The horizon's distance for a typical human being (2 m height) for earth is 5 km, for mars it is 3.7 km, for moon its 2.6 km, and for Diemos it is 0.15 km (all calculations approx).
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).
The complete question is:
" For a typical human height of 2 meters, what is the horizon distance on A) Earth (R=6378 km); B) Mars ( 3,374 km); C) The Moon ( 1,738 km); Mars' moon Diemos ( 6 km) "
Radius touching the line which passes touching the circle (tangent) is perpendicular(to 90°) to it.
Consider the diagram attached below:
The distance D is the distance of horizon from the eyesight of viewer.
The value of h is the height of the observer.
For the triangle ABC, the length of the hypotenuse is: h + R
Other two sides which are mutually perpendicular are of length R and D.
Thus, by using Pythagoras theorem, we get:
[tex]R^2 + D^2 = (h+R)^2\\D = \sqrt{h^2 + R^2 + 2hR -R^2}\\\\D = \sqrt{h^2 + 2hR}\\[/tex]
(positive root as D is representing length, a non-negative quantity).
We're given h = 2, so we get:
[tex]D = \sqrt{4+4R} = 2\sqrt{1+R} \: \rm m[/tex]
A) Earth (R=6378 km);6378 km = 6378000 m
[tex]D = 2\sqrt{6379001} \approx 5051 \: \rm m \approx 5 \: km[/tex]
B) Mars ( 3,374 km);3374 km = 3374000 m
[tex]D = 2\sqrt{3374001} \approx 3674 \: \rm m \approx 3.7 \: km[/tex]
C) The Moon ( 1,738 km);
1738 km = 1738000 m
[tex]D = 2\sqrt{1738001} \approx 2637 \: \rm m \approx 2.6 \: km[/tex]
D)Mars' moon Diemos ( 6 km)
6 km = 6000 m
[tex]D = 2\sqrt{6001} = 154.93 \: \rm m \approx 0.15 \: km[/tex]
Thus, the horizon's distance for a typical human being (2 m height) for earth is 5 km, for mars it is 3.7 km, for moon its 2.6 km, and for Diemos it is 0.15 km (all calculations approx).
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(3 points) Consider the parabola below.
Standard Form
y = ax2 + bx + C
Vertex Form
y = a(x h)? + k
Intercept Form
y = a(x - p)(x - q)
Part A: Write the equation in intercept, vertex, and standard form. For all equations,
a is equal to 1.
Show vour work or explain how
you determined your answer.
Answer:
Step-by-step explanation:
When a = 1,
Standard form:
= x^2 + bx + c.
Intercept form:
= (x - p)(x - q)
Vertex form:
(x - h)^2 + k.
Which answer uses the distributive property to simplify the following? 3 × (5 + 8) A. (3 × 5) + (3 × 8) B. (3 × 5) × (3 × 8) C. 3 + 5 + 8
Answer:
A. (3 x 5) + (3 x 8)
Step-by-step explanation:
The Distributive property distributes the common factor that the numbers in the parenthesis are multiplied with.
Ex. A(B + C) will equal (A x B) + (A x C).
3 x (5 + 8) will equal (3 x 5) + (3 x 8).
Solve for x.
6(x-2)=4
1. X=1
2.x=1 1/3
3. X=2 2/3
Answer:
x = 2 2/3
Step-by-step explanation:
6(x - 2) = 4
6x - 12 = 4
6x - 12 + 12 = 4 + 12
6x = 16
6x/6 = 16/6
x = 2 2/3
Jordan has 28 golf balls. 28 golf balls in 4 rows and 7 columns. Of the 28 golf balls, 17 are yellow. How many golf balls are yellow?
The distribution of the balls is an illustration of proportions, and 4 of the golf balls are yellow
How to determine the number of yellow golf balls?The distribution of the balls are given as:
Total = 28
Yellow = 1/7
The number of yellow balls is given as:
Yellow = 1/7 * Total
This gives
Yellow = 1/7 * 28
Evaluate the product
Yellow = 4
Hence, 4 of the golf balls are yellow
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(long answer needed.)
15 points & brainliest!
1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping, and one color of sprinkles from the chart below. Show all possible outcomes in a tree diagram
Answer:
chocolate, marshmellows, and chocolate sprinkle
Step-by-step explanation:
Answer:
you could do
chocolate,fudge,chocolate
chocolate,marshmallow,rainbow
chocolate,marshmallow,chocolate
chocolate, fudge,rainbow
vanilla, fudge,chocolate
vanilla, fudge,rainbow,
vanilla,marshmallow,rainbow
vanilla marshmallow,chocolate
strawberry,fudge,chocolate
strawberry,fudge,rainbow
strawberry,marshmallow,chocolate
strawberry,marshmallow,rainbow
whinch expression is greater than 250
Answer:D
Step-by-step explanation: All others are fractions of 250 While D is a multiple of 250
Answer:
➡ [tex]9/8[/tex] x 250
➡ [tex]2[/tex] x 250
Greater than 250
solve for x : 13x + 7 = -227
Answer:
-18
Step-by-step explanation:
1. Subtract 7 from both sides:
13x = -234
2. Divide 13 from both sides:
13x/13 = -234/13
x = -18
hope this helps!
Jaylynn draw a hen on graph paper using scale of 1 unit on her graph paper represents 5cm.The hen has height of 11 units in the drawing.
What is the height,in cm,of the actual hen?
Answers:
A.33
B.44
C.55
D.66
Answer:
55
Step-by-step explanation:
There are 11 units used on the paper. If each unit is 5cm, that means you can do 11*5 and get 55 cm.
Answer:
55
Step-by-step explanation:
1 unit = 5cm
we need to find out how much 11 units are so,
we multiply both sides: 1 unit *11 = 5cm*11, 11 units = 55 cm
Ponyboy says 16 years on the streets can teach and show a person all the wrong things. What does he mean by this
There are many things happening on the streets and some of them are bad. There is a high likelihood that if you are on the streets you will see bad things happening.
What is the area of figure abcd? a trapezoid abcd is drawn with length of parallel sides ab and cd equal to 10 inches and 12 inches, respectively. the length of one of the non-parallel sides bc is 6 inches. side bc is perpendicular to dc. a perpendicular line drawn from a to side cd meets cd at e. 54 square inches 60 square inches 66 square inches 72 square inches
Answer: 60 square inches
Step-by-step explanation:
Answer:
66 square inches
Step-by-step explanation:
10 times 6 equals 60 and 60 plus 6 is 66. You add the six because that is the area of the triangle and you get 60 from multiplying 10 and 6 because that is the area of the rectangle.
what is the equation of the line with the slope of -3/5 and an x-intercept of 6
Answer:
Step-by-step explanation:
try
x = -3/5
i might be worng tho
please HELPPPPPPPPPPPPPP
Answer:
q= -rs/t
Step-by-step explanation:
3
10
57:31
Jakob buys lunch at school on Mondays, Wednesdays, and Thursdays. He spends $3.50 for each lunch. Which equation
can be used to find the number of weeks, w, it will take Jakob to spend $84 on lunch?
3.50w-84
O (3x3.50)-84
3w-84
(3+3.50)w-84
Step-by-step explanation:
its say $3.50 each so for a week you multiply $3.50 by 3 because the are 3 days which will be equal to $10.5
the you divide $84 by $10.5
and the answer is =8weeks
Please help, this is due in 20 minutes!! I would greatly appreciate you if you also provided your work and no links!
A 5.0 µC point charge is moved within an electric field and has an electric potential energy change of 10.0 J. What is the electric potential difference before and after the charge was moved? Show work. (µC = 1.0 × 10–6)
Answer:
Step-by-step explanation:
so
V = energy / q
The potential difference * charge = potential energy change of charge
delta V = 10J/(5*10^-6) = 2*10^6 volts
Please helppppppp!! Khan Academy
If X = 18 units, Y = 24 units, and Z = 30 units, what is the sine of
Answer:4 days ago — Click here to get an answer to your question ✍️ If X = 18 units, Y = 24 units, and Z = 30 units, what is the sine of.
Step-by-step explanation:
A bedroom is 10 ft. by 12. ft. with 8 ft. high walls. How much would it cost to put padding and carpet in this room
Answer $2,295.60:
Step-by-step explanation: i just did this assignment and got it right, hope this helps
The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as _____.
Answer:
Statistical Inference
Step-by-step explanation:
Statistical analysis has two main focuses: descriptive statistics and infernetial statistics.
Descriptive statistics summarise data using graphs and summary values such as the mean and interquartile range. Descriptive statistics can help us identify relationships and patterns. Descriptive statistics do not draw conclusions beyond the data we already have. Inferential statistics anaylsis does allow us to make conclusions beyond the data we have.
A defintion of inference is:
The process of drawing conclusions.
which equation is true when c=3
The value of the c that satisfies the equation is 4(c + 2) = 20. Then the correct option is D.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The value of c is 3.
F. 2c + 8 = 31
Then we have
[tex]31 = 2\times 3 + 8 \\\\31 = 6 + 8\\\\31 \neq 14[/tex]
G. 5(7 - c) = 32
Then we have
[tex]32 = 5(7 -3) \\\\32 = 5 (4)\\\\32 \neq 20\\[/tex]
H. 9 - 6c = 0
Then we have
[tex]0 = 9 - 6*3\\\\0 = 9 - 18\\\\0 \neq -9[/tex]
I. 4(c + 2) = 20
Then we have
[tex]20 = 4(3 +2)\\\\20=4*5\\\\20=20[/tex]
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Can you help me with this question Plsss?
helpppp meeeee please
Answer:
?= 35.66º
Step-by-step explanation:
26/32=0.8125
cos 35.66º=0.8125
Answer:
? = 36 degrees
Step-by-step explanation:
Use trigonometry!
since we know the adjacent and hypotenuse sides, use cos.
cos(?) = adjacent/hypotenuse = 26/32
? = arccos(26/32)
? = 35.659
Rounding it up, we get.
? = 36 degrees
Please answer ASAP ........
Answer:
[tex]\sf \boxed{\sf volume=\frac{16}{9} \ ft^3}[/tex]
Explanation:
Cube volume: Length x Width x Height
Volume of the entire cuboid:
Length x Width x Height
(1/3 x 4) x (1/3 x 3) x (1/3 x 4)
4/3 x 1 x 4/3
16/9
Volume of the cuboid
Length ×Breadth×Height(1/3×4)²(1/3×316/9×116/9ft³A rectangular prism has a volume of 240 cubic feet. If the length is 4 feet and the width is 4 feet, what is the height of
the prism?
Answer:
Let's use the formula for the volume of a rectangular prism;
V = l · w · h
Where 'l' represents the length, 'w' stands for the width, and 'h' displays as the height. (V evidently stands for the volume)
What we know:
Volume = 240 ftLength = 4 ftWidth = 4 ftWhat we need to find out:
HeightLet's plug in what we know into the formula:
V = l · w · h
240 = 4 · 4 · h
Now let's solve for h:-
240 = 16 · h
240 = 16h
Get rid of h's co-efficient by dividing 16 from both sides because the inverse operation of multiplication(since 16 is being multiplied by h) is division.
÷16 ÷16
Finally, you would end up with a result of:
15 = h
Hence, the height of this prism is 15 feet.
Jeriel is 1.65 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 28.05 meters. He stands 23.5 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:10.17
Step-by-step explanation:
A courier service charges a $5 pick up fee plus $0.15 per mile. The total charge to deliver a package was $7.85. How many miles did the courier service travel to deliver the package?
*
Answer:
19 miles
Step-by-step explanation:
Find the value of x
………………….
Answer:
x = 5
Step-by-step explanation:
congruent rectangles
4/3 = (x+3)/(2x-4)
8x - 16 = 3x + 9
5x = 9 + 16
x = 25/5
x = 5
Janet has. completed 60% of her eliptical work out. if her entire workout last 1 hr , how many more minutes does she still need to work out?
1 hour = 60 minutes.
60 minutes x 60% = 36 minutes completed.
60 minutes -36 minutes = 24 minutes left
answer: 24 minutes
Answer:
24 min
Step-by-step explanation:
If shecompleted 60% she stil has 40 % of the hour-long (60 minute) workout to go
.40 ( 60 min) = 24 min
please help!! Solve for the hypotenuse and then determine the ratios below. (Show all work)
Answer:
Hypotenuse:
sin x° =
cos y° =
The hypotenuse of the right triangle is 29 units.
The ratios are as follows:
sin x = 20 / 29
cos y = 20 / 29
What is a right angle triangle?Right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios. The sides can also be solved using Pythagoras theorem.
The hypotenuse side is the longest side of a right angle triangle.
Therefore,
c² = a² + b²
c = √20² + 21²
c = √400 + 441
c = √841
c = 29
hypotenuse = 29 units
sin x = opposite / hypotenuse = 20 / 29
cos y = adjacent/ hypotenuse = 20 / 29
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What is the value of f(-3)
Answer:
4
Step-by-step explanation:
the closed circle falls on 4
Miguel is posting photos on a school website . He has 48 photos , and he is allowed to use 12 pages . He wants to put the same number of photos, p. on each page
How many photos are in each page