please help!!! i’m not good at proofs

Answer: I would use the max as 25

Step-by-step explanation: You use the variables of y, for the numbers os the maximum. so i would be high

Answer:

Step-by-step explanation:

Change g(n) to y

y = 2n - 2

2y - 2 = n

2y = n + 2

y = (n + 2)/2

g^-1(n) = 1/2n + 1

solution is B

The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

To find the tangential and normal components of the acceleration vector, we need the velocity vector and the curvature of the path. The tangential component of acceleration (at) represents the change in speed or direction along the path. It is given by the derivative of the velocity vector with respect to time. The normal component of acceleration (an) represents the change in direction perpendicular to the path. It is given by the curvature of the path multiplied by the square of the speed.

In mathematical terms:

at = dV/dt

an = (V^2) / R

where:

V is the velocity vector

t is time

R is the radius of curvature of the path.

The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

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Answer:

x = -3

Step-by-step explanation:

Here, this is a vertical line

What this mean here is that the x-value remains constant irrespective of the y value

For all the y values, we have a single x-value

so what this mean is to simply locate the x-axis. value and equate it to x

We have this as;

x = -3

Answer:

4/15 gallons of juice

Step-by-step explanation:

Total gallon you have = 3/5gallons

Amount consumed = 1/3 gallons

Amount left = Total gallons + Amount consumed

Amount left = 3/5-1/3

Find the LCM

amount left = (3)(3)-5(1)/15

Amount left = (9-5)/15

Amount left = 4/15

Hence 4/15 gallons of juice is left

The brand of cell phone and the number of cell phones sold may have a relationship, but it may be influenced by many other factors and may not be linear.

The relationship between the high temperature of the day and the number of zoo visitors that day could be described using correlation. Correlation measures the strength of the relationship between two variables, and in this case, we can expect that on hotter days, more people may visit the zoo, and on cooler days, fewer people may visit the zoo.

The other relationships listed are not necessarily suitable for correlation analysis because they involve a categorical variable or a variable that does not have a clear linear relationship with the other variable. For example, the number of books read and the gender of a student are categorical variables, and correlation analysis is not appropriate for these types of variables. The number of football games played and the position of a football player could have a relationship, but it may not be linear or straightforward. Similarly, the type of beverage ordered and the time of day it was ordered may have a relationship, but it may not be linear or easily quantifiable. The brand of cell phone and the number of cell phones sold may have a relationship, but it may be influenced by many other factors and may not be linear.

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We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

File < Options < (A) Formulas < Automatic

We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

Therefore, File < Options < (A) Formulas < Automatic

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The complete question is given below:

What would you choose as X in the given series of clicks to calculate formulas automatically: File < Options < X < Automatic?

a. Formulas

b. Language

c. Proofing

d. Advanced

Answer: x = 6

---------------------

a) Using the given values, the integral is ∫√(1+EA) dx = ∫(4+t^2)^-1/2 (200-2t^2) dt. Simplifying the given equation, we have (4+t^2)^-1/2 (200-2t^2) = (2/√(4+t^2)) (100-t^2). Let u = 4+t^2, then du/dt = 2t. The given integral then becomes ∫(2/√u)(100-u) du/(2t). Simplifying this further, we obtain (100/2) ∫u-1/2 du - (1/2) ∫u1/2 du. This gives 100√(4+t^2) - t√(4+t^2) + C = √(1+EA) dx, where C is the constant of integration.

b) Given the function x(t) = tan-1(sinh(t)), we can compute the velocity of the particle as v(t) = dx/dt = sec^2(t) sinh(t)/[1+sinh^2(t)]. Since x only depends on t, we can simplify the velocity expression to v(x) = sec^2(t) sinh(t)/[1+sinh^2(t)], where t = sinh^-1[tan(x)]. Thus, the speed of the particle is given by |v(x)| = √[sec^2(t) sinh^2(t)/[1+sinh^2(t)]^2]. We can use trigonometric identities to further simplify this expression to |v(x)| = √(1-cos^2(t))/cos^2(t) = √(sin^2(t))/cos^2(t) = tan(t). Using the definition of t, we have t = sinh^-1[tan(x)]. Thus, the speed of the particle is given by |v(x)| = tan[sinh^-1(tan(x))] = tan[xln(1+√(1+x^2))]

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Answer:

1) 121 students

2) $330

Step-by-step explanation:

1) 44 percent of 275 is 0.44 * 275 = 121 students

2) 20 percent of 275 is 0.2 * 275 = 55. 275 + 55 = $330

Answer:

P( blue second green first) with replacement= 6/25.... without replacement= 4/15

P(green second blue first) with replacement= 6/25... without replacement= 4/15

Sam is 10 years old, and Gina is 15 years old.

Here's a table to represent the situation:

Person ║   Age

Sam      ║    x

Gina     ║    x+5

In this table, the first column lists the two people in the situation, Sam and Gina. The second column shows their ages in years. According to the problem statement, Gina is 5 years older than Sam, so we can represent Gina's age as x + 5, where x is Sam's age.

To find the solution, we need to use the information given in the problem statement to solve for x, which represents Sam's age. We know that Gina's age is x + 5, so we can set up an equation:

Gina's age = Sam's age + 5

x + 5 = x + 5

Simplifying the equation, we can see that x cancels out:

x + 5 - x = 5

5 = 5

This equation is always true, which means that there are infinitely many possible solutions. However, we can find a specific solution if we are given additional information. For example, if we are told that Gina is 15 years old, we can substitute x + 5 = 15 into the equation and solve for x:

x + 5 = 15

x = 10

Therefore, Sam is 10 years old, and Gina is 15 years old.

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Answer:

2.02

Step-by-step explanation:

Hello, I took the quiz. The correct answer is 2.02

Answer:

\((1.5 \times {10}^{8} )(5.9 \times {10}^{4} ) \\ = 1.5 \times 5.9 \times {10}^{(8 + 4)} \\ = \boxed{8.85 \times {10}^{12}} \)

Answer:

17/8 or 2 and 1/8 in decimal= 2.125

Step-by-step explanation:

5 2/3 Divided by 2 2/3

(5*3) + 2= 17/3

(2*3) + 2= 8/3

17/3 divided by 8/3= 17/3 * 3/8

= 17/8 or 2 1/8

Answer:

see explanation

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) ⇔ \(\frac{1}{a^{m} }\) , then

\(1.5^{-2}\)

= \(\frac{1}{1.5^{2} }\)

= \(\frac{1}{2.25}\)

= 0.4444.....

(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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Answer:

X = > 12 because 15 - 3 = 12 and if X was more than 12 it would be wrong.

Step-by-step explanation:

Answer:

7040

Step-by-step explanation:

C= 2000

B = 20/100 x 2000 = 400 + 2000 = 2400

A= 10/100 x 2400 = 240+2400= 2640

2000 + 2400 + 2640 = 7040

The relation y = (7/8)x is proportional in nature.

In mathematics, two sets of numbers, often experimental data, are proportional- directly or inversely, if their corresponding elements have a constant ratio. This ratio is called the coefficient of proportionality or proportionality constant.

Here, we are given a relation between x and y as follows-

y = (7/8)x

dividing both sides by x we get-

y/x = 7/8

Thus, we see that the ratio y : x will always be equal to 7 : 8. In other words, x and y have a constant ratio. Here, the proportionality constant between x and y is 7 : 8.

This means that they are proportional in nature.

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Answer:

3) =(10,2) is correct because

(d,e) = (10,2) respectively

then, d±e

10±2

12

-d±e

-10±2

-8

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

1.278 x 10²

standard notation = ?

Step 02:

Standard notation

We must move the decimal point 2 spaces to the right.

1.278 x 10² ===> 127.8

The answer is:

127.8

Answer:

The perimeter of parallelogram WXYZ is 2√5 + 2√17 units or also known as about 12.72 units.

Step-by-step explanation:

In the diagram, we have a parallelogram. A parallelogram is a shape with two pairs of congruent sides. So, this means that we only need to find the measurement of two sides. From there, we are going to multiply those individual measurements by 2 because both has another side that is congruent  to them. Lastly, we will add up all of the measurements to find the perimeter.

We can find the lengths by using the distance formula.

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}\)

Let's find the length of WX.

\(WX=\sqrt{(4-0)^2+(0-(-1))^2}\)

\(WX=\sqrt{((4)^2+(1)^2)}\)

\(WX=\sqrt{16+1}\)

\(WX=\sqrt{17}\)

Now, we multiply this number by 2 because ZY is congruent to this side.

√17 × 2 = 2√17

Now, let's find the length of WZ.

\(WZ=\sqrt{(0-(-1))^2+(-1-(-3))^2}\)

\(WZ=\sqrt{(1)^2+(2)^2}\)

\(WZ=\sqrt{1+4}\)

\(WZ=\sqrt{5}\)

Now, we multiply this number by 2 because XY is congruent to this side.

√5 × 2 = 2√5

Now, we add these numbers together to get the perimeter.

2√5 + 2√17 = 12.72

The required perimeter of parallelogram WXYZ is \(2\times \sqrt5 + 2\times \sqrt17 \ units\).

We have to determine, The perimeter of parallelogram WXYZ.

According to the question,

A parallelogram is a shape with two pairs of congruent sides. So, this means need to find the measurement of two sides.

From there, multiply those individual measurements by 2 because both has another side that is congruent  to them. Lastly, add up all of the measurements to find the perimeter.

To find the lengths by using the distance formula,

\(d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WX = \sqrt{(4-0)^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{16+1} \\\\WX = \sqrt{17}\)

Then, multiply this number by 2 because ZY is congruent to this side.

\(\sqrt{17} \times 2= 2 \sqrt{17}\)

Now, let's find the length of WZ by using distance formula,

\(d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WZ = \sqrt{((-1)-(-3))^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{4+1} \\\\WX = \sqrt{5}\)

Now, multiply this number by 2 because XY is congruent to this side.

\(=\sqrt{5} \times 2= 2\sqrt{5}\)

Therefore, adding these numbers together to get the perimeter of parallelogram WXYZ,

Perimeter of parallelogram WXYZ  \(=2\times \sqrt5 + 2\times \sqrt17 \ units\)

Hence, The required perimeter of parallelogram WXYZ is \(2\times \sqrt5 + 2\times \sqrt17 \ units\).

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Answer:

This sum is the sum of an arithmetic sequence.  There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.

A nice approach for this sequence is the following.  Notice  that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.

There are n of these pairs.  So the desired sum is n x (first number + last number).   But the first number is 1 and the last on is 2n.   Thus the desired sum is n(1 + 2n).

Hope this helps!!

Mark Brainleast!!!!!!!!!!!

Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.

Now let's say we wanted to add everything in that set.

What we can do is write out the terms

1, 2, 3, 4, ..., m

then just underneath, we write the reverse of that set

m, ..., 4, 3, 2, 1

Here's an example of what I mean. I'll use m = 7

\(\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}\)

For each column, add straight down

The third row will be nothing but 8's

\(\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}\)

We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.

Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.

-----------------------------

That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.

We could write that as 7(1+7)

Then divide that by 2 to fix the double-counting error.

We have 7(1+7)/2

Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2

Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2

We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.

-----------------------------

The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2

In this case, m = 2n because we want the first 2n natural numbers.

Therefore,

m(1+m)/2

2n(1+2n)/2

n(1+2n)

n(2n+1)

represents the sum 1+2+3+...+n+...+2n

-----------------------------

Try out a value like n = 5 to find that 2n = 2*5 = 10, and,

1+2+3+4+5+6+7+8+9+10 = 55

also

n(2n+1) = 5(2*5+1) = 5*(11) = 55

Showing that the formula works for n = 5. I'll let you try other values of n.

exact form

x=71/8

Decimal Form:

x=8.875

Mixed Number Form:

x=  8    7/8

Answer:

Step-by-step explanation:

8 7/8

Answer:

y=3. (-1)-1

y= -3-1

y= -4

Step-by-step explanation:

The unit tangent vector t(1) at t = 1 is:

t(1) = (4 i + 6 j + 3 k) /\(\sqrt{(61)}\)

To find the unit tangent vector,

we need to calculate the derivative of the position vector r(t) with respect to the parameter t, and then normalize the resulting vector.

Given the position vector r(t) = 4t i + 3t^2 j + 3t k,

we can find the derivative:

r'(t) = d(r(t))/dt

     = 4 i + 6t j + 3 k

Now, we can evaluate r'(t) at t = 1:

r'(1) = 4 i + 6(1) j + 3 k

      = 4 i + 6 j + 3 k

To obtain the unit tangent vector,

we need to normalize r'(1):

t(1) = r'(1) / ||r'(1)||

where ||r'(1)|| represents the magnitude or length of r'(1).

The magnitude of r'(1) is given by:

||r'(1)|| = \(\sqrt{((4^2) + (6^2) + (3^2))}\)

       = \(\sqrt{61}\))

This is the normalized vector representing the direction of the tangent to the curve at the point where t = 1.

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Answer:

I think the answer is 3150 miles

I multiplied 1.50 by 21 and the answer I converted to miles

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