A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.4 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
Answers
Answer:
the length of his shadow on the building is decreasing at the rate of 0.525 m/s
Step-by-step explanation:
From the diagram attached below;
the man is standing at point D with his head at point E
During that time, his shadow on the wall is y = BC
ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e
\(\dfrac{AD}{AB} = \dfrac{DE}{BC}\)
\(\dfrac{8}{12} = \dfrac{2}{y}\)
8y = 24
y = 24/8
y = 3 meters
Let take an integral look at the distance of the man from the building as x, therefore the distance from the spotlight to the man is 12 - x
∴
\(\dfrac{12-x}{12}=\dfrac{2}{y}\)
\(1- \dfrac{1}{12}x = 2* \dfrac{1}{y}\)
To find the derivatives of both sides ;we have:
\(- \dfrac{1}{12}dx = 2* \dfrac{1}{y^2}dy\)
\(- \dfrac{1}{12} \dfrac{dx}{dt} = 2* \dfrac{1}{y^2} \dfrac{dy}{dt}\)
During that time ;
\(\dfrac{dx}{dt }= 1.4 \ m/s\) and y = 3
So; replacing the value into above ; we have:
\(-\dfrac{1}{12}(1.4) = - \dfrac{2}{9} \dfrac{dy}{dt}\)
\(\dfrac{dy}{dt} = \dfrac{\dfrac{ 1.4} {12 } }{ \dfrac{2}{9}}\)
\(\dfrac{dy}{dt} = {\dfrac{ 1.4} {12 } }*{ \dfrac{9}{2}}\)
\(\dfrac{dy}{dt} =0.525 \ m/s\)
Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s
Related Questions
Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answers
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
10. Last year, a state university received 3.560 applications from boys. Of
those applications, 35% were from boys who lived in other states. Part A
How many applications did the university receive from boys who lived in
other states? Show how you found the answer for full credit
Answers
Answer:
1.246
Step-by-step explanation:
First, you divide 3.560 by 100%, which gives you 3.56. Now since you have the number of applications received each, you now multiply 3.56 by 35%, or 0.35, which then gives you 1.246.
If the area of a square inscribed in a circle is
25, what is the area of the circle?
Answers
The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.
To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.
When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.
We are given that the area of the square is 25, so we can find the side length of the square:
Area of square = \(s^2 = 25\)
Taking the square root of both sides, we get:
s = √25 = 5
Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:
Diagonal = Diameter = s√2 = 5√2
The radius of the circle is half the diameter, so:
Radius = 5√2 / 2 = (5√2)/2
Now, we can calculate the area of the circle using the formula:
Area of circle = \(\pi r^2\)
Substituting the value of the radius, we get:
Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2
Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.
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Los puntos A(13, a) y B (4,b) pertenecen a una parábola de vértice V (h, 1) Además el eje focal es paralelo al eje de las abscisas ,su parámetro es p y A, B están
contenidos en la recta 2x - y - 13 = 0. Hallar a" + bP.
Answers
The points on a parabola with the focal axis parallel to the abscissa axis, of parameter p and A, B is -12.
How to calculate parameters?Since A and B are points on the parabola, write two equations using the general form of the parabolic equation:
(x - h)² = 4p(y - 1)
The focal axis is parallel to the x-axis, so the distance from the vertex to the focus is equal to p. Therefore, use the distance formula to write an equation for the distance between the vertex and point A:
√((13 - h)² + (a - 1)²) = p
Similarly, write an equation for the distance between the vertex and point B:
√((4 - h)² + (b - 1)²) = p
A and B lie on the line 2x - y - 13 = 0, so substitute the x and y coordinates of A and B into this equation and solve for a and b:
2(13) - a - 13 = 0
2(4) - b - 13 = 0
Solving these equations gives us a = 3 and b = -5.
Now three equations and three unknowns (a, b, and h):
√((13 - h)² + 4) = p + 1
√((4 - h)² + 36) = p + 1
2h - 3 - 13 = 0
The third equation simplifies to 2h = 16, or h = 8.
Substituting this value of h into the first two equations and squaring both sides:
(13 - 8)² + 4 = (p + 1)²
(4 - 8)² + 36 = (p + 1)²
Simplifying these equations and solving for p gives us p = 3.
Finally, find a" + bP by substituting the values found for a, b, and p:
a" + bP = 3 + (-5)(3) = -12
Therefore, the solution is a" + bP = -12.
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A sine function has the following key features period=12 amplitude=4 midline y=1, y-intercept (0,1)
Answers
The sine function is y = 4 sin[ (π/6)x ] + 1.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
1) The parent function is sin(x)
2) sin(x) has:
Middle line: y = 0
Amplitude: 1 because the function goes from 1 unit up to 1 unit down the midddle line.
Period: 2π because sine function repeats every 2π units.
y-intercept: (0,0) because sin(0) = 0.
Now look how these changes in the function reflect on the parameters:
A sin (ωx + B) + C:
That function will have:
amplitude A, becasue the amplitude is scaled by that factor
Period: 2π / ω, because the function is compressed horizontally by that factor.
It will be translated B units to the left
It will be translated C units up.
And you need
Period = 12 => 2π / ω = 12 => ω = π/6
A = 4
Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => = 1.
Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.
So, the is the function searched>
y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1
Now you can check the amplitude, the period, the middle line and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.
Hence, the sine function is y = 4 sin[ (π/6)x ] + 1.
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Q. Unscramble the following term related to algebra:- ROTPORAE.
Answers
Answer:
operator
Step-by-step explanation:
Operator is represented as any symbol that indicates an operation to be performed.
Examples:
- Square root of√x, which indicates the square root is to be taken
- d/dx, which indicates differentiation with respect to x is to be performed
Answer:
OPERATION
OF ALGEBRA IN MATH
Evaluate the definite integral of sin^5(x)dx from 0 to pi/2.
Answers
Step-by-step explanation:
The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.
Let u = sin(x), then du = cos(x)dx
The integral becomes:
∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)
= (u^6)/6 evaluated at sin(π/2) and 0
= (sin^6(π/2))/6 - 0
= (1^6)/6
= 1/6
So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.
A company's stock was selling at
$30 a share. A month later, it was
selling at $33 a share. What is the
percent gain?
Answers
Answer:
10%
Step-by-step explanation:
Compute P(7,4).Multiple choice:a. 35b. 28c. 210d. 840e. none of these choices
Answers
The correct answer is d. 840
The problem ask us to compute the permutations of 7 objects in groups of 4.
To compute this, we use the formula:
\(P(n,r)=\frac{n!}{(n-r)!}\)Then for P(7,4):
\(P(7,4)=\frac{7!}{(7-3)!}=\frac{5040}{3!}=\frac{5040}{6}=840\)Then P(7,3) = 840
The total revenue for Jane's Vacation Rentals is given as the function R(x)=400x−0.4x2
, where x is the number of apartments booked. What number of apartments booked produces the maximum revenue?
Answers
The vertex of a quadratic function in the form ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, a = -0.4, b = 400, and c = 0.
Using the formula, we can calculate the x-coordinate of the vertex:
x = -b / (2a)
= -(400) / (2 * (-0.4))
= -400 / (-0.8)
= 500
Therefore, the number of apartments booked that produces the maximum revenue is 500.
can you please help me
3. To find the perimeter of a rectangle, use the equation , where P is the perimeter, l is the length and w is the width of the rectangle.
(a) A rectangular garden has a perimeter of 40 yd and a width of 5 yd. Use the equation and the replacement set to find the length of the garden. Show your work.
(b) A rectangular table top has a perimeter of 18.4 ft and a length of 6.75 ft. Use the equation and the replacement set to find the width of the table top. Show your work.
Answers
Answer:
a) 15yd
b)2.45ft
Step-by-step explanation:
P = perimeter, l=length and w = width of the rectangle
P = 2l+2w
a) 40 = 2l+2(5)
40 = 2l+10
30=2l
15=l
b) 18.4 = 2(6.75) + 2w
18.4 = 13.5+2w
4.9=2w
2.45=w
I do not understand these questions please solve them for me
Answers
For the first scenario (choosing 3 balls from 1 to 9):
\(_{9}C_{3} = \frac{9!}{3!(9 - 3)!} \)
For the second scenario (choosing 5 potato chips from 20):
\(_{20}C_{5} = \frac{20!}{5!(20 - 5)!} \)
For the third scenario (choosing 2 team members as captain and co-captain from 24):
\(_{24}P_{2} = \frac{24!}{(24 - 2)!} \)
The first situation is a combination. In a combination, the order of the items does not matter. In this game, it does not matter what order the 3 balls are in, as long as you have the correct numbers in a row. If you choose balls 1, 2, and 3, it's the same as if you choose 3, 2, and 1. A permutation, on the other hand, would require the order of the items to be specific. In this game, the order of the numbers doesn't matter, making it a combination.
The second situation is a combination. In this scenario, you are choosing 5 out of 20 different potato chips, and the order in which you choose them doesn't matter. Whether you choose chips 1, 2, 3, 4, and 5, or chips 5, 4, 3, 2, and 1, the combination is still the same.
The third situation is a permutation. In a permutation, the order of the items matters, meaning the first chosen person will be the captain and the second chosen person will be the co-captain. In this scenario, there are 24 people to choose from, and the order in which they are chosen determines their role as captain or co-captain. A combination, on the other hand, only cares about the items themselves, not the order in which they are chosen. In this scenario, the order matters, making it a permutation.
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Answer this with explanation please
Answers
The measure of angle MTU m∠MTU is 114 degree.
What is the measure of angle MTU?From the figure in the diagram:
Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.
m∠STU = 145°m∠STM = 31°m∠MTU = ?Since, angle STU composes or is the sum of angle STM and angle MTU.
To find angle MTU, simply subract angle STM from angle STU.
m∠STU = m∠STM + m∠MTU
Hence:
m∠MTU = m∠STU - m∠STM
Plug in the given values and simplify
m∠MTU = 145° - 31°
Subtract 31 from 145
m∠MTU = 114°
Therefore, angle MTU measure 114°.
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What the meaning of "f is order-preserving if x < y implies f(x) < f(y)"?
Answers
An order-preserving function is a function that preserves the order of its inputs. In other words, if x is less than y, then f(x) will be less than f(y).
The statement "f is order-preserving if x < y implies f(x) < f(y)" means that if x is less than y, then f(x) must be less than f(y). This is a necessary condition for a function to be order-preserving. However, it is not a sufficient condition. For example, the function f(x) = x^2 is not order-preserving, because 2 < 3, but f(2) = 4 > f(3) = 9.
In summary, order-preserving functions are useful in situations where we need to preserve the order of a set of data.
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What is the Greatest Common Factor of 12 and 28
O2
3
06
4
Answers
Answer:
The GCF of 12 and 28 is 4.
Step-by-step explanation:
hope this helps
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 28 are: 1, 2, 4, 7, 14, 28
Answer:
The GCF is 4.
Step-by-step explanation:
Which statement is always true
Answers
Answer:
No picture so I can’t answer the question
Step-by-step explanation:
Solve for x.
x2.5<10
Answers
Answer:
x < 4
Step-by-step explanation:
The inequality:
\(x2.5 < 10\)
Divide each side by 2.5 to isolate x (make x alone):
\(\frac{x2.5}{2.5} < \frac{10}{2.5} \\x < 4\)
P = kQ
a) direct
b) inverse
c) joint variation
PLEASE HELP!! WILL MARK BRAINIEST!!
Answers
At the bright-as-day light bulb factory, 5 out of each 136 bulbs produced are defective. If the daily production is 2720 bulbs, how many are defective?
Answers
Answer:
100 lightbulbs
Step-by-step explanation:
Basically find the percentage of lightbulbs that are bad. 5/136. So about 3. 6 percent. I'm going to use a more exact form of this percent for my calculations though. Now use the decimal for of this (0.036....) and multiply it by 2720. Using my exact decimal, the answer just so happened to be exactly 100. So there will be 100 defective lightbulbs per day. (Teachers are a stickler for units, so don't forget them if it's for a teacher)
Hope this helps!
What is the unit multiplier for days and weeks?
Answers
Answer:
days 7
weeks 4
Step-by-step explanation:
there are 7DAYS Iin a week
there are 4WEEKS in a month
Find LM.
A.) 5
B.) 17.32
C.) 9
D.) 8.66
Answers
Answer:
Step-by-step explanation:
how many more grains of rice are in a fifty-pound bag of valencia rice than in a fifty pound bag of basmati rice
Answers
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A fifty pound bag of basmati rice has 1.1 * 10³ grains in each ounce of 8 * 10² ounce and fifty pound bag of valencia rice has 1.2 * 10⁶ grains
Difference in number of grains = 1.2 * 10⁶ grains - (1.1 * 10³ grains * 8 * 10² ounce) = 3.2 * 10⁵ grains
Fifty-pound bag of valencia rice has 3.2 * 10⁵ grains more than fifty pound bag of basmati rice
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Mrs. Smith made 6 ¼ dozen cookies for the birthday party. At the end of the party, there were 3 ½ dozen cookies left. How many cookies did the guests eat?
Answers
The guests in the birthday party ate 33 cookies.
How many cookies did the guests eat?We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.
Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.
6 1/4 dozen = 25/4 dozen
3 1/2 dozen = 14/4 dozen
Now we can subtract the number of cookies that were left from the number of cookies that were made:
25/4 - 14/4 = 11/4 dozen
To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.
There are 12 cookies in one dozen, so:
11/4 x 12 = 33
Therefore, the guests ate 33 cookies.
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Anne bought a piece of ribbon that is 7 over 9 m long. She used 3 over 18 m of it to tie a birthday present. She then used the remaining ribbon to form squares of sides 1 over 16 m. What was the maximum number of squares she could form?
Answers
Answer:
9 squares
Step-by-step explanation:
Anne bought a piece of ribbon = 7 over 9 m long = 63 m²
she used = 3 over 18 m = 54 m²
left = 9 m²
maximum number of squares she could form of 1 m = 9
find the following quotient 3 divided by 1107
Answers
Answer:
0.0027100271
Step-by-step explanation:
Answer:
369 and the remainder is 0
Step-by-step explanation:
Click on the measure of the gangle.
Answers
Answer:
34
Step-by-step explanation:
The bottom line is at 180
The top line is at 146
180-146 =34
At first an athlete jogs at 5 miles per hour and then jogs at 8 miles per hour traveling 11 miles in 1.6 hours. How long does the athlete jog at each speed? (Hint: Lett represent the amount of time the athlete jogs at 5 mph. Then 1.6 - t represents the amount of time the athlete jogs at 8 mph)
Answers
Answer:
15
Step-by-step explanation:
Select the correct answer.
Which chart best represents the following information about student results from a class assignment?
Answers
Answer
a) chart
Step-by-step explanation:
a) chart best represents the following information about student results from a class assignment
In art class students are mixing blue and red paint to make purple paint. Isaiah mixes 3 cups of blue paint and 7 cups of red paint. Casho mixes 4 cups of blue paint and 13 cups of red paint. Use Isaiah and Casho's percent of red paint to determine whose purple paint will be redder.
Answers
Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.
To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.
Isaiah's Ratio:
Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.
To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:
Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%
Casho's Ratio:
Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.
To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:
Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)
Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).
Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.
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Select all the expressions equivalent to (4x⁵)(5x⁶).
Answers
Step-by-step explanation:
\( = 4 {x}^{5} \times 5 {x}^{6} \)
\( = (4 \times 5) {x}^{5 + 6} \)
\( = 20 {x}^{11} \)