What is the sum of the first 90 consecutive odd numbers?

Particle moves with its position given by x= cos(2t) and y= sin (t), where positions are given in feet from the origin and time t is in seconds. The speed of the particle at any time t is v = \(\sqrt\)(4sin²(2t) + cos²(t)).

For the speed of the particle, we can calculate the magnitude of its velocity vector.

The velocity vector can be obtained by differentiating the position vector with respect to time.

We have the position of the particle as x = cos(2t) and y = sin(t), we can differentiate these equations to find the corresponding velocity components:

vx = dx/dt = -2sin(2t)

vy = dy/dt = cos(t)

The magnitude of the velocity vector (v) is given by the square root of the sum of the squares of its components:

\(\sqrt\)(vx² + vy²) = \(\sqrt\)((-2sin(2t))² + (cos(t))²)

Simplifying this expression:

v = \(\sqrt\)(4sin²(2t) + cos²(t))

This is the speed of the particle at any given time t.

Note that the speed is not constant but varies with time due to the periodic nature of the sine and cosine functions.

To know more about velocity vector refer here:

https://brainly.com/question/11313073#

#SPJ11

The value of the legs of the triangle would be hypotenuse/√2.

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

Learn more about Trigonometry on

https://brainly.com/question/29002217?referrer=searchResults

#SPJ4

Answer:

• d and f

Step-by-step explanation:

• take an example of;

→ ax + by + 1

\(.\)

True, because dot plots usually look like this

0              0                                        

0              0               0               0               0

__________________________________

1               2               3               4               5    

As you can see, the dots are above the line.        

The sum of the areas of squares K and L equals the area of square P.

The surface of a shape's surface is measured by its area. The length and width of a rectangle or square must be multiplied to determine their respective areas. A has a perimeter of x by y.

The rectangle was chopped diagonally in the diagram, creating two squares and four right triangles.

To discover which statement is true, take the following steps:

Figure 1 shows the areas of four triangles that are identical to one another and the sum of the remaining squares K and L.

The area of the square P is equal to the area of the triangle 4 in Figure 2.

The area of square P is equal to the sum of the areas of squares K and L, as shown by the above conclusion.

To know more about areas visit:-

https://brainly.com/question/19456350

#SPJ1

(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

Learn more about  Equilibrium

brainly.com/question/30694482

#SPJ11

Using addition and subtraction of the fractions with different denominators, we have the following:

1) 13/8

2)  1/8

3) 73/36

4) 29/35

5) 55/216

6) 43/48

7) 5/72

8) 13/8

9) 145/36

10) 275/56

11) 71/70

12) 3/7

For addition and subtraction of fractions with different denominators, we shall first find a common denominator by finding their LCM (Lowest Common Denominator):

1) 7/8 + 3/4:

LCM (the least common multiple) of 8 and 4 is 8.

Next, convert the fractions to get a common denominator:

7/8 + 3/4 = (7/8) + (3/4 * 2/2) = 7/8 + 6/8 = (7 + 6)/8 = 13/8.

2) 7/8 - 3/4:

The LCM of 8 and 4 is 8:

7/8 - 3/4 = (7/8) - (3/4 * 2/2) = 7/8 - 6/8 = (7 - 6)/8 = 1/8.

3) 1 1/12 + 17/18:

First, convert the mixed fraction to an improper fraction.

1 1/12 = (12/12 + 1/12) = 13/12

Find a common denominator for 12 and 18, which is 36.

13/12 + 17/18 = (13/12 * 3/3) + (17/18 * 2/2)

= 39/36 + 34/36 = (39 + 34)/36 = 73/36

4) 3/7 + 2/5:

3/7 + 2/5 = (3/7 * 5/5) + (2/5 * 7/7)

= 15/35 + 14/35 = (15 + 14)/35 = 29/35

5) 15/24 - 10/27 :

15/24 - 10/27 = (15/24 * 9/9) - (10/27 * 8/8)

= 135/216 - 80/216 = (135 - 80)/216 = 55/216

6) 7/12 + 5/16 :

7/12 + 5/16 = (7/12 * 4/4) + (5/16 * 3/3) = 28/48 + 15/48 = (28 + 15)/48 = 43/48

7) 15/27 - 5/24:

15/27 - 5/24 = (15/27 * 8/8) - (5/24 * 9/9) = 120/216 - 45/216 =

(120 - 45)/216 = 75/216 = 5/72

8) 1 1/4 + 3/8 :

1 1/4 = (4/4 + 1/4) =

5/4 + 3/8 = (5/4 * 2/2) + (3/8 * 1/1) = 10/8 + 3/8 = (10 + 3)/8 = 13/8

9) 11/4 + 23/18:

11/4 + 23/18 = (11/4 * 9/9) + (23/18 * 2/2)

= 99/36 + 46/36 = (99 + 46)/36 = 145/36

10) 29/8 + 9/7:

29/8 + 9/7 = (29/8 * 7/7) + (9/7 * 8/8)

= 203/56 + 72/56 = (203 + 72)/56 = 275/56

11) 2 13/35 - 1 5/14:

2 13/35 = (2 * 35/35) + 13/35 = 70/35 + 13/35 = 83/35

1 5/14 = (1 * 14/14) + 5/14 = 14/14 + 5/14 = 19/14

83/35 - 19/14 = (83/35 * 2/2) - (19/14 * 5/5)

= 166/70 - 95/70 = (166 - 95)/70 = 71/70

12) 2/3 + 1/21 - 2/7:

2/3 + 1/21 - 2/7 = (2/3 * 7/7) + (1/21 * 1/1) - (2/7 * 3/3)

= 14/21 + 1/21 - 6/21 = (14 + 1 - 6)/21

= 9/21 = 3/7

Learn more about fractions at brainly.com/question/30154928.

#SPJ1

Answer:

c

Step-by-step explanation:

its c because I just cacuulated it

To determine the next step, we need to slove the expression.

divide both sides by -1:

Square both sides of the equation:

There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

Learn more about degrees of freedom

brainly.com/question/32093315

#SPJ11

There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

Learn more about  t-test

https://brainly.com/question/13800886

#SPJ11

There will be 60 residuals for simple bivariate regression's  60 observations.

According to the statement

We have given that the there is 60 observations and we have to find the number of simple bivariate regression for these observations.

So, For the solution of this problem,

We know that the

A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an outcome variable, specifically with the assumption that the explanatory variable influences the outcome variable, and not vice-versa.

And we know that the it is always same for the number as the number of given observations.

That's why there is 60 residuals.

So, There will be 60 residuals for simple bivariate regression's  60 observations.

Learn more about simple linear regression here

https://brainly.com/question/26755306

#SPJ4

There are two possible outcomes for flipping a coin: heads or tails. Then, there is a probability of 1/2 of flipping tails.

There are six possible outcomes for rolling a dice: 1, 2, 3, 4, 5 or 6. Then, there is a probability of 5/6 of rolling a number greater than 1.

The probability of flipping tails and rolling a number greater than 1 is the product of the probabilities of these two events happening independently:

Therefore, the answer is:

The quiz scores of Rich Borne's Chemistry 101 students are as follows: 24, 31, 47, 29, 31, 16, 48, 41, 50, 54, 37, 22, 54, 38, 7, and 16.the performance of Rich Borne's Chemistry 101 students on the quiz

To analyze this data, we can calculate various descriptive statistics such as the mean, median, mode, range, and standard deviation. The mean (average) score can be obtained by summing up all the scores and dividing by the total number of scores. The median represents the middle value when the scores are arranged in ascending order. The mode refers to the most frequently occurring score. The range is the difference between the highest and lowest scores, indicating the spread of the data. The standard deviation measures the variability or dispersion of the scores around the mean.

By calculating these descriptive statistics, we can gain insights into the performance of Rich Borne's Chemistry 101 students on the quiz and understand the central tendency and variability of their scores.

know more about descriptive statistics :brainly.com/question/30764358

#SPJ11

Answer:

the anserw would be B

Step-by-step explanation:

The relationship that explains the exponential relationship between the year and amount of energy used is: Option B: The amount of energy used decreases by different amount each year.

Rate of an exponential function is  in terms of exponential function itself. It's not constant, and always changing. For example, the rate of \(y = e^x\) with respect to x is \(y' = e^x\) itself, which increases as x increases.

The given table is:

Year(Serial no.)   Amount of energy used (kWh)

          1                      1,000,000

         2                         900,000

         3                         810,000

         4                         792,000
The differences between each consequent years of the amount of energy used is:

1000000 - 900000 = 100000

900000 - 810000 = 90000

810000 - 792000 = 18000

So, we see that the decrement is done by decreasing amount.

So rate of change wasn't constant but continuosly changing.

Thus, Option C is clearly wrong.

We see that 100,000 is 10% of 1,000,000

and 90,000 is 10% of next years amount 900,000

but 18,000 is not 10% of next years amount which is 810,000

Thus, Option A is wrong too.

Option B is correct in its statement, and so as option D because we don't see any immediate pattern in the decrement, except that the energy is just decreasing, so its unexpected.

The rate of exponentially related variables is not unexpected though.

So, its only Option B which is closest (among other options) to the intention of telling that the relation between the year and the amount of energy used is exponential, although it doesn't prove that the relationship is exponential. (because, suppose the function i take is \(y = x^2\), then its rate with respect to x is \(y' = 2x\) and this rate is also non-constant, but the function wasn't exponential).

Thus, the relationship that explains the exponential relationship between the year and amount of energy used is: Option B: The amount of energy used decreases by different amount each year.

Learn more about rates of exponential functions here:

https://brainly.com/question/1497850

Answer:

What is the sum of the measures of the interior anles of a convex 13-gon? There is a formula... the sum of the measures of the interior angles of a convex n-gon is (n-2)180 degrees. For a triangle, n=3, so it's (1)180=180 degrees.

Step-by-step explanation:

180(n-2)

n=number of sides

from question, number of sides=13

substitute 13 into the equation given above

180(13-2)

180(11)

1980 is the answer

For the given function:

Domain:  (2,∞)

Range: negative infinity , and all values less than or equal to 1.

The given logarithmic function is

y = -log(x - 2) + 1

To find Domain of this function

Proceed,

⇒ x - 2 > 0

⇒ x - 2 > 0

⇒ x > 2

Hence,

Domain of it is

⇒ x > 2

Domain set is (2,∞)

The behavior of the logarithmic term as x approaches infinity.

As x becomes very large, the expression x - 2 becomes much larger than 1, and so the logarithm ⇒ negative infinity.

Therefore, as x ⇒ infinity, y ⇒ negative infinity.

Similarly, as x ⇒ 2 from above,

The expression x - 2 ⇒ 0,

And the logarithm approaches negative infinity.

Therefore, as x ⇒ 2 from above, y ⇒ positive infinity.

Thus the logarithm is a decreasing function.

Hence,

The range includes negative infinity (asymptotically approached as x approaches infinity), and all values less than or equal to 1 (attained as x approaches 2 from above).

To learn more about function visit:

https://brainly.com/question/8892191

#SPJ1

Answer: Let's call the time it takes for Mrs. Cunningham to overtake Mr. Cunningham "t".

In that time, Mr. Cunningham will have traveled for 4 more hours than Mrs. Cunningham, so he will have traveled 4 + t hours.

We can set up an equation to represent the distance each person traveled:

distance = rate x time

For Mr. Cunningham:

distance = 46 mph x (4 + t) hours

For Mrs. Cunningham:

distance = 62 mph x t hours

Since they end up at the same place, their distances must be equal:

46 mph x (4 + t) = 62 mph x t

Simplifying this equation:

184 + 46t = 62t

16t = 184

t = 11.5

Therefore, it will take Mrs. Cunningham 11.5 hours to overtake Mr. Cunningham.

Step-by-step explanation:

if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter.

If the sample size is 28 and the population standard deviation is increased, there will be a direct impact on the confidence interval. This is because the confidence interval is calculated based on the sample mean and the standard deviation. If the population standard deviation is increased, it means that there is more variability in the population. This increase in variability will lead to wider confidence intervals.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The width of the confidence interval is determined by the sample size, the standard deviation, and the level of confidence.
In this case, if the population standard deviation is increased, it means that the sample standard deviation will also increase. The sample mean will be relatively more variable than it would be if the population standard deviation was lower. This increase in variability will cause the confidence interval to become wider, as there is more uncertainty in the estimate of the population parameter.
In summary, if the population standard deviation is increased while the sample size is 28, the confidence interval will become wider. This is because there is more variability in the sample mean, and therefore more uncertainty in the estimate of the population parameter. It is important to note that increasing the sample size can help to reduce the impact of increased population standard deviation on the confidence interval, as a larger sample size provides more accurate estimates of the population parameter.

for more questions on confidence interval

https://brainly.com/question/20873848

#SPJ11

Answer:

\(x = 7 \sqrt[3]{2} \)

The perimeter of half of the basketball court is 194 feet.

The basket ball court is divided into two equal halves. The perimeter of the halve of the basket ball court can be calculated as follows:

Therefore, the perimeter is the sum of the whole sides of half of the basket ball court.

Hence,

perimeter of half of the basket ball court = 94 / 2 + 94 / 2 + 50 + 50

perimeter of half of the basket ball court = 47 + 47 + 100

perimeter of half of the basket ball court = 94 + 100

perimeter of half of the basket ball court = 194 feet

learn more on perimeter here: brainly.com/question/12036152

#SPJ1

Answer:

225 ft²

Steps:

(20×10)+5² = 200+25 = 225 ft²

Answer: 225ft^2

Step-by-step explanation:

The zoo had 85 visitors on Grandparents' Day.

To get the number of visitors that visited in the year, we have to divide the total amount of money earned from ticket sales by the cost of each ticket.

Given that:

Total ticket sales = $768

Cost of each ticket = $9

Number of visitors = Total ticket sales / Cost of each ticket

Number of visitors = $768 / $9

Number of visitors = 85.3333333

Number of visitors = 85.33.

Full question:

Once a year, the zoo hosts Grandparents' Day, where only senior citizens are allowed in the zoo. This year, the zoo sold $768 worth of tickets on Grandparents' Day. How many visitors did the zoo have that day? Assume the ticket cost $9 per person.

Read more about cost

brainly.com/question/839029

#SPJ1

The solution of the given equation \((4x-16)^{1/2} = 36\) is 328.

The given equation is:

\((4x-16)^{1/2} = 36\)

The solution of an equation is to find out the numeric value of the variable such that Left-hand side and Right-hand side becomes equal.

Squaring both sides of the given equation.

\([(4x-16)^{1/2} ]^2= (36)^2\)

\(4x-16 = 36^{2}\)

\(4x -16 =1296\)

\(4x =1296+16\)

\(4x = 1312\)

x= 328

Therefore, The solution of the given equation \((4x-16)^{1/2} = 36\) is 328.

To get more about equations visit:

https://brainly.com/question/9423572

Answer:

rate of interest is 6 percent per annum.

Step-by-step explanation:

Formula for simple interest is given

SI = p*r*t/100

where

SI is simple interest

p is principal

r is the rate of interest

t is the time

_______________________________

Given

p = 6400

SI = 768

t = 2 years

r we have to find

lest sue the above formula and plug the given value in it

768 = 6400*r*2/100

=> 768 = 128r

=> r = 768/128 = 6

Thus, r = 6%

thus, rate of interest is 6 percent per annum.

Answer:

122.50

380.80

Step-by-step explanation:

that's both answers have fun go play

Answer:

A. $122.5

B. $340.8

Step-by-step explanation:

A. $24.50 × 5 weeks = $122.5

- He only deposited one time each week so take the amount he puts in every week and multiply it by the amount of times he did it which is 5

B. $85.20 × 4 = $340.8

- 4 friends get the same amount of money just multiply that money amount they earned by all of them which is 4.

A The histogram is the best graph showing the average scores of 5 UCI volleyball teams in UCI history. Because it allows us to divide the data into as many or as few groups as we want and clarify the comparison between them.

We would like to view the average points data of the top 5 UCI basketball players in UCI history. There are two types of charts used to present data. The first is a histogram and the second is a scatterplot. We have to decide which picture is the best. Now, as we know, scatter charts are used to plot observations based on points to show the relationship between two data sets. A histogram is a type of bar chart in which all values are divided. Divides the range of results in the data into classes or groups. It can help identify outliers or gaps in the data. After discussing the features of the two graphs, shows the average score of 5 UCI basketball players in UCI history, the histogram is the best choice here because it allows us to divide and share the difference between clearly.

For more information about Histogram, visit :

https://brainly.com/question/28164315

#SPJ4

complete question:

The above figure complete the question..

you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?

The remaining angle of the triangle ABC is 59° 0'

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

A 110° 50', C= 10° 10', AB=7

The sum of angles in a triangle is 180 degrees

Using the above as a guide, we have the following:

A + B + C = 180

Substitute the known values in the above equation, so, we have the following representation

110° 50' + B + 10° 10' = 180

So, we have

120° 60' + B  = 180

Convert to degrees

This gives

121° + B  = 180

Evaluate the like terms

B = 59

Convert to degree and minutes

B = 59° 0'

Hence, the remaining angle of the triangle ABC is 59° 0'

Read more about triangle at

https://brainly.com/question/14285697

#SPJ4