A ball is thrown upward from the top of a 200 foot tall building with a velocity of 40 feet per second. Take the positive direction upward and the origin of the coordinate system at ground level. What is the initial value problem for the the position, LaTeX: x\left(t\right)\:x ( t ), of the ball at time t
Answers
Answer:
Initial Value Problem: \(\frac{d^2 x}{dt^2} = -32, x(0) = 200, \frac{dx}{dt}(0) = 40\)
\(x(t) = -16t^2 + 40t +200\)
Step-by-step explanation:
The ball is thrown vertically downward, this means that acceleration due to gravity, \(g = \frac{dx^{2} }{dt^{2} } = - 32 ft/s^2\)
The height of the ball at time, t = 0 at the top of the building will be: \(x(0) = 200 ft\)
The velocity at which the ball is thrown from the top of the building, \(\frac{dx}{dt} (0)= 40 ft/s\)
Therefore the initial value problem is written below:
\(\frac{d^2 x}{dt^2} = -32, x(0) = 200, \frac{dx}{dt}(0) = 40\)
Let us solve for x(t)
\(\frac{d^2 x}{dt^2} = -32\\d(\frac{dx}{dt} )= -32 dt\\\)
Integrate both sides
\(\frac{dx}{dt} = -32t + k_1\\\frac{dx}{dt} (0) = 40\\40 = -32(0) + k_1\\k_1 = 0\\\frac{dx}{dt} = -32t + 40\)
Integrate both sides
\(x(t) = -16t^2 + 40t + k_2\\x(0) = 200\\200 = -16(0) + 40(0) + k_2\\k_2 = 200\\x(t) = -16t^2 + 40t +200\)
Related Questions
what multiples 410,000
pls help me
Answers
Write each product using an exponent. number one 20 × 20 number two 4 × 4 × 4 × 4 number three 2 × 2 × 2 × 2 × 2 × 2 × 2 number four 3 × 3 × 3 × 3 × 3 number five 10 × 10 × 10 number six 7 × 7 × 7 × 7 × 7 × 7 number 7 25 × 25 × 25 number 8 5 × 5 × 5 × 5 × 5 × 5 × 5 number 9 6.5 × 6.5 plaease help
Answers
Answer:
1. 20² = 400
2. 4⁴ = 256
3. 2⁷ = 128
4. 3⁵ = 243
5. 10³ = 1,000
6. 7⁶ = 117,649
7. 25³ = 15,625
8. 5⁷ = 78,125
9. 6.5² = 42.25
i wasnt really sure what you meant but i hope this helps
10+11+x+y+12=32, 9+8+x+z+7=37 what is z-y
Answers
Answer: 12
The answer to this equation would be 12, I hope this helps.
which function will have the greatest value at
\(x = 16 \)
\( y = {10}^{16} \)
\(y = {x}^{2} - 17x + 182\)
\(y = {1.17}^{x} \)
Answers
The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.
How to determine the corresponding output value for the given function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;
\(y = 10^{16}\)
y = 10,000,000,000,000,000.
y = x² - 17x + 182
y = 16² - 17(16) + 182
y = 256 - 272 + 182
y = 166.
\(y = 1.17^x\\\\y = 1.17^{16}\)
y = 12.330304108137675851908392069373.
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ₜₕᵢₛ ₕₐₛ ₙₒ ₚₒᵢₙₜ ₜₒ ᵢₜ
Answers
Answer:
Thanks for the points
Step-by-step explanation:
Does standard deviation means independent events
Answers
Standard deviation does not mean independent events.
Does standard deviation means independent events?No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.
Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.
Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.
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Johnson Electronics makes calculators. Consumer satisfaction is one of the top
priorities of the company’s management. The company guarantees the refund of
money or a replacement for any calculator that malfunctions within two years from
the date of purchase. It is known from past data that despite all efforts, 12% of the
calculators manufactured by this company malfunction within a 2-year period. The
company recently mailed 550 such calculators to its customers.
a. Find the probability that exactly 32 of the 550 calculators will be returned for
refund or replacement within a 2-year period.
b. What is the probability that 30 or more of the 550 calculators will be returned for
refund or replacement within a 2-year period?
a. What is the probability that 15 to 35 of the 550 calculators will be returned for
refund or replacement within a 2-year period?
Answers
Answer:
later ill answer this .. read and understand
Solve for the portion. Round to hundredths when necessary.
14.5% of 1,800 is
Answers
The value of 14.5% of 1,800 is 261 by using the concept of percentage.
What is meant by percentage?In mathematics, a percentage is a value or ratio expressed as a fraction of 100.
The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.
A % is a relative figure that indicates one-tenth of a quantity. One percent (symbolized 1%) is the one-hundredth part; consequently, 100 percent denotes the complete amount, and 200 percent specifies twice the supplied amount.
Given,
14.5% of 1,800
=(14.5/100)×1800
=261
Therefore, the answer is 261.
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Find the distance between the two points rounding to the nearest tenth (if necessary). (5,-8) and (-3,-1)
Answers
Answer: \(\sqrt{113}\)
Step-by-step explanation:
You use the Pythagorean Theorem for problems like this.
1. First you figure out the distance between the points.
2. As seen in the picture, the yellow line is 7 units long and the blue line is 8 units long.
3. From here you substitute the numbers into the Pythagorean Theorem. \(7^{2} +8^{2} =c^2\)
4. Now solve. This gives you \(\sqrt{113}\)
Describe at least two advantages to using stemplots rather than frequency distributions
Answers
Answer:
Suppose that a data set has a minimum value of 18 and a max of 83 and that you want 5 classes. Explain how to find the class width for this frequency table. What happens if you mistakenly use a class width of 13 instead of 14?
Step-by-step explanation:
Subtract 150+70x-x^2 +0.5x^3 from 270x-3x^2 and multiple your answer
Answers
Step-by-step explanation:
We start by subtracting the polynomial 150+70x-x^2+0.5x^3 from 270x-3x^2.
270x - 3x^2 - (150 + 70x - x^2 + 0.5x^3)
= 270x - 3x^2 - 150 - 70x + x^2 - 0.5x^3 (distributing the negative sign)
= -0.5x^3 - 2x^2 + 200x - 150
To multiply our answer, let's assume we are multiplying by x:
-0.5x^4 - 2x^3 + 200x^2 - 150x
Therefore, the subtraction and multiplication result in:
(-0.5x^3 - 2x^2 + 200x - 150) * x = -0.5x^4 - 2x^3 + 200x^2 - 150x
(f) 0.7 - 6.32 + (-0.8) + 1.28
Answers
Answer:
=0.7f−5.84
Step-by-step explanation:
Let's simplify step-by-step.
f(0.7)−6.32−0.8+1.28
=0.7f+−6.32+−0.8+1.28
Combine Like Terms:
=0.7f+−6.32+−0.8+1.28
=(0.7f)+(−6.32+−0.8+1.28)
=0.7f+−5.84
Answer:
=0.7f−5.84
Pls Brainliest
Please look at the image.
Answers
Answer:
3
Step-by-step explanation:
because I said so my dude
2. Troy had 3/8 of a pizza left over from his party. He ate 3/4 of the leftover pizza for breakfast. How much of the
whole pizza did Troy have at breakfast?
3. 3/5 of a bag of coffee weighs 6/7 pound. How much does a whole bag of coffee weigh?
Answers
The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds
A fraction is defined as a part of a whole quantity.
1. Leftover pizza = 3/8
Pizza used as breakfast = 3/4 of left-over pizza
= 3/4 of 3/8
The of is calculated by the use of multiplication
The fractions are multiplied as follows:
The numerators of the fractions are multiplied and written as the numerator.The product of the denominators is written as the denominator.Then we simplify the given fraction to get the final result.Pizza used as breakfast = 3/4 * 3/8
= 3 * 3 / 4 * 8
= 9/32
2. 3/5 of bag of coffee weighs = 6/7 pounds
1 bag of coffee weighs = 6/7 ÷ 3/5
The fractions are divided as follows:
The fraction to be divided is reciprocatedThe numerators of the fractions are multiplied and written as the numerator.The product of the denominators is written as the denominator.Then we simplify the given fraction to get the final result.Thus, = 6/7 * 5/3
= 6 * 5 / 7 * 3
= 30/21
= 10/7 pounds
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what is the equation for line b
Answers
Answer:
y=1/2x+1
Step-by-step explanation:
you can literally do rise over run to get the answer
The diameter of a circle is 36cm and a chord of the same circle is 30cm. To the nearest tenth, what is the distance of the chord from the center of the circle?
Answers
Answer:
It would be 2.
Step-by-step explanation:
Emma has money in two savings accounts. One rate is 6% and the other is 14%. If she has $950 more in the 14% account and the total interest is $342, how much is invested in each savings account?
Answers
$1045 was invested at the interest rate 6% whereas $1,995 was invested at 14%
How is interest computed?
Interest is determined as the amount invested multiplied by the interest rate.
Let Y be the amount invested at 6%
Interest=Y*6%
Interest=0.06Y
The amount invested at 14%, which is $950 more , is Y+950
Interest=(Y+950)*14%
Interest=0.14Y+133
Total interest =0.06Y+0.14Y+133
Note that total interest is 342
342=0.06Y+0.14Y+133
342=0.20Y+133
342-133=0.20Y
209=0.20Y
Y=209/0.20
Y=$1,045(amount invested at 6%)
Amount invested at 14%=$1,045+$950
Amount invested at 14%=$1,995
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How many lines of symmetry are there in the object pictured below?
A. 0
B. 2
C. 3
D. 1
Answers
Choose the correct graph of the function
Answers
The perimeter of the figure is 18 units. Complete the statements to find the side lengths.
1. Find the distance from A to B. Explain how you found this distance.
2. Add the distances of the vertical and horizontal segments. These are the distances from A to B, B to C, and C to D. Show how you found the total.
3. Use the perimeter to find the length of segment AD. This is the distance from A to D. Explain how you found your answer.
Answers
Answer:
1.
the distance is 6 units
Explanation: you can just count the squares cince the line is straight and even if you use the Distance Formula... you'll get the same answer.
2.
A to B = 6 units
B to C = 4 units
C to D = 3 units
So...
6+4+3 = 13 units
3.
The distance between A to D is = 5 units
You can find the answer by using the Distance Formula.
What is 2^4+2(10-4)-3?
Answers
Step-by-step explanation:
We have to solve :
\(2^4 + 2 (10 - 4) - 3 \)
BODMAS will be used here,
B = Bracket
O = off
D = Division
M = Multiplication
A = addition
S = Subtraction
First let's solve
\(2^4\)
\(2 \times 2 \times 2 \times 2\)
\(16\)
Now,
Bracket of ,
16 + 2 (6) - 3
16 + 12 - 3
28 - 3
25
16+2•6-3
16+12-3
25
10 Caleb divides powers of 10 using exponents . He says that 0.6 divided by increases the value of the 6. Do you agree with Caleb ? 10 ^ 2 Explain your thinking
Answers
I disagree with Caleb because the value decreased after the quotients are carried out
How to determine the true statement?From the question, the statement is given as
He says that 0.6 divided by 10² increases the value of the 6.
The mathematical expression of the above statement is represented as
0.6 divided by 10²
So, we have
0.6/10²
When the above quotient is evaluated, we have
0.6/10² = 0.006
The above result is different from Caleb's reasoning
This is so because 0.6 divided by 10² decreases the value of the 0.006, instead of increasing the value to 6, as stated by Caleb
Hence, Caleb's reasoning is incorrect
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Complete question
Caleb divides powers of 10 using exponents. He says that 0.6 divided by 10² increases the value of the 6.
Do you agree with Caleb? Explain your thinking
Which numbers are solutions to the inequality 2x –1> X + 2? Check all of the boxes that apply.0 12345
Answers
2x - 1 > x + 2
x is adding on the right, then it will subtract on the left
1 is subtracting on the left, then it will add on the right
2x - x > 2 + 1
x > 3
From the options, the solutions are 4 and 5.
Answer: 4 and 5
Step-by-step explanation:
Use the quadratic formula to find the exact solutions of x2 − 9x + 5 = 0.
x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a
A) x equals negative 9 plus or minus the square root of 101, all over 2
B) x equals 9 plus or minus the square root of 101, all over 2
C) x equals negative 9 plus or minus the square root of 61, all over 2
D) x equals 9 plus or minus the square root of 61, all over 2
Answers
The correct answer is Option D) x equals 9 plus or minus the Square root of 61, all over 2.
The exact solutions of the quadratic equation x^2 - 9x + 5 = 0 using the quadratic formula, we can use the following formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the coefficients of the equation are:
a = 1
b = -9
c = 5
Substituting these values into the quadratic formula:
x = (-(-9) ± √((-9)^2 - 4(1)(5))) / (2(1))
Simplifying:
x = (9 ± √(81 - 20)) / 2
x = (9 ± √61) / 2
Therefore, the exact solutions of the equation x^2 - 9x + 5 = 0 are:
x = (9 + √61) / 2 (Option D)
x = (9 - √61) / 2 (Option D)
So, the correct answer is Option D) x equals 9 plus or minus the square root of 61, all over 2.
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Identify the next number in the following sequence
25 49 97 ?
Select only one answer
- 124
- 171
- 139
- 193
Answers
Answer:
the correct answer is 193
Step-by-step explanation:
25×1-0=25
25×2-1=49
49×2-1=97
97×2-1=193
1.62 was multiplied by a power of ten to get 16.2. What power of ten was it
multiplied by?
10
100
1,000
Answers
Answer:
10
Step-by-step explanation:
Every time you multiply by 10 you move the decimal point one digit to the right. So if you multiply 1.62 by 10 you move the decimal point one digit to the right so it becomes 16.2.
So the answer is 10
Answer:
The answer is 10
Step-by-step explanation:
Every time you multiply by a power of 10 that does not have a negative exponent, the decimal point moves to the right.
How many times, you might wonder. It all just depends on how many zeroes there are. If there's one 0, (10) then the decimal point just moves one over, if were multiplying by 100 then 2 places over, 1000 three places over, and so on.
1.62 * 10 = 16.2, since the decimal point moved one to the right.
10 is therefore the answer, but if you wanted to you could check the other answers as well.
1.62 * 100 = 162
1.62 * 1000 = 1620
Therefore, the answer is 10. Please mark brainliest if possible. Have a nice day.
612,315 in scientific notation
Answers
Answer: 6.12315 × 105
Step-by-step explanation: No worry's just here for the fun of it
F (x)=x+3x find f(2)
f(x)=3x-2 find f(-10)
help please
Answers
Answer:
f(x)=3x-2 is 4x i dont know bout the other one
Step-by-step explanation:
Answer:
1) f(2) = 8
2) f(-10) = -32
Step-by-step explanation:
Whenever you see a problem that asks something like what f(2) or f(-10) is, it is asking you to substitute whatever number is in the parentheses for every x in the given function.
1) So, to find f(2), substitute 2 for every x in the given function, f(x) = x + 3x and solve:
\(f(2) = (2)+3(2)\\f(2) = 2 + 6 \\f(2) = 8\)
Thus, for this function, f(2) = 8.
2) Do the same with the second question. Substitute -10 for every x in the given function, f(x) = 3x - 2.
\(f(-10) = 3(-10) - 2 \\f(-10) = -30-2\\f(-10) = -32\)
Thus, for this function, f(-10) = -32.
An architect uses a scale of 3 4 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?
Answers
Answer:
16 in.
Step-by-step explanation:
We have the ratio
How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of
Now we need to know how many inches there would be if the number of feet is 24:
Cross multiply to get
3x = 48 so
x = 16 in.
The length of the line on the blueprint of the wall will be 18 inches.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
An architect uses a scale of 3/4 inches to represent 1 foot on a blueprint for a building.
Then the scale factor of the blueprint will be
Scale factor = 3/4 inches per foot
If the east wall of the building is 24 feet long.
Then the length of the line on the blueprint of the wall will be
Length = 24 feet x scale factor
Length = 24 x (3/4)
Length = 6 x 3
Length = 18 inches
Thus, the length of the line on the blueprint of the wall will be 18 inches.
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For which of the following displays of data is it not possible to find the mean histogram frequency, table, stem, and leaf plot doc plot
Answers
The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.
A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.
A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.
A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.
A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.
In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
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