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.
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
Related Questions
#1) Catherine takes AC transits to school and the bus travels 35 blocks in 7 minutes. At this rate, how long
should the ride take if Catherine's school is 50 blocks away from her house? Explain how you know.
Answers
Whats the answer for number 12? Thank you!
Answers
It should be B correct me if I'm wrong but it should be B.
5y + 3y + 5 ≤ ‐2(2y + 4) ( pls show work)
Answers
Answer:
y<-13/12
Step-by-step explanation:
12y<-8-5
12y<-13
What is the least common denominator for the fractions below?
4/9
and
2/6
Answers
Answer:
?
Answer · 0 votes
To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how. Let's try it with the fractions 23 and 312 12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also. Now you have the following: 812 and 312 These fractions now have common denominators! Now they're all set for adding or subtracting fractions. Try another: 26 and 35: The least common multiple of 6 and 5 is 30. (the product of the denominators) Transform each fraction by multiplying by "1": 26⋅55 = 1030 and 35⋅66 = 1830 One last problem: 49 and 76 What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the L…
More
Brainly.com
Question
1.What’s the least common multiple (LCM) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 2.What’s the least common denominator (LCD) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5 3.Insert the “equal” sign or the “not equal” sign ( = or ≠) to make each statement true. a. 18/36 _____ 1/2 b. 13/15 _____ 7/10 c. 3/5 _____ 5/9 d. 3/8 _____ 10/16 4.On a hot summer day, John drank 5⁄11 of a quart of iced tea; Gary drank 7⁄10 of a quart; and Carter drank 3⁄5 of a quart. Which man was the most thirsty? 5.What’s the largest fraction in each group? a. 5⁄6 and 29⁄36 b. 5⁄12 and 3⁄8 c. 2⁄5 and 19⁄45 d. 5⁄7, 13⁄14, and 19⁄21 e. 7⁄11 and 9⁄121 f. 1⁄2, 3⁄18, and 4⁄9 6.Reduce each of the following fractions to its simplest form. a. 12⁄18 b. 48⁄54 c. 27⁄90 d. 63⁄77 e. 24⁄32 f. 73⁄365 7.What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .? 8.In each pair, tell if the fractions are equal by using cross multiplication. a. 5⁄30 and 1⁄6 b. 4⁄12 and 21⁄60 c. 17⁄34 and 41⁄82 d. 6⁄9 and 25⁄36 9.This year, a baseball player made 92 hits out of 564 times at bat. Another player made 84 hits out of 634 times at bat. Did the two players have the same batting average? 10.On a test with 80 questions, Bob got 60 correct. On another test with 100 questions, he got 75 correct. Did Bob get the same score on both tests? 11.Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6 12.This handy application of LCMs is used by astronomers. All the planets in our solar system revolve around the sun. The planets occasionally line up together in their journeys, as shown in the illustration. The chart shows the time it takes each planet to make one trip around the sun. Now, imagine that the planets Earth, Mars, Jupiter, Saturn, Uranus, and Neptune aligned last night. How many years will pass before this happens again? (Hint—Find the LCM of the planets’ revolution times.) Solar System Planet Revolution Time Earth 1 year Mars 2 years Jupiter 12 years Saturn 30 years Uranus 84 years Neptune 165 years
Answer · 15 votes
1. a. 30b. 44c. 36d. 402. I don't really remember how to do these but if you cant make the denominator smaller then I belive it's a. 24b. 20c. 4d. 53.a. =b. not =c. not =d. not =4. Gary5. a. 5/6b. 5/12c. 19/45d. 13/14e. 7/11f. 1/26.a. 2/3b. 8/9c. 3/10d. 9/11e. 3/4f. 1/57.a. 36/40b. c. 8.a. yesb. noc. nod. no9. no10. yes11. a. 40b. 48c. 77d. 4812. 4,620
More
Wyzant
Question
what is the common denominator for 3/4 and 2/5
Answer · 0 votes
Hi Elikem! To find the common denominator. First check to see if one of the numbers is divisible by the other. In this case 4 is not divisible by 5 and 5 is not divisible by 4. So the next step is to find the common multiple. You do this by writing out the multiples of each. 4 8 12 16 20 24 28 5 10 15 20 25 When you find a common multiple, in this case 20, you have found the common denominator. Hope this helps!I am available for online tutoring for $35 per hour sessions.
More
Brainly.ph
Question
What is the least common denominator of 2/6 and 5/12
Answer · 3 votes
Answer:12Step-by-step explanation:Rewriting input as fractions if necessary: 2/6, 5/12 For the denominators (6, 12) the least common multiple (LCM) is 12. Therefore, the least common denominator (LCD) is 12. Calculations to rewrite the original inputs as equivalent fractions with the LCD:2/6 = 2/6 × 2/2 = 4/125/12 = 5/12 × 1/1 = 5/12
More
Feedback
People also ask
What is the LCM of 4/6 and 9?
What is the common denominator of 4 and 9?
What is the LCD of 4 and 6?
What is the lowest common denominator of 4 and 9?
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
snsnnsnsnnsnnnsn s s
Find the slope of the line and get a brainliest !!!!!!
Answers
Answer:
m=3
Step-by-step explanation:
Answer: 3/1
Step-by-step explanation: If you look at the very start of the graph you see that the only time the ray touches the right angle of the line is a (1,3) and (0,0). Plugging that into the [tex]m=\frac{y2-y1}{x2-x1}[/tex] you get [tex]\frac{3}{1}[/tex] and turning that into a fraction you get 3 which is the slope.
PLSSSS SOMEONE HELP ME!!!!!!!
Answers
zzzzzz.....
The points (-7, -1) and (r, 1) lie on a line with slope 1/4
Find the missing coordinater.
r =
Answers
Answer:
r = 1
Step-by-step explanation:
Find the missing x-coordinate r.
Use the point-slope formula y - k = m(x - h). We are given the point (-7, -1) on the line and the slope of the line 1/4, and so this general formula becomes
y + 1 = (1/4)(x + 7)
Now substitute the coordinates of the other point (r, 1) to solve for r:
1 + 1 = (1/4)(r + 7)
Multiplying both sides by 4 eliminates the fractional coefficient:
8 = r + 7
It is readily apparent that r must be 1.
Check: If r = 1, then (r, 1) becomes (1, 1). use the point-slope formula again, this time to see if we are correctly predicting the r value 1:
y + 1 = (1/4)(x + 7) becomes 1 + 1 = (1/4)(r + 7), or
2 = (1/4)(r + 7). Multiplying both sides by 4, we get 8 = r + 7, and so r = 1.
EXTRA POINTS -- Find the measure of the angles marked a, b, c, etc. in each diagram below
Answers
b=140°
8) a=74°
b=106°
c=41°
d=115°
Pls help me with this problem
Answers
Answer:
2
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + (2.1)^2 = (2.9)^2
a^2 +4.41=8.41
a^2 = 8.41-4.41
a^2 =4
Take the square root of each side
sqrt(a^2)=sqrt(4)
a=2
A water bottle has a capacity of 1.43 L. What is the bottle's capacity in milliliters?
(1 L = 1,000 mL)
Answers
Answer:
1430
Step-by-step explanation:
just do 1000x1.43 I think this is right but i might be wrong
A jar had 88 coins. 1/3 of the coins were silver. How many coins were gold?
Answers
Answer:
There are 66 gold coins in the jar
Step-by-step explanation:
Let the number of silver coins = X
Then the number of gold coins = 3X (as there are 1/3 number of silver coins as gold)
Total coins =88
Total coins = silver coins + gold coins
Total coins = X + 3X = 88
Total coins = 4X = 88
X = 88/4
X = 22
No. Of silver coins = 22
No. Of gold coins = 3X = 3×22
No. Of gold coins = 3X= 66
Check
Total coins = 3X + X = 88
66+22 = 88
88 = 88
Hope it helps...
Have a great day :P
Answer:
Hello There!!
Step-by-step explanation:
Let the number of silver coins be x and gold coins be 3x which add up to 4x. Make an expression and add 88 with 4x so 4x=88
x=22(88÷4).
So x=22[silver coins]
3x=66(22×3) [gold coins]
hope this helps,have a great day!!
~Pinky~
You flip a coin 30 times, about how many times would you expect to tails to appear?
Answers
Answer:
15 heads out of 30
Step-by-step explanation:
The total number of possible sequences of coin flips can be determined by raising the number of outcomes, which is 2 for any coin (heads or tails), to the power of the number of times the coin is flipped, given by the question as 30. Therefore, 230 is the total number of different sequences for 30 coin flips.
We can use combinatorial math to find the number of sequences with exactly 15 heads, which is 30 choose 15 or (3015) . The probability we are looking for will be the number of sequences with 15 heads divided by the total possible sequences.
Now we can express the whole probability in math notation, and calculate an answer (rounded to 4 decimal places):
(3015)230=1551175201073741824≈0.1445≈14.45%
15 heads out of 30 is the most likely outcome when flipping 30 coins, if you run the same calculation with 14 or 16 heads you will get two equal, but smaller probabilities, same with 13 and 17 heads, and so on. If you graphed all of the outcomes, you will find it follows a normal distribution, or Bell curve, with the outcome of 15 heads, located at the peak.
If the coin is tossed 30 times then the expected value of the tails to appear is 15 which means tails will appear 15 times.
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\[/tex]
You flip a coin 30 times then the expected value will be
The probability of getting tails is 0.5 then the expected value will be
[tex]E(X) = 0.5 \times 30\\\\E(X) = 15\\[/tex]
Learn more about binomial distribution here:
https://brainly.com/question/13609688
Look at the picture.
Answers
Answer:
Answer:Option D will be your answer
Step-by-step explanation:
hope it helps you
have a great day ^-^
A class measured the radius and circumference of various circular objects. The results are plotted on the graph. Does there appear to be a proportional relationship between the radius and circumference of a circle? Explain or show your reasoning. Why might the measured radii and circumferences not be exactly proportional?
Answers
Answer: Because it goes through the origin and the line is straight but there is still the empty space between the 4 and 6
Step-by-step explanation:
Calculate the volume of a rectangular prism with a height of 2 ft, length of 2 ft, and a width of 5.5 ft.
[tex]22ft^{3}[/tex]
[tex]9.5ft^{3}[/tex]
[tex]10,648ft^{3}[/tex]
[tex]11ft^{3}[/tex]
Answers
can someone answer? can someone pls tell me these two graphs i’m confused pls answer i’ll give brainlist and points
Answers
Answer:
you put the 3 and the 1 on the graph a you get your answer
Step-by-step explanation:
Jenny works 30 hours and is paid £318 Calvin works 28 hours and is paid £287 Jenny is paid more per hour than Calvin How much more
Answers
Answer:
£0.35 more per hour.
Step-by-step explanation:
Jenny:
30h = £318
1h = £318 ÷ 30
= £10.60
Calvin:
28h = £287
1h = £287 ÷ 28
= £10.25
Difference:
£10.60 - £10.25 = £0.35
Hope this helps
Write the equation for each circle with the given radius and center.
5. radius: 2, center: (4, -3)
6. radius: 7, center: (-1, 10)
Answers
Answer:
Step-by-step explanation:
Equation of a circle is
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex] where (h,k) is the center and r is radius
#5 Radius 2, Center (4,-3)
[tex](x-4)^{2} +(y+3)^{2} =4[/tex]
#6 Radius 7, Center (-1,10)
[tex](x+1)^{2} +(y-10)^{2} =49[/tex]
A right circular cone is shown. The base of the cone is a circle with the center at point A. The Distance from point A to point C is 16 inches. The distance from point C to point B is 20 inches.
Answers
Answer:
6.4
Step-by-step explanation:
The distance between the point A and B is 12 inches which is the radius of the cone. Thus, The diameter of the cone will be 24 inches.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
A right circular cone is shown.
The base of the cone is a circle with the center at point A.
The Distance from point A to point C is 16 inches.
The distance from point C to point B is 20 inches.
[tex]|BC|^2 = |AB|^2 + |AC|^2 \\\\|20|^2 = |AB|^2 + |16|^2 \\\\AB = \sqrt{400 - 256}\\\\AB = \sqrt{144} \\\\AB = 12[/tex]
Therefore, the distance between the point A and B is 12 inches which is the radius of the cone.
Thus, The diameter of the cone will be 24 inches.
Learn more about Pythagoras' theorem here:
https://brainly.com/question/12105522
#SPJ2
If You Had Three Wishes, What Would You Wish For?
Answers
Answer:
I would wish to be the brainliest, I would wish for more points, and i would wish for more people to answer my questions
Step-by-step explanation:
thats only for brainly though
Answer:
My three wishes would be:
1: Get all staright A's
2: the sickness that starts with C thats going around goes away forever
3: Have some cheesecake.
Step-by-step explanation:
i will mark brainliest if correct pls help
Answers
Answer:
1/6
Step-by-step explanation:
3/18= 1/6. (y-y)/(x-x)
Solve for the letter
96=12r
Answers
96/12=8
...........
Can someone help me with this question. put Into standard form.
Answers
standard form: y=2x^2-28x+109
-48a²/-8a
reduse the equation to its smallest form
Answers
Answer:
the answer is 6a
Step-by-step explanation:
-48/-8=6
a^2/a=a
combine 6 and a to get 6a.
hope it helped
Two forest rangers are standing on a road that runs east-west. One sights a forest fire in the direction 31° east of
north. The other sights the same fire 57° west of north.
Find the distance from each ranger to the forest fire and
the shortest distance from the fire to the road.
Answers
Answer: The forest ranger closest to the fire is at a distance of 9.92 miles (nearest hundredth).
Draw a horizontal line AB of length 15 miles to represent the positions of the two forest rangers.
Point A is to the left and point B is to the right.
Complete triangle ABC so that m∠A = 41° and m∠B = 56°.
The point C represents the location of the fire.
Let x = length of BC. It is the shortest distance from the forest ranger B to the fire because BC is opposite the smaller angle of 41°.
Because the sum of angles in a triangle is 180°,
m∠C = 180° - (41° + 56°) = 83°.
From the Law of Sines,
x/sin(41) = 15/sin(83)
x = 15*[sin(41)/sin(83)] = 9.915 mi
Step-by-step explanation:
Draw a horizontal line AB of length 15 miles to represent the positions of the two forest rangers.
Point A is to the left and point B is to the right.
Complete triangle ABC so that m∠A = 41° and m∠B = 56°.
The point C represents the location of the fire.
Let x = length of BC. It is the shortest distance from the forest ranger B to the fire because BC is opposite the smaller angle of 41°.
Because the sum of angles in a triangle is 180°,
m∠C = 180° - (41° + 56°) = 83°.
From the Law of Sines,
x/sin(41) = 15/sin(83)
x = 15*[sin(41)/sin(83)] = 9.915 mi
Question 1 of 5 Select the correct answer. If the factors of quadratic equation are (x − 7) and (x + 3), what are the x-intercepts? (-7,0) and (-3,0) (-7,0) and (3,0) (3,0) and (7,0) (-3,0) and (7,0)
Answers
Answer:
(7,0) and (-3,0)
Step-by-step explanation:
Given the factors, we want to get the x-intercepts
All we have to do is to get the x values by equating the factors to zero
we have this as;
(x -7) = 0 and (x + 3) = 0
x = 7 and x = -3
The x-intercepts are;
(7,0) and (-3,0)
help me pleaseeeeeeeeee
Answers
Answer:
The diameter is related because it helps find the circumference.
hello ! does anyone know how I could get x and y from this equation :
3x +4y > 2
any help would be appreciated ! :)
Answers
Step-by-step explanation:
x,y£R
x and y are element of real numbers
any number you set for x you get which is strictly greater than 2
2 minus twice a number.
Answers
Answer:
2-2x=y
Step-by-step explanation:
WORTH 24 POINTS PLS HELP
On the blueprints for a new house, a wall measures 3.5 inches. If the map scale is 1.25 inches to 2 feet, how long will the actual wall be?
Answers
Answer:A unit rate is a comparison of two measurements, one of which has a value of ... The unit scale on a map may read \begin{align*}\frac{1}{2}\ inch=100 ... A line 4 inches long would represent an actual line of 800 feet. Unit scales and proportions can be used to calculate actual distances from maps, drawings, ...
Step-by-step explanation: