PLEASE HELP ME WITH PRE CAL!!
A drone is flying over a college campus. The drone spots the cafeteria on the west end of campus at a 27 ° angle of depression and the sports complex on the east end of campus at a 34° angle of depression. If the cafeteria and sports complex are separated by a straight road 2.3 mi long, how high is the drone?
Answers
Answer:
0.67 mi
Step-by-step explanation:
The diagram illustrating the question is shown in the attach photo.
In triangle DCA,
Opposite = H
Adjacent = b
Angel θ = 27°
Tan θ = Opp /Adj
Tan 27° = H/b
Cross multiply
H = b x Tan 27°... (1)
From triangle DSA,
The diagram illustrating the question is shown in attach photo.
In triangle DCA,
Opposite = H
Adjacent = 2.3 – b
Angel θ = 34°
Tan θ = Opp /Adj
Tan 34° = H/ 2.3 – b
Cross multiply
H = Tan 34° (2.3 – b) .. (2)
Equating equation (1) and (2)
b x Tan 27° = Tan 34° (2.3 – b)
0.5095b = 0.6745(2.3 – b)
0.5095b = 1.55135 – 0.6745b
Collect like terms
0.5095b + 0.6745b = 1.55135
1.184b = 1.55135
Divide both side by 1.184
b = 1.55135/1.184
b = 1.31 mi
Substitute the value of b into any of the equation to obtain the height (H). In this case we shall use equation 1.
H = b x Tan 27°
H = 1.31 x Tan 27°
H = 0.67 mi
Therefore, the height of the drone is 0.67 mi
The height of the drone is 0.67 mi
The calculation is as follows:In triangle DCA,
Opposite = H
Adjacent = b
Angel θ = 27°
Tan θ = [tex]Opp \div Adj[/tex]
Tan 27° =[tex]H\div b[/tex]
Now we have to do the cross multiply
[tex]H = b \times Tan 27^{\circ}... (1)[/tex]
Now
From triangle DSA,
In triangle DCA,
Opposite = H
Adjacent = 2.3 – b
Angel θ = 34°
Tan θ = [tex]Opp \div Adj[/tex]
Tan 34° = [tex]H\div 2.3 - b[/tex]
Now we have to do the cross multiply
H = Tan 34° (2.3 – b) .. (2)
Now
Equating equation (1) and (2)
[tex]b \times Tan 27^{\circ} = Tan 34^{\circ} (2.3 - b)[/tex]
0.5095b = 0.6745(2.3 – b)
0.5095b = 1.55135 – 0.6745b
Now
0.5095b + 0.6745b = 1.55135
1.184b = 1.55135
b = 1.31 mi
Now
[tex]H = b \times Tan 27^{\circ}\\\\H = 1.31 \times Tan 27^{\circ}[/tex]
H = 0.67 mi
Find out more information about height here:
https://brainly.com/question/10726356?referrer=searchResults
Related Questions
Find the indicated sum for each geometric series.
S6 for 2 + 1 + 12 + 14
Answers
Answer:435
Step-by-step explanation:
Which expressions are equivalent to - f - 5(2f – 3)?
Choose all answers that apply:
-11f-3
- 11f + 15
None of the above
Answers
Answer:
- 11f + 15
Step-by-step explanation:
- f - 5(2f - 3)
= - f - 10f + 15
= - 11f + 15
1. Escribe como potencia los siguientes productos y luego resuelve como se indica en el ejemplo. a) 6.6.6 = 6 3 = 216 f) 11.11= b) 3.3.3.3 = g) 0.0.0.0.0= c) 17.17= h) 2.2.2.2.2.2= d) 4.4.4.4.4= i) 5.5.5= e) 1.1.1.1.1.1.1= j) 10.10.10.10= 3. Escribe y calcula las potencias. a) Tres al cubo: d) Seis al cubo: b) Cinco al cuadrado: e) Ocho al cuadrado: c) Dos a la quinta: f) Diez a la cuarta:
Answers
Answer:
(Véase la explicación para mayores detalles/See the explanation for further details)
Step-by-step explanation:
a) Tres al cubo (Three to cube):
[tex]x = 3 \times 3 \times 3[/tex]
[tex]x = 3^{3}[/tex]
[tex]x = 27[/tex]
b) Seis al cubo (Six to cube):
[tex]x = 6 \times 6 \times 6[/tex]
[tex]x = 6^{3}[/tex]
[tex]x = 216[/tex]
c) Cinco al cuadrado (Five squared):
[tex]x = 5 \times 5[/tex]
[tex]x = 5^{2}[/tex]
[tex]x = 25[/tex]
d) Ocho al cuadrado (Eight squared):
[tex]x = 8 \times 8[/tex]
[tex]x = 8^{2}[/tex]
[tex]x = 64[/tex]
e) Dos a la quinta (Two to five):
[tex]x = 2 \times 2 \times 2 \times 2 \times 2[/tex]
[tex]x = 2^{5}[/tex]
[tex]x = 32[/tex]
f) Diez a la cuarta (Ten to four):
[tex]x = 10\times 10 \times 10 \times 10[/tex]
[tex]x = 10^{4}[/tex]
[tex]x = 10000[/tex]
Sandra is asked to report on the recent increase in popularity of an application based on the number
of times it is downloaded. Which best describes how Sandra should report this information?
downloads per day
total number of days with downloads
downloads per person
total number of downloads
Answers
Answer:
Step-by-step explanation:
Report the number of downloads per day. By determining how this number is changing / increasing it will be possible to spot and describe an upward trend if there is one.
How far can light travel in 1 year? Remember there are 3.15576 x 10^7 seconds in a single year.
Answers
Answer: [tex]9.465\times 10^{15}\ m[/tex]
Step-by-step explanation:
Given
Seconds in a year is [tex]3.155\times 10^7[/tex]
We know
[tex]Distance=speed\times time [/tex]
Speed of light in vacuum is [tex]3\times 10^8\ m/s[/tex]
So distance traveled [tex]=3\times 10^8\times 3.155\times 10^7[/tex]
[tex]distance=9.465\times 10^{15}\ m[/tex]
Solve the quadratic by factoring.
x2 - 4x = -4x + 4
Answers
Answer:
x=2 or x=-2
Step-by-step explanation:
ax^2+bx+c=0
first we rearrange this equation so we get x^2+(-4+4)x-4=0 so its x^2-4=0 so that means b=0 now we should find two numbers that when we multiply them we get c and when we subtract them we get b so that two numbers are 2 and -2
Find the volume of the prism.
36 m
3 m
5 m
Answers
Answer:=40m
Step-by-step explanation: 36m+3m+5m
Answer:
540m
Step-by-step explanation:
The volume of a rectangular prism is 288 ft3. If its height is 6 feet and its length is 8 feet, what is its width?
a. 6 feet
b. 8 feet
c. 9 feet
d. 12 feet
Answers
Answer:
6 ft
Step-by-step explanation:
Volume = (height) (width) (length), so
(width) = (volume) / [ (height) * (length) ]
Here, the width is:
(width) = (288 ft^3) / [ (6 ft) * (8 ft ) ] = 288/48 ft = 6 ft
The width of the rectangular prism is 6 ft
Quincy folds a piece of cardboard to make the three sides of a triangular prism open at top and bottom. The triangle prism and the piece of cardboard that he used are show below. What is the area of the piece of cardboard?
Answers
This question is incomplete because it lacks the attached diagram.
Find attached to this answer the appropriate diagram
Answer:
500 square centimeters
Step-by-step explanation:
From the question above, we are told that the top and bottom of the triangular prism is open.
Hence, the area of the piece of the cardboard is = Lateral Surface Area of the triangular prism
The formula for Lateral Surface Area of a Triangular Prism = Perimeter of the Triangular prism × Height of the Triangular prism.
Perimeter of the Triangular prism = Side a + Side b + Side c
Where Side a = 9cm
Side b = 9cm
Side c = 7 cm
Perimeter of the Triangular prism = 9cm + 9cm + 7cm
= 25cm
Height of the Triangular prism = 20cm
The Lateral Surface Area of the Triangular prism = 25cm × 20cm
= 500cm² or 500 square centimeters.
Since we are told that Lateral Surface Area = Area of the cardboard,
The Area of the cardboard = 500 cm² or 500 square centimeters.
What is the value of x in the equation 3-2x=-1.5x?
оооо
-6
Answers
Answer:
x=6
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x = 6
Step-by-step explanation:
In this equation, we are told to solve for the value of x. Thus, we must isolate the variable x (poor x... we're always trying to isolate it).
3 - 2x = -1.5x
(I'm going to swap sides to make it easier for me to solve. This doesn't change anything mathematically due to the associative laws. It's purely cosmetic.)
-1.5x = 3 - 2x
First, we can add 2x to both sides of the equation to get all algebraic expressions containing the variable x on one side of the equation alone.
0.5x = 3
For our next part here, let's convert 0.5 to a fraction to make life easier for us.
[tex]\frac{1}{2}[/tex]x = 3
When isolating x in this, we are trying to get rid of 1/2. How can we do this? We can multiply is by 2!
[tex]\frac{1}{2}[/tex]x · [tex]\frac{2}{1}[/tex] = 1x (or simply x)
What we do to one side we must do to another.
x = 3 · 2
x = 6
Our answer is x = 6. Woo!
Select all the equations where =3 is a solution.
Choose 2 answers
Help?
Answers
Answer:
A and C
Step-by-step explanation:
5. Jack and Jill use rain gauges that are the same size and shape to measure rain on top of a hill. Jack
uses a rain gauge marked in fourths of an inch. Jill's gauge measures rain in eighths of an inch. On
Thursday, Jack's gauge measured inches of rain. Jill and Jack both had the same amount of water,
so what was the reading on Jill's gauge on Thursday? Draw a number line and write a sentence to
explain your thinking.
Answers
Answer:
List the multiples
1/4,2/4,3/4,4/4
1/8,2/8,3/8,4/8,5/8,6/8,7/8,8/8
1/4=2/8
2/4=4/8
4/4=8/8
Those numbers are the common fractions so they would be the only fractions that both Jack and Jill could get.
Step-by-step explanation:
The formula to calculate the area of a circle from its circumference is:
A =c2/4π
Answers
Answer:
(if its a true or false question) True
Step-by-step explanation:
We know-
Area of a circle =
A=(π)r2
Circumference of a circle =
C=2(π)r
Where pi is a constant and r is the radius of the circle.
Using these two formulas we can express A in terms of C as follows:
c2=[2(π)r]2
⇒ c2=4[(π)2]r2 ⇒ c2=4(π)[(π)r2]
As (π)r2=A ⇒c2=4(π)A
Therefore:
A=c2/4(π)
Answer:
the answer is b
Step-by-step explanation:
....
Describe what math step you would do to solve this equation ?
Answers
Answer:
Multiply each side by 14.7
Step-by-step explanation:
cos 50 = m / 14.7
Multiply each side by 14.7
14.7 cos 50 = m /14.7 *14.7
14.7cos 50 = m
Answer:
multiply both sides by 14.7
Step-by-step explanation:
Pythagorean theorem
a^2 + b^2 = c^2
X= ?
Answers
[tex]\text{Find the one bottom side of the triangle first}\\\\\text{We know that the total length is 21, but part of it is 11, so subtract}\\\\21-11=10\\\\\text{Divide 10 by 2 because there are two sides for two triangles}\\\\10\div2=5\\\\\text{Now, since we know two of the sides, we would plug in the values}\\\text{into the Pythagorean theorem and solve:}\\\\5^2+b^2=13^2\\\\25+b^2=169\\\\\text{Subtract 25 from both sides}\\\\b^2=144\\\\[/tex]
[tex]\text{Square root both sides}\\\\\sqrt{b^2}=\sqrt{144}\\\\b=12\\\\\text{This means that x = 12}\\\\\boxed{x=12}[/tex]
If t = 24 cm and r = 25 cm, what is the length of s?
Answers
Answer:
24.5
Step-by-step explanation:
middle
Answer:
7cm
Step-by-step explanation:
Hello i need help i only have 20 minutes help mee
Answers
Answer:
The first one
Step-by-step explanation:
Do you really want an explanation :v
Answer:
Can’t really see the end of the question but if it is 3/w it is most likely
c
Step-by-step explanation:
The pot has a diameter of 10 inches a height of 12 inches. there are 120 meatballs each meatball is 2.4 inches. the sauce takes up half the pot already. determine if the sauce overflows or not. pls help its due in an hour! ):
Answers
the answer is c
Step-by-step explanation:
Let a be a rational number and b be an irrational number. Is a + b rational or irrational?
Answers
Answer:
irrational
Step-by-step explanation:
because an irrational number goes on forever so no matter what number is added to it it will always be irrational.
Answer:
Rational
Step-by-step explanation:
I need help very urgent
Answers
Remember: volume=length x width x height
So i think its 15, 15, and neither of them have greater volume.
what expression is equivalent to 3x - (2x+4) + 5
Answers
Answer:
x+1
if it helps let me know by voting
Step-by-step explanation:
Answer:
3x+(-2x-4)+5 would be one of plenty other possibilities, it would help if we knew what x was equal to
Step-by-step explanation:
Need help! Up to 100 points
Link or something. It's has been a nightmare with these questions...
Answers
Answer:
Part B
Part 1 describes a quartic function that's been reflected over the x-axis and translated up and to the right. (It's quartic because it has those bumps; it's like a quadratic in that its end behavior is down-down, but it has more bumps than a quadratic.)Part 2 describes an exponential decay function that approaches a horizontal asymptote. (This one looks just like Part 3 in the previous graph.)Part C
You're going to have to do this scatter plot on your own with the given software, because I don't know how your software works, but I can tell you that #1 will look like a quadratic, #2 a cubic, #3 a quartic, #4 a really fun third root that looks like a cubic on the y-axis instead of the x-axis.
Part D
You can look on Worldometer for graphs of the coronavirus; they have graphs in every individual country. I advise using the total cases on a logarithmic scale, because the question specified that it can't be linear.
write an equation that represents the points (2,6)(0,3) but a linear kind of an equation in any form
Answers
Answer:
y=[tex]\frac{3}{2} x+3[/tex]
Step-by-step explanation:
Story: The Escalator Ratio Task: Ty took the escalator to the second floor. The escalator is 12 meters long, and he rode the escalator for 30 seconds. (Things to consider: 60 seconds = 1 minute; 60 minutes = 1 hour; 24 hours = 1 day). Question: True or False? He traveled 2 meters ever 5 seconds. Answer T or F and tell (or show) how you know you are correct.
Answers
Answer: True
Step-by-step explanation:
YES, HE TRAVELLED 2 METRES EVERY 5 SECONDS
PROOF:
TOTAL RIDE TIME = 30 SECONDS
Length of elevator = 12 METRES
Distance moved per second can be calculated by = (length of elevator / total ride time)
( 12 METRES / 30 seconds) = 0.4 metres per second
Therefore, distance covered in 5 seconds :
0.4 × 5 = 2 metres.
Hence, the proof
He traveled 2 meters ever 5 seconds
Two rectangular prisms, M and N, are mathematically similar. The volumes of M and N are 17 cm^3 and 136 cm^3, respectively. The height of N is 18 cm. Find the corresponding height of M.
Answers
We have been given that two rectangular prisms, M and N, are mathematically similar. The volumes of M and N are 17 cm^3 and 136 cm^3, respectively. The height of N is 18 cm. We are asked to find the height of M.
First of all, we will find the ratio between sides of rectangle M and N using proportions.
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{ Volume of N}}{\text{ Volume of M}}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{136\text{ cm}^3}{17\text{ cm}^3}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{8\text{ cm}^3}{1\text{ cm}^3}[/tex]
Now we will take cube root on right side to find length in cm.
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\sqrt[3]{\text{8 cm}^3}}{\sqrt[3]{\text{1 cm}^3}}[/tex]
[tex]\frac{\text{Side of N}}{\text{Side of M}}=\frac{\text{2 cm}}{\text{1 cm}}[/tex]
Therefore, sides of rectangle N is 2 times greater than sides of rectangle M.
To find height of rectangle M, we will divide side of rectangle N by 2.
[tex]\text{Height of rectangle M}=\frac{18}{2}=9[/tex]
Therefore, height of rectangle M is 9 cm.
ASSIGNMEN
Solve the following linear system of equations using substitution.
y = 3x - 5
y = 2x - 6
O (3, 2)
0 (-5, -6)
(-1,-8)
(1, -2)
DONE
Answers
Answer:
(-1,-8)
Step-by-step explanation:
Write the ratio of the first measurement to the second measurement. Compare in millimeters. Diameter of ball A: 44 mm diameter of ball B: 7.2 cm The ratio of the diameter of ball A to the diameter of ball B is
Answers
Answer:
11:18
Step-by-step explanation:
Here, we are interested in calculating the ratio of diameter of ball A to that of ball B
what to do here is to ensure that both diameters have measurements that are same units.
Thus, mathematically;
44 mm to 7.2cm
But, mathematically;
10 mm = 1 cm
Thus 7.2cm = 7.2 * 10 = 72mm
Thus, our ratio becomes;
44:72
divide through be 4, we have
44/4 : 72/4
= 11 : 18
Answer:
11:19
Step-by-step explanation:
You leave school and walk 1.237 miles west. Your friend leaves school and walks 0.56 miles east. How far apart are you and your friend? Justify your answer.
Answers
Answer:
You and your friend are 1.797 miles apart. Since east and west are opposite directions, we just add the distances.
Step-by-step explanation:
They are walking on opposite directions, so to see how far apart, we add how much each of you walked.
We have that:
You walk 1.237 miles west.
He walks 0.56 miles.
1.237 + 0.56 = 1.797.
You and your friend are 1.797 miles apart. Since east and west are opposite directions, we just add the distances.
please please answer these five questions !!!!!!!!!
Answers
Answer: 1. V≈603.19
2. V≈103.67
3. V≈513.13
Step-by-step explanation: i only know those sorry :(
Steve has 2 and one half cups of flour for one of his recipes requires one 8th cup of flour, what is the maximum number of times Steve can complete the recipe.
Answers
Answer:
20 times
Step-by-step explanation:
We know that the recipe requires an eighth of a cup of flour (1/8 or 0.125) but in total Steve has 2 and a half, that is (2 1/2 or 2.5). To know the result we must divide the total amount by what is needed for 1 recipe, that is:
2.5 / 0.125 = 20
Which means that Steve with the flour he has can make the same recipe a total of 20 times
Answer: the answer is 20
Step-by-step explanation:
