A student is standing next to a vertical flagpole. The top of the student's shadow
coincides with the top of the flagpole's shadow as shown.
not to scale
The student is 62 inches tall. The student estimates that the distance from the flagpole
to the point where the student is standing is between 21 and 22 feet. The student also
estimates that the length of the student's shadow is between 7 and 7 feet.
Based on the given information, what are the least and greatest possible heights, in
feet, of the flagpole? Explain how you arrived at your answers.
Answer:
The least possible height of the flagpole is 227.33 inches and the greatest possible height is 248 inches
Step-by-step explanation:
Given
See attachment for the system
Required
Determine the least and greatest heights of the flagpole
From the question, we have:
[tex]AB = 7\ to\ 7\frac{1}{2} ft[/tex]
[tex]BE =62in[/tex]
[tex]BC = 20\ to\ 21ft[/tex]
Convert AB and BC to feet (multiply by 12)
[tex]AB = 84in\ to\ 90in[/tex]
[tex]BC = 240in\ to\ 252in[/tex]
The height of the flagpole is represented as: CD
To calculate CD, we make use of the following equivalent ratios:
[tex]CD : AC = BE : AB[/tex]
Express as fraction
[tex]\frac{CD }{ AC } = \frac{BE }{ AB}[/tex]
Make CD the subject
[tex]CD = \frac{BE }{ AB} * AC[/tex]
From the attachment:
[tex]AC = AB + BC[/tex]
Where:
[tex]AB = 84in\ to\ 90in[/tex]
[tex]BC = 240in\ to\ 252in[/tex]
The possible values of AC are:
[tex]AC = 84 + 240 =324in[/tex]
[tex]AC = 84 + 252 =336in[/tex]
[tex]BC = 90 + 240 = 330in[/tex]
[tex]AC = 90 + 252 =342in[/tex]
So:
[tex]CD = \frac{BE }{ AB} * AC[/tex]
[tex]BE =62in[/tex]
When AC = 324 ; AB = 84
[tex]CD = \frac{62}{84} * 324[/tex]
[tex]CD = \frac{62* 324}{84}[/tex]
[tex]CD = \frac{20088}{84}[/tex]
[tex]CD = 239.14in[/tex]
When AC = 336 ; AB = 84
[tex]CD = \frac{62}{84} * 336[/tex]
[tex]CD = \frac{62* 336}{84}[/tex]
[tex]CD = \frac{20832}{84}[/tex]
[tex]CD = 248in[/tex]
When AC = 330 ; AB = 90
[tex]CD = \frac{62}{90} * 330[/tex]
[tex]CD = \frac{62 * 330}{90}[/tex]
[tex]CD = \frac{20460}{90}[/tex]
[tex]CD = 227.33in[/tex]
When AC = 342 ; AB = 90
[tex]CD = \frac{62}{90} * 342[/tex]
[tex]CD = \frac{62* 342}{90}[/tex]
[tex]CD = \frac{21204}{90}[/tex]
[tex]CD = 235.6in[/tex]
So, we have:
[tex]CD = 239.14in[/tex]
[tex]CD = 248in[/tex]
[tex]CD = 227.33in[/tex]
[tex]CD = 235.6in[/tex]
The least possible height of the flagpole is 227.33 inches and the greatest possible height is 248 inches
The given range of the length of the shadow and distance of the student
from the tree of between 7 and [tex]7\frac{1}{2}[/tex] feet and 21 and 22 feet gives;
The greatest possible height of the flagpole in feet ≈ 21.8 feet
The least possible height of the flagpole in feet = 19.3 feet
How can the height of the tree be calculated?Height of the student = 62 inches = [tex]5\frac{1}{6}[/tex] feet
Distance of the flagpole to the student = 21 to 22 feet = 252 to 264 inches
Length of the student's shadow = Between 7 and [tex]\mathbf{7\frac{1}{2}}[/tex] feet = Between 84 and 90 inches
Required:
The least and greatest height of the flagpole.
Solution;
By using similar triangles formed by the student and the flagpole, we
have;
[tex]\dfrac{Height \ of \ the \ student}{Length\ of \ the \ student's \ shadow} = \mathbf{\dfrac{Height \ of \ the \ flagpole}{Length\ of \ the \ flagpole's \ shadow}}[/tex]
Which gives;
[tex]\dfrac{62}{84 \ or \ 90} =\mathbf{ \dfrac{h}{252+(84 \ or \ 90) \ or \ 264 + (84 \ or \ 90)}}[/tex]
Based on the method of cross multiplication, h will be the greatest
possible value, when we have, the largest possible value for the
denominator on the right hand side and the least possible value for the
denominator on the left hand side of the equation, and vice versa.
Which gives;
[tex]\dfrac{62}{90} = \mathbf{\dfrac{h_{min}}{252 + 84}}[/tex]
[tex]h_{min} \ in \ feet = \mathbf{\dfrac{\dfrac{62}{90} \times (252 + 84)}{12}} \approx 19.3[/tex]
The least possible height of the flagpole in feet, [tex]h_{min}[/tex] ≈ 19.3 feet
Similarly. we have;
[tex]\dfrac{62}{84} = \mathbf{\dfrac{h_{max}}{264 + 90}}[/tex]
Which gives;
[tex]h_{max} = \dfrac{62}{84} \times (264 + 90) \approx 261.3[/tex]
[tex]h_{max} \ in \ feet \approx \dfrac{261.3}{12} \approx\mathbf{ 21.8}[/tex]
The greatest possible height of the flagpole in feet, [tex]h_{max}[/tex] ≈ 21.8 feet
Learn more about the characteristics of similar triangles here:
https://brainly.com/question/10703692
LOOK AT THE PIC BELOW
Answer:
144 i think
Step-by-step explanation:
triangular prism calculator
Sally is making a
square quilt with 49
squares and each square is
4 inches. What is the
length of the quilt?
Answer:
784
Step-by-step explanation:
you take the 49 and times is by 16
there are 4 sides
Find the value of x.
US_
Diagram NOT
accurately draw
(x + 1)cm
(3 - x) cm
(2x + 5) cm
The diagram shows a cuboid of volume V cm3
(a) Show that V = 15 + 16x - x (squared) - 2x (cubed)
Answer:
Step-by-step explanation:
Length of the cuboid = ((2x + 5) cm
Width of the cuboid = (3 - x) cm
Height of the cuboid = (2x + 5) cm
Since, volume of the cuboid = Length × Width × Height
= (2x + 5)(3 - x)(x + 1)
= [2x(3 - x) + 5(3 - x)](x + 1)
= (6x - 2x² + 15 - 5x)(x + 1)
= (-2x² + x + 15)(x + 1)
= x(-2x² + x + 15) + 1(-2x² + x + 15)
= -2x³ + x² + 15x - 2x² + x + 15
= -2x³ - x² + 16x + 15
≈ 15 + 16x - x² - 2x³
To find one half of 56 you would use what operation ?
Answer:
Division to get 28
Step-by-step explanation:
Sophia bought snacks for her team's practice. She bought a bag of popcorn for $1.98
and a 10-pack of juice bottles. The total cost before tax was $12.48. Write and solve
an equation which can be used to determine j, how much each bottle of juice costs?
Answer:
j = $1.05
Step-by-step explanation:
($12.48 - $1.98) / 10 = j
(Total cost - popcorn cost) / number of juice boxes = cost of one juice box
Answer:
10j+1.98=12.48
j= 1.05
Step-by-step explanation:
Please I need quick help, Solve for X
Answer:
10
Step-by-step explanation:
Since it's a right angle, it's already 90 degrees. So, you add 48 + 32 which gives you 80. 80 minus 90 equals 10.
48 + 32 = 80
90 - 80 = 10
Select the correct answer from each drop-down menu. Describe the relationship between the area of a circle and its circumference. The (area, diameter, or radius) is (1/3, 1/2, 2, or 3) times the (area, diameter, or radius) times the circumference. (PLEASE HELP ME)
Answer:I got the answer correct because i have to take the test
Step-by-step explanation:
The relation between the area and the circumference is given by:
"The area is 1/2 times the radius times the circumference".
How to find the measures of a circle?
We know that for a circle of radius R we have:
Circumference = P = 2*pi*RArea = A = pi*R^2.If you take the quotient between the area and the circumference, you get:
A/P = (pi*R^2)/(2*pi*R) = R/2
So the area is R/2 times the circumference, or, using the terms given in the list:
"This means that the area is 1/2 times the radius times the circumference"
If you want to learn more about circles, you can read:
https://brainly.com/question/25306774
Miss Lianto mowed 2/7 of her lawn. Her son mowed 1/4 of it. Who mowed most of the lawn? How much of the lawn still needs to be mowed?
HURRY AND BE CORRECT PLEASE!!!
Answer: 2/7 = 8/28
1/4 = 7/28
Therefore Mr Pham mowed more.
8+7 = 15 so 15/28 of lawn has been mowed, therefore 13/28 of the lawn is left still to be mowed.
Mr. Pham mowed more of the lawn than his son.
it still needs ¹³/₂₈ of the lawn to be mowed.
Step-by-step explanation:
Answer: 1/4 is greater than 2/7 mowed most of the lawn.
Step-by-step explanation:
First, draw a fraction model for [tex]\frac{2}{7}[/tex] and [tex]\frac{1}{4}[/tex] and partition it. Then, how ever many you get write it as a fraction. Then, see whose answer is greater.
What is the formula for volume? (Select all that apply) *
v=Lwh (volume = length x width x height)
V = Lw (volume = length x width)
V = Bh (volume = base x height)
V=L+W+L+W (length + width + length + width)
Answer: v=Lwh (volume = length x width x height)
Step-by-step explanation: it would be the first answer, to find volume, it’s finding the amount of space in a 3D object, kind of like area, but multiply the height to the area (bxh)
solve for x 4x = -29 gove your answer as an improper fraction in its simplest form
PLEASE ANSWER ALL BIG REWARD
Dilations involve ________ the scale factor and the pre–image ordered pair(s)? *
adding
dividing
subtracting
multiplying
All dilations produce _______. *
similar figures
vertical figures
congruent figures
supplementary figures
The rule to describe a dilation is written in _________. *
a list
scale factor
arrow notation
slope-intercept form
Which of the rules below would create a reduction/compression? *
(x, y) (–3x, –3y)
(x, y) (3.2x, 3.2y)
(x, y) (x + 9, y + 9)
(x, y) (0.23x, 0.23y)
Which of the following rules below do NOT represent a dilation? *
(x, y) --> (2x, 4y)
(x, y) --> (–8x, –8y)
(x, y) --> (1/2x, 1/2y)
(x, y) --> (3x, 3y)
(x, y) --> (1.2x, 1.2y)
In the diagram below, triangle ABC will be dilated with the origin as the center of dilation by a scale factor of 1/2. What will be the coordinates of A'? *
Captionless Image
(0, 3/2)
(12, 6)
(3, – 3/2)
(–1, –5/2)
A line segment with endpoints D (–6, –5) and E (3, –4) is dilated by a scale factor of 2. Which statement below is true? *
The line segment has become longer with endpoints D' (-12, -10) and E' (6 -8).
The line segment has become shorter with endpoints D' (-12, -10) and E' (6 -8).
The line segment has become longer with endpoints D' (-3, -5/2) and E' (3/2, -2).
The line segment stays the same length with endpoints D' (-3, -5/2) and E' (3/2, -2).
Write a rule to describe the dilation below. *
Captionless Image
(x, y)→ (1/2x, 1/2y)
(x, y)→ (1/3x, 1/3y)
(x, y)→ (3x, 3y)
(x, y)→ (2x, 2y)
If the scale factor k = 1/9 the resulting dilation will be a/an *
enlargement
reduction
If the scale factor k = 3 the resulting dilation will be a/an *
enlargement
reduction
Answer:
multiplying similar figures scale factor (x, y) (–3x, –3y) and (x, y) (0.23x, 0.23y) (x, y) --> (2x, 4y) Need diagramA. The line segment has become longer with endpoints D' (-12, -10) and E' (6 -8).Need imageReductionEnlargementgood luck, i hope this helps :)
In a school, 30% of the students arrived by private car, 15 travel by taxi and the remainder walk to school. If the school has a population of 230, how many more students walk to school than arrives by car?
Answer:
57.5 students
Step-by-step explanation:
Given that
The 30% students would be arrived by private car
So 15% would be travelled by taxi
And, the remaining i.e. 55% would be walk to school
Since the population of the school is 230
So by car, the students would be
= 230 × 0.30
= 69
By walk, the students would be
= 230 × 0.55
= 126.50
Now the more students would be
= 126.50 - 69
= 57.5 students
Jase wrote the prime factorization of 99. Which expressions could he have written?
Select all that apply.
A. 32 x 11
B. 9x9
C 3 x 3 x 3 x 11
D. 34
E.
3 x 3 x 11
Answer:
A and d is the correct answer
Step-by-step explanation:
A and d is matter fact correct answer
What does 602.93+9.5%=
Which expression is equivalent to 120x2 - 48x?
F 12(10X - 4)
G 12x(10x + 4)
H 12X(-10X - 4)
J 12x(10x - 4)
Mr. Snyder begins traveling east on Interstate 90 from Spokane with a full tank of gasoline. His car has a 15-gallon gas tank and gets 30 miles per gallon during highway travel. Let m = the number of miles Mr. Snyder has driven Let g = the number of gallons of gas remaining in his tank Select in the letter of the equation that describes the relationship between the number of miles Mr. Snyder has traveled and the number of gallons remaining in his gas tank.
Answer:
[tex]g = 15 - \frac{1}{30}m[/tex]
Step-by-step explanation:
Given
[tex]Initial = 15[/tex]
[tex]mpg = 30[/tex] --- miles per gallon
Required
Determine an equation for this trip
First we have to get the number of gallons per mile from [tex]mpg = 30[/tex]
[tex]\frac{miles}{gallon}=30[/tex]
Inverse the equation
[tex]\frac{gallon}{miles}=\frac{1}{30}[/tex]
This represents the rate in gallons/mile
So, the equation is:
[tex]g= Initial - Rate * m[/tex]
[tex]g= 15 - \frac{1}{30} * m[/tex]
[tex]g= 15 - \frac{1}{30}m[/tex]
csc pi/3 exact value ?
Answer:
Exact Form:
2√3/3
Decimal Form:
1.15470053
Step-by-step explanation:
Multiply
2√3
and
√3√3.2√3√
3
√
3
Raise
√
3
to the power of
1
.
2
√
3
√
3
1
√
3
Raise
√
3
to the power of
1
.
2
√
3
√
3
1
√
3
1
Use the power rule
a
m
a
n
=
a
m
+
n
to combine exponents.
2
√
3
√
3
1
+
1
Add
1
and
1
.
2
√
3
√
3
2
Rewrite
√
3
2
as
3
.
Tap for fewer steps...
Rewrite
√
3
as
3
1
2
.
2
√
3
(
3
1
2
)
2
Apply the power rule and multiply exponents,
(
a
m
)
n
=
a
m
n
.
2
√
3
3
1
2
⋅
2
Combine
1
2
and
2
.
2
√
3
3
2
2
Cancel the common factor of
2
.
Cancel the common factor.
2
√
3
3
2
2
Divide
1
by
1
.
2
√
3
3
1
Evaluate the exponent.
2
√
3
3
A bus averages 2miles per hour faster than a motorcycle. If the bus travels 165miles in the same time it takes the motorcycle to travel 155miles, then what is the speed of each?
Answer:
speed of bus = 33 mi/hr
speed of motorcycle = 31 mi/hr
Step-by-step explanation:
Let the speed of the motorcycle be x mi/h.
Now, we are told that the bus averages 2 mi/hr faster than the motorcycle. Thus, speed of bus = (x + 2) mi/hr
Formula for time is; t = distance/speed
Since distance covered by bus is 165 miles, then t_bus = 165/(x + 2)
Since distance covered by motorcycle is 155 miles, then t_motorcycle = 155/x
We are told that the bus and the motorcycle used the same time to cover their respective distances. Thus;. t_bus = t_motorcycle
Thus;
165/(x + 2) = 155/x
Cross multiply to get;
165x = 155(x + 2)
165x = 155x + 310
165x - 155x = 310
10x = 310
x = 310/10
x = 31 mi/hr
Then speed of bus = 31 + 2 = 33 mi/hr
A sports team is holding a banquet.
The total cost of supplies for the banquet event is $1000. The cost per ticket is set so that 100 tickets will cover the cost of the banquet event.
Based on this information, what is the cost of ONE ticket?
One ticket for this banquet costs $
Answer:
$10
Step-by-step explanation:
1000 divided by 100 = 10
so $10 is the answer
then 100 tickets = $1000
PLEASE MARK BRAINLIEST AND GIVE 5 STARS.
A tent originally cost $90 and is on sale for 60 % off .
Answer:
$36
Step-by-step explanation:
60% of 90 is 54
With $54 off, you'd only pay $36
Is this correct please help will mark brainliest
Answer:
yes i believe it is correct
Step-by-step explanation:
Lottie and Ollie shared some money in the ratio 5:1.
Ollie received £15.
How much did Lottie receive?
Answer:
=£75
Step-by-step explanation:
ratio=5(lottie):1(Ollie)
we do 15/1 which will stay the same as 15
15/1=15
Then we times 15 by 5( lotties share)=75
15*5=75
Therefore lottie got £75
=£75
Answer:
75 : 15
Step-by-step explanation:
Please help with this
Answer:
What is your question?
______________________________
Please rate my answer and say thanks!
write a function with an initial value of 5 and increasing exponentially by 18%.
Answer:
f(x)=5(1.18)^x
Solve for the missing side
Answer:
The answer would be
Sin 60°=x/14
X=7v3
Lesson 2 Practice Problems
1. In 1990, the value of a home is $170,000. Since then, its value has increased 5% per
year.
a. What is the approximate value of the home in the year 1993?
Answer:
$3,400,000
Step-by-step explanation:
170,000/ 5% for the increase
170,000/ 5% = $3,400,000
If a flock of ducks is growing by 6% per year and starts with a population of 68 how many ducks will be in the flock after 10 years
Suppose that appoximately 261,000,000 people live in the united states. Of these people 37,600,000 speak a language other than english at home who speak another lanague at home over 45 percent speak spanish
Answer:
16,920,000 people speak Spanish at home in the United States, which represents 6.48% of the country's population.
Step-by-step explanation:
Given that approximately 261,000,000 people live in the United States, and of these people 37,600,000 speak a language other than English at home, of which over 45 percent speak Spanish, to determine the number of people who speak Spanish in the United States, the following calculation has to be done:
37,600,000 x 0.45 = X
16,920,000 = X
261,000,000 = 100
16,920,000 = X
16,920,000 x 100 / 261,000,000 = X
6.48 = X
Thus, some 16,920,000 people speak Spanish at home in the United States, which represents 6.48% of the country's population.