

The angle for the triangle will be 150/2 = 75°.

The diagram for such a triangle is given as below,

Now, OC = 1 × Sin B

⇒ OC = Sin 75°

And, BC =  1 × Cos B

⇒  BC = Cos 75°

Then, AB = 2BC = 2Cos 75°

Area of the triangle is given as,

1/2 × base × height

⇒ 1/2 × Sin 75° × 2Cos 75°

⇒ 0.25

Now, the area of the regular 12-gon inscribed in a unit circle is given as,

12 × 0.25 = 3 square units.

Hence, the area of a regular 12-gon inscribed in a unit circle is 3 square units.

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A- The fitted line or the fitted linear regression model is:[tex]y=2625.385462-36.96179663*x[/tex]

B- [tex]s^{2} = 9811.21237[/tex]

C- [tex]y_{20} = 1886.14953[/tex]

A fundamental and widely used form of predictive analysis is linear regression. Regression analysis' main goal is to look at two things: (1) Is it possible to accurately forecast an outcome (dependent) variable using a set of predictor variables? (2) Which individual variables—as shown by the size and sign of the beta estimates—are highly important predictors of the outcome variable, and how do they affect the outcome variable? The link between one dependent variable and one or more independent variables is explained using these regression estimations.

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The correct answer is c. The null hypothesis would be rejected at both the 0.05 and 0.01 levels.

A p-value is a probability of obtaining a result that is at least as extreme as the one observed in the sample data, given that the null hypothesis is true. The smaller the p-value, the less likely it is that the observed result occurred by chance, and the more likely it is that the null hypothesis is false.

In this case, the p-value of 0.002 is less than both the 0.05 and 0.01 significance levels, which means that it is highly unlikely that the observed result occurred by chance if the null hypothesis is true. Therefore, the null hypothesis should be rejected at both the 0.05 and 0.01 levels.

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Answer:

C) 2.400L

Step-by-step explanation:

A) 2.280L - 2.300L = -0.020L

B) 2.291L - 2.300L = -0.009L

C) 2.400L - 2.300L = 0.100L

D) 2.302L - 2.300L = 0.002L

E) 2.300L - 2.300L = 0.000L

The greatest difference in absolute value between the measurement and the actual volume is 0.100L.

Answer: C)

for two dices, there are 36 possible combinations, the probability of getting these results a sum of greater than or equal to 11 is 3/36 = 12

What is probability and example?

Example: toss a coin 100 times, how many Heads will come up? Probability says that heads have a ½ chance, so we can expect 50 Heads. But when we actually try it we might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.

The only way to get 11 or more is getting 5 with one dice and 6 with another or getting 6 with both dices.

Therefore, there are only three combinations that satisfy this condition: (5,6), (6,5), and (6,6).

Since, for two dices, there are 36 possible combinations, the probability is 3/36 = 12

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the result we get is statistically significant. We reject the null hypothesis.

The null hypothesis in the given question is 'the mean annual consumption of high fructose corn syrup by a person in the United States is 48.8 pounds' and the alternative hypothesis in the given question is 'the population standard deviation is 3.6 pounds.'

Population mean = 48.8 pounds

Sample size = 120

Sample mean = 49.5 pounds

Population standard deviation = 3.6

α = 0.05

The standardized statistic z is:

z = (Sample mean - Population mean) x (√n / standard deviation)

z = (49.5 - 48.8) x (√120/3.6)

z = 2.13

The standardized statistic P is:

P = 2 - 2 x Φ(z)

P = 2 - 2 x 0.983

P = 0.034

Since, the result we get is statistically significant. We reject the null hypothesis.

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In view of Molly's three types of bills

Therefore the first equation is    [tex]1x+5y+10z=96[/tex]

Therefore the second equation is [tex]x+1=y+z[/tex]

Therefore the third equation is [tex]x+y+z=23[/tex]

As per the details share in the above question as as follow,

x for the no, of $1 bills

y for the no. of $5 bills.

z for the no. of $10 bills.

We have to find the first, second and third equations.

Therefore worth of x $1 bills is [tex]1 \times x[/tex]

So of y for the no. of $5 bills is [tex]5 \times y[/tex]

And z for the no. of $10 bills is [tex]10 \times z[/tex]

The total worth in molly wallet is $96.

So the equation will be,

[tex]1x+5y+10z=96[/tex]

Now further is molly has one more  $1 bill then the number of $1 bill will be same as.

Therefore the second equation is [tex]x+1=y+z[/tex]

Now she had 23 bills,

We also know that she has one-dollar, five-dollar, and ten-dollar notes, with x denoting the quantity of each, Y the number of the five-dollar bill, and Z the number of the ten-dollar bill.

Therefore the third equation is [tex]x+y+z=23[/tex]

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If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94

As we can see here,

20N force which is passing through the center O will not produce any torque about point O

For 30N force which is acting at 45 angles with the x−axis, its x−component will pass through the origin, hence its horizontal component will also not cause any torque about O

Hence, torque because of 20N force which is acting in a tangential direction :

τ1=r⊥F=0.1×30=3N-m

Torque produced by y component of 30N force acting at angle 45:

τ2=r⊥F=0.05×30sin45∘

=0.05×30×1/√2=1.5/√2Nm⨀

Torque produced by 20N force acting in negative y direction:

τ3=r⊥×F=0.05×20

τ=1Nm⨀

Hence, the Net torque produced on O

τnet=τ1+τ2+τ3

τnet=−3+(1.5/√2)+1

τnet=−0.94Nm

or

|τnet|=0.94Nm

So  If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94

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Answer:

B. 0

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As per the polar coordinates, the limits of the integration is written as ∬Df(rcos⁡(θ),rsin⁡(θ))rdrdθ.

What is meant by polar coordinates?

In math, polar coordinates refer a pair of coordinates locating the position of a point in a plane, the first being the length of the straight line ( r ) connecting the point to the origin, and the second the angle ( θ ) made by this line with a fixed line.

Here we have  the limits of integration and evaluate the integral to find the volume. for the polar coordinates.

Here we have the polar representation of a point P is the ordered pair (r,θ) where r is the distance from the origin to P and θ is the angle the ray through the origin and P makes with the positive x-axis.

Then the polar coordinates r and θ of a point (x,y) in rectangular coordinates satisfy

=> r=x² + x²      and      tan⁡(θ)=yx;

Here the rectangular coordinates x and y of a point (r,θ) in polar coordinates satisfy and x=rcos⁡(θ) and y=rsin⁡(θ).

Then the area element dA in polar coordinates is determined by the area of a slice of an annulus and is given by dA=rdrdθ.

Here we have to convert the double integral ∬Df(x,y)dA to an iterated integral in polar coordinates,

Now, we have to substitute rcos⁡(θ) for ,x, rsin⁡(θ) for ,y, and rdrdθ for dA to obtain the iterated integral

=> ∬Df(rcos⁡(θ),rsin⁡(θ))rdrdθ.

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The simplified expression of [(b - 3)/(b² + 2b)] + [b/(4b + 8)] is (b² - 12 + 4b)/[(4b)(b + 2)]

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

[(b-3)/(b^2+2b)]+[b/(4b+8)]

Rewrite the exponents

[(b - 3)/(b² + 2b)] + [b/(4b + 8)]

So, we have

(b - 3)/(b² + 2b) + b/(4b + 8)

Factor out b and 4

(b - 3)/b(b + 2) + b/4(b + 2)

Factor out 1/(b + 2)

1/(b + 2) * ((b - 3)/b + b/4)

So, we have

1/(b + 2) * (4(b - 3) + b²)/(4b)

This gives

1/(b + 2) * (4b - 12 + b²)/(4b)

Rewrite as

1/(b + 2) * (b² - 12 + 4b)/(4b)

Lastly, we have

(b² - 12 + 4b)/[(4b)(b + 2)]

Hence, the solution is (b² - 12 + 4b)/[(4b)(b + 2)]

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