A floodlight is on the ground 45 meters from a building. A thief 2 meters tall runs from the floodlight directly towards the building at 6 meters per second. How rapidly is the length of his shadow on the building changing when he is 15 meters from the building
Answers
When the thief is 15 meters from the building, the rate of change of the length of his shadow on the building is 19.63 m/s.
Let AB be the height of the building, and TC be the length of the shadow cast by the thief when he is 15 meters from the building. Also, let BD be the length of the thief's shadow at the given instant.Since the distance between the building and the floodlight is 45 meters, we have AC = 45 meters.
At a given instant, let x be the distance from the thief to the floodlight.
Then, we have TC = 1/2 * BD ...........(1) (By AA similarity)
Thus, we need to find dB/dt when x = 15 meters.
Differentiating equation (1) with respect to time t, we get:(dT_C)/(dt) = 1/2 * (dB)/(dt)
Since the thief is moving towards the building, we have x = 45 - 15 = 30 meters.
So, using Pythagoras theorem, we have:
AB² = AC²+ BC²=> AB² = 45²+ BD²=> AB² = 2025 + BD²
Differentiating with respect to time, we get:
2AB(dAB)/(dt) = 2BD(dBD)/(dt)=> (dBD)/(dt) = (AB/(BD)) * (dAB)/(dt)...........(2)
Putting AB² = 2025 + BD², we get:
AB = √(2025 + BD²)
Putting AB = 47.53 m and BD = 8.66 m (using x = 15 m), we get:
d(BD)/(dt) = (47.53/(8.66)) * (dAB)/(dt)
d(BD)/(dt) = 5.487(dAB)/(dt)
Using the similar triangles ABD and ACT, we get:
AB/BD = AC/TC=> (AB/BD) = (AC/TC) => AB = (AC/TC) * BD
Substituting the value of AB = 47.53 m, AC = 45 m and TC = BD/2, we get:
(BD/2) = (45/47.53) * BD=> BD = 17.94 meters
Substituting BD = 17.94 m in equation (2), we get:
d(BD)/(dt) = (47.53/(8.66)) * (dAB)/(dt)
d(17.94)/(dt) = 5.487(dAB)/(dt)
AB= 19.63
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Related Questions
students who study for 7 hours over the course of a week will perform better than students who cram for 7 hours the night before the exam. the dependent variable in this hypothesis is:
Answers
The dependent variable in this hypothesis is test performance.
What is a dependent variable?
In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, one‘s values are examined under the assumption as well as demand that they are dependent on the value of another variable due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not thought to be depending on other variables. Time, space, specific gravity, mass, fluid flow rate and previous values of certain observed value of interest (such as the size of the human population) are examples of common independent variables that can be used to forecast future value systems (the dependent variable).
The outcome of this hypothesis is the dependent variable.
Hence, the dependent variable in this hypothesis is test performance.
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7.[–/1 Points]DETAILSALEXGEOM7 9.1.004.MY NOTESASK YOUR TEACHERConsider the triangular prism shown. A triangular prism is shown.(a)How many vertices does it have? (b)How many edges (lateral edges plus base edges) does it have? (c)How many faces (lateral faces plus bases) does it have?
![7.[/1 Points]DETAILSALEXGEOM7 9.1.004.MY NOTESASK YOUR TEACHERConsider the triangular prism shown. A](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/VoqRpBtqQE7IavlzZ9edcz6isob5YsEU.jpeg)
Answers
Step 1
Vertices in shapes are the points where two or more line segments or edges meet (like a corner). The singular of vertices is vertex.]
A)
\(The\text{ triangular prism has 6 vertices}\)The edge is the side of a polygon or a line segment where two faces of a solid figure meet.
B)
\(The\text{ triangle prism has 9 edges}\)A prism is a 3-dimensional shape with two identical shapes facing each other. These identical shapes are called “bases”. The bases can be a triangle, square, rectangle or any other polygon. Other faces of a prism are parallelograms or rectangles.
C)
\(The\text{ triangular prism has 5 faces}\)Use Euler's Method with a step size of h = 0.1 to find approximate values of the solution at t = 0.1,0.2, 0.3, 0.4, and 0.5. +2y=2-ey (0) = 1 Euler method for formula Yn=Yn-1+ hF (n-1-Yn-1)
Answers
Using Euler's Method with a step size of h = 0.1, the approximate values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 are as follows:
t = 0.1: y ≈ 0.805
t = 0.2: y ≈ 0.753
t = 0.3: y ≈ 0.715
t = 0.4: y ≈ 0.687
t = 0.5: y ≈ 0.667
To apply Euler's Method, we need to use the given formula:
Yn = Yn-1 + hF(n-1, Yn-1)
In this case, the given differential equation is 2y = 2 - e^(-y) and the initial condition is y(0) = 1.
We can rewrite the differential equation as:
2y = 2 - e^(-y)
2y + e^(-y) = 2
Now, let's apply Euler's Method using a step size of h = 0.1.
For t = 0.1:
Y1 = Y0 + hF(0, Y0)
= 1 + 0.1(2 - e^(-1))
≈ 0.805
For t = 0.2:
Y2 = Y1 + hF(0.1, Y1)
≈ 0.753
For t = 0.3:
Y3 = Y2 + hF(0.2, Y2)
≈ 0.715
For t = 0.4:
Y4 = Y3 + hF(0.3, Y3)
≈ 0.687
For t = 0.5:
Y5 = Y4 + hF(0.4, Y4)
≈ 0.667
Using Euler's Method with a step size of h = 0.1, we have approximated the values of the solution at t = 0.1, 0.2, 0.3, 0.4, and 0.5 to be approximately 0.805, 0.753, 0.715, 0.687, and 0.667, respectively.
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The names of the automobile manufacturer of the car that you drive is what type of variables ( scales of measurement)
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The type of variable that represents the names of the automobile manufacturers would be the categorical variable.
What are variables in research work?A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.
There are various types of variables that include the following:
categorical variables.Nominal variables. Ordinal variables. Numeric variables. Continuous variables. Discrete variables.Learn more about variables here:
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Function g is defined as g(x)=kf(x). What is the value of k?
Answers
Pick an x value like x = 2
Note that f(2) = 1 and g(2) = 2. This shows we've doubled the f(x) value to get g(x). Therefore k = 2.
Or you could pick on x = 4 to see f(4) = 2 and g(4) = 4. The output of f(x) has been doubled as well.
It doesn't matter what x is since we'll have this doubling effect go on. I recommend picking x values where the points on the blue graph land perfectly on a grid location. Something like x = 5 seems a bit tricky.
Answer:
K = 2
Step-by-step explanation:
I just took a test with this question on it and got it right.
Hope this helps! :)
use determinants to find out if the matrix is invertible.| 5 -2 3|| 1 6 6||0 -10 -9|the determinant of the matrix is
Answers
The determinant is non-zero (-30 ≠ 0), the matrix is invertible.
To find the determinant of the matrix, we can use the Laplace expansion along the first row:
| 5 -2 3 |
| 1 6 6 |
| 0 -10 -9 |
= 5 * | 6 6 | - (-2) * | 1 6 | + 3 * | 1 6 |
| -10 -9 | | 0 -9 | | 0 -10 |
= 5[(6*(-9)) - (6*(-10))] - (-2)[(1*(-9)) - (60)] + 3[(1(-10)) - (6*0)]
= -30
Since the determinant is non-zero (-30 ≠ 0), the matrix is invertible.
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The determinant of the given matrix is 132.
To find the determinant of the matrix, we can use the formula for a 3x3 matrix:
| a b c |
| d e f |
| g h i |
Determinant = a(ei - fh) - b(di - fg) + c(dh - eg)
In this case, the matrix is:
| 5 -2 3 |
| 1 6 6 |
| 0 -10 -9 |
Using the formula, we can calculate the determinant as follows:
Determinant = 5(6(-9) - (-10)(6)) - (-2)(1(-9) - (-10)(6)) + 3(1(-10) - 6(0))
Simplifying the expression, we get:
Determinant = 5(-54 + 60) - (-2)(-9 + 60) + 3(-10 - 0)
= 5(6) - (-2)(51) + 3(-10)
= 30 + 102 + (-30)
= 132
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a box with a square base and open top must have a volume of 42592 c m 3 . we wish to find the dimensions of the box that minimize the amount of material used. first, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [hint: use the volume formula to express the height of the box in terms of x .] simplify your formula as much as possible. wyzant
Answers
a formula for the surface area of the box in terms of only x , the length of one side of the square base is A = x² + 170368 cm³/x
The volume of the box with square base is V = x²h where x = length of side of square base and h = height of box.
Now, the area of the of box open at the top with dimensions of length, l , width, w and height, h are
A = 2lh + lw + 2wh
Now for a box of square base, l = w = x.
So, A = 2xh + x² + 2xh
A = x² + 4xh
Since V = x²h and V = 42592 cm³,
h = V/x² = 42592/x²
substituting h into A, we have
A = x² + 4xh
A = x² + 4x(42592 cm³/x²)
A = x² + 4 × 42592 cm³/x
A = x² + 170368 cm³/x
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Please look at photo. Help please. Algebra 1 problem.
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Answer:
set up equations, then explain. use u as
Step-by-step explanation:
A microbiologist is growing bacteria cultures in the lab. After 5 minutes, a bacteria colony has 1.3 million organisms. After 12 minutes, the same colony has 41.5 million organisms. After 15 minutes, the colony has grown to 101.3 million organisms. Is this a proportional or non-proportional relationship?
Answers
Answer: Non proportional
Step-by-step explanation:
To know if the values given are proportional or not, we will use the formula:
y = kx
where
y = number of organisms
x = number of minutes
k = constant of proportionality
After 5 minutes, a bacteria colony has 1.3 million organisms. Using the formula, y = kx
1,300,000 = 5k
k = 1,300,000 / 5
k = 260,000
After 12 minutes, the same colony has 41.5 million organisms. Using y= kx
41,500,000 = 12x
x = 41500000 / 12
x = 3458333.8
After 15 minutes, the colony has grown to 101.3 million organisms.
y = kx
101,300,000 = 15k
k = 101,300,000 / 15
k = 6753333.8
It is a non-proportional relationship as the constant of proportionality is different for each.
Shahid bought 1.25 kg of apples, 500g bananas and some grapes. In total he bought 2 kg of fruits. What is the weight of the grapes?
Answers
Determine the largest integer value of xx in the solution of the following inequality.
2x−8≤-19
Answers
Answer:
x≤-11/2
Step-by-step explanation:
Hope this helps!
Brain-List?
if you drive for 2 hours, at 60 miles per hour, you will have traveled 120 miles. this is a very common type of calculation, involving three quantities: distance, rate and time. if you know just two of these three quantities, you can always calculate the third. thus, if you want to know how much time it is going to take you to get somewhere, and you know that the distance is 120 miles and you will drive at a rate of 60 miles per hour, you can divide the 120 miles by the 60 miles per hour and obtain a time of 2 hours. for this exercise, you will be relating distance, rate and time. the distance we will work with is the depth of happy valley. (remember that even more rock has been removed than the depth of the valley, because the site of the modern valley once was higher than the site of the modern mountain, and the site of the modern mountain has been lowered somewhat as well. and, the rocks had to be deposited, raised and bent before the erosion could occur. so, you're calculating how much time was involved in a small part of the much longer history of central pennsylvania.) we can measure how rapidly rock is being dissolved and washed out of happy valley, and use some fairly simple physical ideas to turn that into the rate at which the valley floor is being lowered. that gives you a distance (the valley depth) and a rate ( the speed at which the valley floor is being lowered), allowing you to calculate the time that has been used in the lowering. to get the correct answer, you will calculate the time from which equation: group of answer choices
Answers
The equation that can be used to calculate the time in this scenario is:Time = Distance / Rate
In this case, the distance refers to the depth of Happy Valley, and the rate refers to the speed at which the valley floor is being lowered. By dividing the distance by the rate, you can determine the time that has been used in the lowering of the valley floor.
In the given scenario, we are trying to calculate the time it takes for the valley floor to lower in Happy Valley. We have two quantities: the distance (depth of Happy Valley) and the rate (speed at which the valley floor is being lowered).
To calculate the time, we can use the formula:
Time = Distance / Rate
This formula applies to situations where you have two known quantities and want to find the third. In this case, by dividing the distance (depth of Happy Valley) by the rate (speed at which the valley floor is being lowered), we can determine the time it has taken for the valley floor to lower.
By applying the same principle as the example of driving at a certain speed for a certain distance, we can calculate the time involved in the geological process of the valley floor lowering in Happy Valley.
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A uniformed U.S. Marine conducts an in-person survey at a social event to determine the proportion of Americans that say "yes" to the question: "Should the U.S. Government reduce military funding?" Of the 100 people surveyed, 99 of the respondents said "no." Identify the type of bias in this poll and state whether the sample proportion overestimates or underestimates the true proportion of Americans that believe that the U.S. Government should reduce military funding.
Answers
The type of bias in this poll is selection bias and the sample proportion underestimates the true proportion of Americans that believe the U.S. Government should reduce military funding.
Selection bias is a form of bias that arises when the sample being studied is not genuinely representative of the entire population, resulting in some aspects of the population being over- or under-represented in the sample. In other words, selection bias occurs when specific groups or subgroups within the population are more likely to be included in the sample. The individuals conducting the survey may have selected a group that is not representative of the entire population. In the given problem, the Marine selected a group of people at a social event, which may not be representative of the entire population.Therefore, the type of bias in this poll is selection bias, and the sample proportion underestimates the true proportion of Americans that believe that the U.S. Government should reduce military funding.
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The decay of 249 mg of an isotope is given by A=249e−0.015t , where t is time in years. Find the amount after 43 years.
Answers
Answer:
A≈676.2
Step-by-step explanation:
1. Exponentially solve equation
A=249e-0.0015t as t = 43 years (Unless conversion to seconds)
A≈676.2
2. Solve graphically = intersect = (43, 676.2) x axis is time y axis is amount.
5y + 3= 14
pleaseeeee help
Answers
Answer:
5y + 3= 14
subtract 3 from each side
5y=11
divide each side by 5
5y/5=11/5
y=11/5 or 2.2 or 2 1/5
Hope This Helps!!!
Answer:
2.2
Step-by-step explanation:
Properties needed:
Subtraction Property of EqualityDivision Property of Equality
First we need to subtract 3 from both sides because of subtraction property of equality to make both sides equal.
5y + 3 = 14
-3 -3
5y = 11
Then we need to divide 5 from both sides (division property of equality) to get y.
\(\frac{5y}{5} = \frac{11}{5}\)
And we get 2.2
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I hope this helps!
Have a great day!
Tony received a $20 gift card for school supplies. Paper is $5 per pack and notebooks are $3 each. Which inequality represents the number of packs of paper, p, and notebooks, n, Tony may purchase?
Answers
The inequality 5p + 3n ≤ 20 represents the purchase of Tony
Tony received a $20 gift card for school supplies. Paper is $5 per pack and notebooks are $3 each. Which inequality represents the number of packs of paper, p, and notebooks, n,
We can start by using the data provided in the question to address this problem.
A $20 gift card for school supplies was given to Tony.
A pack of paper costs $5, while a notepad costs $3.
Let n be the number of notebooks Tony may buy and p be the number of packs of paper he may buy.
The paper costs five pence in total.
The price of notebooks is n dollars in total.
Tony has a $20 gift certificate, so we can write:
5p + 3n ≤ 20
This disparity shows how many notebooks and paper packs Tony is allowed to buy.
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How can systems of linear equations with two variables be solved using algebraic methods?
Answers
Answer: The systems are solved by solving for one variable in one of the equations, then substituting that equation into the second equation. Solve for a in the second equation, then substitute the second equation into the first. The Elimination Method: Both equations are in standard form: Ax + By = C.
Your teacher wants to use a point system to select the winning pet. She wants each pet to get a certain number of points for each 1st choice vote and a certain number of points for each 2nd choice vote.
Your teacher decides to use these rules for her point system:
Points need to be positive whole numbers
Points for a 1st choice vote have to be greater than or equal to the points for a 2nd choice vote.
Determine point values for the 1st and 2nd choice that would result in the turtle winning. Use words and numbers to explain how this point system results in the turtle winning
Answers
In the above case, the possible point system will be:
1st choice vote: 4 points
2nd choice vote: 2 points
What is the point system?In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:
The point got to be positive entire numbersThe point for a 1st choice vote need to be more noteworthy than or rise to to the focuses for a 2nd choice voteLets say:
1st choice vote: 4 points
2nd choice vote: 2 points
Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.
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what is the answer?
Answers
Answer:
24.5%
Step-by-step explanation:
Which describe all decimal that te rational number
Answers
Explanation: Any decimal number that terminates or ends at some point is a rational number.
The slope of a line is 1/7 and it passes through the point (21, 14). What is
the equation of the line in point-slope form?*
Answers
Answer: the equation of the line is y=1/7x+11
Find the cos 35
Thanks
Answers
Answer:
0.8192
Step-by-step explanation:
in a game of poker, what is the probability that a five-card hand will contain (a) a straight (five cards in unbroken numerical sequence)
Answers
The probability that a five-card hand will contain a straight = 5/1274
There are 52 cards in a deck from which each 13 cards are from 4 different suits (clubs, diamonds, spades and hearts) in a game of poker.
Each 13 cards from high to low are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. So a straight of five cards, i.e., five cards in unbroken numerical sequence would be got only from 10 cards in a sequence.
So the possible ways to get a single straight five from all four suits = \(4^5\)
Now as we doesn't need all 5 cards from a single suit, we can ignore 4 ways from the above number. i.e., \(4^5-4 = 1020\) ways.
Hence the possible ways to get a straight five from 10 cards from all four suits = 10 x 1020 = 10200 ways
Total number of ways to select 5 cards from 52 cards = 52C5
Thus,
The probability that a five-card hand will contain a straight = 10200 / 52C5
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For each sum or product, determine whether the result is a rational number or an irrational number.
Then choose the appropriate reason for each.
Answers
The appropriate reasons for each. are:
1. Rational/The sum of two rational is always rational
2. Irrational/ the sum of a rational and an irrational is always irrational
3. Irrational/The product of a nonzero rational and an irrational is always irrational
4. Rational/The product of two rational is always rational
What are the Rational sum?A rational number is simply a number that can be written as a fraction of two integers, as long as the denominator is not equal to zero. There are numerous rational numbers, like 1/2, -3/4, and 5, for instance.
Rational numbers comprise of both whole numbers and fractions while the irrational numbers, on the other hand, are those that bear radical signs above them. Once you have known if the two numbers are rational or irrational, the solution can be found among the other area of the solutions.
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Solve for x. Rolind to the nearest hundredth.
Answers
cos(51°) = x/7
x = 7 • cos(51)
x = 4.4052 = 4.41
Choose all the expressions that are equal to 45×67 4 5 × 6 7. A. 2435 24 35 B. 4×75×6 4 × 7 5 × 6 C. 4×56×7 4 × 5 6 × 7 D. 6×54×7 6 × 5 4 × 7 E. 6×45×7 6 × 4 5 × 7
Answers
None of the given expressions (A, B, C, D, E) are equal to 45 x 67.
How to find which expressions are equal to multiplication?To find which expressions are equal to 45 x 67, we simply need to simplify each of the expressions given.
Starting with option A, 24 x 35, this is not equal to 45 x 67.Moving on to option B, we have 4 x 75 x 6. Simplifying this, we get 1,800, which is not equal to 45 x 67.Option C is 4 x 56 x 7, which simplifies to 1,568, not equal to 45 x 67.Option D is 6 x 54 x 7, which simplifies to 2,268, not equal to 45 x 67.Finally, option E is 6 x 45 x 7, which simplifies to 1,890, also not equal to 45 x 67.Therefore, none of the expressions are equal to 45 x 67.
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Change the negative exponent to a positive exponent
Answers
Answer:
\( \frac{1}{ {6}^{8} } \)
Step-by-step explanation:
when the is a base raised to a negative power.....put it under 1 and the negative power now becomes a positive power
Example: 5^-2 = 1/5^2
Find the volume of a sphere with a surface area of 2916 squared pi
Answers
Answer:
it would be somewhere around 29161231
Step-by-step explanation:
it is m8
Write each equation in slope-intercept form of the equation of a line. Underline the slope and circle the y-intercept in each equation.
2x+y=1 Answer:
Answers
Bill rented a truck for one day. There was a base fee of $16.95, and there was an additional charge of 82 cents for each mile driven. Bill had to pay$222.77 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer:
251 miles
Step-by-step explanation:
To answer this, we first must subtract the total Bill ended up paying by the base fee:
222.77 - 16.95 = 205.82
Now, we divide this total by 82 cents:
205.82 / 0.82 = 251
So, Bill drove the truck 251 miles
Hope this helps :)