can someone help me?​

a. The velocity at time t is v(t) = t² + 2t - 15 m/s.

b. The distance travelled during the given time interval is \(\frac{25}{3}\) meters (or approximately 8.33 meters).

(a) To find the velocity at time t, we need to integrate the acceleration function a(t) from 0 to t and add the initial velocity v(0):

\(v(t) = \int a(t) \, dt + v(0) = \int (2t + 2) \, dt - 15 = t^2 + 2t - 15\)

So the velocity at time t is v(t) = t² + 2t - 15 m/s.

(b) To find the distance travelled during the given time interval, we need to integrate the velocity function v(t) from 0 to 5:

s(5) - s(0) = ∫v(t) dt from 0 to 5

Using the formula for v(t) from part (a), we have:

s(5) - s(0) = ∫(t² + 2t - 15) dt from 0 to 5

\(\int_{0}^{5} \left( \frac{t^3}{3} + t^2 - 15t \right) \, dt\)

\(= \frac{25}{3}+25-75-\frac{0}{3}+0-0=\frac{25}{3}\)

As a result, the distance covered in the allotted time is \(\frac{25}{3}\), or roughly 8.33 metres.

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Answer:

CIAE

Step-by-step explanation:

Answer:

Step-by-step explanation:1/9

Therefore, the height of the flagpole, rounded to the nearest foot, is approximately 47 feet.

To calculate the height of the flagpole, we can use trigonometry and the concept of similar triangles. Let's denote the height of the flagpole as h and the distance from the base to the point where the angle of elevation is measured as x. In this case, x = 22 feet.

We have a right triangle formed by the flagpole, the distance from the base, and the line of sight to the top of the flagpole. The angle of elevation is the angle between the line of sight and the horizontal ground. We can use the tangent function to relate the angle of elevation to the height and the distance from the base:

tan(angle of elevation) = h / x

Rearranging the equation to solve for h:

h = x * tan(angle of elevation)

Substituting the values:

h = 22 * tan(65°)

Using a scientific calculator or trigonometric table, we find:

h ≈ 22 * 2.14450692051

h ≈ 47.1791532511 feet

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The median of the given list of numbers is 87.

To find the median of a list of numbers, we arrange them in ascending order and identify the middle value.

If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

First, let's arrange the numbers in ascending order:

65.9, 68, 70, 74, 75, 78, 84, 86, 87, 90, 93, 93, 95, 96, 97, 380, 486, 680

There are 17 numbers in the list, which is an odd number. The middle number is the 9th number in the list, which is 87.

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Answer:

Hello,

x=5

Step-by-step explanation:

\(Since\ \overrightarrow{AD}=\overrightarrow{BC}, ABCD\ is\ a\ parallelogramm\\\\12x+60=150-6x\\\\18x=90\\\\x=\frac{90}{18} \\\\\boxed{x=5}\\\)

The two vectors that are equivalent are AB and JK

Given data ,

AB with A(-8, 8) and B(-5, 6)

To check if two vectors are equivalent, we need to compare their components. In this case, we compare the differences in x-coordinates and y-coordinates between the initial and terminal points of each vector.

For vector AB:

x-component: Difference between x-coordinates of B and A: -5 - (-8) = 3

y-component: Difference between y-coordinates of B and A: 6 - 8 = -2

Similarly, for vector JK:

x-component: Difference between x-coordinates of K and J: 13 - 16 = -3

y-component: Difference between y-coordinates of K and J: -2 - (-4) = 2

Comparing the components of AB and JK, we can see that they have the same differences in both x and y coordinates:

AB: x-component = 3, y-component = -2

JK: x-component = -3, y-component = 2

Hence , vector AB and vector JK are equivalent

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The given statements are correct or incorrect is given below:

1) Correct.

2) Correct.

3) Correct.

4) Correct.

5) Correct.

6) Incorrect.

7) Correct.

8) Correct.

9) Correct.

10) Incorrect.

Here, we have,

1) Correct. In a simple graphical method, a graph is plotted to show the relationship between water usage and population.

2) Correct. The pressure in a distribution system needs to be sufficient to allow for adequate hydrant flows in case of a fire.

3) Correct. The term "distribution system" refers to the infrastructure and facilities used to supply water from its source to the point of usage.

4) Correct. Brackish water is water that has a higher salinity level than fresh water and even higher than seawater.

5) Correct. Monthly variation in water usage can impact the design and capacity requirements of storage reservoirs.

6) Incorrect. Jordan is considered a "Water Scarce" country, as it faces significant challenges in terms of water availability and scarcity.

7) Correct. During a fire, a significant quantity of water needs to be supplied over an extended period, necessitating a high rate of hourly supply.

8) Correct. The Manning equation is commonly used in the design and evaluation of sanitary sewers.

9) Correct. If the diameter (d) is less than 200 mm, the pipe's final diameter (D) is set at 200 mm.

10) Incorrect. The diameter of the interceptor pipe is typically larger than the diameter of the lateral pipe. The interceptor pipe carries wastewater from multiple lateral pipes.

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Rae's new balance after making the new transaction is $3422.40.

With the help of the interest rate formula, we can calculate the interest rate, which is the percentage of the principle sum that the lender or bank would charge the borrower in exchange for using its assets or money for a given period of time.

Interest Rate = (Simple Interest 100)/(Principal Time) is the formula for calculating interest rates.

To calculate Rae's new balance after making a new transaction, we need to take into account the interest accrued on the unpaid balance as well as the new transaction. The interest accrued can be calculated as:

interest = unpaid balance * (APR/12)

where APR is the annual percentage rate and is divided by 12 to get the monthly rate. So, for Rae's current balance of $1,938 and APR of 15.1%, the monthly interest rate is:

interest rate = 15.1%/12 = 0.01258

Hence, the interest accrued on the unpaid balance is:

interest = 1938 * 0.01258 = $24.40

So, Rae's balance before the new transaction is:

balance before = 1938 + 24.40 = $1962.40

Now, when Rae makes a new transaction of $1460, her balance becomes:

balance after = balance before + new transaction = 1962.40 + 1460 = $3422.40

Therefore, Rae's new balance after making the new transaction is $3422.40.

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Answer:

A. 7

Step-by-step explanation:

f(x) = 3(3) - 2

f(x) = 9 - 2

f(x) = 7

good luck, i hope this helps :)

Answer:

B = -2

Step-by-step explanation:

Infer means to guess or reach a conclusion, especially based on an indirect hint.

The passage suggests that the main reason the narrator considers Great Expectations to be the best gift he ever received is that reading the book convinced him that he wanted to be a writer.

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Answer:

3, 7, 20, 1, -4, 9

Step-by-step explanation:

wrilvkdfjaerlbvuabvcs

The circumference of the circular test track is 3.3 km. When a car travels around the track from the southernmost point to the northernmost point, it covers the entire circumference of the track.

To calculate the distance traveled by the car, we can use the formula: distance = circumference.

In this case, the distance traveled by the car is equal to the circumference of the track, which is 3.3 km.

So, when the car completes one full lap around the track, it will have traveled a distance of 3.3 km.

If the car completes multiple laps around the track, the total distance traveled will depend on the number of laps. For example:

- If the car completes 2 laps, the total distance traveled will be 2 times the circumference, which is 2 * 3.3 km = 6.6 km.
- If the car completes 3 laps, the total distance traveled will be 3 times the circumference, which is 3 * 3.3 km = 9.9 km.

Therefore, the distance traveled by the car around the circular test track depends on the number of laps completed.

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Answer:

3/4

Step-by-step explanation:

since they already have a common denominator you'd add the numerators and keep the denominator. you'd get 6/8. Then you'd divide both the numerator and denominator by 2. 3/4 is your final answer.

Answer:

i think its 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

No. of pockets = 625

No. of toffees in each pocket = 100

Total no. of toffees = 625 × 100 = 62500

Hope this helps

Plz mark as brainliest!!!!!!!!

Answer:

62500

Step-by-step explanation:

if each pocket of toffee has 100 in 625 pockets then 100x625 will =62500

Answer:

\(t = 2.86 \: s\)

The ball remains in the air for 2.86 seconds.

Step-by-step explanation:

A baseball is hit into the air, and its height above the ground is described by the function

\(H(t) = -16t^2 + 45t + 2\)

Where H(t) represents the height of the ball t seconds after it is hit.

The ball remains in the air before it hits the ground.

When the ball hits the ground,

\(H(t) = 0\)

So,

\(0 = -16t^2 + 45t + 2\)

The equation may be solved using the quadratic formula.

\($t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$\)

Where

\(a = -16 \\\\b = 45 \\\\c = 2 \\\\\)

So,

\(t=\frac{-(45)\pm\sqrt{(45)^2-4(-16)(2)}}{2(-16)} \\\\t=\frac{-45\pm\sqrt{(2025 - (-128)}}{-32} \\\\t=\frac{-45\pm\sqrt{(2153}}{-32} \\\\t=\frac{-45\pm 46.4004}{-32} \\\\t=\frac{-45 + 46.4004}{-32} \: and \: t=\frac{-45 - 46.4004}{-32}\\\\t= -0.04 \: and \: t = 2.86 \\\\\)

Since the time cannot be negative, discard the negative value and accept the positive value

\(t = 2.86 \: s\)

Therefore, the ball remains in the air for 2.86 seconds.

The perimeter of the triangle is 23.623 units.

What is perimeter of triangle?

Finding the distance around a triangle entails determining its perimeter. The distance formula can be used to calculate the side lengths if you don't already know all of them. The simplest way to find a triangle's perimeter is to add up all of its sides' lengths.

The distance between two points (x1,y1) and (x2,y2) can be determined using the following formula: √(x₂-x₁)² + (y₂ - y₁)²

Let the given vertices are (-7, -2), (-2, -5) , and (2, 3).

Distance formula for two points is = √(x₂-x₁)² + (y₂ - y₁)²

Using the formula,

AB = √((-2)-(-7))² +((-5)-(-2))²

= √(-2+7)² + (-5+2)²

= √5² + (-3)²

= √25 + 9

= √31

Similarly, BC = √(2 - (-2))² + (3-(-5))²

= √(2+2)² + (3+5)²

= √4² + 8²

= √16+64

= √80

CA = √((-7)-2)² + (-2 + 3)²

= √(-9²) + 1

= √81+1

=√82

Perimeter of triangle = AB + BC + CA

= √31 +√81 +√82

= 5.5677 + 9 + 9.0553

= 23.623

Therefore, the perimeter of the triangle is 23.623 units.

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Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

The "dead spot" is 19.04 thousand miles from the center of the earth

To find the "dead spot" where no net gravitational force acts upon the object, we need to find the value of x that makes F equal to 0.

We know that F = −K x2 + 0.012K (239 − x)2

So, we set F equal to 0 and solve for x:

0 = −K x2 + 0.012K (239 − x)2

0 = −K x2 + 0.012K (239 − x)2

K x2 = 0.012K (239 − x)2

x2 = 0.012 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 (239 − x)2

x2 = 2.888 x2 - 676.8 x + 568.976

x2 - 2.888 x2 = 676.8 x - 568.976

-1.888 x2 = 676.8 x - 568.976

x2 = 361.6 x - 303.504

x = √(361.6 x - 303.504)

x = √(361.6 x - 303.504)

x = 19.04

So the "dead spot" is 19.04 thousand miles from the center of the earth

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To compute the z-score for the applicant, we can use the formula:

z = (x - μ) / σ

Where:

x is the applicant's score

μ is the mean

σ is the standard deviation

Given that the applicant's score is 21.0, the mean is 18.0, and the standard deviation is -3.0, we can substitute these values into the formula to calculate the z-score.

z = (21.0 - 18.0) / (-3.0)

z = 3.0 / -3.0

z = -1.0

Therefore, the z-score for the applicant is -1.0.

The correct option is O-10.

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So,

A) → (11 + 25 ) -2

Solve :- ( 36 ) -2

B) → (11 + 25) ÷ 2

Solve :- (36) ÷2

Answer:

Step-by-step explanation:

M<2=m<3*2

Answer:

y = -6x + 3

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = slope

b = y-intercept

Because the x value is increasing while the y value is decreasing, the slope is negative.

To find the slope, first find 2 points on the line:

(-1 , 8) and (0, 2)

Since the y value decreases by 6 in the same amount that the x value increases by 1, the slope is -6.

To find the value of b, locate the point at which the line intersects the y-axis:

(0 , 3)

The y-intercept is the value of y when x = 0. Because the y-intercept is 3, b = 3.

So, to put this into slope-intercept form, plug in the values:

y = mx + b

y = -6x + 2

The equation of the line in slope-intercept form is y = -6x + 2.

The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.

A square is a four sided polygon with 4 equal angles and length.

The fourth corner = 90° - 36°

= 54°

Recall,

Alternate angles are equal

So,

(4x + 4)° = 36°

substract 4 from both sides

4x = 36 - 4

4x = 32

divide both sides by 4

x = 32/4

x = 8

(4y + 10)° = 54°

substract 10 from both sides

4y = 54 - 10

4y = 44

divide both sides by 4

y = 44/4

y = 11

In conclusion, the value of the following given equations are:

(4x + 4)° = 36°

4(8) + 4 = 36

32 + 4 = 36

36° = 36°

(4y + 10)° = 54°

4(11) + 10 = 54

44 + 10 = 54

54 ^= 54°

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As per the question, 33 boys tried the track and 87 boys didn't, whereas 12 girls tried the track and 68 girls didn't.

Total number of boys = 120

Total number of girls = 80

Students who tried out for track = 45

Students that were girls = 45

If 12 were girls, therefore,

Total number of boys -

= 45 - 12

= 33

This means that 33 boys tried the track

Now, since 12 girls tried the track

Boys who did not try the track -

= 120 - 33

= 87

Girls who did not try the track -

= 80 - 12

= 68

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The last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.

Let's assign symbols to represent the statements in the argument:

P: The boss snaps at you.

Q: You make a mistake.

R: The boss is irritable.

The argument can be symbolically represented as follows:

[(P ∧ Q) → R] ∧ ¬P → ¬R

To determine the validity of the argument, we can construct a truth table:

P | Q | R | (P ∧ Q) → R | ¬P | ¬R | [(P ∧ Q) → R] ∧ ¬P → ¬R

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

T | T | T |      T      |  F |  F |          T          |

T | T | F |      F      |  F |  T |          T          |

T | F | T |      T      |  F |  F |          T          |

T | F | F |      F      |  F |  T |          T          |

F | T | T |      T      |  T |  F |          F          |

F | T | F |      T      |  T |  T |          T          |

F | F | T |      T      |  T |  F |          F          |

F | F | F |      T      |  T |  T |          T          |

The last column represents the evaluation of the entire argument. If it is always true (T), the argument is valid; otherwise, it is invalid.

Looking at the truth table, we can see that the last column evaluates to "T" in all rows. Therefore, the argument is valid since the conclusion always follows from the premises.

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Answer:

X = 0, Y= -2

Step-by-step explanation:

Compare the x and y coordinate values

3x + 2y =-4_______(1)

2x - y = 2 ________(2)

Multiply the (2) with 2

4x - 2y = 4

and add the new equation to (1)

3x + 2y =-4

4x - 2y = 4

____________

7x = 0

X = 0

Substitute x value into (1)

3 *0 + 2y = -4

0 + 2y =-4

2y =-4

Y= -2

If the sample size in part c is larger, then the sample standard deviation will be a better estimate of the population

standard deviation.  If the sample size is smaller, then the sample standard deviation will be less reliable and may not

be a good estimate of the population standard deviation.

To describe the standard deviation in part c relative to the population standard deviation from which the samples were

generated, you can use the concept of the sample standard deviation.

The sample standard deviation is a measure of the variation in a set of data that is calculated by taking the square root

of the variance of the data set. The variance is the average of the squared differences from the mean. It is important to

note that the sample standard deviation is an estimate of the population standard deviation, which is the true measure

of the variability in the population. The larger the sample size, the closer the sample standard deviation will be to the

population standard deviation. Therefore, if the sample size in part c is larger, then the sample standard deviation will

be a better estimate of the population standard deviation.

Conversely, if the sample size is smaller, then the sample standard deviation will be less reliable and may not be a

good estimate of the population standard deviation.

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