A helicopter flies between two islands that are 20 miles apart. The angle of elevation with one island is 15o and 35o with the second island. What is the mileage of the helicopter? Round your answer to the nearest tenth of a mile. (Law of Sines or Law of Cosines Problem)
Answers
Answer:
Step-by-step explanation:
From the figure attached,
A helicopter is flying at a height 'h' and angle of elevations from two islands C and B are 35° and 15° respectively.
Let the measure of BD = x miles
From ΔABD,
tan(15) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{h}{x}[/tex]
h = x.tan(15) ---------(1)
From ΔACD,
tan(35) = [tex]\frac{h}{12-x}[/tex]
h = (12 - x).tan(35) ------(2)
By equating the values of h from equations (1) and (2),
x.tan(15) = (12 - x).tan(35)
[tex]\frac{x}{12-x}=\frac{\text{tan}35}{\text{tan}15}[/tex]
[tex]\frac{x}{12-x}=2.613[/tex]
x = 2.613(12 - x)
x + 2.613x = 31.386
3.613x = 31.386
x = 9.914 ≈ 9.9 miles
From equation (1),
h = x.tan(15)
= 9.9[tan(15)]
= 2.65 ≈ 2.7 miles
Therefore, helicopter is flying at the vertical height = 2.7 miles and horizontal distance of the helicopter from the island B = 9.9 miles.
Answer:
2.7
Step-by-step explanation:
I took the quiz and got it right :)
Related Questions
y varies directly as x = 1/2 and y = 5/4. what is x when y is 60
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Answer:
X is 24
Step-by-step explanation:
mark me brainliest!!!!
find the length and breadth of a rectangular plot whose area is 660square metre and perimeter is 104metre
Answers
Answer:
Step-by-step explanation:
let length=l
breadth=b
l×b=660
2(l+b)=104
l+b=104/2=52
b=52-l
l×(52-l)=660
52l-l²=660
l²-52l+660=0
l²-22l-30l+660=0
l(l-22)-30(l-22)=0
(l-22)(l-30)=0
l=22,30
when l=22,b=52-22=30
when l=30,b=52-30=22
l>b
so l=30m
b=22m
Answer:
W = 22 m
L = 30 m
Step-by-step explanation:
given:
area is 660square metre and perimeter is 104metre
find:
the length and breadth of a rectangular plot
----------------------------------------------------------------
1. area of rectangle (A) = L x W
2. Perimeter of a rectangle (P) = 2L + 2W
where:
A = 660 m²
P = 104 m
solve for L using formula 1.
A = L x W
660 = L x W
L = 660 / W
solve W using formula 2 and use L = 660 / W
P = 2L + 2W
104 = 2 (660) + 2W
W
104W = 1320 + 2 W²
-2W² + 104W = 1320
solve W using quadratic equation:
W = 22 m; ( 30 m = L)
plugin W=22 into L = 660 / W to solve L:
L = 660 / 22
L = 30 m
The formula A = Pe^rt gives the balance A of an account earning what type of interest?
The formula A = Pert gives the balance A of an account earning interest compounded daily.
The formula A = Pert gives the balance A of an account earning interest compounded monthly.
The formula A = Pert gives the balance A of an account earning interest compounded continuously.
The formula A = Pert gives the balance A of an account earning interest compounded quarterly.
Answers
From the given options, Option (C) shows the type of compound interest earned.
Formula for the compound interest earned continuously is given by,
[tex]A=P.e^{rt}[/tex]
Here, [tex]A=[/tex] Final amount
[tex]P=[/tex] Principal amount
[tex]r=[/tex] rate of interest
[tex]t=[/tex] Time
Therefore, Option (C) will be the correct option.
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The robotics team needs to purchase $350 of new equipment. Each of the students on the team plans to fundraise and contribute equally to the purchase. Which expression represents the amount that each student needs to fundraise? Which expression represents the amount that each student needs to fundraise? Explain your thinking.
Answers
Answer:
s = students, m = money they pay
S(M)=350
The expression that represents the amount that each student needs to fundraise is - y = [tex]$\frac{350}{x}[/tex]
We have robotics team who needs to purchase $350 of new equipment.
We have to determine the expression which represents the amount that each student needs to fundraise.
In a class of 50 students, it was asked to collect a total of $3000 for NGO funding. Find the amount contributed by each student assuming they all pay the equal amount.Assume the amount paid by each student be x. Then -
50x = 3000
x = $60
According to the question, we have -
Assume that the number of students in the robotics team are x.
Assume that the money contributed by each member is $y.
Then, the expression represents the amount that each student needs to fundraise is -
xy = 350
y = [tex]$\frac{350}{x}[/tex]
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What is the length of AB? Round your answer to the nearest
hundredth. Hint: The nearest hundredth means the second place to
the right of the decimal point. This is not the answer! For example,
12.06
Ay
B
2.
х
-2
O
-2
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How to calculate the sin, cos, and tan. (Trigonometry)
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Answer:
Please see the attached picture for full solution.
solve for v bellow. 8(z-5)=16
Answers
Answer:
z=7
Step-by-step explanation:
8(z-5)=16
Divide by 8
8/8(z-5)=16/8
z-5 = 2
Add 5 to each side
z-5+5 = 2+5
z = 7
Answer:
z = 7
Step-by-step explanation:
Expand 8 ( z - 5 ) = 16 first.
8z - 40 = 16
Move 40 to the other side.
8z = 40 + 16
8z = 56
z = 7
what is a number expression that equals 68
Answers
4+5
134_75
56.4+6
68/8.7_2+1
evaluate the expression -8 + (-15)
Answers
Hey there!
ANSWER: [tex]-23[/tex]EXPLANATION:[tex]-8+(-15)[/tex]
To easily solve this, try removing the negative and add 8 + 15.
[tex]8+(15)=23[/tex]
Now add back the negative.
[tex]-8+(-15)=-23\\-23(ANSWER)[/tex]
Hope this helps and have a great weekend!
[tex]\text {-TestedHyperr}[/tex]
if 20 percent of item is 360,what is 85 percent of the item
Answers
() + -8= -6 what is the awnser
Answers
Answer:x=2
Step-by-step explanation:
change () to x
x + -8= -6
-6+8=2
x=2
Find the coordinates of the vertex of g(x) = |x + 1| - 2.
A. (-2, -1)
B. (-2, 1)
C. (-1, -2)
D. (1, -2)
Answers
Answer:
The vertex will be at ( -1,-2)
Step-by-step explanation:
g(x) = |x + 1| - 2.
The vertex of g(x) = |x | is ( 0,0)
y = f(x) + C C < 0 moves it down
y = f(x + C) C > 0 moves it left
We shift this to the left 1 unit and down 2 units
( 0 -1, 0-2)
The vertex will be at ( -1,-2)
Given: g(x) = |x + 1| - 2.
We start at g(x) = |x| at (0, 0)
c < 0 moves it down
y = f(x) + c
2 units down
c > 0 moves it left
y = f(x + c)
1 unit to the left
After the shift, we see the vertex being at (-1, -2).
Best of Luck!
please answer i need it fast!!!!!!!!
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145 is the answer bruh i cant type
Eliza's backpack weighs 18 and StartFraction 7 over 9 EndFraction pounds with her math book in it. Without her math book, her backpack weighs 14 and StartFraction 7 over 8 EndFraction pounds. How much does Eliza's math book weigh?
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its B sorry if Im wrong have a nice day
I’m trying to do the math but I keep getting mixed up. I keep forgetting wether or not I should add a zero.
This is the question by the way:
1.09 x 5.4
Answers
Find the distance between the points L(7, -1) and M(-2, 4).
Answers
Answer:
(5-5)
Step-by-step explanation:
hope this helped
Answer:Not correct
Step-by-step explanation:
Mrs. Start's class paid $5.60 for 4 5 yd of lace for an art project. Later, the class decided to buy another 7 3 4 yd of the same lace to make costumes for the school musical. How much money do they need for this second purchase?
Answers
Faucet A flows at a rate of 100 liters per 5 minutes and Faucet B flows at a rate of 100 liters per 4 minutes into an empty pool. How many minutes do the two faucets take to fill a pool with 9,000 liters of water?
Answers
Answer:
It will take both faucets 200 minutes to fill a pool with 9,000 liters of water
Step-by-step explanation:
Here, we want to know the time it will take for both faucets to fill a pool with 9,000 liters of water
What we need here is to have a joint rate for both faucets;
For the first faucet, we have a rate of 100 liters per 5 minutes so this means in a minute;
100/5 = 20 liters per minute
For the second faucet, the per minute rate will be 100/4 = 25 liters per minute
So therefore, the joint rate will be;
25 liters per minute + 20 liters per minute = 45 liters per minute
So the time needed to fill 9,000 liters of water in a pool will be ;
9000 liters/ 45 liters per minute = 200 minutes
The volume of a box 4inches wide and 2 inches high and 5 inches long is
Answers
Answer:
40
Step-by-step explanation:
4x2x5=40, the formula for volume is LxWxH=V length times width times height
I need a fast answer !! A bag has 7 blue marbles and 3 red marbles. What is the probability of drawing two red marbles, if the first marble is replaced after it is drawn? A. 1/7 B. 1/3 C. 3/10 D. 9/100
Answers
Answer:
Step-by-step explanation:
9/100 i believe as you would multiply 3/10 by 3/10 due to the fact the marble is being replaced so the probability of getting a red marble the second time will be more unlikely. If I'm right please thank me or give me brainly. Hope this helps :)
The probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.
What is Probability?
It is a branch of mathematics that deals with the occurrence of a random event.
The probability of drawing a red marble on the first draw is 3/10, since there are 3 red marbles out of a total of 10 marbles.
Since the first marble is replaced before the second draw, the probability of drawing a red marble on the second draw is also 3/10.
To find the probability of drawing two red marbles in a row, we multiply the probabilities of the individual events, since they are independent:
P(drawing two red marbles) = P(red on first draw) × P(red on second draw)
P(drawing two red marbles) = (3/10) × (3/10)
= 9/100
Therefore, the probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.
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1.) 6 quarts liters *(1 QUART = 0.946 LITERS) help please
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Answer:
Let me figure it out first then I will give you the answer.
Three boys cut out hundredths decimal models. Luke shades three fourths of one model. Owen shades four small squares of one model. Jacob shades two full models and nine tenths of another model. What decimal represents the amount each boy shades?
Answers
Answer:
Luke = 0.75
Owen = 0.04
Jacob = 2.9
Step-by-step explanation:
A model = 100 small squares
100 small squares = 1
Luke shades three fourths of one model.
Luke = 3/4 of 1 model
= 3/4 × 1
= 0.75
Owen shades four small squares of one model.
Owen = 4/100
= 0.04
Jacob shades two full models and nine tenths of another model
Jacob = 2 + 9/10
= 2 + 0.9
= 2.9
Luke = 0.75
Owen = 0.04
Jacob = 2.9
The purple shape is a dilation of the black shape. What is the scale factor of the dilation?
Answers
Am I correct with this?
Answers
Answer:
no
Step-by-step explanation:
u can cut the trapesoid in half and make it into a rectangle then get ur answer
It costs $200 for 12 piano lessons . Solve for unit rate or price per one lesson . Can someone help me please ?
Answers
Answer:
it is 16 dollars
Step-by-step explanation:
if you divide 200 by 12 it is 16 aka i used my calculator
Answer:
each lesson would cost $16.70
Lilyworks for a florist. She worked 20hours last week and earned $200.00. At that rate, how much will she earn if she works for 10 hours?
Answers
Answer:
$100
Step-by-step explanation:
Answer:
$100
Step-by-step explanation:
She will earn $100 because since 20 is just 10 times 2, she will earn half as much as she did in 20 hours. 200/2 is 100.
Carina spent a total of $5.27 buying a pineapple for $3.40 and some tomatoes that were on sale for $0.85 per pound. To determine the number of pounds of tomatoes that she bought, x, Carina wrote and solved the equation as shown below.
3.40 + 0.85 x = 5.27. 0.85 x = 8.67. x = 10.2 pounds.
Where, if anywhere, did Carina make an error?
Carina did not make any errors.
The initial equation that Carina wrote was incorrect.
Carina should have subtracted 3.40 from 5.27.
Carina should have divided 8.67 by 0.85.
Answers
Answer:
C. Carina should have subtracted 3.40 from 5.27
Step-by-step explanation:
I'm just smart like that
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The mistake that Carina made is she should have subtracted 3.40 from 5.27.
How many pounds of tomatoes was bought?The equation that represents the total amount spent is: $5.27 = $3.40 + $0.85x
In order to determine the value of x, take the following steps:
Combine similar terms: 5.27 - 3.40 = 0.85Add similar terms: 1.87 = 0.85xDivide both sides of the equation by 0.85: 2.2 poundsTo learn more about addition, please check: https://brainly.com/question/349488
Use elimination to solve and match each system of equations to the correct solution.
2x-9y=-51
2x-3y=-9
Answers
Answer:
2x-9y=-51
2x-3y=-9
subtract question ii from i we get
-6y = -42
y =7
put value of y in 1
2x - 63 = -51
2x= 8
x=4
-1/8n= -2/7 whats the n value?
Answers
Answer:
16 /7
Step-by-step explanation:
multiply both sides by -8 then simplify
8x^2+5=22x Need help learning factoring please put work so I can understand
Answers
Answer: (2x - 5) • (4x - 1)
STEP 1 : Equation at the end of step 1
(23x2 - 22x) + 5
STEP 2 : Trying to factor by splitting the middle term
2.1 Factoring 8x2-22x+5
The first term is, 8x2 its coefficient is 8 .
The middle term is, -22x its coefficient is -22 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 8 • 5 = 40
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is -22 .
-40 + -1 = -41
-20 + -2 = -22 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and -2
8x2 - 20x - 2x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (2x-5)
Add up the last 2 terms, pulling out common factors :
1 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(4x-1) • (2x-5)
Which is the desired factorization
Final result : (2x - 5) • (4x - 1)