A 6-foot tall person standing with her back to the sun casts an 8-foot long shadow. To the nearest degree, what angle does the sun make with the ground?
Answers
α≈37 °
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
Let us suppose the sun has angle of elevation x
The triangle formed will be a right triangle, so
[tex]tan x= \frac{opposite}{adjacent}[/tex]
[tex]tanx = \frac{6}{8}[/tex]
taking tan inverse
[tex]x=tan^{-1}(\frac{6}{8} )[/tex]
[tex]x=36.87[/tex]
To the nearest degree, the angle will be 37 degrees. : Answer
Hope it will help :)
Related Questions
one angle of a triangle is 2 / 3 of a right angle . the greater of the other to exceed the lesser by 20 degree. Find the angles of the triangle in grades.
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2x + 80 = 180, so 2x = 100 and x = 50. The angles are 50, 70 and 60 (degrees)
What do you mean by "grades?"
A traveler is walking on a moving walkway in an airport The Traveler must walk back on the walkway to get a bag he forgot the Travelers ground speed is 2ft/s against the walkway and 6ft/s with the walkway what is the Travellers speed off the walkway what is the speed of the moving walkway
Answers
x+y=6....i
x-y=2....ii
adding the above equation we get:
2x=8
thus
x=4 ft/s
and
y=6-4=2 ft/s
thus the speed off the walk way is 4 ft/s
the speed of the moving walkway is 2 ft/s
The speed of the traveler off the walkway is 4ft/s, while the speed of the moving walkway is 2ft/s. This is found by simultaneously solving the equations formed by the given speeds of the traveler with and against the walkway.
Explanation:The speed of the traveler, independent of the moving walkway, as well as the speed of the moving walkway itself can be determined using the given speeds of the traveler with the walkway and against it. When the traveler walks in the same direction as the moving walkway, their speeds add together, which is given as 6ft/s. Conversely, when the traveler walks against the movement of the walkway, their velocities subtract which is given as 2ft/s.
That is to say, if we denote the traveler's speed as *T* and the walkway's as *W*, then we have these two equations: *T* + *W* = 6, and *T* - *W* = 2. Solving these equations simultaneously, we find that *T* = 4ft/s, which is the traveler's speed off the walkway, and *W* = 2ft/s, which is the speed of the moving walkway
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A pattern that can be folded to form a solid figure is a
Answers
pretty sure
In a scale drawing a plane has a length of 35 centimeters. The actual length of the plane is 87.5 feet. What is the scale of the drawing?
Answers
1 cm : x
cross multiplying
35 cm X = 1 cm x 87.5 ft
x= 87.5 ft. cm /35 cm
x = 2.5 ft
therefore, the scale is 1 cm : 2.5 ft
Using proportions, it is found that the scale of the drawing is of 1 ft:0.4 cm.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that 35 cm represent 87.5 ft. How many cm represent a ft?
The rule of three is given by:
35 cm - 87 ft
x cm - 1 ft
Applying cross multiplication:
[tex]87x = 35[/tex]
[tex]x = \frac{35}{87}[/tex]
[tex]x = 0.4[/tex]
Hence, the scale of the drawing is of 1 ft:0.4 cm.
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Evaluate.
7 with a 3 on top
A) 21
B) 49
C) 81
D) 343
Answers
What is the net force here and what direction will the object accelerate ?
Answers
since there is force being applied in opposite directions, the net force is found by subtracting the 2
100 - 10 = 90 N ( Net Force)
and because the higher force is pushing the box to the right, the direction will accelerate to the right.
What are the constants in x-3+2/3-y/2
Answers
In an equation, the constants are the numbers that are by themselves. In this problem, the numbers -3 and 2/3 are by themselves therefore they are constants.
Student Stars Mazie 7 Chris 4 Jenni -3 Scott 0 Michael 2 Zoe 4 Liza -5 Thomas -1 Benjamin 6 Josie 1 Chase 8 David -4 Students in Mr. Miller's class gain and lose stars for behavior during the day. At the end of the week, any students with a negative star value must stay for detention. According to the chart who must serve detention?
Answers
A lawn is shaped like a parallelogram with a base of 32 feet and a height of 15 feet. Covering the lawn with grass will cost $2.60 per square foot. How much money will it cost to cover the lawn with grass?
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To find the total cost, we need to first find the area of the parallelogram. To find the area, we need to multiply the base and height.
Then, we need to multiply the total area by the cost of $2.60.
32 x 15 x 2.6 = 1248
Answer:
$1248.
Step-by-step explanation:
area = base x height.
then
area x cost
b h c
32 x 15 x 2.6 = 1248
BRAINLIEST to the correct answer Which measure(s) of center best derceibe(s) the data Explain. {10,10,10,10,1010,10,60} Mean Median or Mode
Answers
Mode.
The number that appears the most is 10, so it's mode.
PLEASE HELP MEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
= 6(5x - 3)
multiply 6 by each term in parentheses
= (6 * 5x) + (6 * -3)
multiply inside each parentheses; remember a negative times a positive equals a negative
= 30x - 18
ANSWER: 30x - 18
Hope this helps! :)
Find the measure of JEF
A)16
B)74
C)82
D)164
Answers
Its because the final angle in the quadrangle is 164 degrees (you can get this by knowing all the angles add up to 360). Then note that the angles are complementary.
Answer:
16
Step-by-step explanation:
I just submitted it on USA Test Prep
How do you find the diameter of 12 inches
Answers
12x12=144
Judy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of the cone and no more. the cone has a height of 4.5 inches and a radius of 1.5 inches
Answers
V = 1/3x pi x r^2 x h
1/3 x 3.14 x 1.5^2 x 4.5
V = 10.6 cubic inches
The volume of ice cream that the cone can hold is approximately 10.6 in.³.
1. Write the rule for finding a point translated vertically k units up.
2. Use this rule to find the coordinates for (−3, −6) when translated 5 units up.
Answers
(x, y) -------> (x, y + k) ------> (x ', y')
Where,
k: number> 0
Substituting values we have:
(-3, -6) -------> (-3, -6 + 5) ------> (-3, -1)
Answer:
the rule for finding a point translated vertically k units up is:
(x, y + k)
The new coordinates are:
(-3, -1)
one hundred grams of radium are stored in a container. The amount R of radium present after t years can modeled by R=10e^-0.00043t. After how many years will only 5 grams of radium be present? round your answer to the nearest whole year.
Answers
To determine after how many years only 5 grams of radium will be present, we use the decay equation [tex]R = 100e^{-0.00043t}[/tex] to solve for t when R equals 5 grams, yielding approximately 1,605 years.
Explanation:To determine after how many years only 5 grams of radium will be present, we can use the provided equation for radioactive decay: R = [tex]100e^{-0.00043t}[/tex]. We need to solve for when R equals 5 grams. Here are the steps:
Set the equation equal to 5: [tex]5 = 100e^{-0.00043t}.[/tex]Divide both sides by 100: [tex]0.05 = e^{-0.00043t[/tex]}.Take the natural logarithm (ln) of both sides to solve for t: [tex]ln(0.05) = ln(e^{-0.00043t}) = -0.00043t.[/tex]Divide both sides by -0.00043 to isolate t: [tex]t = ln(0.05) / -0.00043.[/tex]Use a calculator to find the value of t: [tex]t \approx 1,605.11[/tex] years.Round to the nearest whole year: t ≈ 1,605 years.After approximately 1,605 years, only 5 grams of radium will be present.
To find the time after which only 5 grams of radium remain, the exponential decay equation [tex]R = 10e^{-0.00043t[/tex] is solved using natural logarithms, yielding an approximate time of 1608 years.
To determine after how many years only 5 grams of radium will be present, we need to solve the exponential decay equation provided, R = [tex]10e^{-0.00043t[/tex], for t when R = 5 grams. We can do this using logarithms.
Set up the equation with R = 5: 5 = [tex]10e^{-0.00043t[/tex]
Divide both sides by 10 to isolate the exponential term: 0.5 = [tex]e^{-0.00043t[/tex]
Take the natural logarithm (ln) of both sides: ln(0.5) = ln([tex]e^{-0.00043t[/tex]), which simplifies to ln(0.5) = -0.00043t because the natural logarithm and the exponential function are inverses of each other.
Divide by -0.00043 to solve for t: t = ln(0.5) / -0.00043
Use a calculator to find the value of t: t ≈ 1608 years (rounded to the nearest whole year)
After approximately 1608 years, there will only be 5 grams of radium present in the container.
Explain what happens at the saturation point when adding salt to water at room temperature
Answers
Which of the following is not a perfect square?
A) 49
B) 121
C) 75
D) 64
Answers
Therefore, the correct answer is C.
Two acute angles can be which of the following?
I. congruent
II. adjacent
III. complementary
IV. supplementary
A. I and II
B. I and III
C. I, II, III
D. I, II, and IV
Answers
Two angles are adjacent when they have a common side and a common vertex.
Complimentary angles- either of two angles whose sum is 90
Congruent angles have the same angle.
Supplementary angles- either of two angles whose sum is 180
It is not supplementary because you can not add two acute angles together. To make a supplementary angle you must add an acute and obtuse or two right angles.
An Obtuse angle is an angle with a sum more than 90.
A Right angle is an angle with a sum of only 90.
Locate the prepositional phrase and type it in the blank. Then, identify the function of the phrase. Above the door hung a horseshoe. prepositional phrase: function of phrase: (Type adjective or adverb ).
Answers
The function of this prepositional phrase is adverbial, specifically it acts as an adverbial phrase of place, modifying the verb "hung". It answers the question "where?" in relation to the action of hanging.
The prepositional phrase in the sentence "Above the door hung a horseshoe" is "above the door".
This phrase describes the location of the horseshoe relative to the door. It specifies that the horseshoe is positioned vertically higher than the door. Prepositional phrases function as adjectives or adverbs by providing additional information about nouns (in this case, "door") or verbs (in this case, "hung"). In this context, "above the door" modifies the action of "hung" by indicating where the horseshoe is located.
Complete answer
Locate the prepositional phrase and type it in the blank. Then, identify the function of the phrase. Above the door hung a horseshoe. prepositional phrase: function of phrase: (Type adjective or adverb ):
3h/h^2-12h+36 -18/h^2-12h+36
Answers
[tex] \frac{3h}{h^2-12h+36} - \frac{18}{h^2-12h+36} = \frac{3h-18}{h^2-12h+36} [/tex]
Notice that we have a common factor, 3, in the numerator, so lets factor that out:
[tex]\frac{3h-18}{h^2-12h+36}= \frac{3(h-6)}{h^2-12h+36} [/tex]
Next, we can factor the denominator:
[tex]\frac{3(h-6)}{h^2-12h+36} = \frac{3(h-6)}{(h-6)^2} [/tex]
Now we can cancel the common factor [tex]h-6[/tex] in both numerator and denominator:
[tex]\frac{3(h-6)}{(h-6)^2}= \frac{3}{h-6} [/tex]
We can conclude that the result of 3h/h^2-12h+36 -18/h^2-12h+36 is: [tex] \frac{3}{h-6} [/tex]
3h/h^2-12h+36- 18/h^2-12h+36=3h-18/h^2-12h+36
Let us factor the common termsx(h-6)/h^2-12h+36= 3(h-6)/(h-6)^2
So since h-6 are similar, we can cancel the numerator and cancel 1 term in the denominatorso,3(h-6)/(h-6)^2=3/h-6
SO the answer of 3h/h^2-12h+36 -18/h^2-12h+36 is 3/h-6
4 1/4 divided by 1 1/2
Answers
Final answer:
The division of 4 1/4 by 1 1/2, when converted to improper fractions, results in 17/6, or 2 5/6 as a mixed number.
Explanation:
The question asks us to find the result of the division 4 1/4 divided by 1 1/2. To tackle this problem, we need to convert the mixed numbers into improper fractions and then perform the division by multiplying by the reciprocal. Here's how it is done step-by-step:
Convert mixed numbers to improper fractions:
4 1/4 = (4×4 + 1)/4 = 17/4 and
1 1/2 = (1×2 + 1)/2 = 3/2.
Divide the fractions by multiplying by the reciprocal of the divisor:
(17/4) × (2/3) = 34/12.
Simplify the result:
34/12 can be simplified to 17/6, or as a mixed number, 2 5/6.
Therefore, the answer to 4 1/4 divided by 1 1/2 is 2 5/6.
Which set is more variable? How do you know?
Please please help me ASAP like RIGHT NOW this is my last question and the only question I have left so please help me super quick!!!!!!!!!!
Answers
To determine which set is more variable, calculate their measures of variability such as range and standard deviation. Sets with larger range and standard deviation are considered more variable.
Explanation:To determine which set is more variable, you need to calculate the measures of variability for both sets. The measures of variability commonly used are the range and standard deviation. The set with a larger range and standard deviation is considered to be more variable.
For example, if we have two sets of data: Set A (2, 4, 6, 8, 10) and Set B (3, 5, 7, 9, 11), we can calculate the range for both sets. The range of Set A is 10 - 2 = 8, while the range of Set B is 11 - 3 = 8. Both sets have the same range, so we need to calculate the standard deviation to determine which set is more variable.
By calculating the standard deviation, we find that Set A has a standard deviation of 2.83, while Set B has a standard deviation of 2.83 as well. Again, both sets have the same standard deviation, so in this example, both sets are equally variable.
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Which of the graphs displays the expression |5|? A) B) C) D)
Answers
Answer:
Step-by-step explanation:
Which of the graphs displays the expression |5|?
A)
B)
C)
D)
The answer id ( D )
have a great and hope this helps :)!
By using the number line below, a graph that displays the expression |5| is: D) graph D.
What is a number line?In Mathematics and Geometry, a number line is a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values that are located at equal intervals along its length.
This ultimately implies that, every number line would primarily increase in numerical value towards the right from 0 and decrease in numerical value towards the left from 0.
Based on the information provided above, we can logically deduce that the absolute value of 5 is equal to 5, which represents a distance of 5 units from the point zero (0);
|5| = 5
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can someone help me
Answers
what is the slope of the line???
Answers
[tex]m=\dfrac{7}{4}[/tex]
Could somebody please help me I dont understand how to do this problem
Answers
107 + 2x-5 +x = 180
solve for x
112 + 3x = 180
-112 -112
3x = 68
x = 22.6667 degrees
Y=-4x+10 what is the perpendicular equation that contains (4,-6)
Answers
The slopes are usually a fraction and a whole number. If the first slope is a whole number, it changes to a fraction, and vice versa. Also, if the first slope is negative, the perpendicular slope is positive and vice versa.
The y intercepts in this case are 10 (first slope) and 5 (dividing by 2) since it has to go through (4,-6). See graph below.
I hope this helps!
Let f(x) = -5x -4 and g(x) = 6x -7. Find f(x) + g(x)
Answer options
-11x = 3b
x - 11
-11x - 11
x + 3
Answers
[tex]6x - 5x - 4 - 7[/tex]
Answer:
Second option.
Step-by-step explanation:
f(x) + g(x) = -5x-4 + 6x-7 = -5x + 6x - 4 - 7 = x - 11.
The word pluralistic contains the root pour which means more what does pluralistic mean?
The pluralistic culture of the United States encourages people from around the world to apply for citizenship
A) patriotic
B) diverse
C) receptive
D) unified
Answers
The word pluralistic means diverse.
Pluralistic:
'Anything pluralistic involves a diversity of different ideas or people. A pluralistic society is a diverse one, where the people in it believe all kinds of different things and tolerate each other’s beliefs even when they don’t match their own'
According to the given question,
'The diverse culture of the United States encourages people from around the world to apply for citizenship.'
Hence, we can conclude that that diverse is the correct meaning for pluralistic.
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