a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 15 ft from the base of the pole?
Answers
The speed of the tip of her shadow would be 5.714 ft/sec. ft/sec.
let H, be the height of the pole = 20 ft.
h, be the height of the woman = 6 ft.
x, be the length of the woman's shadow,
and s, be the distance from the pole to the woman = 15
by using the equation of similar triangles,
[tex]\frac{H}{h} = \frac{(s+x)}{x}[/tex] or Hx = h(x+s)
differentiating, [tex]H\frac{dx}{dt} = h (\frac{ds}{dt} + \frac{dx}{dt} )[/tex]
[tex]20\frac{dx}{dt} = 6(4 + \frac{dx}{dt} ) = 24 + 6 \frac{dx}{dt}[/tex]
[tex]14\frac{dx}{dt} = 24[/tex],
[tex]\frac{dx}{dt} = \frac{24}{14}[/tex] ≈ 1.714 ft/sec, is how fast her shadow is lengthening.
the speed of the tip of her shadow would be the speed of shadow lengthening + speed of her traveling = 1.714 + 4 = 5.714 ft/sec.
thus, a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. the speed of the tip of her shadow would be 5.714 ft/sec.
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Related Questions
What is the solution to this inequality? x - 1 . 5 > 2 . 5 Question 1 options: x < 4 x < 1 x > 1 x > 4
Answers
The solution to the inequality is X > 4
InequalityInequality is a set of mathematical expression which the individual side is not equal to other side
To solve for x in the inequality x - 1 . 5 > 2, we followed the step;
Step 1: Add 1.5 to both sides
x - 1.5 + 1.5 > 2 . 5 + 1.5
X > 4
Therefore, the solution to the inequality is X > 4
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Determine which integer(s) from the set S:{−24, 2, 20, 35} will make the inequality five sixths m minus five is less than one half m plus 3 false.
S:{−24, 2}
S:{35}
S:{−24, 2, 20}
S:{20}
Answers
The inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The set of integers:
S:{−24, 2, 20, 35}
Plug the value 35 in the inequality:
= 5/6(35 - 5) < 1/2(35 + 3)
= 5/6(30) < 1/2(38)
= 25 < 19 (False)
Thus, the inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.
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Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios. A 2-column table has 3 rows. Column 1 is labeled Silver paints (parts) with entries 3, blank, blank. Column 2 is labeled Green paint (parts) with entries 4, blank, blank. Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check all that apply. 4:5 6:8 5:6 9:12
Answers
The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.
What are Equivalent Ratios?Equivalent ratios can be described as ratios that have the same values when compared to each other. For example, 8/16, 4/8 and 1/2 re equivalent ratios because:
8/16 = 1/2
4/8 = 1/2
Therefore, 8:16 = 4:8 = 1:2.
Given the table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, the ratio is: 3:4.
This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.
Therefore:
6/8 = 3/4
9/12 = 3/4
6/8 = 9/12 = 3/4
This implies that 6:8, 9:12 and 3:4 are all equivalent ratios.
Therefore, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
see the attachment photo!
If the statement is rewritten as a conditional statement in if-then form, which best describes the hypothesis? Two lines in a plane intersect at a point.
Answers
When the statement is rewritten as a conditional statement in if-then form, the option that best describes the hypothesis is B. Two lines intersect at a point
What is a conditional statement?A conditional statement is one that has the form "If P then Q," where P and Q are sentences. P is referred to as the hypothesis in this conditional statement, and Q is referred to as the conclusion. "If P then Q" implies that Q must be true whenever P is true.
There is a conditional statement. We will not play if it is raining. Let's say A: it's raining and B: we're not going to play. If A is true (it is raining) and B is false (we played), then the statement A implies B is false.
If the original sentence is restated as an if-then conditional statement, the hypothesis is best described as two lines intersecting at a point. As a result, the statement "Two lines intersect at a point" is the correct option (B) and the best option.
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Complete question
If the statement is rewritten as a conditional statement in if-then form, which best describes the hypothesis?
Two lines in a plane intersect at a point
A. Two lines in a plane intersect
B. Two lines intersect at a point
C. A point exists
D. Points are in a plane
Pls help due tomorrow!!!!!!!!!!:
Answers
The answer is 15ab
Step-by-step explanation:
Since (x + y)² = (x + y)(x + y) = x² + 2xy + y²
(3a + 2.5b)²
9a² + 2(3a)(2.5b) + 6.25b²
9a² + 15ab + 6.25b²
Hence, (3a + 2.5b)² = 9a² + 6.25b² + 15ab
x + y = 5
–3x + 2y = 5
Answers
Step 1: multipy both sides by 3
3x+3y=15
-3x+2y=5
Step 2: add the equation eliminating the x variable
5y=20
Step 3: divide both sides by 5
y=4
Step 4: substitute the y value with 4
x+4=5 so x=1
Answer: (1, 4)
There are 14 students in the school that like vanilla ice cream best. This represents 20% of the total number of students at the school. How many students are there in the school in total?
Answers
There are 70 students in the school in total
A hat factory makes 3 types of hats. Each day, the factory makes 4,000 of each type of hat. How many hats does the factory make each day?
Answers
Answer:
The factory makes 12,000 (12k) hats each day
Step-by-step explanation:
4000
× 3
--------
12,000
the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing (in mm3/s) when the diameter is 80 mm? (round your answer to two decimal places.)
Answers
Increase in volume is 802424.77 cubic mm/s when the diameter is 80 mm.
Let the radius of the sphere be R.
So, the volume of the sphere is given by,
V = [tex]\frac{4}{3}\pi r^3[/tex]
Differentiating the above relation with respect to time 't' we get,
dV/dt = 4[tex]\pi r^2[/tex]. dr/dt
Given that, the change of radius (dr/dt) = 4 mm/s
When the diameter is 80 mm, then the radius = 80/2 = 40 mm
So the volume change when the diameter is 80 mm is given by,
dV/dt [tex]=4\pi\times40^2\times4\approx 802424.77[/tex] cubic mm/s
Hence the volume increase in 802424.77 cubic mm/s.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The point -3/5 , -4/5 in the third quadrant corresponds to angle θ on the unit circle.
The value of sec θ is ____
, and the value of cot θ is _____
.
Answers
The value of sec θ is -5/3 ,and the value of cot θ is 3/4 in the unit circle.
Given:
The point -3/5 , -4/5 in the third quadrant corresponds to angle θ on the unit circle.
here x = -3/5 and y = -4/5
radius r = [tex]\sqrt{(-3/5)^{2}+(-4/5)^{2} }[/tex]
= [tex]\sqrt{9/25 + 16/25}[/tex]
r = 1.(which is hypotenuse in unit circle).
sec θ = hypotenuse / adjacent
= 1/-3/5
sec θ = -5/3
cot θ = adjacent / opposite
= -3/5 / -4/5
= 3*5/5*4
= 15/20
cot θ= 3/4
Therefore the value of sec θ is -5/3 ,and the value of cot θ is 3/4.
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A tortoise and a hare run in the NYC marathon (26.2 miles). The hare crosses the finish line first in a time of 4 hours and 30 minutes. How fast did the hare run?
Answers
The hare ran 5.8 mph to win the race.
What is Speed?Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.
Given that, a tortoise and a hare run in the NYC marathon for 26.2 miles, the hare crosses the finish line first in a time of 4.5 hours.
Speed = distance/time
Speed of hare = 26.2/4.5 = 5.8 mph
Hence, The hare ran 5.8 mph to win the race.
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For each equation, explain what you could do first to each side of the equation so that there would be no fractions.
Answers
To simplify the equations so that there would be no fractions, we
1. Multiply both sides by 8
2. Multiply both sides by 12
3. Multiply both sides by 10
4. Multiply both sides by 30
Simplifying an equation so that there would be no fractionsFrom the question, we are to determine what we could do first to each side of the equations so that there would be no fraction
1. (4x -4)/8 = (x +2)/4
Multiply both sides by the LCM of the denominators
The denominators are 8 and 4
The LCM of 8 and 4 is 8
Thus,
Multiply both sides by 8
8 × (4x -4)/8 = 8 × (x +2)/4
4x -4 = 2(x +2)
2. 3(4 - r)/6 = (4 + r) /4
Multiply both sides by the LCM of the denominators
The denominators are 6 and 4
The LCM of 6 and 4 is 12
Thus,
Multiply both sides by 12
12 × 3(4 - r)/6 = 12 × (4 + r) /4
2 × 3(4 - r) = 3(4 + r)
6(4 - r) = 3(4 + r)
3. (5q + 3)/10 = (q + 2)/5
Multiply both sides by the LCM of the denominators
The denominators are 10 and 5
The LCM of 10 and 5 is 10
Thus,
Multiply both sides by 10
10 × (5q + 3)/10 = 10 × (q + 2)/5
(5q + 3) = 2(q + 2)
4. 4(b - 7)/15 = (b + 3)/10
Multiply both sides by the LCM of the denominators
The denominators are 15 and 10
The LCM of 15 and 10 is 30
Thus,
Multiply both sides by 30
30 × 4(b - 7)/15 = 30 × (b + 3)/10
2 × 4(b - 7) = 3(b + 3)
8(b - 7) = 3(b + 3)
Hence, we will multiply both sides of the equation by 30
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The Cozo family has 5 children. While on vacation, they went to a play. They bought 5 tickets at the child’s price of $10.25 and 2 tickets at the adult’s price. If they spent a total of $89.15, how much was the price of each adult ticket?
Answers
Answer:
$18.95
Step-by-step explanation:
5(10.25) + 2x = 89.15
51.25 + 2x = 89.15 Subtract 51.25 from both sides
2x = 37.90 Divide both sides by 2
x = 18.95
Check:
5(10.25) + 2( 18.95) = 89.15
51.25 + 37.90 = 89.15
89.15 = 89.15
89.15 - 5(10.25)
= 37.9
37.9/2
= 18.95 dollars for each parent
Which of the following is true about the constant of proportionality? Select all that apply. Multiple select questions. cross out
A) The constant of proportionality is also the unit rate. cross out
B) The constant of proportionality is always equal to 1. cross out
C) The constant of proportionality is always equal to 0. cross out
D) There is no constant of proportionality in a nonproportional relationship. cross out
E) If two quantities are proportional, the constant of proportionality is the constant ratio between them.
Answers
Answer:
D
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality
How to identify the correct representations of the inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
Given: the inequality –3(2x – 5) < 5(2 – x)
First, we have to solve for x in the inequality
–3(2x – 5) < 5(2 – x)
Clear the parenthesis:
-6x + 15 < 10 - 5x
Collect like terms:
-6x + 5x < 10 - 15
-x < -5
Divide both sides by -1:
x > 5 ( Note: Divide both sides by -1 will change the < to > )
This is what will determine our answer
Since our answer is x > 5. An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)
Therefore, the correct representations of the inequality is an open circle is at 5 and a bold line starts at 5 and is pointing to the right r
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i NEED HELP NOW dane is selling popcorn for a fundraiser if each bag of popcorn he sells cost $4.75 what equation can he use to calculate the total amount of money he raised if he sold x number of bags
Answers
Answer:
Step-by-step explanation:
Take the amount, $4.75, multiplied by x will give you the total amount of money raised and just put that into the equation format:
$4.75 (x) = total amount of money raised
f(x) = 11 – x Find the range of f for x > 4.
Answers
Answer:
Step-by-step explanation:
Comment
The graph below shows or implies that you start at very close to 4 and move downward and to your right
To find the beginning of the range, substitute 4 into the given equation
f(4) = 11 - 4
f(4) = 7
The range is
7 <y <-∞
Last year, the student population at Haley Elementary School was 360 students. After rezoning this year, the student population is 10% smaller. HOW MANY STUDENTS ATTEND HALEY ELEMENTARY THIS YEAR?
Answers
Answer:
360 of 10%
360 x 10/100
36
now, 360 - 36 = 324
therefore, 324 students attended haley elementry this yr.
What is the slope of the line?
Answers
Answer:
8/2 or 4/1
Step-by-step explanation:
To find the slope, you simply count how high up one point is from another (0,0 to 2,8) and then how far over. Since 2,8 is 8 points up from 0,0 the numerator of our slope would be 8; and since 8,2 is two over from 0,0 the denominator is 2. Simplify this to 4/1.
What is the remainder of the following division problem?
x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
x
1
0
–1
Answers
The remainder of the long division problem (x + 1)/x is given as follows:
1.
What is a long division?The representation of a long division problem is given as follows:
di(x)/d(x) = q(x) + (r(x)/b(x))
In which the meaning of each symbol is listed as follows:
di(x) is the dividend of the division operation.d(x) is the divisor of the division operation.q(x) is the quotient of the division operation.r(x) is the remainder of the division operation.In the context of this problem, the operation is presented as follows:
(x + 1)/x.
This division can be separated into two divisions that are added, hence:
(x + 1)/x = x/x + 1/x = 1 + 1/x.
Comparing to the standard symbols, we have that:
The quotient of the division operation is of 1.The remainder of the division operation is of 1.Missing informationThe expression is:
(x + 1)/x.
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Answer:
B 1
Step-by-step explanation:
Arun spends some of the money from his monthly salary on food, travelling and entertainment and the rest of the money he deposits in the bank. (i) The money he spends on food, travelling and entertainment is in the Ratio, food : travelling : entertainment = 4 : 2 : 3. If he spends on food $160 more than travelling calculate the amount he spends on entertainment.
(c) If he deposits 1/7 of his monthly salary , calculate his monthly salary
Answers
The amounts are given as follows, using proportions:
i) Amount spent on entertainment: $240.
c) Monthly salary: $840.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem along with basic arithmetic operations such as multiplication or division to find the desired amounts.
The ratio of food : travelling : entertainment = 4 : 2 : 3 means that:
4/9 of the investment was in food.2/9 of the investment was in travelling.3/9 of the investment was in entertainment.The amount spent on food $160 more than travelling, the total amount is obtained as follows:
(4/9 - 2/9)x = 160
2/9x = 160
2x = 160 x 9
x = 80 x 9
x = 720.
Then the amount invested in entertainment was of:
3/9 x 720 = 1/3 x 720 = $240.
He invests 6/7 of his monthly salary, as 1/7 is deposited, hence:
6x/7 = 720
6x = 720 x 7
x = 120 x 7 (simplifying both sides of the equality by 6)
x = $840.
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why do we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test?
Answers
we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test whne When the variances of both populations are the same
The standard error for the distinction within the proportions is calculated utilizing the population proportions but in cases where the population proportions are unknown, we utilize the test proportions to calculate the standard error. In the case of hypothesis testing, we are mindful of the population proportions whereas in evaluating the confidence interval for the distinction between the proportions we have no thought of the population proportions. So, the standard error for a hypothesis test of distinction in two proportions is distinctive from the standard error for a certain interval of the difference in two proportion.
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2.3 Find measure of angle by finding x first
Solve for x.
I need help I have forgotten how to solve for x..
Answers
Answer:
x=5
Whole angle/9x=45
Step-by-step explanation:
sum of all three angles in a triangle is 180 degrees so we can add all of these angles together and set it equal to 180 like this
9x+65+70=180
Simplify
9x+135=180
Subtract both sides of 135
9x+135=180
-135. -135
9x=45
since 9x equals 45 that is how much the angle is
Divide both sides by 9 to find x
9x=45
/9. /9
x=5
Hopes this helps please mark brainliest
PLEASE HELP ME!!!!!!!!!!!!
Answers
together, katya and mimi have 480 pennies in their piggy banks. after katya loses 1/2 and mimi losses 2/3of her pennies, they have an equal number of pennies left. how many pennies did they lose altogether?
Answers
The number of pennies they lose altogether is 288 pennies.
How to find the number of pennies they lost together?
Together, Katya and Mimi have 480 pennies in their piggy banks.
Therefore, there total amount of pennies is 480.
After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.
Therefore,
let
x = number of pennies Katya have
y = number of pennies Mimi have
Hence,
x + y = 480
x = 480
Katya pennies left = x - 1 / 2x = 1 / 2x
Mimi pennies left = y - 2 / 3 y = 1 / 3 y
1 / 2 x = 1 / 3 y
2y = 3x
y = 3 / 2 x
Substitute the value in equation(i)
x + 3 / 2 x = 480
2.5x = 480
x = 480 / 2.5
x = 192
Therefore,
192 + y = 480
y = 480 - 192
y = 288
The number of pennies they lose can be calculated as follows;
Katya losses = 1 / 2 × 192 = 96
Mimi losses = 2 / 3 × 288 = 192
Therefore, they lost 96 + 192 = 288 pennies altogether.
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Ty bought three and four-sixths pounds of coffee. He gave five-sixths of a pound to his grandma. Estimate how much coffee Ty has left.
5 pounds
four and one-half pounds
3 pounds
two and one-half pounds
Answers
Ty has 2 5/6 pounds of coffee left after giving 5/6 pounds of coffee to his grandma
What is fraction?Fraction is a numerical quantity that is not a whole number
From the question,
Ty bought 3 4/6 pounds of coffee
converting 3 4/6 to improper fraction
we have 22/6
Ty gave his friend 5/6 pound of coffee to his grandma
To estimate how much coffee Ty has left
We substract Coffee given to his grandma from Coffee bought
That is,
22/6 - 5/6
= 17/6
= 2 5/6 pounds of coffee left
Ty has 2 5/6 pounds of toffee left. He gave 5/6 of what he bought to his grandma.
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Identify x-intercepts, the vertex, and axis of symmetry of the graph f(x)= 1/4x (x-1)(x+7)
Answers
x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
What is, axis of symmetry, vertex and x - intercept?
A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.
A line's x-intercept is the location at which the x-axis is crossed.
Consider, the given equation,
[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]
Let,
[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex] ..(1)
To find x - intercept, plug y = 0 in above equation,
[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]
Therefore, x = 1 and x = -7 are the x - intercepts.
Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.
So,
[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]
Plug x = -3 in equation (1)
[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]
Therefore, the vertex is, (-3, -4).
The x - coordinate of the vertex is the axis of symmetry.
Therefore, axis of symmetry is x = -3.
Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.
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Shandra is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 8 minutes after being turned on? What is the temperature of the oven tt minutes after being turned on?
Answers
Answer:
x=145 at 8 minutes
im not sure what tt means but please read my note at the end.
Step-by-step explanation:
if the initial temp is 65 and it increases at a rate of 10 per min the use
65+10(x)
let x be the number of minutes
65+10(8)
65 +80= 145
after 8 minutes the oven will be at 15 degrees. im not sure what tt is suppose to mean, but to find any other solution just plug it into x multiply x by 10 and add it to 65
a plane has a cruising speed of 250 miles per hour when there is no wind. at this speed, the plane flew miles with the wind in the same amount of time it flew miles against the wind. find the speed of the wind.
Answers
The speed of the wind is 50 mph.
Define speed.Speed, expressed in terms of meters per second, is the rate at which an object's position changes. A thing moves one metre in one second, for instance, if it starts at the origin and moves three metres in three seconds. The formula for speed is as straightforward as dividing a distance by a time.
Given,
250 mph for the plane's speed when there is no wind
v is the wind speed.
Think about how the plane will move against the wind:
V' = the rate of flight of the aircraft against the wind = V + v = 250 + v
300 miles is the distance travelled in d'.
T is the passage of time over the distance.
The distance's travel time is specified as
t' = d'/V'
t' = 300/(250 + v) eq-1
Think about how the plane moves when flying against the wind:
V" is the speed of a plane travelling against the wind and equals V - v. This equals 250 - v.
D" = 200 miles of distance travelled
t" is the passage of time over the distance.
The distance's travel time is specified as
t'' = d''/V''
t'' = 200/(250 - v) eq-2
Due to this:
travelling time of 300 time required to drive 200 miles in miles
t' = t''
using eqs 1 and 2
300/(250 + v) = 200/(250 - v) (250 - v)
3/(250 + v) = 2/(250 - v) (250 - v)
750 - 3 v = 500 + 2 v
5 v = 250
v = 50 mph
The speed of the wind is 50 mph.
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