Find the first 5 terms of the arithmetic sequence given that: an = 2n - 2

The angle between the curve c(t) = (et cos(4t), et sin(4t)) and its derivative c'(t) is constant at 90 degrees.

To show that the angle between the curve c(t) = (et cos(4t), et sin(4t)) and its derivative c'(t) is constant, we first need to find the derivative c'(t).

To find c'(t), we differentiate each component of c(t) with respect to t:

c'(t) = (d/dt(et cos(4t)), d/dt(et sin(4t))).

Using the chain rule, we can differentiate the exponential term:

d/dt(et) = et.

Differentiating the cosine and sine terms with respect to t gives:

d/dt(cos(4t)) = -4sin(4t),

d/dt(sin(4t)) = 4cos(4t).

Now we can substitute these derivatives back into c'(t):

c'(t) = (et(-4sin(4t)), et(4cos(4t)))

= (-4et sin(4t), 4et cos(4t)).

Now, let's find the angle between c(t) and c'(t) using the dot product rule:

The dot product of two vectors, A = (a₁, a₂) and B = (b₁, b₂), is given by:

A · B = a₁b₁ + a₂b₂.

Applying the dot product rule to c(t) and c'(t), we have:

c(t) · c'(t) = (et cos(4t), et sin(4t)) · (-4et sin(4t), 4et cos(4t))

= -4et² cos(4t) sin(4t) + 4et² cos(4t) sin(4t)

= 0.

Since the dot product of c(t) and c'(t) is zero, we know that the angle between them is 90 degrees (or π/2 radians).

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Answer:

2

Step-by-step explanation:

3 = 5x - 13 + 3x

3 + 13 = 5x + 3x

16 = 8x

16 ÷ 8 = 8x ÷ 8

2 = x

Answer:

\(5x - 13 + 3x = 3 \\ 8x = 3 + 13 \\ 8x = 16 \\ x = \frac{16}{8} \\ x = 2\)

The geometric sequences in the options are:

1, 5, 25, 125, 625...

2, 4, 8, 16, 32...

1, -1, 1, -1, 1...

Geometric sequence is a type of sequence in which the ratio of every two successive terms is a constant.

This ratio is  also called the common ratio of the geometric sequence. In other words, in a geometric sequence, every term is multiplied by a constant which results in its next term.

Let's check if the common ratios are constant (the same):

Sequence 1:

Common ratio; 65/64  ≠ 66/65   [No]

Sequence 2:

Common ratio: 5/1 = 25/5 (i.e. 5)  [Yes]​

Sequence 3:

Common ratio: 4/2 = 8/4 (i.e. 2)  [Yes]

Sequence 4:

Common ratio: 3/2  ≠ 5/3  [No]​ ​

Sequence 5:

Common ratio: -1/1 = 1/(-1) (i.e. -1)  [Yes]

Sequence 6:

Common ratio: 8/14 ≠  2/8  [No]

Sequence 7:

Common ratio: 1/1 ≠ 2/1  [No]

Sequence 8:

Common ratio: 8/5 ≠  11/8  [No]

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just try your best!!!!!!!!!!!!!!!!!!!!!!

Answer:

Step-by-step explanation:

\(7+x\le 19\\ \\ 7-7+x\le 19-7\\ \\ x\le 12\)

Answer:

x = Any number 11 or below!

Step-by-step explanation:

It has to be less than 12 because 7 + 12 = 19 and the result should be less than 19

Hope that helps!

Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.

Given a regression equation is y = 5000 + 7.25x, where y is the predicted sales value (in dollars) and x is advertising budget (in dollars).To find the predicted difference in sales of two stores which differ by $30,000 in advertising budget. Here, the slope of the line is 7.25. This means that for every dollar increase in advertising budget, sales will increase by $7.25. Therefore, a $30,000 difference in advertising budget will lead to a difference in sales of:7.25 × 30,000 = 217,500Therefore, the predicted difference in sales between two women's clothing stores differing by $30,000 is $217,500, which is option E.

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Using the branch and bound method, we can solve the given linear programming problem to maximize Z = 50x₁ + 10x₂, subject to the constraints x₁ + x₂ ≤ 8 and 3x₁ + x₂ ≤ 20, with the additional requirement that x₁ and x₂ are integers and both are less than or equal to 20.

The branch and bound method involves systematically dividing the feasible solution space into smaller subspaces and bounding the optimal solution within each branch.

To solve the linear programming problem using the branch and bound method, we start with an initial branch representing the entire feasible solution space.

We calculate the objective function Z for the current branch and obtain a fractional solution. Since the problem requires integer solutions, we branch further by creating subproblems that enforce different constraints or bounds on the variables.

In this case, we can consider two scenarios: one where x₁ takes the value of the lower integer bound (0) and another where x₁ takes the value of the upper integer bound (8).

For each subproblem, we apply the same branching process to x₂, resulting in a total of nine subproblems.

Next, we compute the objective function Z for each subproblem and compare the values obtained. We update the upper bound of Z based on the maximum Z value found so far.

If the upper bound of Z is less than or equal to the current maximum Z value, we prune that branch as it cannot produce a better solution.

By iteratively branching and pruning the subproblems, we eventually reach a solution that satisfies all the constraints and maximizes the objective function Z.

The optimal solution obtained using the branch and bound method provides the values of x₁ and x₂ that maximize Z while satisfying the given constraints.

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Answer:

y = 13

Step-by-step explanation:

First, find the value of x.

The 2 other angles with x values are alternate exterior angles, meaning they are congruent. Set up an equation setting them equal to each other:

10x - 17 = 8x + 1

Solve for x:

2x - 17 = 1

2x = 18

x = 9

Then, plug in 9 as x into the angle measure next to the one with y values:

8x + 1

8(9) + 1

72 + 1

= 73

This angle and the one with the y value will be supplementary. To find the measure of the angle with the y value, subtract 73 from 180:

180 - 73

= 107

So, it is equal to 107. Lastly, set the angle measure equal to 107 and solve for y:

6y + 29 = 107

6y = 78

y = 13

Answer:

First cone: 29.32

Steps:

1. 3.14(2^2)7/3

2. 3.14(4)7/3

3. 12.56(7/3)

4. 12.56(2.3

5. 29.32

Second cone: 1526.81

Divide 18 in half and so same steps as above to get the answer! :)

Have a great day!!

Please rate and mark brainliest!!

Answer:

Cone 1 = 29.32mi || Cone 2 = 1526.81

Step-by-step explanation:

Step 1) Apply formula (volume of cone)

V= 1/3 * π * r^2 * h [OR] V= π * r^2 * h/3

Step 2) Insert numbers. (cone 1)

V= π * 2^2 * 7/3

Step 3) Insert numbers. (cone 2)

V= π * 9^2 * 18/3 (r=9 because r=1/2 base diameter of circle, 18/2=9)

Step 4) Plug and solve.

Step 5) CHECK YOUR ANSWER BEFORE SUBMISSION. Do it a few times just to make sure it checks out, and then continue!

Step-by-step explanation:

Let b be base and h be height

b = 11+h

Then the area would be hx b = h(11+h) = 11h + h^2

Perimeter = 2h + 2b

= 2h + 2(11+h)

= 2h + 22 + 2h

= 4h + 22

Answer:

x=54

Step-by-step explanation:

55+54= 109

180-109=71

x+17=71

=54

Answer:

nine minus x square

Answer:

4/5 x 2 1/2 < 2 1/2

Step-by-step explanation:

1/5 x 2 1/5 is 1/2 of 2 1/2 so 2 1/2 would be greater.

Answer:

6x + 24

Step-by-step explanation:

Distributive property: a (b + c) = ab + ac.

6 (x + 4) = 6x + 6(4) = 6x + 24.

Answer:

\((5^3)^5=5^1^5\)

\((5^3)*5=625\)

Step-by-step explanation:

If the problem was \((5^3)^5\)

When you raise a power to another power, you can keep the original base and multiply the exponents

\(5^1^5\)

If the problem was \((5^3)*5\)

then you find the value of the exponential number and multiply it by 5

\(625\)

brainliest pls

The simplified value of the expression  (5³)5 is 625 or 5⁴.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An exponential expression (5³)5.

We know 5³ = 5×5×5.

Therefore,

(5³)5.

= 5×5×5×5.

= 25×25.

= 625 or 5⁴.

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Answer:

A

Step-by-step explanation:

the line hits the point between the 6 and 8 notch marks so the y-intercept is (0,7).

a line increasing goes upward from left to right, so the line is increasing from x = -10 to x = -2 if you follow the notches down/up.

then you follow where the line starts decreasing (downward left to right) and you see its from the points x = -2 to x = 10.

i hope this helps :))

The total distance that Kayla walked on Tuesday and Wednesday will be 3/4 miles.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Kayla walked 1/2 miles on Tuesday and then walked 1/4 miles on Wednesday. The total distance that Kayla walked on Tuesday and Wednesday will be:

= 1/2 + 1/4

= 3/4 miles.

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Complete question

Kayla walked 1/2 miles on Tuesday and then walked 1/4 miles on Wednesday. What was the total distance that Kayla walked on Tuesday and Wednesday?

answer is 0.2 using cross multiplication.

Answer:

in 2 seconds, the snail will only move 0.2 centimeters or 2 millimeters. And after 2.5, 0.25 centimeters, or 2.5 millimeters.

Step-by-step explanation:

The options that are true about the two triangles are

△XYZ ~ △X'Y'Z';

XZY ≅ Y'Z'X'

XZ = 2X'Z'

The options are:

△XYZ ~ △X'Y'Z'

XZY ≅ Y'Z'X'

YX ≅ Y'X'

XZ = 2X'Z'

mYXZ = 2mY'X'Z'

W are told that △XYZ is reflected over a vertical line, then dilated by 1/2 to form X'Y'Z'. This means that X'Y'Z' = ¹/₂XYZ

The side lengths of triangle X'Y'Z' is half the side lengths of the original triangle XYZ. The triangles are similar and the angles are congruent.

The side lengths of XYZ are twice the side lengths of X'YZ'.

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A: The percentage of respondents who like hamburgers but dislikes burritos is 46.34%

B: Marginal relative frequency  of all who like hamburgers is 0.65.

C:Lowest joint frequency is of the respondents who like both.

The word "relative" is used to describe how something is being viewed in connection to or in comparison to another event. How frequently an event occurs can be determined by looking at its frequency. On the other hand, relative frequency is a means to compare the frequency of a specific event to all other occurrences.

The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency.

Two facts must be known in order to determine the relative frequency:

>>Number of total events/trials

>>Frequency count for a category/subgroup

                             Like Ham↓  Does Not Like Ham    Total↓

Likes burritos →                 39           38                         77

Does not like burritos →    95           33                        128

Total →                               134           71                        205

So, according to the above table, a total of 77 customers like burritos, out of which 38 do not like hamburgers, hence, the remaining 39 like Hamburgers.

A total of 128 customers do not like burritos, out of which 95 do like hamburgers, hence, the remaining 33 do not like Hamburgers.

A total of 134 customers like hamburgers, but 71 do not like it, hence, the total respondents are 205.

A:

Total people who liked hamburgers are 134 and those who doesnot like burritos and liked hamburgers are 95 and the total people participated in the survey are 205.

So the percentage of people is \(\frac{95}{205}*100\) = 46.34%

B:

The marginal relative frequency is nothing but total people who like hamburgers out of the total respondents.. which is

\(\frac{134}{205}\) = 0.65

C:

The category that has lowest joint relative frequency is

Case 1:

Likes both burritos and hamburgers:

\(\frac{39}{134}=0.29\)

Likes burritos and dislikes hamburgers:

\(\frac{38}{71} = 0.53\)

Likes hamburgers and dislikes burritos:

\(\frac{95}{134} = 0.71\)

Who dislike both are:

\(\frac{33}{71}=0.47\)

So the category which lowest joint frequency is Likes both burritos and Hamburgers.

A: The percentage of respondents who like hamburgers but dislikes burritos is 46.34%

B: Marginal relative frequency  of all who like hamburgers is 0.65.

C:Lowest joint frequency is of the respondents who like both.

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Answer:

look at the link so you can get the straight up answers



Step-by-step explanation:

I did the same test got it all right

PLS give BRAINLIST mean the world

Answer:

MN ≈ 92.1

Step-by-step explanation:

given the figures are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{MN}{IJ}\) = \(\frac{KL}{GH}\) ( substitute values )

\(\frac{MN}{21}\) = \(\frac{57}{13}\) ( cross- multiply )

13 MN = 21 × 57 = 1197 ( divide both sides by 13 )

MN ≈ 92.1 ( to the nearest tenth )

Answer:

c.3.95 gallons hopes this helps

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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Answer:

Step-by-step explanation:

m2 + 3m + 2

m2 + m + 2m + 2

m (m + 1) + 2(m + 1)

(m + 1) and (m + 2) are the factors

The slope of all the given options  are equal and it is equal to slope of given equation .

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

Given

Equation of a given line is x+2 y=6

Lets find out slope m by writing the equation in \($y= \mathbf{m}+\mathbf{b}$\) form

\($$\begin{aligned}& x+2 y=6 \\& 2 y=-x+6 \\& y=\frac{-1}{2} x+6\end{aligned}$$\)

The slope of the line is \($\frac{-1}{2}$\)

Now we find slope of each option using formula \($m=\frac{y_2-y_1}{x_2-x_1}$\)

Lets pick two points from the graph to find out slope

Pick (0,3) and (6,0)

\($$\begin{aligned}& m=\frac{y_2-y_1}{x_2-x_1} \\& m=\frac{0-3}{6-0}=\frac{-1}{2}\end{aligned}$$\)

Now pick two points from option \($\mathbf{B}$\) to find slope

(-10,-3) and (0,-8)

\(m=\frac{-8+3}{0+10}=\frac{-1}{2}$$\)

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The volume of the triangular prism is 60 cm³

A solid figure is a three dimensional shape that has length, width and height. Example of solid figures are cube, pyramid, prism, sphere and so on.

The volume of a triangular prism is given as:

Volume = area of base * height

The area of the prism base = (1/2) * base * height = 1/2 * 5 * 8 = 20 cm²

Volume = area of base * height = 20 cm² * 3 cm = 60 cm³

The volume is 60 cm³

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Yes, any sentence written using addition has its own subtraction equivalent. This is done using the example below.

This can be done using Linear Algebra. Linear Algebra is a branch of mathematics that deals with linear combinations. It includes transformation properties and deals with vectors, planes, mappings, and other spaces.

We can use linear algebra to write equations as discussed in the problem. For example, let's take an unknown variable whose quantity we have to find, which will be x. If we add 13.5 to this variable we get 67.89 as the result.

⇒ x + 13.5 = 67.89    (i)

According to the properties of linear algebra, we can bring the 13.5 on the LHS to the RHS to solve this equation. The 13.5 will become negative in this process -

⇒ 67.89 - 13.5 = x  (ii)

Hence, here we have equation (ii) which is the subtraction equivalent of equation (I). We can solve the equation for the value of x as well and the equations would still be the same.

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Answer:

£48

Step-by-step explanation:

Area of walls = area of four rectangular walls + area of two triangular shape at front and back

Area of a rectangular wall = l *w = 8 * 4 = 32 m²

Area of 4 rectangular walls = 4 *32 = 128 m²

Triangle:

Base = 6m

height = h = 7 - 4 = 3 m

Area of triangle = (1/2)*b*h

                          \(= \dfrac{1}{2}*6*3 = 3*3 = 9 \ m^{2}\)

Area of 2 triangles = 2*9 = 18 m²

Area of four walls = 128 + 18 = 146 m²

Number of paint tins required = 146 ÷ 25 = 5.84 = 6

6 tins are required.

Cost of 6 tins = 8 * 6 = £48

There is about a 7.3% probability that it will take Zach 555 or more throws to score his first ringer.

To solve this problem, we can use a geometric distribution, which models the number of trials it takes to get a success in a series of independent Bernoulli trials (trials with two outcomes: success or failure) with a fixed probability of success.

In this case, the probability of success is 40% (the probability of scoring a ringer), and the probability of failure is 60% (the probability of not scoring a ringer). We can use the formula for the probability mass function of a geometric distribution to calculate the probability that it takes Zach 555 or more throws to score his first ringer:

P(X ≥ 555) = 1 - P(X < 555)

= 1 - (P(X = 1) + P(X = 2) + ... + P(X = 554))

= 1 - (0.4 + (0.4 * 0.6) + (0.4 * 0.6^2) + ... + (0.4 * 0.6^554))

To calculate this probability, we can use a computer to sum up the series, or we can use a calculator with a geometric distribution function. Using a calculator, we get P(X ≥ 555) ≈ 0.073, or about 7.3%.

This means that there is about a 7.3% probability that it will take Zach 555 or more throws to score his first ringer.

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In this case, the probability of success is 40% (the probability of scoring a ringer), and the probability of failure is 60% (the probability of not scoring a ringer). We can use the formula for the probability mass function of a geometric distribution to calculate the probability that it takes Zach 555 or more throws to score his first ringer:

P(X ≥ 555) = 1 - P(X < 555)

= 1 - (P(X = 1) + P(X = 2) + ... + P(X = 554))

= 1 - (0.4 + (0.4 * 0.6) + (0.4 * 0.6^2) + ... + (0.4 * 0.6^554))

To calculate this probability, we can use a computer to sum up the series, or we can use a calculator with a geometric distribution function. Using a calculator, we get P(X ≥ 555) ≈ 0.073, or about 7.3%.