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
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Related Questions
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
ill give a brainliest :)
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Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Charge your computer!!
can someone tell me how to do this
Answers
Answer:
must not be
Step-by-step explanation:
The whole thing equals 360 degrees
Angle B and Angle D are equal; which equals 190 degrees.
Add Angle A to 190 degrees; which is 86 + 190 = 276.
Subtract 360, which is what the whole thing equals, and 276, which is the known angle added together, and you get 56.
In order for this to be a parallelogram, the opposite angles need to be equal.
Since they are not, the answer is must not be.
Jessie installed 12 more axles than the number of engine blocks her friend Gus installed yesterday. Write an equation for g, the number of engine blocks Gus installed yesterday.
Answers
Answer:
g = j - 12
Step-by-step explanation:
We know that if g is Gus' number of engine quantity, then j is Jessie's number of engine quantity, from this statement we have that Jessie made 12 more than Gus, therefore:
j = g + 12
if we solve for g:
g = j - 12
which is the same as saying that Gus made 12 number of engine less than Jessie
Answer:
g = x - 12
where x is the number of axles installed by Jessie
Step-by-step explanation:
Using a simple analogy. If a man has 7 cars while his friend has 3 cars, The statement may be written as the man has 4 cars more than his friend. The 4 cars being the difference between the number of cars he has and the number his friend has.
As such, if the number of engine blocks installed by Gus is g and Jessie installed 12 more axles than the number of engine blocks Gus installed yesterday, where Jessie must have installed x axles,
x = g + 12
Such that
g = x - 12
Unit 5. 6) Please help. A block of wood has a density of 2.7 grams per cubic centimeter. If the block has a mass of 54 grams, what is its volume?
Answers
Answer:
V = 20 cm^3
Step-by-step explanation:
density = mass / volume
2.7 grams/ cm^3 = 54 grams / V
Multiply V on each side
V *2.7 grams/ cm^3 = 54 grams / V *V
Divide each side by 2.7
V = 54 grams / 2.7
V = 20 cm^3
Answer:
The correct answer is option 2, 20cm.
A jar contains 666 red jelly beans, 444 green jelly beans, and 444 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the probability that the first jelly bean will be blue and the second will be blue as well?
Answers
Answer:
Step-by-step explanation:
P(first blue) = 444/ 1554
P(second blue) = 443/1553
P(first blue + second blue) = 444/ 1554 * 443/1553 = 0.08
The circular ring of the fountain has a radius of 9 feet. What is the area of the ring?
Answers
Answer:
about 254.47
Step-by-step explanation
Circle are equation: pi(r)^2
pi(9)^2 = 254.47
The growth of a population of bacteria can be modeled by an exponential function. The graph models the population of the bacteria colony P(t) as a function of the time t, in weeks, that has passed. The initial population of the bacteria colony was 500. What is the domain of the function? What does the domain represent in this context?
Answers
Answer:
t ≥0
Step-by-step explanation:
Given the information:
The initial population: 500
The graph models the population of the bacteria colony P(t) as a function of the time t, in weeks,
=> our function is: P(t) =500*[tex]b^{t}[/tex] where b is the base number and it is ≥0
What is the domain of the function?The domain of exponential functions is all real numbers greater than zero
<=> t ≥0 (because t present for the time and time can not have negative value)
What does the domain represent in this context?t is the independent variable is this exponential function and the population of bacteria depends on the change of t.
Because it is the growth function so the range (the population of bacteria) increase over its domain (the time)
Hope it will find you well.
which of the following statements correctlydescribes the points
Answers
The first statement is correct
To calculate the distance we have to substrate the values of the Y axis only since X values are constant so the distance IS 4 - - 7=4+7=11
Answer:
The first answer. The distance is 11.
3
Find the volume of the prism. *
1.5 m
2 m
4 m
Answer choices are:
A) 8m^3
B) 12m^3
C)10m^3
6m^3
Answers
Answer:
[tex]12m^{3}[/tex]
Step-by-step explanation:
Multiply all the variables together to get the answer (only for rectangular prism).
So I basically did 4 x 2 x 1.5 = 12 Then I applied the unit of measurement and cubic meters as it is volume.The formula is length x width x heightA taxi charges $3, plus $1.50 for each mile traveled. Mr. Hill rode in the taxi
from his home to the airport and was charged $30. How many miles does
Mr. Hill live from the airport?
Answers
Answer:
18 miles from the airport
Answer:
18
Step-by-step explanation:
30-3=27 divided by 1.50=18
Y=12x+7 find an equation for the inverse relation
Answers
Answer:
y= 5x
Step-by-step explanation:
I hope this helps and that it is correct.
Consider the system of equations. 5x + 2y = 6, 10x + 4y = 12 Which equation is equivalent to the first equation of the system and can be used to solve the system using the linear combination method
Answers
Step-by-step explanation:
(5x+2y=6)2
10x+4y=12
10x+4y=12 then substract
10x+4y=12
0=0 true so, it have infinite s/n
I need help pleaseeee
Answers
Answer:
20cm
Step-by-step explanation:
pythagorean theorem
15^2 + b^2 = 25^2
225 + b^2 = 625
b^2 = 400
b = 20
Answer:
20 cm
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem
a^2 +b^2 = c^2
where a and b are the legs and c is the hypotenuse
15^2 +b^2 = 25^2
225+b^2 = 625
Subtract 225 from each side
225+b^2 -225 = 625-225
b^2 = 400
Take the square root of each side
sqrt(b^2) = sqrt(400)
b = 20
HELPPP I NEED IT I DONT KNOW WHAT TO DO
Answers
Answer:
3/2
Step-by-step explanation:
Its because its saying the largest box to the smallest.
since the largest box has a side of 3 it should be on top and the smallest is 2, should be on the bottom.
Ignore all negetive fraction because they are useless.
Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast, to $3 in the mid-US, to $5 on the west coast. B On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price?
Answers
Answer:
A) The amount of gas they bought on each coast;
East Coast = 35 gallons
Mid-US = 100 gallons
West Coast = 15 gallons
B) The amount of gas they bought on each coast on the return journey;
East Coast = 37 gallons
Mid-US = 116 gallons
West Coast = 21 gallons
Step-by-step explanation:
Complete Question
Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast to $3 in the mid-US, to $5 on the west coast.
(a) If they used twice as much gas in the mid-US than on either coast combined, and they spend $515 on gas to purchased 150 gallons of gas, how many gallons of gas did they buy at each price?
The answer to this question is East Coast - 35 gal, Mid-US - 100 gal, West Coast - 15 gal.
(b) On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price? I don't know the answer to this one
Solution
Let the amount of fuel bought on the east coast = x gallons
Let the amount of fuel bought on the mid-coast = y gallons
Let the amount of fuel bought on the west coast = z gallons
a) - They used twice as much gas in the mid-US than on either coast combined
y = 2(x + z) = 2x + 2z (eqn 1)
- They spend $515 on gas to purchase 150 gallons of gas.
Total gallons purchased = x + y + z = 150
Total amount spent = 4x + 3y + 5z = 515
From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations
x + y + z = x + 2x + 2z + z = 150
3x + 3z = 150
Divide through by 3
x + z = 50 (eqn *)
4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 515
4x + 6x + 6z + 5z = 515
10x + 11z = 515 (eqn **)
x + z = 50
10x + 11z = 515
Solving the simultaneous equation,
x = 35 gallons
z = 15 gallons
y = 2x + 2z = 2(35 + 15) = 100 gallons
B) On the return journey, the ratio between x, y and z is still the same, but the total gallons and total amount spent is now different.
They used twice as much gas in the mid-US than on either coast combined
y = 2(x + z) = 2x + 2z (eqn 1)
- They spend $601 on gas to purchase 174 gallons of gas.
Total gallons purchased = x + y + z = 174
Total amount spent = 4x + 3y + 5z = 601
From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations
x + y + z = x + 2x + 2z + z = 174
3x + 3z = 174
Divide through by 3
x + z = 58 (eqn *)
4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 601
4x + 6x + 6z + 5z = 601
10x + 11z = 601 (eqn **)
x + z = 58
10x + 11z = 601
Solving the simultaneous equation,
x = 37 gallons
z = 21 gallons
y = 2x + 2z = 2(37 + 21) = 116 gallons
Hope this Helps!!!
50. Express
-44 in the form bi where b is a real number.
TIME SENSITIVE‼️‼️‼️
Answers
Answer:
A
Step-by-step explanation:
i is the same as negative squareroot of one. Then you have 2 squareoot of 11 which is the same as squareroot of 44
State the degree of each expression.
1) 10x10 + x
Answers
Answer:
10x10x10
Step-by-step explanation:
Thus, shown in long form, a power of 10 is the number 1 followed by n zeros, where n is the exponent and is greater than 0; for example, 106 is written 1,000,000. When n is less than 0, the power of 10 is the number 1 n places after the decimal point; for example, 10−2 is written 0.01. if im not right i tried to fix the math question
I NEED HELP FAST, 20POINTS
Which of the following statements is true?
| A | < | D |
A + B = D
C ≥ D
| B | > C
Answers
Answer:
| A | < | D |
Step-by-step explanation:
| A | is going to be 4 units since A = -4
| D | i sgoing to be 3 units since D = 3
Answer:
The answer is |A|< |D|
Step-by-step explanation:
Just did it and it was right
Miguel stated that any monomial can be a cube root. Sylvia disagreed and said that a monomial cube root must have exponents divisible by 3. Who is correct, and why?
Sylvia is correct. Any variable term, when it is cubed, always has an exponent divisible by 3.
Miguel is correct. Any monomial can be a perfect cube root because, when it is cubed, the variables will have exponents divisible by 3.
Sylvia is correct. In order for the cube to have exponents that are divisible by 3, the cube root has to be divisible by 3.
Miguel is correct. Sylvia confused the perfect square root with the perfect cube root.
Answers
Option B. is correct
Polynomial equation are equation of number independent variables having relationship with dependent variable.
Since,
A monomial can have higher exponents so its exponents has probability to get divisible by 3 so when cube root for monomial performed.
for example [tex]\sqrt[3]{x^3}[/tex] = x
Thus, Miguel is correct. Any monomial can be a perfect cube root because, when it is cubed, the variables will have exponents divisible by 3.
Learn more about polynomial here:
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#SPJ2
Answer:
option B
Step-by-step explanation:
edge 2023
What is the negative square root of 4,900?
Answers
Answer: -70
Step-by-step explanation: hope I helped
The United States five-dollar bill are 155.956 mm long and 66.294 wide. A stack of these bills fits inside a 156 x 66.3 x 66.3 mm box and uses up 258,473.68 cubic millimeters of volume.
Part A: How much money is in the box?
Part B: What percent of the box’s volume is taken up by the five-dollar bills?
Answers
Answer:
A) $5 × 25 = $75
B) 37.69%
Step-by-step explanation:
The dimension of five dollar bill:
Length = 155.956mm
Width = 66.294
Volume of box being occupied by 5 dollar bill = 258,473.68mm^3
Dimension of box :
156 x 66.3 x 66.3 mm
If volume of the 5—dollar bill is 258,473.68mm^3
Then, the Thickness of the five dollar stack equals :
Volume = Length × width × height
258,473.68mm^3 = 155.956mm × 66.294 × height
258,473.68 = 10338.947064 × h
h = (258473.68/10338.947064)
h = 25.000000003288 = 25
Therefore, the amount of money in the box is:
$5 × 25 = $75
Percentage of box volume taken up by $5 bill
Volume of the box:
156 x 66.3 x 66.3 mm = 685727.6399mm^3
Volume of box being occupied by 5 dollar bill = 258,473.68mm^3
(258,473.68 / 685727.6399) × 100
=37.69%
Identify the outlier of the data set.
3,4,4,5,5,6,6,7,7,7,8,20
a
20
b
8
oooo
C
6.8
d
3
Answers
Answer:
a.20
Step-by-step explanation:
20 is standing out from the rest of the numbers
the lines below are parallel. If the green line has a slope of 5, what is the slope of the red line? Enter your answer as an integer or fraction in lowest terms
Answers
Answer: 5
Step-by-step explanation: As a rule, parallel lines will always have the same slope. What that means is that if you're told that 2 lines are parallel, the slopes will be exactly the same for both of them.
So if the green line has a slope of 5, the red
line also has a slope of 5.
Jimmy pumps 288,000 cubic centimeters of air into a spherical balloon. What is the radius of the balloon?
There are no options to choose from
Answers
Answer:
r: radius of balloon
V = (4/3)*pi*r^3 = 288000
=> r^3 = 288000*(3/4)/pi
=> r^3 = 68754.94
=> r = [tex]\sqrt[3]{68754.94}[/tex] = ~40.97 cm
Una caja grande cuesta lo mismo que tres pequeñas. Si 7 cajas grandes y 4 pequeñas cuestan $12 más que 4 grandes y 7 pequeñas ¿Cuál es el sistema de ecuaciones que modela el sistema?
Answers
Answer:
[tex] x = 3y [/tex]
[tex]7x+4y= 12 + 4x+7y[/tex]
Step-by-step explanation:
Para resolver la pregunta, basta con definir variables adecuadas y traducir cada relación. Sea x el costo de una caja grande e y el costo de una caja pequeña. Tenemos que el costo de una caja grande es igual a 3 cajas pequeñas. Es decir, x = 3y. Luego, tenemos que
[tex]7x+4y= 12 + 4x+7y[/tex]
pues al sumarle 12 al costo de 4grande y 7 pequeñas obtenemos el costo de 7 grande y cuatro pequeñas. De aquí, el sistema de ecuaciones que modela el sistema es
[tex] x = 3y [/tex]
[tex]7x+4y= 12 + 4x+7y[/tex]
Please help!
Find the interval of convergence for:
Please note: The 2 in the picture must actually also be an exponent, so n^2^n.
Answers
Answer:
-∞ < x < ∞
Step-by-step explanation:
∑ xⁿ / n^(2ⁿ)
Apply ratio test:
lim(n→∞) | [xⁿ⁺¹ / (n+1)^(2ⁿ⁺¹)] / [xⁿ / n^(2ⁿ)] |
lim(n→∞) | [xⁿ⁺¹ / (n+1)^(2ⁿ⁺¹)] × [n^(2ⁿ) / xⁿ] |
lim(n→∞) | x n^(2ⁿ) / (n+1)^(2ⁿ⁺¹) |
0
The series converges for all values of x.
What is the slope of the line
Answers
the slope of the line above is -2
The original price of a jacket is $75 , you have a 25% off coupon, how much will you pay for the jacket
Answers
Answer:
18.75
Step-by-step explanation:
75 is the 100% price. If you divide 75 by two you will get the 50% price. Which is 37.5. If you divide that by two you will get the 25% price which is 18.75
The area of the quadrilateral below can be found be adding the areas of the distinct figures.
