NO LINKS!!! Please help me with this problem. PART 9
THIS IS NOT MULTIPLE CHOICE!!
a. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 100 feet from the base of the tower?
b. How long should a second guy wire be if it is to connect from the base on the flat side?
Answers
Answer:
a. 493 ft.
b. 269 ft.
Step-by-step explanation:
Please see the attached pictures.
a. Since we are interested in the length of AD, and ∆ABD does not have a right angle, we should think about using sine rule or cosine rule. We are only given two lengths in ∆ABD thus let's find one more angle, ∠ABD.
∠ABD= ∠ABC -∠CBD
∠CBD= 10° (given)
Since the tower should be vertically upright from the ground, we can assume that ∠ABC is 90°.
∠ABD= 90° -10°
∠ABD= 80°
With 2 lengths and 1 angle, we can apply cosine rule to find the length of the 3rd side:
[tex]\textcolor{steelblue}{{ {c}^{2} = {a}^{2} + {b}^{2} - 2abcosC}}[/tex]
(AD)²= 500² +100² -2(500)(100)(cos80°)
After simplifying and taking the square root of both sides, we obtain:
AD= 492.58 (5 s.f.)
AD= 483 (3 s.f.)
Thus, the guy wire has to be [tex]\textcolor{red}{{483 ft}}[/tex].
__________
b. Here, we make the assumption that the 500 ft. is excluding the height of the antenna and each square unit has the same height.
The tower is made up of 12 boxes, while the second guy wire is connected to the 6th box of the tower from the ground.
12 boxes ----- 500 ft
6 boxes ----- 500 ÷2= 250 ft
Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
Applying Pythagoras' Theorem,
x²= 100² +250²
x²= 72500
Taking the square root of both sides:
x= 269.26 (5 s.f.)
x= 269 (3 s.f.)
Thus, the length of the second guy wire is [tex]\textcolor{red}{{269 ft}}[/tex].
Answer:
a) 493 ft (nearest foot)
b) 269 ft (nearest foot)
Step-by-step explanation:
Part a
The guy wire creates a triangle with the tower with the following:
longest side = 500 ftshortest side = 100 ftangle between longest side and shortest side = 90 - 10 = 80°Therefore, as we have an angle with 2 adjacent side lengths, we can use the cosine rule to find the length of the unknown side opposite the angle.
cosine rule: c² = a² + b² - 2ab cos C
(where C is the angle, a and b are the sides adjacent the angle, and c is the side opposite the angle)
Substituting given values into the equation and solving for c:
c² = a² + b² - 2ab cos C
⇒ c² = 500² + 100² - 2(500)(100) cos(80°)
⇒ c² = 260000 - 100000cos(80°)
⇒ c = √[260000 - 100000cos(80°)]
⇒ c = 492.5801277...
Therefore, the length of the guy wire that is connected to the top of the tower and is secured at a point on the sloped side 100 ft from the base of the tower is 493 ft (nearest foot).
Part b
From inspection of the diagram, we can see that the second (left) guy wire is attached halfway up the height of the tower.
This guy wire creates a right triangle with the tower with the following:
height = 500 ÷ 2 = 250 ftbase = 100 ftTherefore, as we have the length of both legs of a right triangle, we can use Pythagoras' Theorem to find the length of the wire:
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Substituting given values into the equation and solving for c:
a² + b² = c²
⇒ 100² + 250² = c²
⇒ c² = 72500
⇒ c = √(72500)
⇒ c = 269.2582404...
Therefore, the length of the second guy wire is 269 ft (nearest foot)
Related Questions
I will mark brainlyist
What are the values of the variables in the triangle below?
Answers
Answer:
x=9
y=3√3
Use trig ratios
Answer:
x = 3sqr3, y = 9
Step-by-step explanation:
Use SOH CAH TOA, to solve this.
Here I know the hypotenuse, so I could use either SOH either CAH or both to find the 2 unknowns.
To find y, I would use SOH, which is Sin(angle) = opposite/hypotenuse.
When I rearrange it, I get Sin(angle)*hypotenuse = opposite. Now let's fill in with the values to give:
Sin(30)*6sqr3 = 3sqr3
And then to find x, let's use CAH, which is Cos(angle) = adjacent/hypotenuse.
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Cos(30)*6sqr3 = 9
I Need help on this question .
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x^2-y^2
Step-by-step explanation:
Foil (x+y)(x-y)=
x^2-xy+xy-y^2=
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What is the 6th term in the following sequence 48 40 32 24
Answers
Answer:
8
Step-by-step explanation:
48 - 8 = 40
40 - 8 = 32
...
so we can conclude that the next number in the sequence is the one before minus 8
24 - 8 = 16
16 - 8 = 8
2. A mountain climber descends a cliff at a rate of 2.5 ft/second.
a
Write an equation modeling the change in elevation c after s seconds.
Answers
Answer:
c=-2.5s
Step-by-step explanation:
The equation modeling the change in elevation c after s seconds is
c = -2.5s
Given,
A mountain climber descends a cliff at a rate of 2.5 ft/second.
We need to write an equation modeling the change in elevation c after s seconds.
How do we represent elevation and descent?Elevation means going up so we take it as a positive distance.
Descent means going down so we take it as a negative distance.
Find the rate at which the climber descents.
2.5 ft = 1 second
Find the equation that represents the descents c in seconds.
We have,
2.5 ft = 1 second
So,
s x 2.5 ft = s x 1 seconds
2.5 s ft = s seconds
This means,
In s seconds we will have a 2.5s distance descended.
We can write this as an equation:
c = change in elevation
c = - 2.5s
Thus the equation modeling the change in elevation c after s seconds is
c = -2.5s
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how do you do this?
Answers
========================================================
Explanatoin:
There are a number of ways to do this type of problem. One way is to divide the figure as shown in the diagram below. See the attached image.
I'm splitting the irregular shape into two rectangles and a triangle.
The upper rectangle is 10 miles by 9 miles to get an area of 10*9 = 90 square miles. Let A = 90 so we can use it later.
The lower rectangle is 4 miles by 19 miles. Its area is 4*19 = 76 square miles. Let B = 76.
The total vertical height of the figure is 9+4+10 = 23 miles.
Notice along the column that has "8 miles" up top over "9 miles" down below, we have a gap of some distance which I'll call x. This x adds to 8 and 9 to get the 23 mentioned.
x+8+9 = 23
x+17 = 23
x = 23-17
x = 6
This helps find the height of the triangle which is 9+x = 9+6 = 15 miles.
The triangle has a base of 9 miles.
The area of the triangle is base*height/2 = 9*15/2 = 135/2 = 67.5 square miles. Let C = 67.5
--------------
We found that:
A = 90 = area of the upper rectangleB = 76 = area of the lower rectangleC = 67.5 = area of the triangleThe total area is: A+B+C = 90+76+67.5 = 233.5 square miles.
Convert 4.5% to a decimal
Answers
Answer:
0.045
Hope this helpful! Have a great night/day!
Answer:
0.045
Step-by-step explanation:
To convert a percent to a decimal, just move the decimal point 2 spaces to the left.
......................
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Answer:
the answer is in the picture
Which values are solutions to the inequality x < 15
Answers
Answer:
{x|x<15}
Step-by-step explanation:
all real numbers less than 15
pls brainliest im hardstuck ambitious
What is the solution to the equation below? 5^x=26
Answers
log5 5^x = log5 26
(log 5 & 5 cancel out)
x = log5 26
use change of base formula
x = (log 26)/(log 5)
^ if you need an exact number just put that into any calculator
Suppose that the water level of the McBride River is at 34 feet above flood stage and that it is receding
(going down) at a rate of 0.3 ft per day.
Write a linear equation to represent the how far the McBride River is above flood stage.
Answers
Answer:
y= -0.3x + 34
Step-by-step explanation:
y=mx+b
y= -0.3x + 34
Is 32 cm bigger than 315 mm
Answers
Answer:
Yes! 32 cm is 320 mm. I hope this helps you
Step-by-step explanation:
Answer:
32 centimeters are equal to 320 millimetres, so if compare the two:
315 __ 320
315 < 320, therefore 32 centimeters is bigger than 315 millimetres
) Lori and Jayden open 6 packs of baseball cards. They have 72 cards in all.
They want to know how many cards, c, were in each pack.
Answers
Answer:
12
Step-by-step explanation:
Since there are 6 packs in all, and a total of 72 cards, we can multiply 6×12=72
There were 12 cards in each pack if they have 72 cards in all.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Lori and Jayden crack open six packs of baseball cards. They have a total of 72 cards.
As per the given question, the required solution would be as;
Lori and Jayden have 6 packs × c cards/pack = cards in total.
This means that there are c = 72 cards / 6 packs = 12 cards in each pack.
Therefore, there were 12 cards in each pack.
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WHO CAN FILL IN THE VALUES OF THE TABLE. i dont understand. please, please help.
If you can also tell me what "employment-to-population ratio" is, what "labor force participation rate" is, "unemployment rate" all using the values of the table, i will make you brainiest.
Answers
Answer:
Total Population = Young & Institutionalized + Working Age Population
Working-Age Population = Labor Force + Not in the Labor Force
Labor Force = Employed + Unemployed
Total population = 400
Working Age Population = 300
Young & Institutionalized = 100
Not in Labor Force = 100
Labor Force = 200
Employed = 150
Unemployed = 50
Employment-population ratio = (Employed ÷ Working Age Population) x 100%
= (150 ÷ 300) × 100%
= 50%
Labor force participation rate = (Labor Force ÷ Working Age Population) x 100%
= (200 ÷ 300) × 100%
= 66.7% (nearest tenth)
Unemployment rate = (Unemployed ÷ Labor Force) x 100%
= (50 ÷ 200) x 100%
= 25%
look for numbers in place of the letters such that the following mathematical expression hold PRQ/3=OV UVW/6=OV MNO/9=OV
Answers
Answer:
PRQ/3
Step-by-step explanation:
it is done by adding the first two
Factor completely.
x2−14x+48
Answers
Answer: -14x
48+x
2
−14x
I will mark brainlyist if correct Please help!
Answers
Answer: C: 5r + 12
Step-by-step explanation:
2(3r + 7) - (2 + r)
6r + 14 - 2 - r
5r + 12
Which function is shown in the graph below?
Answers
Answer:
B
Step-by-step explanation:
From the graph, we know when x -> -∞, y -> 3
Note x -> -∞, 2^x -> 0
so only A and B may be right.
Note y-intercept is 7 when x = 0, so only B is right
A basket of goods and services is used to calculate CPI. Assume that the basket contains 5 toothbrushes and 2 tubes of toothpaste. The prices for those goods are shown in the table.
Year Toothbrush Tube of Toothpaste
year 1 $1.00 each $2.00 each
year 2 $1.25 each $2.10 each
What will the CPI for year 2 be?
A.
9.00
B.
10.45
C.
86.00
D.
116.11
Answers
The Consumer Price Index for the year 2 be 116.11.
How do we calculate Consumer Price Index?This is calculated by adding together a sampling of product prices from a previous year.
We then add together the current prices of the same products and divide the total of current prices by the old prices, then multiply the result by 100.
Given data
Year 1 = $9
Year 2 = $10.45
Year 2 / Year 1 = $10.45 / $9.00
Year 2 / Year 1= 1.6111
CPI for year 2 = 1.61 x 100
CPI for year 2 = 116.11
Therefore, the Option D is correct.
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I bought x cans of fruit cocktail and two more cans of mushrooms than cans of fruit cocktail. A can of mushrooms cost $.80 and a can of fruit cocktail cost $.90. How much money did I spend?
Answers
Answer:
0.9x + 0.8(x + 2)
Step-by-step explanation:
# of cans of fruit cocktail: x
# of cans of mushrooms: 2 more than x, or x + 2
$ of can of mushroom: $0.80
$ of can of fruit cocktail: $0.90
To find out how much money you spent, you need to multiply the # of cans by their respective prices. Therefore:
The price of the cans of fruit cocktail = 0.90 * x
= 0.9x
The price of the cans of mushrooms = 0.80 * (x + 2)
= 0.8(x + 2)
Total price = 0.9x + 0.8(x + 2)
If 32 − x = 16, what is the value of x?
Answers
Answer:
32-16=x
x=16 that's your answer
Answer ๑•ᴗ•๑
[tex]32 - x = 16 \\ - x = 16 - 32 \\ - x = - 16 \\ x = 16[/tex]
solve using the zero product property:
10x^2 - 13x = 3
with explanation pls; will give brainliest
answer should be: -1/5 and 3
Answers
10x^2 - 13x = 3 a = 10, b = -13, c = -3 (quadratic formula? icba to write it sos!!)
-3 both sides
10x^2 - 13x - 3 = 0 -3 x 10 = -30 (products of -30 and equal to -13 are 15, -2 (so we use this))
10x^2 - 2x + 15x - 3 = 0
factorising now
2x (5x - 1) + 3 (5x - 1)
the brackets have to be the same
(2x + 3) (5x - 1)
2x - 3 = 0 ——— 5x + 1 = 0 (switch the signs forgot y tbf)
add 3 to both sides ——— minus 1 on sides
2x = 3 ——— 5x = -1
divide by 2 both sides ——— divide both by 5
x = 3/2 ——— x = -1/5
naw cus I spent so long on this for the answer to be wrong dam-n
11. Suppose ∆ ≅ ∆. Which choice below shows corresponding parts to congruent triangles that are
congruent? Explain your answer.
Answers
Answer:
CStep-by-step explanation:
Cross out B and D, because angle D does not correspond with Y and Angle F does not correspond with X (order matters).
It comes down to either A or C, so look at the sides.
DF does not correspond to XY, again, the order it is displayed matters.
D is the first letter and F is the last, while X is the 2nd letter of the triangle, while it should be the first letter to correspond with D
Thus by Process of Elimination the answer is C.
(Also DF DOES correspond with WY)
Use the Pythagorean Theorem to
find the distance between
(1,1) & (-5,-4)
Answers
Answer:
Use the formula which is shown above.
Find the missing angle
Answers
Answer:
Step-by-step explanation:
2x + 3x = 90
5x = 90
Divide both sides by 5
x = 90/5
x = 18
Angles are: 3x = 3*18 = 54°
2x = 2*18 = 36°
What kind of building material has the cheapest premiums?
helllllllllllllllllllllp me
Answers
Answer:
well theres prefabricated panel, concrete sheets, reclaimed wood, bamboo, brick those are the cheapest materials you could use
Step-by-step explanation:
Gabe is in a hot air balloon that has taken off and is floating now 7 meters above it's launching point. Adele is standing on the ground, 6 meters away from the launching point. How far apart are Gabe and Adele? If necessary, round to the nearest tenth.
[I need help]
c^{2} = b^{2} +a^{2}
use a right triangle
Answers
Answer:
9.2 m
Step-by-step explanation:
The right triangle model is shown in the attachment. The lengths 6 m and 7 m are the legs of the triangle, and the requested distance is the hypotenuse. The given Pythagorean theorem equation can be used to find the desired distance:
c² = a² +b²
c² = 7² +6² = 49 +36 = 85
c = √85 ≈ 9.2
Gabe and Adele are about 9.2 meters apart.
a quadrilateral is a polygon with 4 sides. A rhombus is a quadrilaterial with 2 sets of parallel sides and 4 congruent sides. Which of the following is both.a quadrilateral and a rhombus
Answers
need more info to help need the picture
The line plot above shows the distance in miles Luna runs each day. What is the difference in distance between the fewest miles she ran and the most miles she ran in a day?
Answers
Answer:
The answer is 4
Step-by-step explanation:
The formula d= 2a relates the area (A) of a square and its diagonal length (d). What is the area
of a square if its diagonal has a length of 50 centimeters?
Answers
Answer:
my answer is 24 and this question is somehow a hard for me because I'm just saying yes to
Aiden has a gross income of $63,000 and takes the standard deduction. Their total taxes due are $6,847.50.
What is their taxable income?
What is their marginal tax rate?
What is their effective tax rate? Round to the nearest hundredth of a percent.
Answers
If their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.
Taxable incomea. Taxable income:
Taxable income=Gross income - Total taxes due
Taxable income=$63,000-$6,847.50
Taxable income=$56,152.5
b. The marginal tax rate for taxable income under the income bracket of of $40,526 to $86,375 is 22%.
c. Effective tax rate:
Effective tax rate = Total taxes due/ Taxable income×100
Effective tax rate =$6,847.50/$56,152.5×100
Effective tax rate =10.869%
Effective tax rate =10.87% (Approximately)
Inconclusion if their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.
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