Answer:
(dy/dt) = - 0.45 m/s (the minus sign indicates that the height of the shadow decreases as the man moves towards the wall).
Step-by-step explanation:
An image of the problem is presented in the attached file to this solution. The image shows the exact moment when the 2m tall man is 4m away from the wall.
First of, when the man is 4m away from the wall, he is 8m away from the spotlight, that is, x = 8m
Using the concept of similar triangles, we can obtain the value of y at this point.
(x/2) = [(x+4)/y]
x = 8
(8/2) = (12/y)
y = 3m when x = 8m
From the image,
But generally, for x and y at any point,
(x/2) = (12/y)
xy = 24
Differentiating with respect to t
(d/dt)(xy) = (d/dt)12
y (dx/dt) + x (dy/dt) = 0
x (dy/dt) = - y (dx/dt)
At x = 8m, y = 3m, (dx/dt) = 1.2 m/s
8 (dy/dt) = - 3 (1.2)
(dy/dt) = - 3.6/8 = - 0.45 m/s
The minus sign indicates that the height of the shadow decreases as the man moves towards the wall.
Using unit concepts, it is found that:
- a) Grams.
- b) Grams.
- c) Grams squared.
- d) Grams squared.
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- For a data-set, the standard deviation has the same unit as the data-set, both for the sample and the population.
- The variance has the unit squared, both for the sample and the population.
- For example, if the data-set is in metres, the standard deviation will be in metres while the variance will be in squared metres.
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In this question, the data-set is in grams.
- The standard deviation, both for the sample and the population, in items a and b, will be in grams.
- The variance, both for the sample and the population, in items c and d, will be in grams squared.
A similar problem is given at brainly.com/question/14524219
Answer:
g/cm²
Step-by-step explanation:
First, we need to find the volume of the prism. The volume of a square pyramid is V = Bh/3
B = 100 cm²
h = 6 cm
V = 100 cm² * 6 cm /3
V = 600 cm³ /3
V = 200 cm³
Next, we need to solve for the density based on the desired volume and mass.
m = mass = 300 g
V = volume
density = m/V
density = 300 g / 200 cm³
density = 3/2 g/cm³
The lowest possible density of the material to make the paperweight would be g/cm²
The solution to the algebraic expression is: 23e - 21g - 14j + 32
What are algebraic expressions?
Algebraic expressions are mathematical expressions that contain variables, coefficients, and arithmetic operations such as addition, subtraction, division, and multiplication.
Solving algebraic expressions are an important part of mathematics as it helps to improve the aptitude and solving skills of the students.
From the given information, we have;
23j - 21g + 20e - 13 + 52e - 37j + 45 - 49e
let's rearrange by taking the like terms to the same sides;
= 23j -37j - 21g + 20e + 52e - 49e - 13 + 45
= -14j - 21g + 23e + 32
= 23e - 21g - 14j + 32
Therefore, we can conclude that the solution to the algebraic expression is: 23e - 21g - 14j + 32
Learn more about solving algebraic expressions here:
brainly.com/question/4344214
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