X square +1/2x+blank= 2+ blank

For your question: "The path of a seat on a new Ferris wheel is modeled by: What is the maximum height a rider will experience?"

The answer is B. 55 feet.

I got this through working this on my own. Let me know if you have any other questions down below.

The path of a seat on a new Ferris wheel is modeled by the function. the maximum height a rider will experience is 55 feet.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function,

if results in negative output, then at that point, there is maxima.

If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

The path of a seat on a new Ferris wheel is modeled by

\(x = -25sin( \dfrac{ \pi} {30}t)\\\\y= -25cos( \dfrac{ \pi} {30}t)+ 30,\)

To find its maximum, we will derivate this function and equalize it to 0.

\(y'(t)= \dfrac{5}{6}\pi cos( \dfrac{ \pi} {30}t)\\\\y''(t)= \dfrac{1}{36}\pi^2 cos( \dfrac{ \pi} {30}t)\)

Now given that we have an arbitrary critical point,

If   \(y''(t) > 0\) then we will have a minimum at tn.

If  \(y''(t) < 0\) then we will have a maximum at tn.

by replacing the equation with the critical points.

y(30) = 55

y(-30) = 55

We found out that the maximum height a rider will experience is 55 feet.

The answer is B. 55 feet.

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Solution for the question 2 :

It is given that ,

The population after n years is given by exponential function ,

Population after 9 years is calculated as,

Thus the population after 9 years is 956 .

To construct a truth table for the expression `(x+y′)(x′+z′)(y′+z)`, follow the steps given below:

Step 1: Write the given expression, `(x+y′)(x′+z′)(y′+z)`.

Step 2: List out all possible combinations of the given variables in a table. There are three variables x, y and z, so there will be 2³ = 8 combinations. Let's list them as follows: x=0, y=0, z=0 x=0, y=0, z=1 x=0, y=1, z=0 x=0, y=1, z=1 x=1, y=0, z=0 x=1, y=0, z=1 x=1, y=1, z=0 x=1, y=1, z=1

Step 3: Evaluate the expression `(x+y′)(x′+z′)(y′+z)` for each combination of variables, and write the output values in the truth table. To do this, substitute the given variable values in the expression and then simplify to get the output.

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Step-by-step explanation:

Perimeter = Sum of all sides

\(\longrightarrow\) 11 + 5 + 10 + 2

\(\longrightarrow\) 16 + 12

\(\longrightarrow\) 28 cm

Area of Rectangule = Length × Breadth

\(\longrightarrow\) 2 × 5

\(\longrightarrow\) 10 in²

Volume of cube = (Side)³

\(\longrightarrow\) (1)³

\(\longrightarrow\) 1 ft³

Perimeter = Sum of sides

\(\longrightarrow\) 4 + 5 + 5

\(\longrightarrow\) 14 cm

Area of triangle = 1/2 × Height × Base

\(\longrightarrow\) 1/2 × 5 × 8

\(\longrightarrow\) 5 × 4

\(\longrightarrow\) 20 mm²

Answer:

75%

Step-by-step explanation:

Answer: The axis of reflection is x

Step-by-step explanation:

Answer:

1 : 27

Step-by-step explanation:

Radius of sphere one = r₁ = x units

Radius of sphere 2 = r₂ = 3*x = 3x units

Ratio of area of two sphere's = r₁³ : r₂³

                                                = x³ : (3x)³

                                                \(= \frac{x^{3}}{3^{3}*x^{3}}\\\\= \frac{1}{3^{3}}\\\\= \frac{1}{27}\)

                                                 = 1 : 27

The present value is approximately $624,732.39. To determine which method would give Ms. Lucy Brier the highest winnings, we need to calculate the present value of each option .

Using the appropriate opportunity cost of 8% p.a. compounded quarterly. The method with the highest present value will result in the highest winnings. a) For $30,000 each quarter for 6 years with the first payment received immediately, we can calculate the present value using the formula for the present value of an ordinary annuity: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $30,000; r = Annual interest rate = 8% = 0.08; n = Number of compounding periods per year = 4 (quarterly compounding); t = Number of years = 6. Using the formula, the present value is approximately $151,297.11. b) For $500,000 received immediately, the present value is simply the same amount, $500,000. c) For $120,000 each year for 5 years with the first payment in 1 year's time, we can calculate the present value of an ordinary annuity starting in 1 year: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $120,000; r = Annual interest rate = 8% = 0.08; n = Number of compounding periods per year = 4 (quarterly compounding); t = Number of years = 5.

Using the formula, the present value is approximately $472,347.55. d) For $37,000 each quarter for 4 years with the first payment in 3 months' time, we can calculate the present value of an ordinary annuity starting in 3 months: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $37,000. r = Annual interest rate = 8% = 0.08. n = Number of compounding periods per year = 4 (quarterly compounding). t = Number of years = 4.Using the formula, the present value is approximately $142,934.37. e) For $75,000 each year for 11 years with the first payment in 1 year's time, we can calculate the present value of an ordinary annuity starting in 1 year: Present Value = C * (1 - (1 + r/n)^(-n*t)) / (r/n). Where: C = Cash flow per period = $75,000; r = Annual interest rate = 8% = 0.08; n = Number of compounding periods per year = 4 (quarterly compounding); t = Number of years = 11. Using the formula, the present value is approximately $624,732.39. Comparing the present values, we can see that option e) with $75,000 each year for 11 years starting in 1 year's time has the highest present value and, therefore, would give Ms. Lucy Brier the highest winnings.

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Therefore, the first term of the sequence is 3.

A sequence is an ordered list of numbers, usually generated by a pattern or a rule. Each number in the sequence is called a term, and the position of a term in the sequence is called its index. Sequences can have a finite or infinite number of terms, and they can be defined in various ways, such as recursively (where each term is defined in terms of the previous terms) or explicitly (where the formula for each term is given).

Here,

The given sequence is an arithmetic sequence, where the common difference between consecutive terms is 4. To find the first term, we can use the formula for the nth term of an arithmetic sequence, which is:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the position of the term in the sequence, and d is the common difference.

For this sequence, we know that a6 = 23 (since 23 is the last term given in the sequence), n = 6, and d = 4. Substituting these values into the formula, we get:

a6 = a1 + (6 - 1)4

23 = a1 + 20

a1 = 23 - 20

a1 = 3

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Complete question:

What’s the first term for the given sequence: 3, 7, 11, 15, 19, 23?

No, it does not matter who will go first as the probability of getting both head and tail after flipping a coin is equal to ( 1 / 2 ).

As given in the question,

Number of players playing the game = 2

Number of coins to flip = One

Possible outcomes after flipping a coin = { Head , Coin }

Probability of getting a head

= (Number of favourable outcomes) / ( Total number of outcomes)

= 1 / 2

Probability of getting a tail

= 1 / 2

Either you tossed first or second chances are fifty percent.

Therefore, it does not matter who will go first as probability of getting head and tail is ( 1 / 2) after flipping a coin.

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Answer:

m<ECB = 65°

Step-by-step explanation:

<ACB and <ACD are vertical angles. That means they are congruent and have equal measures.

m<ECB = 65°

Vector subtraction is done by arranging head to tail.

Vector subtraction is the process of finding the vector that results from taking away one vector from another. To perform vector subtraction, we arrange the vectors head to tail, with the tail of one vector touching the head of the other vector. We then draw a new vector from the tail of the first vector to the head of the second vector. The resulting vector is the difference between the two vectors. This can be mathematically represented as:

a - b = a + (-b)

where "a" and "b" are vectors, and (-b) is the additive inverse of b, which is the vector with the same magnitude as b but opposite in direction.

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Answer:

To find the value of n that makes the fraction A have the largest value, we can take the derivative of A with respect to n, set it equal to zero, and solve for n.

First, let's rewrite the fraction A as:

A = 1 + \frac{1}{n^{2}+1}

Next, let's take the derivative of A with respect to n:

dA/dn = 0 - 2n/(n^2+1)^2

Setting dA/dn equal to zero, we get:

0 = -2n/(n^2+1)^2

Multiplying both sides by (n^2+1)^2, we get:

0 = -2n

Therefore, n = 0 is a critical point of A. However, n cannot equal 0 because the denominator of A would be zero, which is undefined.

Instead, let's consider the limit of A as n approaches infinity. We have:

lim A = lim (1 + 1/(n^2+1)) = 1

Therefore, as n approaches infinity, A approaches 1.

On the other hand, as n approaches negative infinity, A approaches -1 because the denominator of A becomes negative while the numerator remains positive.

Therefore, the largest value of A occurs at n = infinity, and A approaches 1 as n approaches infinity.

In conclusion, the value of n that makes the fraction A have the largest value is infinity.

Answer:

C. Supplementary Angles

One way to remember that is that C is the top half of S and Complementary Angles =90 and Supplementary angles =180. 90 is one half of 90

B makes sense.

On the first play, they gained 6 yards.

On the 2nd play, they lost 8 yards, which can be shown as + (-8)

On the 3rd play, they lost two yards, which can be shown as + (-2)

If you input it in a calculator, you'd find that the answer is a negative, which makes sense considering that they lost more yards than they gained.

Answer:

We know that there are 5,569,500 strings of length 14 over the alphabet {a, b, c, d} that have exactly three a's or exactly three b's or both

Step-by-step explanation:

We can use the principle of inclusion-exclusion to count the number of strings of length 14 over the alphabet {a, b, c, d} that have exactly three a's or exactly three b's or both.

First, let's count the number of strings with exactly three a's. We can choose the positions for the three a's in ${14 \choose 3}$ ways, and for each choice, we can fill the remaining 11 positions with any of the three remaining letters (b, c, or d) in $3^{11}$ ways. Therefore, the number of strings with exactly three a's is ${14 \choose 3} \times 3^{11}$.

Similarly, the number of strings with exactly three b's is ${14 \choose 3} \times 3^{11}$.

To count the number of strings with both three a's and three b's, we can choose the positions for the three a's in ${14 \choose 3}$ ways, and choose the positions for the three b's among the remaining 11 positions in ${11 \choose 3}$ ways. Then, we can fill the remaining 8 positions with any of the two remaining letters (c or d) in $2^8$ ways. Therefore, the number of strings with both three a's and three b's is ${14 \choose 3} \times {11 \choose 3} \times 2^8$.

By the principle of inclusion-exclusion, the total number of strings with exactly three a's or exactly three b's or both is:

(

14

3

)

×

3

11

+

(

14

3

)

×

3

11

−

(

14

3

)

×

(

11

3

)

×

2

8

(

3

14

​

)×3

11

+(

3

14

​

)×3

11

−(

3

14

​

)×(

3

11

​

)×2

8

Simplifying this expression gives:

2

×

(

14

3

)

×

3

11

−

(

14

3

)

×

(

11

3

)

×

2

8

2×(

3

14

​

)×3

11

−(

3

14

​

)×(

3

11

​

)×2

8

Plugging in the values gives us:

2

×

(

14

3

)

×

3

11

−

(

14

3

)

×

(

11

3

)

×

2

8

=

5

,

569

,

500

2×(

3

14

​

)×3

11

−(

3

14

​

)×(

3

11

​

)×2

8

=5,569,500

Therefore, there are 5,569,500 strings of length 14 over the alphabet {a, b, c, d} that have exactly three a's or exactly three b's or both

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To determine whether the sequence is bounded, we can consider its behavior as n gets larger and larger. As n increases, 2^n grows exponentially, which means that a_n will also grow exponentially. However, no matter how large n gets, there will always be a constant term of 8 added to the result, which means that the sequence will never become unbounded. In other words, the sequence is both monotonic and bounded.

To determine the boundedness and monotonicity of the sequence a_n = 2^n + 8, n≥1, we can start by considering its first few terms:
a_1 = 2^1 + 8 = 10
a_2 = 2^2 + 8 = 12
a_3 = 2^3 + 8 = 16
a_4 = 2^4 + 8 = 24
From this, we can see that the sequence is increasing, as each term is larger than the one before it. This means that the sequence is monotonic.

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The answer is 21

I just took the test

Answer:

21.25

Step-by-step explanation:

took the test

The quotient is 1111. The process continues until the result is less than the divisor.

To perform the division using the restoring-division algorithm with the given divisor and dividend, follow these steps:

Step 1: Initialize the dividend and divisor

Divisor: 00011

Dividend: 1011

Step 2: Append zeros to the dividend

Divisor: 00011

Dividend: 101100

Step 3: Determine the initial guess for the quotient

Since the first two bits of the dividend (10) are greater than the divisor (00), we can guess that the quotient bit is 1.

Step 4: Subtract the divisor from the dividend

101100 - 00011 = 101001

Step 5: Determine the next quotient bit

Since the first two bits of the result (1010) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

Step 6: Subtract the divisor from the result

101001 - 00011 = 100110

Step 7: Repeat steps 5 and 6 until the result is less than the divisor

Since the first two bits of the new result (1001) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100110 - 00011 = 100011

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100011 - 00011 = 100001

Since the first two bits of the new result (1000) are still greater than the divisor (00011), we guess that the next quotient bit is 1.

100001 - 00011 = 011111

Since the first two bits of the new result (0111) are less than the divisor (00011), we guess that the next quotient bit is 0.

011111 - 00000 = 011111

Step 8: Remove the extra zeros from the result

Result: 1111

Therefore, the quotient is 1111.

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The inference is that the person will tell the friend that he did manifest coding and he should have recorded the base.

The options are:

He did manifest coding.

He did latent coding.

He should have recorded the base.

He did manifest coding and he should have recorded the base.

It should be noted that an inference simply means the conclusion that can be deduced based on the information given.

In this case, the friend was interested in determining whether the news media noticed campus events and decided to do a content analysis of the local paper.

Therefore, the the person will tell the friend that he did manifest coding and he should have recorded the base.

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You told your friend: d. he did manifest coding and he should have recorded the base.

The missing options are:

a. he did manifest coding.      b. he did latent coding.

c. he should have recorded the base.

d. he did manifest coding and he should have recorded the base.

e. he did latent coding and he should have recorded the base.

From the question, we understand that:

As a general rule, manifest coding include making use of the contents at the surface gotten from available data and questionnaires.

Because the stories that mentioned the university name can be gotten from publications, it means that your friend used manifest coding

Hence, the true statement is (d) he did manifest coding and he should have recorded the base.

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Answer:

12 is 85.714285714286% of 14.

Answer:

thanks

Step-by-step explanation:

I don't understand this problem. will look at and edit my answer if get it.

Step-by-step explanation:

2πr^2h

2*22/7*6*6*3

2*22/7*36*3

2*22/7*108

Answer:

A. 120 degrees.

Step-by-step explanation:

The two angles are alternate angles, which means they are congruent. So, x is also 120 degrees.

Hope this helps!

The area of the region bounded above by y = 3x and below by y = 9x^2 is 270 square units.

To use Green's Theorem to calculate the area of the region bounded above by y = 3x and below by y = 9x^2, we need to first find a vector field whose divergence is 1 over the region.

Let F = (-y/2, x/2). Then, ∂F/∂x = 1/2 and ∂F/∂y = -1/2, so div F = ∂(∂F/∂x)/∂x + ∂(∂F/∂y)/∂y = 1/2 - 1/2 = 0.

By Green's Theorem, we have:

∬R dA = ∮C F · dr

where R is the region bounded by y = 3x, y = 9x^2, and the lines x = 0 and x = 6, and C is the positively oriented boundary of R.

We can parameterize C as r(t) = (t, 3t) for 0 ≤ t ≤ 6 and r(t) = (t, 9t^2) for 6 ≤ t ≤ 0. Then,

∮C F · dr = ∫0^6 F(r(t)) · r'(t) dt + ∫6^0 F(r(t)) · r'(t) dt

= ∫0^6 (-3t/2, t/2) · (1, 3) dt + ∫6^0 (-9t^2/2, t/2) · (1, 18t) dt

= ∫0^6 (-9t/2 + 3t/2) dt + ∫6^0 (-9t^2/2 + 9t^2) dt

= ∫0^6 -3t dt + ∫6^0 9t^2/2 dt

= [-3t^2/2]0^6 + [3t^3/2]6^0

= -54 + 324

= 270.

Therefore, the area of the region bounded above by y = 3x and below by y = 9x^2 is 270 square units.

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The Volume of crystals is 160 mm³ while the area of the base is 20 mm².

Volume is the amount of space occupied by a three dimensional shape or object.

Area of triangle = (1/2) * DF * height

Height = 10 - 6 = 4 mm, DF = AC = AB + BC = 2 + 3 = 5 mm

Area of triangle = (1/2) * 5 * 4 = 10 mm²

Volume of triangle prism = Area of triangle * AG = 10 * 4 = 40 mm³

Volume of rectangular prism = A to F * AC * AG = 6 * 5 * 4 = 120 mm³

Volume of crystals = 120 + 40 = 160 mm³

Area of base = AC * AG = 5 * 4 = 20 mm²

The Volume of crystals is 160 mm³ while the area of the base is 20 mm².

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Answer: R  = (4600 - 200x) ( 9 + 1x)

Step-by-step explanation:

We have that

Revenue  =  Members  *  (Cost Per Member)

Where x represents the number of $1  increases

The percentage rate of increase in Joshua wages is 17%

Rate of increase or decrease is often referred to as rate of change. Rate of change refers to how quickly something changes over time.

To calculate the rate of decrease we subtract the original value from the new value, then divide the result by the original value. Multiply the result by 100. The answer is the percent increase.

This means percentage rate in increase = (new wage - original wage )/original wage × 100

= (14-12)/12 ×100

= 2/12 ×100

= 100/6 = 17% ( nearest percent)

Therefore the percentage increase in Joshua wage is 17%

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-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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