A man walks along a straight path at a speed of 3 ft/s. A searchlight is located on the ground 4 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 3 ft from the point on the path closest to the searchlight
Answers
Answer:
0.48 rad/sec
Step-by-step explanation:
From the diagram:
We can find 'x' using trigonometry :
Tanθ = opposite / Adjacent
Opposite = x ; adjacent = 4
Tanθ = x / 4
x = 4tanθ
Let u = 4 and v = tanθ
If dx/dt = 3ft/s ;
dθ/dt when x = 3ft
Differentiate x with respect to t
dx/dt (4tanθ)
Let d/dθ tanθ = sec^2θ
Sec^2θ = 1 / cos^2θ
dθ/dt = 1/4cos^2θdx/dt
dθ/dt = 1/4cos^2θ(3)
dθ/dt = 3/4cos^2θ
When x = 3ft
Cosθ = Adjacent / Hypotenus
Hypotenus = √(4^2 + 3^2
Hypotenuse = √16 + 9 = √25 = 5
Cosθ = 4/5
dθ/dt = 3/4(4/5)^2
dθ/dt = 3/4(16/25)
dθ/dt = 48/100 = 12/25 = 0.48 rad/sec
Related Questions
Can someone help me
Answers
The scale factor that was used to convert triangle ABC into the image in A ' B ' C ' is 1 / 2.
How to find the scale factor ?To find the scale factor, you need to find the length of a side of triangle ABC and then the length of the corresponding side in A ' B ' C '.
The side length we will pick is AB which is:
= 6 - 2
= 4 units
The side length of the other triangle is A' B' :
= 3 - 1
= 2 units
The scale factor is:
= 2 / 4
= 1 / 2
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Newton's Law of Gravitation states that two bodies with masses m1 and m2 attract each other with a force F, where r is the distance between the bodies and G is the gravitational constant. F = G(m_1m_2)/r^2 Use Newton's Law of Gravitation to compute the work W required to propel a 1100 kg satellite out of the earth's gravitational field. You may assume that the earth's mass is 5.98✕1024 kg and is concentrated at its center. Take the radius of the earth to be 6.37✕106 m and G = 6.67✕10-11 Nm2/kg2. (Round your answer to three significant digits.)
Answers
The two bodies are being drawn together by a force of 10812 N, according to Newton's Law of Gravitation.
Every particle in the universe is drawn to every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation from one another, according to Newton's Law of Universal Gravitation.
Symbolically, Newton came to the following conclusion on the strength of the gravitational force:
F = G(m₁ × m₂) / r²
F is the gravitational force between two bodies, m1 and m2 are the bodies' masses, r is the distance between their centres, and G is the gravitational constant of the universe.
According to the query,
satellite's mass is m1 = 1100 kg.
mass of earth = 5.98 ×10²⁴ kg
Radius of the earth = 6.37 × 10⁶ m
G = 6.67 × 10⁻¹¹ Nm² / kg²
Force = G(m₁ × m₂) / r²
Substituting the values,
F = 6.67 × 10⁻¹¹( 1100 × 5.98 ×10²⁴) /( 6.37 × 10⁶)²
=> F = 6.67 × 1100 × 5.98 × 10¹³ / 40.58 × 10¹²
=> F = 43,875.26 × 10 / 40.58
=> F = 10812 N
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Which of the following is a like radical to
6 3*/2x
A: 6 3*/x
B: 6 4*/2x
C:-5 3*/2x
D:6 3*/2x 2*
Answers
The third option C: -5∛2x is a like radical to the expression 6∛2x.
What are radicals?In mathematics, the symbol √ is used to represent or show that a number is a radical. Radical expression is defined as any expression containing a radical (√) symbol.
The expression 6∛2x can be expanded into two factors which bare 6 and ∛2x
Also for the third option C, the expression -5∛2x can be expanded into two factors which are -5 and ∛2x
By observation, we will notice the two expressions 6∛2x and -5∛2x have same factor ∛2x which make them like radical expressions.
In conclusion, the expression -5∛2x is a like radical expression to 6∛2x.
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URGENT!!!!!!!!
The diameter of circle P is 12 inches. The diameter of circle S is 16 inches. Anise wants to find the difference between the circumference of the circles.
Which two statements are true? \
Select TWO correct answers.
A The circumference of circle P is about 24π
inches.
B The circumference of circle S is about 50.24 inches.
C The difference between the circumferences of the two circles is 12.56 inches.
D The circumference of circle S is about 8π
inches.
E The circumference of circle P is about 75.36 inches.
F The difference between the circumferences of the two circles is 28π
inches.
Answers
Answer:
The answer are
B and C
Step-by-step explanation:
r=d/2=12/2=6
r=16/2=8
Circumference=2pir
C=2×6pi
C=12pi
C=2pir
C=2×8pi
C=16pi
Sierra is growing tomato plants.
Which situation is represented by the inequality 48≤4+0.75
?
CLEAR CHECK
Sierra starts with a tomato plant that is 4
inches tall.
The plant grows 0.75
inches each week.
She wants to grow the plant to be at least 48
inches tall.
Sierra starts with a tomato plant that is 0.75
inches tall.
The plant grows 4
inches each week.
She wants to grow the plant to be at least 48
inches tall.
Sierra starts with a seed planted 4
inches below ground.
The tomato plants grow 0.75
inches each week.
She wants to grow the plant to be at least 48
inches tall.
Sierra starts with a seed planted 0.75
inches below ground.
The tomato plants grow 4
inches each week.
She wants to grow the plant to be at least 48
inches tall.
Answers
The situations represented by the inequality 48 ≤ 4 + 0.75x is given as follows:
Sierra starts with a tomato plant that is 4 inches tall.The plant grows 0.75 inches each week.She wants to grow the plant to be at least 48 inches tall.How to understand the inequality?The inequality for this problem is defined as follows:
48 ≤ 4 + 0.75x.
Considering the linear function 4 + 0.75x, we have that:
Sierra starts with a tomato plant that is 4 inches tall.The plant grows 0.75 inches each week.The inequality has the signal at least = greater of equal, hence:
She wants to grow the plant to be at least 48 inches tall.
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Luna is selling balloon animals at the park. She began with 35 balloons, and she has sold
2
5
of them so far. If Luna charges $1.75 for each balloon animal, how much money has she made so far?
Answers
Answer:
$12.25
i hope this helps
Step-by-step explanation:
5+2=7
1.75×7=12.25
Answer:24.50
Step-by-step explanation:
HELP WITH MATH PLEASE
1. The formula A = L x W gives the area of a rectangle R. The area of a rectangular garden is 5000sqm.
What is the garden's length in terms of width?
2. The formula for the area of a triangle is A = ½ bh, where b is the length of the base, and h is the height. Solve for b
3. The formula for an object’s final velocity is f = i – gt, where i is the object’s initial velocity,
g is acceleration due to gravity, and t is time. Solve for t.
4. Make your own question and solve it for your chosen variable:
Answers
Answer:
1. Length in terms of width is 5000/W meters
2. Solving for b gives us: \(b = \frac{2A}{h}\)
3. Solving for t gives us: \(t = \frac{i-f}{g}\)
4. Solving for P gives us:
\(W = \frac{P}{2} - L\)
Step-by-step explanation:
1. The formula A = L x W gives the area of a rectangle R. The area of a rectangular garden is 5000sqm. What is the garden's length in terms of width?
Given that
\(A= L*W\)
Also given that A = 5000 square meters.
Now,
\(5000 = L * W\)
Dividing both sides by W
\(\frac{L*W}{W} = \frac{5000}{W}\\L = \frac{5000}{W}\)
So,
Length in terms of width is 5000/W meters
2. The formula for the area of a triangle is A = ½ bh, where b is the length of the base, and h is the height. Solve for b
The given formula is:
\(A = \frac{1}{2}bh\)
Solving it for b means that the we have to isolate b
So,
\(A = \frac{1}{2}bh\\2A = 2. \frac{1}{2}bh\\2A = bh\\\frac{2A}{h} = \frac{bh}{h}\\b = \frac{2A}{h}\)
Solving for b gives us: \(b = \frac{2A}{h}\)
3. The formula for an object’s final velocity is f = i – gt, where i is the object’s initial velocity, g is acceleration due to gravity, and t is time. Solve for t.
Given
\(f = i-gt\\Now\\f+gt = i\\gt = i-f\\\frac{gt}{g} = \frac{i-f}{t}\\t = \frac{i-f}{t}\)
Solving for t gives us: \(t = \frac{i-f}{g}\)
4. Own Question: The perimeter of a rectangle is given by P = 2(L+W). Solve for width.
\(P = 2(L+W)\\\frac{P}{2} = \frac{2(L+W)}{2}\\\frac{P}{2} = L+W\\\frac{P}{2} - L = W\)
Solving for P gives us:
\(W = \frac{P}{2} - L\)
Solve each system of equations by GRAPHING. Clearly identify your solution.(4x-y=3)(3x+y=4)
Answers
By graphying
The solution is the point where both lines crosses.
For this system of equations the solution is (1, 1)
Polygons in the Plane I Move to Bottom Parallelogram Rectangle Square Trapezoid Identify the shape when the points are plotted in the coordinate plane. 1. ( 5, 5 ), ( 9, 5 ), ( 9, 1 ), ( 5, 1 ) when graphed is a 2. ( 2, 4 ), ( 3, 7 ), ( 7, 7 ), ( 6, 4 ) when graphed is a 3. ( 2, 7 ), ( 8, 7 ), ( 8, 3 ), ( 2, 3 ) when graphed is a 4. ( 4, 7 ), ( 7, 7 ), ( 10, 4 ), ( 1, 4 ) when graphed is a
Answers
Answer:
It is a Number between 1 - 100
Step-by-step explanation:
It helps if you pay attention in class
(a) Compute two lines of regression from the following data:
r = 0.68, x = 68, y = 52, Sx = 5.12, Sy = 5.6
Answers
Answer:
can you write this on paper and send me? i have feeling ik this but i don't understand what u need
PLEASE HELP ME! thank you
Translate this phrase into an algebraic expression.
Nine less than the product of 18 and Chrissy's savings
Use the variable c to represent Chrissy's savings
Answers
Answer:
18c - 9
Step-by-step explanation:
Which of the following types of data are likely to be normally distributed? Check all that apply.
A. The number of times Americans have been struck by lightning
B. The distance of an archer's shots from the center of a target
C. The time it takes for an airliner to fly from Los Angeles to New York
D. The outcomes of rolling a single fair die
Answers
Answer:
B. The distance of an archer's shots from the center of a target
C. The time it takes for an airliner to fly from Los Angeles to New York
Step-by-step explanation:
According to the Question,
B & C should each have a range of values that cover most occurrences with outlying values that decrease in number as they move further away from the dominant value range, which is the definition of a normal distribution.
Therefore, The answer is C the time it takes for an airliner to fly from Los Angeles to New York City, and B the distance of an archer's shot from the center of a target.The table below shows data for a class's midterm and final exam. Use the table to answer the following questions.
What is the 5 number summary for the class's Midterm Exam?
Minimum
Lower Quartile
Median
Upper Quartile
Maximum
Answers
The five-number summary of the class, determined by the results of the final test, is:
Minimum = 60
Lower quartile = 71.5.
Median = 85.
Upper Quartile = 94.
Maximum = 98
What is median?The median, a measure of the center of gravity, reflects the center of value in the collection when values are sorted in either ascending or descending order. The value that distinguishes the lower 50% of the information from the upper 50% of the data is, in other words, the value.
The lowest score is 60, which is the minimum. The highest score, 98, will serve as the maximum.
The formula: can be used to determine the lower quartile.
= (Second score + Third score) / 2
= (65 + 78) / 2
= 71.5.
The upper quartile is:
= (Third to last score + Second to last score) / 2
= (93 + 95) / 2
= 94
The median is:
= (5th score + 6th score) / 2
= (82 + 88) / 2
= 85
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The table shows the number of miles driven and the number of gas used in 4 cars.Which car drives the most miles per gallon of gas
Answers
Answer:
Car C
Step-by-step explanation:
Miles per gallon = miles traveled / gallon of gas used
Miles per gallon :
Car A = 19 / 1 = 19 miles per gallon
Car B = 39 / 3 = 13 miles per gallon
Car C = 42 / 2 = 21 miles per gallon
Car D = 48 / 3 = 16 miles per gallon
Car with most miles per gallon is car C
Name the property illustrated by each equation.
(6.8)x5 = 6x(8.5)
Answers
Answer:
Commutative Property Of Multiplication
Which statement is true about the function f(x) = 6x7?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = –f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
Answers
Answer: The function is odd because f(–x) = –f(x).
Step-by-step explanation:
\(f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)\)
The function is odd because f(–x) = –f(x).
How to determine the true statement?The function is given as:
f(x) = 6x^7
A function is odd if the following is true
f(-x) = -f(x)
Calculate f(-x)
f(-x) = 6(-x)^7
f(-x) = -6x^7
Calculate -f(x)
-f(x) = -6x^7
By comparison;
f(-x) = -f(x) = -6x^7
Hence, the function is odd because f(–x) = –f(x).
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The ratio of Andrew's money to Paul's money was 5: 2 at first. After Andrew gave $30 to Paul, they had an equal amount of money each. How much money did they have altogether?
Answers
Step-by-step explanation:
Let's assume that Andrew had $5x at first, and Paul had $2x.
After Andrew gave $30 to Paul, Andrew has $5x-$30, and Paul has $2x+$30.
We are told that they had an equal amount of money each after the transaction. This means:
5x - 30 = 2x + 30
Solving for x, we get:
3x = 60
x = 20
So Andrew had $5x = $100 at first, and Paul had $2x = $40.
After the transaction, Andrew had $100-$30 = $70, and Paul had $40+$30 = $70.
Together, they had $70+$70 = $140.
Therefore, they had $140 altogether.
A number is between 40 and 45 . It has prime factors of 2 and 11. What is the number?
Answers
Answer: 42
Step by step:
42 is divisible by both 7 and 2
Answer:
44
Step-by-step explanation:
4 x 11 = 44
2 x 22 = 44
Solve for X
1/5 X + 1/2 = 1
Answers
Answer:
X = 5/2
Step-by-step explanation:
I will assume that you meant (1/5)X + 1/2 = 1. The LCD is 10.
Multiplying both sides by 10, we get:
2X + 5 = 10, or 2X = 5, or X = 5/2
please help
every package of a certain caculator also includes 4 batteries. select all equations that represent the relationship between the number of packages and the number of batteries
a.) p = 4b
b.) b = 4p
c.) p=1/4b
d.)b= 1/4p
Answers
Answer:
c
Step-by-step explanation:
A group of 12 students is deciding whether to go to the science center or the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.
How much will a group of 12 students save by choosing the science center?
Enter your answer in the box.
Answers
ANSWER:
$6
ExPLANATION:
Step 1:
36.75 × 4 = 147
Step 2:
51 × 3 = 153
Step 3:
153 - 147 = 6
The group of 12 students will save $6 by visiting the science center instead of the Zoo.
Science center fee :
3 tickets = $36.75 Total cost of visiting Science center = (12/3) × 36.75 = $147Zoo Fee :
4 tickets = $51Total cost of visiting Zoo = (12/4) × 51 = $153The difference in the total amount spent :
Total cost of Zoo - Total cost of Science center $153 - $147 = $6Therefore, the group will save $6 by visiting the science center.
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What type of triangle can an equilateral be?
isosceles triangle
right triangle
acute triangle
obtuse triangle
Answers
Answer:
Acute triangle
Step-by-step explanation:
road trip
What is the Pennington's rate of change (slope)?
What is the Williams' rate of change (slope)?
Which family is traveling faster?
Answers
Pennington's rate of change is; 80 miles per hour.
William's rate of change is; 60 miles per hour.
The family which is travelling faster is; Pennington's family.
What is the rate of change in each case?It follows from the task content that the rate of change, otherwise termed slope is to be determined for each of Pennington and Williams.
For Pennington;
As evident in the given graphs; the distance travelled and time of travel are proportional.
Hence, by observation; Pennington's family travelled 40 miles in 0.5 hours and hence;
the rate of change = Distance / time is;
= 40/0.5
= 80 miles per hour.
For Williams;
As evident in the given graphs; the distance travelled and time of travel are proportional.
Hence, by observation; William's family travelled 180 miles in 3 hours and hence;
the rate of change = Distance / time is;
= 180/3
= 60 miles per hour.
On this note, the Pennington's family are traveling faster as their rate of change is greater.
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One number is four times as large as another and their sum is 5285 what are the two numbers
Answers
Answer:
One number is equal to 4228 and the other is equal to 1057
Step-by-step explanation:
1. Let's consider the number that four times the other X, and the other as N
2. We can write X as 4N to make it easier
3. Next, we can form a simple equation X + N = 5285 and substitute the value of X to get 4n + n = 5285
4. We get 5n = 5285
5. To get N we divide 5285 by 5 to get 1057
6. 5285 - 1057 = 4228
Therefore, one number is equal to 4228 and the other is 1057
Never mind i got it!
Answers
Answer:
OOk
Step-by-step explanation:
11/12 - 5/8 in simplest form
Answers
Answer:
7/24
Step-by-step explanation:
11/12 - 5/8
Get a common denominator of 24
11/12 * 2/2 = 22/24
5/8 *3/3 = 15/24
22/24 -15/24 = 7/24
a) You have a piece of string that is 36m long. find the areas of all the shapes you can make which have a perimeter of 36m. b) A piece of land has an area of 100m². How many meters of wire fencing is needed to enclose it?
Answers
a. The areas of the square is 81m² and for rectangle is 72m²
b. The perimeter of the square is 40m
What are the areas of all the shapes you can make which have a perimeter of 36m?a. To determine the area of the shapes in which we have that have a perimeter of 36m, we can consider rectangle and square.
For a square;
Perimeter of square = 4L
36 = 4L
L = 9m
The area of the square will be L² = 9² = 81m²
For a rectangle;
The perimeter of rectangle is;
P = 2(L + W)
We can assume that two numbers which will represent the length and width are;
L = 12m, W = 6m or L = 6m, W = 12m
A = 12 * 6 = 72m²
b.
The area of the wire is 100m², the perimeter for this can be calculated when we consider square and rectangle;
Perimeter of square = 4L
Area of square = L² = 100m²
L = 10m
The perimeter of the wire is 4(10) = 40m
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What the meaning of "\(\bigcup X\) = sup X"?
![What the meaning of "[tex]\bigcup X[/tex] = sup X"?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/l99zHqmK4sXkq4hL7ZPX00J81Q5xivhA.jpeg)
Answers
"UX = sup X," means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.
Understanding Set NotationIn set theory, the symbol "∪" denotes the union of sets. So, when we say "∪X," it represents the union of all the elements in the set X.
On the other hand, "sup X" stands for the supremum (or least upper bound) of the set X. The supremum of a set is the smallest ordinal number that is greater than or equal to all the elements in the set.
Therefore, when it is stated that "UX = sup X," it means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.
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What percentage of 4m is 20m
Answers
Answer:500%
Step-by-step explanation:
The solution is in the file below
The answer is 20%
ILL GIVE YOU A BRAILLEST???
Answers
Answer:
K= 4
Step-by-step explanation:
Cross multiply
Answer:
k = 4
Step-by-step explanation:
To solve ANY proportion, you can cross multiply. For example, in this case, you can multiply 7 x 32 and k x 56. Remember, a proportion is always equal, so 7 x 32 = k x 56. That means 224 = 56k. Which means k = 4. Hope that helped!