a street light is mounted at the top of a -ft-tall pole. a man ft tall walks away from the pole with a speed of along a straight path. how fast is the tip of his shadow moving when he is ft from the pole?
Answers
The tip of the man's shadow is moving at the speed of 2.25m/s.
Here, we are given-
Length of the pole = 6 meters
Height of the man = 2 meters
Speed of the man = 1.5 m/s
we can form a diagram as shown in the figure below.
Now as the two triangles are similar, the ratio of their sides will be equal-
2/ b = 6/ (a + b)
2(a + b) = 6b
2a + 2b = 6b
2a = 4b
a = 2b
Now, differentiating both sides with respect to time-
da/ dt = 2db/ dt
(1/2)(da/dt) = db/dt
Let a + b = c
⇒ dc/ dt = da/dt + db/dt
dc/ dt = da/dt + da/2dt
dc/ dt = 3/2 × da/ dt
Now, we know that the speed of the man is 1.5m/s ⇒ da/dt = 1.5
dc/dt = 3/2 × 1.5
= 2.25
Thus, the tip of the man's shadow is moving at a speed of 2.25m/s.
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a street light is mounted at the top of 6 a -ft-tall pole. a man 2 ft tall walks away from the pole with a speed of 1.5m/s along a straight path. How fast is the tip of his shadow moving when he is 10ft from the pole?
Related Questions
A line passes through the point (9,
- 4) and has a slope of 3/4
Write an equation in slope-intercept form for this line.
Answers
5. The first five terms of a sequence are -7.7, -7.4, -7.1, -6.8, -6.5.
a. Find an expression for the nth term.
Answers
The expression of the nth term of the given sequence is
-7.7 + (n - 1)0.3
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
-7.7, -7.4, -7.1, -6.8, -6.5
This is an arithmetic sequence.
Now,
a = -7.7
d = -7.4 + 7.7 = 0.3
The nth term of an arithmetic sequence.
= a + (n - a)d
Now,
a + (n - a)d
= -7.7 + (n - 1)0.3
Thus,
The nth term is -7.7 + (n - 1)0.3.
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please answer I have limited time!!!!
Answers
Answer:
First second and third
Step-by-step explanation:
A function can only have one output for every input
Answer:
2, 3, 4
Step-by-step explanation:
an input can only have 1 output
Hassan buys an apartment for $78 000.
After one year the value decreases by 5%.
Work out the new value of Hassan’s apartment.
Answers
Answer:
3900 is decreased.$74100 is new value
Step-by-step explanation:
5% of 78000 subtracted by 78000...
3x + 5 < 2x - 8 is:
all values more than -13.
all values less than -13. all values less than 3. all values less than -3.
Answers
Answer:
all values less than -13
Step-by-step explanation:
3x + 5 < 2x - 8
3x + 5 - 5 = 2x - 8 - 5 ==> isolate x by subtracting 5 on both sides
3x < 2x - 13 ==> simplify
3x - 2x < 2x - 2x - 13 ==> subtract 2x from both sides to move x to the left
side of the inequality
x < -13 ==> simplify
Hence, the answer is all values less than -13.
Need help with this question
Answers
The figure S is translatation and then followed by rotation to map it into
figure T.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The figure S is translated (moved a fixed amount from the preimage)
and then followed by rotation(the preimage is rotated to create the final image) to map it into figure T.
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Write a system of equations and then solve by the method of your choice: substitution or elimination
Answers
There are 30 questions for 2 points and 10 questions for 4 point.
What is elimination method?
The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.
Given that, the total number of equations is 40. Total point on the paper is 100 points.
There are two types questions, one type question contains 2 points and other type question contains 4 points.
Assume that, there are x questions for 2 points and y questions for 4 points.
The total number of questions is x + y.
The total point is 2x + 4y.
Therefore,
x + y = 40 ......(i)
2x + 4y = 100 .....(ii)
Multiply 2 with equation (i)
2x + 2y = 80
2x + 4y = 100
___________
-2y = -20
Divide both sides by -2:
y = 10
Putting y = 10 in equation (i)
x + 10 = 40
x = 30
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Explain three of seven phases of the impulse purchase cycle
Answers
Three of the seven phases of the impulse purchase cycle. The other phases include antecedent, search, and selection.
The impulse purchase cycle is a model that describes the process of making an impulsive purchase. It is typically divided into seven phases:
Antecedent: This phase is characterized by a need or desire for something. It can be triggered by a variety of factors, such as boredom, hunger, or a sudden craving for a particular product.
Search: In this phase, the consumer begins to actively search for a product that will satisfy their need or desire. They may search online or in physical stores, and they may consider various options before deciding on a product.
Selection: In this phase, the consumer narrows down their options and selects a specific product that they want to purchase. They may consider factors such as price, quality, and convenience when making their decision.
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John spread 45 minutes after school reviewing his notes before taking a 15 minute break for a snack. After that snack, he continues reading his notes for the other 30 minutes. What would you add to find the total time that John studied?
Answers
Answer:
its A
Step-by-step explanation:
Ben
Anil completes the 72km journey between Bristol and Cardiff in 48 minutes. He then drives 69km from Cardiff to Swansea at an average speed of 60km/h
Work out Anil's average speed (in km/h) for his total journey from Bristol to Swansea.
(with working out pls)
Answers
Answer:
75 km/h
Step-by-step explanation:
48 minutes = 48/60
(48 : 12)/(60:12)
4/5
0.8 hours
average speed between Bristol and Cardiff = 72/0.8 = 90 km/h
average speed of the journey = (60 + 90)/2 = 150/2 = 75 km/h
Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for 7, and do not round your answers. Be sure to include the correct units in your answers.
Answers
Answer:
Area :153.86 m
Circumference: 43.96 m
Step-by-step explanation:
Area: 3.14 x r^2
or, A= 3.14 x 7^2
Therefore, A= 153.86m
Circumference: 2 x 3.14 x r
or, C= 2 x 3.14 x 7
Therefore, C= 43.96 m
Hope this helps:)
(btw I put so much time and effort in this answer as it is hard to type mathematical problems in mobile, so I hope I can get marked as brainliest, I have written all the answer that needs to be written in an exam. Anyone can copy it and their work is done.)
A parabola is the set of all points in the plane that are equidistant from a fixed point called the ____ and a fixed line called the ____ of the parabola.
Answers
Caroline drinks 2 cups of milk per day. She buys 4 quarts of milk. How many days will her 4 quarts of milk last?
Answers
Answer:
4 quarts of milk will last her 8 days.
We can solve this by finding how many cups are in a quart.
1 quart=4 cups
4 quarts= 16 cups
Since Caroline drinks 2 cups a day, divide 16 by 2.
16/2=8
4 quarts will last her 8 days.
Hope this helps! :D
Step-by-step explanation:
Kayla works at a trampoline gym that hosts birthday parties. Parties are priced at $75 plus $12.50 per guest. Kayla rang up a customer who paid $200 for a party. How many guests were at the party?
Write and solve an equation to find the answer
Answers
Answer:
10 Guests
Step-by-step explanation:
200 - 75 = 125 (We need to find a number that will spend 125 dollars)
125 / 12.50 = 10
12.50 x 10 = 125
So the answer is 10
The Valdez family left at noon for a 4-hour trip to viit relative. They topped 1 hour for lunch and 2 hour to viit an amuement park. What time did they get to their relative' houe?
Answers
The Valdez family left at noon for a 4-hour trip to visit relative. They topped 1 hour time for lunch and 2 hour to visit an amusement park.The Valdez family would have arrived at their relative's house at 5 pm.
1. The Valdez family left at noon, so they had 12 hours to get to their relative's house.
2. They stopped for 1 hour for lunch, so they had 11 hours left.
3. They then stopped for 2 hours at the amusement park, so they had 9 hours left.
4. 9 hours later would be 9 pm.
5. However, since it is summer, the clocks are set to daylight savings time and it is currently one hour ahead, so the time is actually 5 pm.
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Write the following as an algebraic expression. Then
simplify.
The perimeter of a triangle whose sides are of
lengths 6x, 6x + 6, and x.
Answers
Answer:
[tex]6x + 6x + 6 + x = 13x + 6[/tex]
(4.8)/(2z+15)=(0.2)/(5) PLS HELP! SHOW STEPS TOO IF POSSIBLE!
Answers
Answer:
z = 52.5
Step-by-step explanation:
You want the solution for (4.8)/(2z+15)=(0.2)/(5).
Cross multiplyMultiplying by 5(2z +15) we have ...
5(4.8) = 0.2(2z +15)
24 = 0.4z +3 . . . . . . . . . . simplify
21 = 0.4z . . . . . . . . . . . . subtract 3
z = 21/0.4 = 52.5 . . . . divide by the coefficient of z
The value of z is 52.5.
<95141404393>
7(3x+5)-11x simply the expression
Answers
Answer:
10x + 35
Step-by-step explanation:
7(3x+5)-11x
21x + 35 - 11x
10x + 35
Ticket to a baketball game can be ordered online for a et price per ticket plu a $5. 50 ervice fee. The total cot in dollar for ordering 5 ticket i $108. 0. Which linear function repreent c, the total cot, when x ticket are ordered? (A ervice fee i a ingle fee applied to the total, no matter the number of ticket purchaed). C(x) = 5. 50 20. 50x
c(x) = 5. 50x 20. 50
c(x) = 5. 50 21. 60x
c(x) = 5. 50x 21. 60
Answers
The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
The total cost for ordering 5 tickets is $108.00. This means that each ticket costs $20.50 plus a service fee of $5.50.
Therefore, we can create a linear function that represents the total cost when x tickets are ordered. The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
When x = 5, then c(x) = 5.50 + 21.60x = 5.50 + 21.60(5) = 108.00, which matches the given total cost.
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when the angle of an incline with a block resting on it increases the normal support force? A) decreases B) increases C) stays the same
Answers
Answer:
normal force decreases
Step-by-step explanation:
N=mgcosθ, and cosine decreases as theta increases
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Answer:
A) decreases
Step-by-step explanation:
As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.
sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.
Answers
The equation x²/3 + y²/3 = 4 represents an ellipse in the shown graph below and the length of the given ellipse is 8 units.
The equation x²/3 + y²/3 = 4 represents an ellipse centered at the origin with a major axis along the x-axis and a minor axis along the y-axis.
The equation can be rewritten as x²/4 + y²/12 = 1 to highlight the lengths of the semi-major and semi-minor axes.
The semi-major axis length is given by the square root of the denominator of the x-term, which is 4, so the semi-major axis length is 2.
The semi-minor axis length is given by the square root of the denominator of the y-term, which is 12, so the semi-minor axis length is 2√3.
Based on the symmetry of the ellipse, we can determine that it is symmetric with respect to both the x-axis and the y-axis.
This means that the length of the entire ellipse can be found by multiplying the semi-major axis length by 4, since there are 4 identical sections due to symmetry.
Length of the ellipse = 4 * semi-major axis length
= 4 * 2
= 8.
Therefore, the length of the given ellipse is 8 units.
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The correct question is as follows:
Sketch the curve with the equation x²/3 + y²/3 = 4 and use symmetry to find its length.
8.
For which set of data is the median greater than the mean?
A.
B.
C.
D.
{8, 12, 14, 14, 20}
{8, 12, 14, 14, 22}
{9, 13, 14, 15, 19}
(9, 13, 14, 15, 20}
Answers
Answer:
B
Step-by-step explanation:
For a set of data to have a median that is greater than the mean, it must have an odd number of values and be skewed to the right. This means that the majority of the values in the set must be smaller than the median, with a few larger values on the right side of the distribution.
Out of the given options, the only set of data that satisfies these conditions is (B) {8, 12, 14, 14, 22}. This set has an odd number of values, and the median of 14 is greater than the mean of 14.4. The other options have either an even number of values, or are not skewed to the right.
Therefore, the correct answer is (B) {8, 12, 14, 14, 22}.
Jeremy's mother deposited $1,200 into a
savings account as a college fund when he
was born. How much will Jeremy have in
this account after 18 years at a yearly
simple interest rate of 4.25%?
A) $51.00
C) $918.00
B) $10,380.00
D) $2,118.00
Answers
Answer: D) $2,118.00
Step-by-step explanation:
1 year = 4.25% interest rate
18 years = 76.5% interest rate
76.5% = 0.765
Take 1200 times 0.765 = $918.00
$918.00 is the interest money he will receive after 18 years. We have to add both numbers to find the total.
$1,200 + $918.00 = $2118.00
Given that the measurement is in inches find the circumference of the circle to the nearest tenth use 3.14 for
Answers
The circumference of the circle is 25.12 inches
How to determine the circumference?From the question, we have the following parameters that can be used in our computation:
Radius = 4 inches
The circumference of a circle can be calculated using
C = 2πr
Substitute the known values in the above equation, so, we have the following representation
C = 2 * 3.14 * 4
Evaluate
C = 25.12
Hence, the circumference is 25.12 inches
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Use the image below to answer the identify the following: One pair of vertical angles: One pair of adjacent angles: One pair of supplementary angles:
Answers
A pair of vertical angles is; Angle 1 and Angle 4
A pair of supplementary angles are; Angle 2 and angle 1
How to identify angle properties?Vertical Angles are defined as the angles that are opposite each other when two lines cross each other.
Two angles are defined as adjacent angles when they share the common vertex and side.
Two angles are defined as supplementary angles if they sum up to 180 degrees.
By those definitions above, we can say that;
Angle 1 & 2 as well as angle 3 & 4 are pairs of supplementary angles.
We can also say that;
Angle 4 and 1 are vertical angles while angle 2 and 3 are vertical angles as well.
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The scale below is balancedwhch meas they are equal
The addentical ball and small box weigh the same amount as the big box
How much does each ball weigh?
Answers
Answer:
x weigh of ball
2x+40=160
2x=120
x=60g
The solution is 60 grams
The size of each of the balls is given by the equation x = 60 grams
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the size of the balls be represented as = x
The number of balls = 2
So , the total size of the balls = 2x
Now , the equation will be
The weight of all the elements = 160 grams equation (1)
The weight is balanced by = 40 grams + 2x equation (2)
Now , equation (1) = equation (2)
Substituting the values in the equation , we get
160 = 2x + 40
On simplifying the equation , we get
Subtracting 40 on both sides of the equation , we get
2x = 120
Divide by 2 on both sides of the equation , we get
x = 60 grams
Therefore , the value of x is 60 grams
Hence , the size of the ball is 60 grams
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Work out the base of a square with area,
A
= 64cm2.
Answers
Answer: 8cm
Step-by-step explanation:
Square root 64 to get 8
Answer:
8cm
Step-by-step explanation:
A base is either the length or the width of the square (doesn't matter because square has 4 equal lengthed sides). To find the area from the base, square it. To find the base from the area, square root it (inverse operations.)
[tex]\sqrt{64cm^2}[/tex]
8cm
One week, 100 tudent purchaed item from the tudent tore and the tore made a profit of $500. The next week, when 80 tudent purchaed item, the profit wa $460. Write a linear equation relating profit, to the number of tudent,
Answers
A linear equation relating profit, to the number of student is shown below.
y = 2x + 500
Linear equation is used to present the elements in mathematic. A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
To write a linear equation relating profit to the number of students, we need to find the slope and the y-intercept of the line.
The slope of the line can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
In this case, we can use the two data points given to find the slope:
slope = (460 - 500) / (80 - 100) = -40/ -20 = 2
The y-intercept of the line is the point where the line crosses the y-axis, which is the profit when the number of students is 0. In this case, the y-intercept is 500, since that is the profit when 100 students purchase items.
Using these values, we can write the linear equation in slope-intercept form:
y = 2x + 500
This equation can be interpreted as follows: the profit (y) is equal to 2 times the number of students (x) plus 500.
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4
The volume of a spherical balloon (V=4/3pir^3) is increasing at a constant rate of 0.78 inches per minute. At the instant when the radius is 3.20 inches, the radius is
increasing at a rate of…
Answers
The rate at which the radius is increasing is; 0.006 in/min
How to find the rate of increase of radius?We are given that the formula for the volume of a spherical balloon is;
V = ⁴/₃πr³
where r is the radius
The volume is increasing at the constant rate of 0.78 inches per minute. Thus;
dV/dt = 0.78
Now, differentiating with respect to t gives;
dV/dt = ⁴/₃(3πr²)(dr/dt)
At radius of 3.2 inches, we have;
0.78 = 4π * 3.2² * dr/dt
dr/dt = 0.78/(4π * 3.2²)
dr/dt = 0.006 in/min
This is therefore the rate at which the radius is increasing.
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Jordan and Raj each bake 7 batches of muffins. Jordan makes 18 muffins per batch, and Raj makes 15 muffins per batch. They combine their muffins and put all of them into boxes. They fill as many boxes as possible with 6 muffins each. They place the remaining muffins in the last box. How many full boxes do they make, and how many muffins will be in the last box?
Answers
Answer:
38 full batch with a remainder of 3
Step-by-step explanation:
18*7 + 15*7 = 231
231/6 = 38 r3