Evaluate each expression.
12! / 6!
Answers
The value of the expression 12! / 6! is approximately 665,280.
To evaluate the expression 12! / 6!, we need to calculate the factorials of 12 and 6 and then divide them.
Factorial (!) is the product of an integer and all the positive integers below it.
12! (read as "12 factorial") is calculated as follows:
12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
= 479,001,600
6! (read as "6 factorial") is calculated as follows:
6! = 6 × 5 × 4 × 3 × 2 × 1
= 720
Now, we can evaluate the expression:
12! / 6! = 479,001,600 / 720
≈ 665,280
Therefore, the value of the expression 12! / 6! is approximately 665,280.
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Related Questions
Submarines use sonar systems, which are similar to radar systems, to detect obstacles. Sonar systems use sound to detect objects underwater.
a. You are traveling underwater in a submarine. The sonar system detects an iceberg 4000 meters ahead, with an angle of depression of 34∘ to the bottom of the iceberg. How many meters must the submarine lower to pass under the iceberg?
The submarine must lower at least ____ meters.
Question 2
b. The sonar system then detects a sunken ship 1500 meters ahead, with an angle of elevation of 19∘ to the highest part of the sunken ship. How many meters must the submarine rise to pass over the sunken ship?
The submarine must rise at least ____ meters.
Answers
Answer:
a. tan(34)= O/4000 and follow the solving to get the distance it must be lowered
b. (Same idea as a) tan(19)=1500/A and solve to get the distance
The submarine must lower at least 2698 meters and the submarine must rise at least 516.45 meters.
Given that, the sonar system detects an iceberg 4000 meters ahead, with an angle of depression of 34∘ to the bottom of the iceberg.
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.
a) We know that, tan θ = (Perpendicular/Base)
Let the number of meters must the submarine lower to pass under the iceberg be x.
tan θ = x/4000
⇒ tan 34° = x/4000
⇒ 0.6745 = x/4000
⇒ x = 0.6745 × 4000
⇒ x = 2698 meters
b) Let the number of meters must the submarine rise to pass over the sunken ship be y.
tan θ = y/1500
⇒ tan 19° = y/1500
⇒ 0.3443 = y/1500
⇒ y = 0.3443 × 1500
⇒ y = 516.45 meters
Therefore, the submarine must lower at least 2698 meters and the submarine must rise at least 516.45 meters.
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acute angle between the hours hand and the minute hand at 1pm
Answers
Answer: 30 degrees
Step-by-step explanation:
1 hour = 60 min = 360 degree
1 min = 360/60 degree
1 min = 6 degree
and the gap of hour hand and minute hand at 1pm, is of 5 min
therefore acute angle formed is 5 X 6 = 30 degrees.
:-)
Answer:
30 degrees
Step-by-step explanation:
1 hour = 60 min = 360 degree
1 min = 360/60 degree
1 min = 6 degree
and the gap of hour hand and minute hand at 1pm, is of 5 min
therefore acute angle formed is 5 X 6 = 30 degrees.
in a chi-square test for the equality of population proportions, how many categories or populations do you need to be able to perform this analysis?
Answers
In a chi-square test for the equality of population proportions, you need at least two categories or populations to be able to perform the analysis.
Chi-Square Test For ProportionsA chi-square test for the equality of population proportions is used to determine if there is a significant difference between the proportion of observations in different categories or populations. In order to perform this test, you need at least two categories or populations to compare the proportions. If you only had one category or population, there would be no basis for comparison and the test would not be meaningful.
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If 111 is divided into pieces that are each \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction of a whole, how many pieces are there?
1\div\dfrac19=1÷
9
1
=1, divided by, start fraction, 1, divided by, 9, end fraction, equals
Answers
The results of dividing 1 into pieces that are each 1/9 of a whole is 9
Division of fraction1 ÷ 1/9
multiply by the reciprocal of 1/9 which is 9/11 ÷ 1/9
= 1 × 9/1
= (1 × 9) / (1 × 1)
= 9/1
= 9
Complete question:
If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there
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Steven and Anna start running from the school. Steven starts 15
seconds before Anna and runs at a rate of 3 feet per second. Anna runs at
a rate of 4 feet per second. Write an equation that represents this
situation.
Answers
Complete question :
Steven and Anna start running from the school. Steven starts 15
seconds before Anna and runs at a rate of 3 feet per second. Anna runs at
a rate of 4 feet per second. Write an equation that represents this
situation.
Which equation could you solve to find when Anna will catch up to Steven.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Steve starts 15s before Anna and runs at a rate of 3ft per second
Anna runs at a rate of 4 feets per second
Let Anna's time = t
Anna's speed = 4ft/s
Then Steve's time = t + 15
Steve's speed = 3ft/s
Distance = speed * time
Anna's distance = Steve's distance
4t = 3(t + 15)
4t = 3t + 45
4t - 3t = 45
t = 45
Anna will catch up. With Steve after 45 seconds
If point B is reflected across the y axis, what are the coordinates of the new point?
(-3,2)
(-2,-3)
(-2,3)
(3,-2)
Answers
Answer: (3,-2)
Step-by-step explanation: We're reflecting to the y-axis, thus, we're going to reflect to the right.
(-x,-y) ⇒ (x,-y)
Our current coordinate is (-3,-2)...let's convert it now...
(3,-2)
I hope this helps!
Answer:
(3, -2).
Step-by-step explanation:
When you reflect across the y axis the y coordinate stays the same and the x axis changes sign : (x, y) --> (-x, y).
So B (-3, -2) --> (3, -2).
Suppose X is a continuous random variable with range range(X) = ℝ, whose density fx is proportional to |x|e^(-x^2) (a) Find and plot the density fx. (b) Compute the cumulative distribution function Fx. (c) Compute the probability of X ∈ [1, 3] (approximate to 4-th decimal place). (d) Find the expected value and variance of X.
Answers
The density function of the continuous random variable X, with a range of ℝ, is given by fx ∝ |x|e^(-x^2). To find the density function, we need to determine the constant of proportionality. Since the density function must integrate to 1 over the entire range, we can calculate the constant by integrating the density function from negative infinity to infinity and setting it equal to 1. This gives us the normalized density function fx = (2/√π) |x|e^(-x^2). Plotting this density function will show a symmetric, bell-shaped curve centered around 0.
To compute the cumulative distribution function (CDF), Fx, we integrate the density function fx from negative infinity to x. Integrating fx = (2/√π) |x|e^(-x^2) with respect to x gives Fx = (1/√π) (x^2/2 + 1/2) for x ≥ 0 and Fx = (1/√π) (-x^2/2 + 1/2) for x < 0. The CDF Fx takes on different forms depending on the sign of x.
To compute the probability of X ∈ [1, 3], we evaluate Fx at the upper and lower bounds and take the difference: P(1 ≤ X ≤ 3) = Fx(3) - Fx(1). Substituting the values, we can approximate this probability to the desired decimal place.
The expected value, or mean, of a continuous random variable can be found by integrating x times the density function fx from negative infinity to infinity. In this case, the expected value of X is 0 since the density function is symmetric. The variance of X can be calculated by integrating (x - E[X])^2 times the density function fx. Since the expected value is 0, the variance simplifies to the second moment, which can be evaluated using integration.
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During the firs 4 months of employment, the monthy seies S (in thousands of dolars) for a new salerperson depend en the number of hours x of tiaining, as follows. −5=S(x)= 5/x+10+x/2+x≥2 (8) find lima→1 5(x), thousends of doliars
(b) find limx→2 s(x). thousands of celiars
Answers
a. The one-sided limits from the left and right sides are not equal, the limit lim(x→1) S(x) does not exist.
b. lim(x→2) S(x) is equal to 13.5 thousand dollars.
To find the limits, we substitute the given values into the function:
(a) lim(x→1) S(x) = lim(x→1) [5/x + 10 + x/2]
Since the function is not defined at x = 1, we need to find the one-sided limits from the left and right sides of x = 1 separately.
From the left side:
lim(x→1-) S(x) = lim(x→1-) [5/x + 10 + x/2]
= (-∞ + 10 + 1/2) [as 1/x approaches -∞ when x approaches 1 from the left side]
= -∞
From the right side:
lim(x→1+) S(x) = lim(x→1+) [5/x + 10 + x/2]
= (5/1 + 10 + 1/2) [as 1/x approaches +∞ when x approaches 1 from the right side]
= 5 + 10 + 1/2
= 15.5
Since the one-sided limits from the left and right sides are not equal, the limit lim(x→1) S(x) does not exist.
(b) lim(x→2) S(x) = lim(x→2) [5/x + 10 + x/2]
Substituting x = 2:
lim(x→2) S(x) = lim(x→2) [5/2 + 10 + 2/2]
= 5/2 + 10 + 1
= 2.5 + 10 + 1
= 13.5
Therefore, lim(x→2) S(x) is equal to 13.5 thousand dollars.
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please help me please will give brainliest to anyone who is right
Answers
Answer:
A (?)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
if you look at the graph the area thats purple for texas is farther up it meaning the tempature is higher.
PLEASE HELP. FIRST (CORRECT) ANSWER GETS BRAINLIEST
Simplify the expression
12 - 4 x 3 / 7 + 13 x 15
Answers
Answer:
the answer is 240 multiply and divide
Answer:240
Step-by-step explanation:
Use the order of operations. (PEMDAS)
Parenthesis
Exponent
Multiply
Divide
Addition
Subtraction
Hope this helped dude
he top and bottom margins of a poster are 2 cm and the side margins are each 12 cm. if the area of printed material on the poster is fixed at 778 square centimeters, find the dimensions of the poster with the smallest area.
Answers
The width is (12√389 + 24) units and the height is (√389/6+ 4) units.
By dimension definition, it is a measure of a point or line extended in one direction. Every shape around us has some dimensions.
The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by,
Dimensional Formula: Q = MaLbTc
The area of printable area is wh.
wh = 778
The poster has width w + 2*12 (as there are margins on both sides) and height h + 2 * 2.
We seek to minimize the area of the poster =
(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)
As wh = 778, we may substitute h = 778/w
Then, A = (w + 24)(778/w + 4) is the size of the poster which we seek to minimize.
(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =
4w + 874 + 18672/w
We minimize this by calculating
dA/dw = 4 - 18672/w² and setting it equal to 0
4 - 18672/w^2 = 0
4w^2 = 18672
w^2 = 18672/4
w = √4668 = 12√389
h = 778/(12√389) = √389/6
Note how h and w have the same ratio as the margins.
Then, since the problem asks for the width and height of the poster,
Width = 12√389 + 24
Height = √389/6+ 4
Thus, the width is (12√389 + 24) units and the height is (√389/6+ 4) units.
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The width is (12√389 + 24) units and the height is (√389/6+ 4) units.
By dimension definition, it is a measure of a point or line extended in one direction. Every shape around us has some dimensions.
The dimensional formula of any quantity is the expression showing the powers to which the fundamental units are to be raised to obtain one unit of a derived quantity. If Q is any physical quantity, the expression representing its dimensional formula is given by,
Dimensional Formula: Q = MaLbTc
The area of printable area is wh.
wh = 778
The poster has width w + 2*12 (as there are margins on both sides) and height h + 2 * 2.
We seek to minimize the area of the poster =
(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)
As wh = 778, we may substitute h = 778/w
Then, A = (w + 24)(778/w + 4) is the size of the poster which we seek to minimize.
(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =
4w + 874 + 18672/w
We minimize this by calculating
dA/dw = 4 - 18672/w² and setting it equal to 0
4 - 18672/w² = 0
4w² = 18672
w² = 18672/4
w = √4668 = 12√389
h = 778/(12√389) = √389/6
Note how h and w have the same ratio as the margins.
Then, since the problem asks for the width and height of the poster,
Width = 12√389 + 24
Height = √389/6+ 4
Thus, the width is (12√389 + 24) units and the height is (√389/6+ 4) units.
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The common stock of Dayton Rapur sells for $48 49 a shame. The stock is inxpected to pay $2.17 per share next year when the annual dividend is distributed. The company increases its dividends by 2.56 percent annually What is the market rate of retum on this stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, eg-32.16.)
Answers
The market rate of return on the Dayton Rapur stock is approximately 4.59%.
To calculate the market rate of return on the Dayton Rapur stock, we need to use the dividend discount model (DDM). The DDM calculates the present value of expected future dividends and divides it by the current stock price.
First, let's calculate the expected dividend for the next year. The annual dividend is $2.17 per share, and it increases by 2.56% annually. So the expected dividend for the next year is:
Expected Dividend = Annual Dividend * (1 + Annual Dividend Growth Rate)
Expected Dividend = $2.17 * (1 + 0.0256)
Expected Dividend = $2.23
Now, we can calculate the market rate of return using the DDM:
Market Rate of Return = Expected Dividend / Stock Price
Market Rate of Return = $2.23 / $48.49
Market Rate of Return ≈ 0.0459
Finally, we convert this to a percentage:
Market Rate of Return ≈ 0.0459 * 100 ≈ 4.59%
Therefore, the market rate of return on the Dayton Rapur stock is approximately 4.59%.
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i dont know help me i am so confused?
Answers
Answer:
the answer should be 16, if you're looking for X that is
A particular manufacturing design requires a shaft with a diameter of 21.000 mm, but shafts with diameters between 20.989 mm and 21.011 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 21.002 mm and a standard deviation of 0.005 mm. Complete parts (a) through (d) below. a. For this process, what is the proportion of shafts with a diameter between 20.989 mm and 21.000 mm? The proportion of shafts with diameter between 20.989 mm and 21.000 mm is (Round to four decimal places as needed.) . b. For this process, what is the probability that a shaft is acceptable? The probability that a shaft is acceptable is (Round to four decimal places as needed.) c. For this process, what is the diameter that will be exceeded by only 5% of the shafts? mm. The diameter that will be exceeded by only 5% of the shafts is (Round to four decimal places as needed.) d. What would be your answers to parts (a) through (c) if the standard deviation of the shaft diameters were 0.004 mm? . If the standard deviation is 0.004 mm, the proportion of shafts with diameter between 20.989 mm and 21.000 mm is (Round to four decimal places as needed.) T. If the standard deviation is 0.004 mm, the probability that a shaft is acceptable is (Round to four decimal places as needed.) mm. If the standard deviation is 0.004 mm, the diameter that will be exceeded by only 5% of the shafts is (Round to four decimal places as needed.)
Answers
In a manufacturing process, shaft diameters are normally distributed with a mean of 21.002 mm and a standard deviation of 0.005 mm. We need to calculate various probabilities and proportions related to shaft diameters.
a. To find the proportion of shafts with a diameter between 20.989 mm and 21.000 mm, we calculate the z-scores for these values using the formula: z = (x - μ) / σ, where x is the diameter, μ is the mean, and σ is the standard deviation. The z-score for 20.989 mm is z1 = (20.989 - 21.002) / 0.005, and for 21.000 mm, z2 = (21.000 - 21.002) / 0.005. We then use the z-scores to find the proportion using a standard normal distribution table or calculator. b. The probability that a shaft is acceptable corresponds to the proportion of shafts with diameters within the acceptable range of 20.989 mm to 21.011 mm. Similar to part (a), we calculate the z-scores for these values and find the proportion using the standard normal distribution.
c. To determine the diameter that will be exceeded by only 5% of the shafts, we need to find the z-score that corresponds to the cumulative probability of 0.95. Using the standard normal distribution table or calculator, we find the z-score and convert it back to the diameter using the formula: x = z * σ + μ.
d. If the standard deviation of the shaft diameters were 0.004 mm, we repeat the calculations in parts (a), (b), and (c) using the updated standard deviation value. By performing these calculations, we can obtain the requested proportions, probabilities, and diameters for the given manufacturing process.
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There are 223 freshman in this school of 845 students what percent of students at this high school belong to classes other than freshman class? show all work
Answers
Answer:1884.35
Step-by-step explanation: it’s just 223% of 845. Might not be what ur looking for but I dk
845 - 223 = 622
622 / 845 = 73.6/100
73.6% are non freshman
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On Feb. 19th, 2010, 4.13% of the randomly selected spots had potamogeton (a type of seagrass). Is 4.13% a statistic or a parameter?
Answers
A statistic is, 4.13%.
Given that;
On Feb. 19th, 2010, 4.13% of the randomly selected spots had potamogeton (a type of seagrass)
Since, A parameter is a value that is determined from all of the data, whereas a statistic is a value that is produced from a sample of the data.
Here, The percentage of spots containing portamento in this instance was solely determined from a randomly chosen sample, making it a statistic.
Hence, It would be a parameter if the percentage was determined using the whole population of spots.
Thus, 4.13% is a statistic.
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I need help with please and FAST ( I’m willing to give out a Brainliest to anyone who gets it correct )
Answers
Answer:
x=3
6x-3 = 15
Step-by-step explanation:
The sides with the lines means they are the same length
The perimeter is
6x-3 + 6x -3 + 32 = 62
Combine like terms
12x+26=62
Subtract 26 from each side
12x+26-26 =62-26
12x =36
Divide by 12
12x/12 = 36/12
x = 3
The missing side length 6x-3 = 6*3 -3 = 18-3 = 15
Please help me out! And please show your work!
Answers
x/24=0.25
x=6
Are 0.34 and 3/4 equivalent? Explain your answer in complete sentences.
Answers
Answer:
No because 3/4 is equal to 0.75 and 0.75 is not equal to 0.34
Step-by-step explanation:
Answer:
No. 3/4 is equavilent to 0.75 not 0.34.
Trigonometry Question
Answers
AB^2 + BC^2 = AC^2
6^2 + BC^2 = 10^2
36 + BC^2 = 100
BC^2 = 64
BC = 8
If AC = 10, CD and AD = 5
Tan = opp/adj
Tan = 5/8
Triangle BCD is a 45-45-90 triangle
CD = BD = 5
Sec = inverse cos
sec = hyp/adj
Sec = 8/5
Riley answered 42 questions correctly on her multiple choice science final and earned a grade of 35%. How many total questions were on the final exam?
Answers
Answer:
120 questions
Step-by-step explanation:
The total number of questions in the exam was 120.
As mentioned in the question, Riley answered 42 questions correctly on her multiple-choice science final and earned a grade of 35%.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the total number of questions be x,
According to the question,
35% of x = 42
0.35 × x = 42
x = 42 / 0.35
x = 120
Thus, the total number of questions in the exam was 120.
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Estimate 84.839 + 55.65 by first rounding each number to the nearest whole number.
Answers
Answer:
140.489
Step-by-step explanation:
If x is an integer, what is the minimum value of x that satisfies the inequality below?
6x−3(2x−1)>7−4(x+2)
Answers
FIRST STEP TO A ANSWER THIS QUESTION IS TO SIMPLIFY THE INEQUALITY.
\(6x - 6x + 3 > 7 - 4x - 8 \\ 3 > 7 - 4x - 8 \\ 4x > 7 - 8 - 3 \\ 4x > - 4 \\ \frac{4x}{4} > \frac{ - 4}{4} \\ x > - 1\)
IF THEY SAY X IS AN INTEGER THEREFORE THE MINIMUM VALUE OF X TO SATISFY THE INEQUALITY IS 0
x=0 is the answer
6x-6x+3>7-4x-8
2) Simplify
3>-1-4x
3) Add 1 on both sides
4>-4x
4) Divide both sides by -4 (Dividing a negative number flips the sign)
-1
X must be greater than -1 to satisfy the inequality
A line passes through the point (4, -7) and has a slope of -5/4 write an equation in point slope form for this line
Answers
Answer:
y + 7 = -5/4(x - 4)
Step-by-step explanation:
The formula for point slope form is [ y - y1 = m(x - x1) ].
We are already given all the information needed so fill it in into the formula.
y - (-7) = -5/4(x - 4)
y + 7 = -5/4(x - 4)
Best of Luck!
Allison earns $8.50 an hour at her job serving at iHop, and also earns $9 each hour she tutors her little brother in math. She graphs the amount of hours
she works at her iHop job (x) and the number of hours she tutors (y) to determine how to eam at least $870. Which type of boundary line should she use in
her graph?
Answers
Answer:
i
Step-by-step explanation:
How many positive factors of 96 are also multiples of 12?
Answers
The number of positive factors of 96 which are also multiples of 12 are 4 which are 12,24,48, and 96.
Positive factors of 96 = 1,2,3,4,6,8,12,16,24,32,48 and, 96
Multiples of 12 upto 96 = 12,24,36,48,60,72, 84 and 96
Common numbers between the two are 12,24,48 and 96.
Hence, there are only 4 positive factors of 96 which are also the multiples of 12
Factors
Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left.
Multiples
A multiple is a result obtained by multiplying a number by an integer(it shouldn’t be a fraction). The multiples of the whole number are obtained by taking out the product of the counting numbers and that of whole numbers.
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Express in the form
1
:
n
.
Give
n
as a fully simplified fraction.
9
:
6
Answers
Answer:
Step-by-step explanation:
\(\frac{1}{n} =\frac{9}{6} \\9n=6\\n=\frac{6}{9} =\frac{2}{3} \\1:n=1:\frac{2}{3}\)
Answer:
3:2
In fraction form :
Step-by-step explanation:
Pls mark as brainliest
The velocity of a particle moving along the x-axis is modeled by a differentiable function v, where the position is measured in meters, and the time I is measured in seconds. Selected values of (t) are given in the table below. The particle is at position x = 7 when I = 0 seconds. NC0 8 20 25 32 40 1 (seconds)t (v) t (meters per second) 3 5 -10 -8 -4 7 a) Estimate the acceleration of the particle at 1 = 36 seconds. Show the computations that lead to your answer. Indicate units of measure. b) Using correct units, explain the meaning of v(e)dt in the context of the problem. Use a trapezoidal sum with the three subintervals indicated by the data to approximate Sa(tdt. c) For OSIS 40, must the particle change direction in any of the subintervals indicated by the data in the table? If so, identify the subintervals and explain your reasoning. If not, explain why not. d) Suppose the acceleration of the particle is positive for O
Answers
The acceleration of the particle at t = 36 seconds is 11/8 meters/s2
Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt
using the second derivative of a and to find the time at 36 seconds is
a(36)=v'(36)=\(\frac{v(40)-v(32)}{40-32} \\\)
=7-(-4)÷8
a(36)=11/8 meters/s^2
The Trapezoidal Rule:
This is a rule that defines the area under the curves by dividing the total area into smaller trapezoids rather than using rectangles.
The formula for the trapezoidal rule:
T n = 1 2 Δ x ( f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + ⋯ + 2 f ( x n − 1 ) + f ( x n ) )
∫v(t) dt is the particle’s change in position in meters from time
t = 20 seconds to time 40 t = seconds.
\(\int\limits {v(t)} \, dx =\frac{v(20)+v(25)}{2}*5+\frac{v(25)+v(32)}{2} *7+\frac{v(32)+v(40)}{y} *8 \\\\=\frac{-18*5}{2} +\frac{-12*7}{2} +\frac{24}{2} \\\\=\frac{-90}{2} +\frac{-84}{2} +\frac{24}{2} \\\\=-45-42+12\\=-75\)
∫v(t) dt=-75meters.
For 0 ≤t≤40, must the particle change direction in any of the subintervals indicated by the data in the table
since v(t) is differentiable, v(t) is continuous.
Particle changes direction is v(t) changes sign.
The particle must change direction in (8,20) and (32,40)
v(8)=5>0 and v(20)=-10<0 for this v(t) changes sign for same C for8<C<20.
v(32)=-4<0 and v(4)=7>0 for this v(t) changes sign for some d for 32<d<40
the above is true due to the Intermediate Value theorem.
since v(t) changes sign in (8,20) and in (32,40)
The particle changes sign in (8,20) and in (32,40)
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A straight line p through A(-2,1) and B(2,k) the line is perpendicular to a line 3y + 2x =5. Determine the value of k
Answers
Answer:
k = 7
Step-by-step explanation:
To solve this, first, you need to find the slope of the line. To do this, you can convert it into point-slope form.
3y = -2x + 5
y = - 2/3x + 5/3
The slope is -2/3, so the perpendicular slope in 3/2
You find the difference between the x - values (2 - -2 = 4), then multiply that by the slope (4 x 3/2 = 6) finally, you add that to the y value of point one.
1 + 6 = 7
Guess the number! it is less than 300 000. there is a 1 in the thousands place. the digit in the thousands place is half the ones. the digit in the ones place is the same as the hundred thousands place. the digit in the ten thousands place is double the digit in the ones place. the digit in the tens and thousands place add to make 10. the digit in the hundreds place is the difference between the digits in the tens and ones places. drag the numbers into the boxes to show the mystery number.
Answers
If the difference is 2, then the hundreds place would be 2. If the difference is 4, then the hundreds place would be 4, and so on.
1. The digit in the thousands place is half the ones place. Since the ones place is not specified, let's consider all possible values. If the ones place is 2, then the thousands place would be 1. If the ones place is 4, then the thousands place would be 2, and so on.
2. The digit in the ones place is the same as the hundred thousands place. Since the ones place is the same as the hundred thousands place, it means the number is a palindrome. So, if the ones place is 2, then the hundred thousands place would be 2 as well. If the ones place is 4, then the hundred thousands place would also be 4, and so on.
3. The digit in the ten thousands place is double the digit in the ones place. If the ones place is 2, then the ten thousands place would be 4. If the ones place is 4, then the ten thousands place would be 8, and so on.
4. The digit in the tens and thousands place add to make 10. Let's consider all possible pairs of digits that add up to 10. For example, if the tens place is 6, then the thousands place would be 4. If the tens place is 8, then the thousands place would be 2, and so on.
5. The digit in the hundreds place is the difference between the digits in the tens and ones places. Let's consider all possible differences between the tens and ones places.
Based on these clues, we can have multiple relevant and creative answers, such as:
\(- 124421- 244842- 364763\)
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