The height of the pole above the level of the observer's eyes is 31.42 ft
Let the angle of elevation of the top of the pole from a point 47 ft away be α.
Let the angle of elevation of the top of the pole from the point 13 ft away be β.
Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.
If the height of the pole above the level of the observer's eye is h, we have that
tanβ = tan2α = h/13 and tanα = h/47
From trigonometric identities tan2α = 2tanα/(1 - tan²α)
Substituting the values of the variables into the equation, we have
tan2α = 2tanα/(1 - tan²α)
h/13 = 2h/47 ÷ [1 - (h/47)²]
Dividing through by h, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
Cross-multiplying, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
1 - (h/47)² = 2/47 × 13
1 - (h/47)² = 26/47
(h/47)² = 1 - 26/47
(h/47)² = (47 - 26)/47
(h/47)² = 21/47
Taking square-root of both sides, we have
h/47 = √(21/47)
Cross-multiplyng, we have
h = √(21/47) × 47
h = √(21 × 47)
h = √987
h = 31.42 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
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Forty minutes of hot yoga and 10 minutes of jumping jacks burns 510 calories. Thirty minutes at hot yoga and 20 minutes of jumping jacks burns 470 calories. How many calories are burned per minute of yoga? How many calories are burned per minute of jumping jacks
Answer:
Step-by-step explanation:
ur answer I have the link
PLEASE HELP ⁉️ POR FAVOR SOMEONE IM DESPERATE tHIS IS DUE IN THE mORiNG!
Answer:
Just in case you want me to answer all the questions, I will
Step-by-step explanation:
Question 1): answer is 25
Question 2): answer is 24
Question 3): answer is 100%
24/25 = 96/100
Box Question 1): 21/25 = 84/100
Box Question 2): 15/20 = 75/100
Box Question 3): 47/50 = 94/100
Box Question 4): 28/30 = 93.3/100
Box Question 5): 19/45 = 42.2/100
Box Question 6): 3/4 = 75/100
If a digit is underlined, put a line ONLY over the underlined digit, it is repeating
I'm not completely sure if this is correct, but I really think it is..
I hope this helps!
tisha and her academic team are working
Answer:b equals T minus a minus c minus d all over 3 ⇒ 3rd answer
Step-by-step explanation:
- Tisha and her academic team have had three local matches
# Assume that the points of the local matches are a , c , d
- They will attend a district match
- District match points count for three times the number of points
than local matches do
# Assume that the points of the district match is b
- T is the total points they will earned in the four matches
∵ The points in the local matches are a , c , d
∵ The point in district mach is 3b
∴ T = a + c + d + 3b
* Lets find b in terms of a , c , d , T
∵ T = a + c + d + 3b
- Subtract a from both sides
∴ T - a = c + d + 3b
- Subtract c from both sides
∴ T - a - c = d + 3b
- Subtract d from both sides
∴ T - a - c - d = 3b
- Divide both sides by 3
∴
∴ b equals T minus a minus c minus d all over 3
Find the distance from point $A\left(15,-21\right)$ to the line $5x+2y\ =\ 4$ . Round your answer to the nearest tenth.
The distance from point (15,-21) to the line 5x + 2y = 4 is 27.5 units
Given the coordinate (15, -21) and the line 5x + 2y = 4
In order to get the point on the line 5x + 2y =4, we can a point on the line
Let x = 0
5(0) + 2y = 4
2y = 4
y = 2
The point (0, 2) is on the line.
Find the distance between the point (15, -21) and (0, 2) using the distance formula
[tex]D=\sqrt{(2+21)^2+(0-15)^2} \\D=\sqrt{23^2+15^2}\\D=\sqrt{754}\\D= 27.46units[/tex]
Hence the distance from point (15,-21) to the line 5x + 2y = 4 is 27.5 units
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The sum of 13 and 3 times a number is 31. What is the number?
Answer:
6
Step-by-step explanation:
yeah-ya ............... right?
Answer: 6
Step-by-step explanation:
13 + 3 × n = 31
n represents unknown number
13 + 3n = 31
-13 -13
3n = 18
/3 /3
n=6
What are the slope and y-intercept on the graph of the linear equation on the grid?
Answer:
simple look at y intercept then look at slope or you can solve two points by using the formula y2-y1/x2-x1
but your formula is
y =1/2 +5 so b would be your answer
1. Michael serves 1.5 quarts of juice for eight people if he’s going to serve 128 people how much juice does he need?
2. five out of nine people at Hawaiian Falls have a season pass if there are 360 people at the pool how many have a season pass?
Answer:
1. 24 qt
2. 200 people
Step-by-step explanation:
1. Use a proportion.
1.5 qt to 8 people = x qt to 128 people
1.5/8 = x/128
Cross multiply.
8x = 1.5 × 128
8x = 192
x = 24
Answer: 24 qt
2.
5/9 of number of people have a season pass.
number of people at pool = 360
5/9 × 360 = 200
Answer: 200 people
please hurry this is timed and I only have 20 mins left!!!
Answer:
x = 6 2/3 The supplementary pair of angle is 78 degree and z = 112degree = 180 degree First step is where we can also see z its opposite angle is vertical opposite angle to 112 degree given and label as vertical angle - where we see a line through the 180 degree line at any angle we can call the pair supplementary- Pairs OR sets of angles an only be called consecutive when they are grouped with a set of parallel line across a straight line and it is only because they add up to 180 they could be either terms so as there isn't parallel shown ; we know we an call a pair of angles upon a straight line supplementary.angles.
Step-by-step explanation:
6 x +38 (+112) = 180 degree as angles on a straight line add up to 180 6 x +38 (+112) = 180 6 x +140 = 180 6 x + 140- 140 = 180-140 6 x = 40 x = 40/6 x = 6.66666667 x = 6 2/3 Proof (6( 6 2/3)) + 38 + 112 = 180 = (40+38)+112 = 180 = 78 +112 = 180 Proves the supplementary angle is 78 degree.
Jane Rose’s semimonthly salary is $750. Her yearly salary is A.$9000 B. $12,500 C. $18,000 D. $19,500 E. $21,000
Answer:
C. $18,000
Step-by-step explanation:
Given that her semimonthly salary is $750, find her yearly salary.
Semimonthly means twice a month, meaning that she will receive 24 paychecks every year.
750x24=18,000
=$18,000
Hope this helps :)
no link no bot right answer
The function f(x) = In(x) has a domain of all real numbers greater than zero and a range of all real numbers. The
inverse of this function is f^-1(x) = e^x
Which conclusion can be drawn by comparing the two functions?
The domain of f^-1(x) is all real numbers and the range is all real numbers.
The domain of f^-1(x) is all real numbers greater than 0 and the range is all real numbers.
The domain of f^-1(x) is all real numbers and the range is all real numbers greater than 0.
The domain of f^-1(x) is all real numbers greater than 0 and the range is all real numbers greater than 0.
Answer:
The domain of f–1(x) is all real numbers and the range is all real numbers greater than 0.
Step-by-step explanation:
I REALLY NEED HELP CAN SOMEBODY PLZZZ HELP MEEEE
What is the prime factorization of 144?
2
O 2x62
O 22 x 34
x
O 23 x 32
х
0 24 x 32
Х
Help pls thx
Answer:
2
Step-by-step explanation:
Hi do you have a photo? i’m confused with the listing
Simplify the algebraic
expression
4(x + 1) + 7(x + 3).
a. 11x + 4
b. 2x + 215
C. 11x + 25
d. 5x + 11
Someone help pleaseeee
Answer:
C.
Step-by-step explanation:
4(x + 1) + 7(x + 3)= 4*x+4*1 + 7*x+7*3 = 4x+4 +7x +21 = 11x + 25
C
Step-by-step explanation:
4x+4+7x+21
11x+25
you have to combine like terms
(-x+ 4) (3х^2 + 3х + 5)
Answer:
-3x^3 + 9x^2 + 7x + 20
Step-by-step explanation:
this is the expression simplified
Find the geometric mean between 18 and 7. Write your answer in radical form.
• 3 square root of 14
• 126
• 9 square root of 7
• 128
Answer: Choice A
Work Shown:
[tex]m = \text{geometric mean of x and y}\\\\m = \sqrt{x*y}\\\\m = \sqrt{18*7}\\\\m = \sqrt{9*2*7}\\\\m = \sqrt{9}*\sqrt{2*7}\\\\m = 3\sqrt{14}\\\\[/tex]
What are 5 rules to follow in a science lab?
Answer:
Step-by-step explanation:
1. Wear safety glasses
2. Be accompanied by an adult
3. Wear proper lab clothing
4. Alert Lab instructor if an accident were to happen
5. Follow all instructions given by lab instructor
The GDP per capita of ten arab countries is given in US Dollars. Find the median: 22865, 37749, 3046, 5738, 69687, 3980, 29266, 3345, 17791, 1249 (1 Point 12057 O None of these 0 11764.5 O 17791
Answer:
11764.5Step-by-step explanation:
Given numbers:
22865, 37749, 3046, 5738, 69687, 3980, 29266, 3345, 17791, 1249Put the numbers in ascending order:
1249, 3046, 3345, 3980, 5738, 17791, 22865, 29266, 37749, 69687Since the set is even, the median is the average of the middle numbers:
(5738 + 17791)/2 = 11764.5what integer does 378 need to be divided by to equal -21
Answer:
-18
Step-by-step explanation:
just divide 378 by 21 to get the missing integer:18
since multiplying 2 negatives makes a positive, the same applies for division, so it would be -18
describe the domain and range of function D
pls help <3
Answer:
Domain- [0,7], Range- [0,20]
Step-by-step explanation:
Last year at a certain high school, there were 100 boys on the honor roll and 60 girls on the honor roll. This year, the number of boys on the honor roll decreased by 11% and the number of girls on the honor roll decreased by 10%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
-11 boys -6 girls
Step-by-step explanation:
Suppose Set A contains 19 elements and Set B contains 69 elements. If the total number elements
in either Set A or Set B is 75, how many elements do Sets A and B have in common?
B u A = 48
B = 45
The part of set B not included in A is B - A∩B = 45 - 7 = 38
Since B u A = 48, A must have 48-38 = 10 elements (3 exclusive of B, 7 shared with B).
------
Alternatively, the inclusion-exclusion principle may be used: A + B - (A ∩ B) = A u B
A + 45 - 7 = 48
A = 48 - 45 + 7
A = 10
NOTE that I'm using A and B to indicate the number of elements in each set, respectively.
More formally, one would write |A| and |B| to indicate the cardinality (number of elements) of the set.
day!
Altea is making pumpkin spice cupcakes.
She needs 15 ounces of pureed pumpkin
for each batch. If she makes 16 batches of
the cupcakes, how many ounces of the
pureed pumpkin will she need?
o
Answer:
240oz.
Step-by-step explanation:
15oz=1batch
She needs 16 batches.
15oz. x 16batches = 240oz.
Hope this helps :)
dur rn help pls ))))))))))
Answer:
A is correct good luck bud
Step-by-step explanation:
2.(04.05)
Kelsey painted 1/4
of her bedroom in 3/7
of an hour. At this rate, how long would it take her to paint the entire room?
A.3/28 of a hour
B.28/3 of an hour
C.12/7 of an hour
D.7/17 of an hour
Answer:
1/4 in 3/7th of an hour
1/4 = 3/7
multiply by 4
1 (whole room) = 12/7 (of an hour)
Answer:
12/7 of an hour
Step-by-step explanation:
I couldnt do the asnwer earlier but here it is the person above gave the answer worked out
0.9627281873+783,840,183=??!!
plzzz help
My dinner at San Felipe cost $8.20 before tax and $9.96 after tax. What was the sales tax rate?
*Round to the nearest whole percent.
Show Your WorK
Answer:
Sale tax rate = 21.46%
Step-by-step explanation:
Sale Tax % = ( Amount after sale tax - Original cost) ÷ original × 100
Sale Tax % = ( $9.96 - $8.20) ÷ $8.20 × 100
Sale Tax % = $1.76 ÷ $8.20 × 100
Sale Tax % = .2146341463 × 100
Sale Tax % = 21.46
solve pls brainliest
Answer:
Mixed Number = 2 9/10
Improper Fraction = 29/10
Step-by-step explanation:
Mixed Number = 29/10 = 2 9/10
Improper Fraction = 29/10
Show this situation on a vertical number line
what is the situation to your question
Answer:
What is the situation?
Step-by-step explanation:
Proxima Centauri, our nearest star except for the sun, is about 4·1013 km from Earth. Find to one decimal place its distance in parsecs.
Step-by-step explanation:
The conversion for parsecs into meters is
1 parsec (pc) = [tex]3.09×10^{16}\:\text {m}[/tex]
So if Proxima Centauri is [tex]4×10^{13}\:\text{m}[/tex] away, then in terms of parsecs, this distance is
[tex]4×10^{13}\:\text{m}×\left(\dfrac{1\:\text{parsec}}{3.09×10^{16}\:\text{m}}\right)[/tex]
[tex]\;\;\;\;\;= 1.2×10^{-3}\:\text{parsec}[/tex]