A helicopter is flying at an elevation of 575 feet directly above a horizontal highway. Two motorists are driving cars on the highway. The angle of depression to one car is 28° and the angle of depression to the other car is 35°. How far apart are the cars to the nearest foot?
Answers
Answer:
Distance between cars rounded to the nearest foot is : 1903 ft
Step-by-step explanation:
Notice that two right triangles can be used to represent the diagram of this situation. One between the car whose angle of depression is [tex]28^o[/tex], and the other with the car with angle of depression [tex]35^o[/tex] (see attached image)
Each triangle in the attached image is depicted with a different color. and as one can see, the distance between both cars is the addition of the side "x" in one triangle, to the side "y" in the other.
Notice as well that the information known for both right-angle triangles is one acute angle, and the side opposite to it. And what one needs to find is the side adjacent to this acute angle. Then, the function to use in both triangles, is the tangent:
a) For the [tex]28^o[/tex] [orange] triangle :
[tex]tan(28^o)=\frac{575}{y} \\y=\frac{575}{tan(28^o)} \\y=1081.42\,\,ft[/tex]
b) For the [tex]35^o[/tex] [green] triangle:
[tex]tan(35^o)=\frac{575}{x} \\y=\frac{575}{tan(35^o)} \\y=821.19\,\,ft[/tex]
Therefore the total distance between cars is:
1081.42 ft + 821.19 ft = 1902.61 ft
which to the nearest foot can be rounded as: 1903 ft
Both the cars driven by the motorists on the highway are 1903 feet apart.
Angle of eleveation and angle of depression: Angle of elevation or depression is the angle between the line of sight and the horizontal line. Angle of elevation and angle of depression form an observer are equal in measure for the same object.
Given in the question,
Helicopter is flying at point A from which two cars at C and D are being observed. Elevation of the helicopter is 575 feet. Angle of depressions of both the cars are 35° and 28°.From right triangle ABC,
[tex]\text{tan}(35^\circ)=\frac{AB}{BC}[/tex]
BC = [tex]\frac{AB}{\text{tan}35^\circ}[/tex]
= [tex]\frac{575}{\text{tan}35^\circ}[/tex]
= 821.19 feet
From right triangle ABD,
[tex]\text{tan}(28^\circ)=\frac{AB}{BD}[/tex]
[tex]BD=\frac{575}{\text{tan}28^\circ}[/tex]
= 1081.42 feet
Distance between the cars (CD) = BC + BD
= 821.19 + 1081.42
= 1902.61 feet
≈ 1903 feet
Therefore, distance between the cars is 1903 feet.
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Related Questions
Please help me in this question.Tell me if it is good. And if it is not good then do it for me please.
Answers
Answer:
Y = 170, Z = 64.
Step-by-step explanation:
Since y is the external angle to x, which you got right, it is in fact, 180-10, = 170 degrees. And since z is the external to our unknown angle, that means it is equal to the sum of the other two angles in the triangle. That means z is 54 + 10, which is 64.
22 points !!! multiply. express your answer as a fraction simplest form. 8.33 x 144
Answers
Answer:
100
Step-by-step explanation:
Let's convert both numbers into fraction form.
let x=8.33 bar
x=8.33 bar
10x=83.33 bar
9x=75
x=25/3
[tex]\sqrt{144}=12[/tex]
[tex]\frac{25}{3}*\frac{12}{1}=25*4=100[/tex]
The value of 8.33 x ✓144, when expressed as a fraction in its lowest term will be 100.
Since the expression given is 8.33 x ✓144 l, we have to convert them to fraction firstly and this will be:
= 25/3 × √144
= 25/3 × 12/1
= 25 × 4
= 100
Therefore, the value is 100.
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The lateral area of a cone is 86 cm squared. The radius is 18 cm. Find the slant height to
the nearest tenth.
Answers
Answer:
1.5 cm
Step-by-step explanation:
The lateral area is given by ...
LA = πrh
86 cm^2 = π(18 cm)h
h = (86 cm^2)/(18π cm) ≈ 1.5 . . . cm
_____
Comment on the problem
The geometry described here is impossible. The slant height cannot be less than the radius of the cone. We suspect a typo in the problem statement.
whats the middle number in between 12 and 17
Answers
Answer:
The middle number would be (14+15)/2 = 14.5
How I found that is I did (14+15)/2.
pls mark as branliest
There are 2076 people at a concert.One third of the people at the concert are under thirty years old.How many people are under thirty years old?
Answers
= 1/3*2076
= 693 people were under 30 years old
Hope it helped !!!!
Comment below
The people are under thirty years old is 692.
It is required to find the people are under thirty years old.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
There are 2076 people at a concert.
One third of the people at the concert are under thirty years old.
According to given question we have,
Total number of people at a concert= 2076
Multiply 2076 by 1/3 we get,
= 1/3*2076
= 692 people were under 30 years old
Therefore, the people are under thirty years old is 692.
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Terry has a credit card that uses the average daily balance method. For the first 18 days of one of his billing cycles, his balance was $350
Answers
Complete question:
Terry has a credit card that uses the average daily balance method. For the first 18 days of one of his billing cycles, his balance was $350, and for the last 12 days of the billing cycle, his balance was $520. If his credit card's APR is 14%, which of these expressions could be used to calculate the amount Terry was charged in interest for the billing cycle?
(0.14/365 31)(18 $350 + 12 $520 / 31)
(0.14/365 30)(18 $350 + 12 $520 / 30)
(0.14/365 30)(12 $350 + 18 $520 / 30)
(0.14/365 31)(12 $350 + 18 $520 / 31)
Answer:
(0.14/365 30)(18 $350 + 12 $520 / 30)
Step-by-step explanation:
Number of days in a year = 365
Number of days in billing cycle = (18 + 12) = 30
Interest rate per year = 14% = 0.14
Amount charged monthly :
(Monthly rate × average daily balance)
MONTHLY RATE:
(Annual interest / number of days in year) * days in billing cycle
(0.14 / 365) × 30
Average daily balance :
First 18 days ; balance = $350
Last 12 days ; balance = $520
Sum of balance / days in billing cycle
[(18 × $350) + (12 × 520)] / 30
THEREFORE, MONTHLY INTEREST CHARGE :
((0.14 / 365) × 30) ((18 × $350) + (12 × 520) / 30)
Which statement correctly relates the standard deviation of the two data sets below? Data set 1 Data set 2 1 2 2 2 3 3 3 3 6 4 4 Answer choices: A.) The standard deviation of Data Set 1 is less than the standard deviation of Data Set 2. B.) The standard deviation of Data Set 1 is equal to the standard deviation of Data Set 2. C.) The standard deviation of Data Set 1 is about twice the standard deviation of Data Set 2.
Answers
Answer:
C.) The standard deviation of Data Set 1 is about twice the standard deviation of Data Set 2.
Step-by-step explanation:
Data Set 1: 1,2,3,3,6Data Set 2: 2,2,3,3,4,4Data Set 1
[tex]\mu =\dfrac{1+2+3+3+6}{5}= \dfrac{15}{5}=3[/tex]
[tex]S$tandard Deviation, \sigma =\sqrt{\dfrac{\sum (x-\mu)^2}{N}}[/tex]
[tex]\sigma =\sqrt{\dfrac{(1-3)^2+(2-3)^2+(3-3)^2+(3-3)^2+(6-3)^2}{5}}\\=\sqrt{\dfrac{4+1+0+0+9}{5}}\\=\sqrt{\dfrac{14}{5}}\\\\=1.67[/tex]
Data Set 2
[tex]\mu =\dfrac{2+2+3+3+4+4}{6}= \dfrac{18}{6}=3[/tex]
[tex]\sigma =\sqrt{\dfrac{(2-3)^2+(2-3)^2+(3-3)^2+(3-3)^2+(4-3)^2+(4-3)^2}{6}}\\=\sqrt{\dfrac{1+1+0+0+1+1}{6}}\\=\sqrt{\dfrac{4}{5}}\\\\=0.89[/tex]
0.89 X 2=1.78 which is close to 1.67
Therefore, the standard deviation of Data Set 1 is about twice the standard deviation of Data Set 2.
Which equation represents a line that passes through (2, –left-parenthesis 2, negative StartFraction one-half EndFraction right-parenthesis.) and has a slope of 3?
Answers
Answer:
I'm not sure what your choices are or if you have any choices. Try y+ 1/2 = 3(x-2)
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
on edg2021
Which investment account can be used to save for post-secondary education? traditional IRA, 403(b), flexible spending account (fsa), 529 plan, or 401(k)
Answers
Answer:
529 plan
Step-by-step explanation:
The 529 plan investment account is a type of account used to save for future education purposes and are sponsored by educational institutions and the state. They are of two types, The prepaid tuition plan and the education saving plan. The prepaid tuition plan is used to pay for future tuition fee at present rates while the education saving plan are used to pay for qualified education expenses
Answer:
529 plan
Step-by-step explanation:
A 529 college savings plan works much like a Roth 401(k) or Roth IRAby investing your after-tax contributions in mutual funds, ETFs and other similar investments. Your investment grows on a tax-deferred basis and can be withdrawn tax-free if the money is used to pay for qualified higher education expenses.
A rancher has 4,200 feet of fencing available to enclose a rectangular area bordering a river. He wants to separate his cows and horses by dividing the enclosure into two equal areas. If no fencing is required along the river, find the length of the center partition that will yield the maximum area.
Answers
Answer:
The center portion's length will be "700 ft".
Step-by-step explanation:
Let the center will be "x".
Given that, Length = 4200 feet
Now, Length
⇒ [tex]L=3x+y[/tex]
⇒ [tex]4200=3x+y[/tex]
⇒ [tex]y=4200-3x[/tex]
As we know,
Area,
⇒ [tex]A=Length\times breadth=x\times y[/tex]
⇒ [tex]=x(4200-3x)[/tex]
⇒ [tex]=4200x-3x^2[/tex]
So that the length or center portion or the area will be greater or maximum when:
⇒ [tex]x=-\frac{4200}{2\times (-3)}[/tex]
⇒ [tex]=\frac{-4200}{-6}[/tex]
⇒ [tex]=700 \ ft[/tex]
Solve the exponential equation. 16x = 0.5 -4 -1/4 1/4
Answers
Answer:
x = -1/4
Step-by-step explanation:
16 ^x = 1/2
Rewiting as
2^4^x = 2 ^ -1
We know that a^b^c = a^(b*c)
2 ^ (4x) = 2^ -1
The bases are the same so the exponents are the same
4x = -1
Divide by 4
4x/4 = -1/4
x = -1/4
Ginger's puppy weighed pounds when she first took him home. The veterinarian said the puppy cannot eat dry dog food until he weighs pounds. How many pounds must the puppy gain before he can eat dry dog food?
Answers
Answer:
For someone to be able to answer this question you need to include the weights. Im trying to help but we cant help unless you give the amount of weight. :(
Step-by-step explanation:
Answer:51-75 Pounds
Step-by-step explanation:
(16) 1/2+16
can someone help me with this question?
Answers
Answer:
24
Step-by-step explanation:
16(1/2)+16
8+16
24
Answer: 24
Step-by-step explanation:
16 times 1/2 is 8
Then 8+16= 24
Which property of equality was used to solve this equation? x − 5 = -14 x − 5 + 5 = -14 + 5 x = -9 A.) addition property of equality B.) subtraction property of equality C.) multiplication property of equality D.) division property of equality
Answers
To solve the given equation, we will use the addition property of equality.
What is the addition property of equality?The addition property of equality states that when the same quantity is added to both sides of an equation, it produces an equivalent equation.
For numbers a, b, and c, if a = b then a + c = b + c.
Given is an equation, x - 5 = -14,
We are asked to identify, that, which property of equality was used to solve this equation,
Solving the equation,
x - 5 = -14
Add 5 to both sides,
x-5+5 = -14+5
x = -9
Since, we used addition, therefore, this property is addition property of equality.
Hence, to solve the given equation, we will use the addition property of equality.
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Which equation is the inverse of y=x^2 + 4?
Answers
Answer:
y = √(x - 4)
Step-by-step explanation:
To find the inverse, simply swap x and y in your equation, then solve for in terms of y. Keep in mind that this isn't the true inverse of y = x² + 4 because y = √(x - 4) has a restricted domain.
Answer:
B. y = √(x - 4)
Step-by-step explanation:
Edge 2020 2021
Please help me solve number 14 and 15
Answers
Answer:
Step-by-step explanation:
Similarity property,
" If the two triangles are similar then their corresponding sides will be proportional."
14). If ΔPQR ~ ΔUVW,
[tex]\frac{PQ}{UV}=\frac{QR}{VW}=\frac{PR}{UW}[/tex] [Statement}
[tex]\frac{15}{10}=\frac{9}{6}=\frac{6}{4}[/tex]
[tex]\frac{3}{2}=\frac{3}{2}=\frac{3}{2}[/tex] [True}
Therefore, ΔPQR ~ ΔUVW [Theorem - SSS]
15). If ΔFHE ~ ΔDHG,
[tex]\frac{EH}{HG}=\frac{HF}{DH}[/tex] [Statement]
[tex]\frac{24}{6}=\frac{36}{9}[/tex]
4 = 4
Therefore, ΔFHE ~ ΔDHG [Theorem - AA]
Using the frequency table below, what is the probability of people that are not boys? 10% 20% 30% 50%
Answers
Answer:
50%
Step-by-step explanation:
Out of the 200 total people, 100 of them are not boys (the only people on this table who are not boys are girls) so the probability is 100 / 200 = 1 / 2 = 50%.
pls answer. i will mark as branliest
Answers
Answer:
The supplement to 101° is 79° (since 180 - 101 = 79) so that means, using the exterior angle formula, we can write:
x = 38 + 79 which simplifies to x = 117°.
Answer:
117 degrees
Step-by-step explanation:
38* is one inside angle
to find the other you got to find the rest if you do 180-101 you get 79.
all interior angles of a triangle add up to 180 aswell so 38+79=180 so subtract 180 from those 2 added up and you get 63* now that is the right bottom angle but don't forget a line is 180* so now we do 180-65 and you get 117
OK sorry i had it wrong apparently i cant read
Mark wants to fence 4 rectangular gardens, each with a length of 9 1/4 feet and a width of 4 1/2feet. What is the length of fencing mark needs to surround all 4 gardens
Answers
Answer:
110 ft
Step-by-step explanation:
The length of fencing is four times the perimeter of one garden.
The formula for the perimeter of a rectangle is
P = 2l + 2w
The total perimeter for all four rectangles is
P = 4× (2l + 2w) = 8l + 8w
Data:
l = 9¼ ft
w = 4½ ft
Calculation:
P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft
The total length of fencing is 110 ft.
Dan rolls 2 fair dice and adds the results from each. Work out the probability of getting a total less than 3. Answer pls its my h/w
Answers
Answer:
There are 6 * 6 = 36 total outcomes from throwing 2 dice. Of those, there is only 1 that will give you a sum less than 3 (1 + 1) so the answer is 1 / 36.
(I'LL MARK U BRAINLIEST BUT PLS HELP FIRST)
Care packages cost $6.25 each and certificates cost $4.50 each. Mr. Fernandes has a budget of $550 to purchase both care packages and certificates. If he purchases 45 certificates, what is the maximum number of care packages he can purchase?
A) State maximum number of care packages he can purchase
B)Explain how you got it
Answers
Answer:
55
Step-by-step explanation:
find how much it costs to buy 45 certificates, subtract that from the original budget then divide that by 6.25 and remove the decimals
Answer:
He can buy up to 55 care packages
Step-by-step explanation:
c = certificates
p = packages
6.25p + 4.50c ≤ 550
c = 45
6.25p + 4.50(45) ≤ 550
6.25p + 202.50 ≤ 550
Subtract 202.50 from each side
6.25p + 202.50 -202.50 ≤ 550-202.50
6.25p ≤ 347.50
Divide each side by 6.25
6.25p/6.25 ≤ 347.50/6.25
p ≤ 55.6
Since we cannot buy part of a care package
p ≤55
MY BRAIN IS DEAD! PLS HELP MEH ITS THE LAST ONE! TYSM! Time taken for 6 people to build a house is 30 days. How many days will it take for 2 people to build the same house ? (You need to think if this is a direct or inverse proportion problem).
Answers
Answer:
2 people will take 90 days to complete the same house
Step-by-step explanation:
Given:
T1 = 30 days
P1 = 6
T2 = x
P2 = 2
This is an inverse proportion because if there are more people, less time will be taken to complete the house and vice versa.
So, We'll write it in the order of :
=> T1:T2 = P2:P1
=> 30:x = 2:6
Writing in fraction form
=> [tex]\frac{30}{x} = \frac{2}{6}[/tex]
Cross Multiplying
=> 2x = 180
Dividing both sides by 2
=> x = 90 days
So, 2 people will take 90 days to complete the same house
Answer:
90 days
Step-by-step explanation:
6 people- 30 days
1 person- 30*6= 180 days
2 people- 180/2= 90 days
Which of the following graphs does not show a linear relationship?
Answers
Answer:
The answer is graph B
Step-by-step explanation:
Linear relationships mean that the lines on the graphs would be a straight line with a slope. But if the line were to be zigzagging like I'm graph B that means it's not a linear equation, doesn't have a linear relationship, or a linear graph. Hope this helps!
Which is a valid prediction about the continuous function f(x)?
Answers
Answer:
The answer is "f(x) ≥ 0 over the interval [-1, 1] and f(x) ≥ 0 over the interval [5, ∞)".
Step-by-step explanation:
In the given question function choices were missing so, the correct choices can be defined as follows:
f(x) ≥ 0 over the interval [-1, 1]
f(x) ≥ 0 over the interval [5, ∞]
The correct choice can be described in the following attachment table.
Answer:
A. f(x) ≥ 0 over the interval [5, ∞).
Step-by-step explanation:
I'll give BRAINLIEST!!
Answers
Answer:3
Step-by-step explanation:
The domain is the input (x) value look for 4 in the domain area and find the value in the range are that the arrow is pointing at.
The answer is 3
Jill earned $40 from a carpool plus $9 per hour (h) babysitting this week. Which of the following expressions best represents Jill's income for the week?
9 + 40h
9 + h + 40
9h + 40
9 + 40
Answers
Answer:
9h+40
Step-by-step explanation:
Jill is Guaranteed exactly 40$ so that stays the same. She will also earn 9$ every hour. This can be represented as 9 x number of hours or simply 9h.
So altogether, her original 40$ and her 9$ from every hour can be written together as 40 + 9h or 9h + 40.
(ps. this is my first answer, I apologise if Its not very detailed.)
The expressions best represent Jill's income for the week is 9h+40. The correct option is C.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that Jill earned $40 from a carpool plus $9 per hour (h) babysitting this week. The expression will be written as below:-
Jill is Guaranteed exactly 40$ so that stays the same. She will also earn 9$ every hour. This can be represented as 9 x the number of hours or simply 9h.
Her original 40$ and her 9$ from every hour can be written together as below:-
40 + 9h or 9h + 40.
Therefore, the expressions best represent Jill's income for the week is 9h+40. The correct option is C.
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Dalton has $44,759 in a savings account that earns 9% annually. The interest is not compounded. How much will he have in 1 year? Use the formula i=prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in a years.
Answers
Answer: total amount after 1 year will be 44759 + 4028.31 = 48,787.31
Step-by-step explanation:
SI = prt / 100
= 44759 x .09 x 1
= 4028.31
what is the value of sin teta if sec teta =-9/4 and teta is in the second quadrant
Answers
Answer:
Sin θ = √65/9
Step-by-step explanation:
Sec θ = -9/4
Sec θ = hypotenuse/base
So, hyp = 9, base = -4
Using Pythagorean Theorem to find perp
81 = 16 + P²
P² = √65
Now
Sin θ = Perp/Hyp
Sin θ = √65/9
Answer:
sin θ = [tex]\frac{\sqrt{65} }{9}[/tex].
Step-by-step explanation:
Remember that:
sec θ is the reciprocal of cos θ. Therefore:
cos θ = -4/9.
From this, we can derive that:
Adjacent side = -4.
Hypotenuse = 9
Use the Pythagorean Theorem to solve for the 'Opposite' side:
9² = (-4)² + b²
81 = 16 + b²
65 = b²
b = √65
sin θ = O/H, so:
sin θ = [tex]\frac{\sqrt{65} }{9}[/tex]
How do you combine radicals
Answers
Answer:
the numbers outside of the radical get multiplied together and the numbers under the radical get multiplied together. Then see if you can simplify more.
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIEST IF CORRECT
To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?
Answers
Answer:
Option (1)
Step-by-step explanation:
Diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 to 0.2 cm greater than 1.5 cm.
Let the diameter of the bolt = x cm
Then the value of x will be,
(1.5 - 0.2) cm < x < (1.5 + 0.2) cm
When we plot the possible measures of the diameter of the bolt on a number line,
Measures of x will be between 1.3 cm to 1.7 cm
Option (1) will be the answer.
Answer:
A
Step-by-step explanation:
Its pretty self explainatory, it tells you that the line has to be anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm, so if you look at the graphs A is the only one that maches with what the question in asking.