A 170 ft tower is located on the side of a mountain that is inclined 19° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 46 ft downhill from the base of the tower. Find the shortest length of wire needed.
Answers
The shortest length of wire is 74.9 feet.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
Given:
A 170 ft tower is located on the side of a mountain that is inclined 19° to the horizontal.
A guy wire is to be attached to the top of the tower and anchored at a point 46 ft downhill from the base of the tower.
The visual representation of the phrase is given in the attached image.
Let b = 46 feet.
h = 70 feet.
And angle θ = 180 - 19 = 161°.
a = 46cos(161)
c = 46sin(161)
Then, the shortest length of the wire,
x = √{(h +c)²+(a)²}
x = √{(46 + 46sin (161))²+(46cos(161))²}
x = 74.9 feet
Therefore, the shortest length is 74.9 feet.
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Related Questions
The earth is approximately 93,000,000 miles from the sun how long does it take from the Sun to reach the earth use the speed of light to be 1.86×10^5 Miles per second
Answers
The light from the sun takes 8 minutes 20 seconds to reach the earth.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: The distance is 93,000,000 miles and the speed of light as 1.86×10⁵ miles per hour.
Now we know speed = Distance/ time
Thus we have Time taken = 93000000/1.86×10⁵
= 8 minutes 20 second (approx)
Hence, The light from the sun takes 8 minutes 20 seconds to reach the earth.
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(Look at picture) ty btw :)!!!!! <3
Answers
Answer:
Step-by-step explanation:
6
. The difference between two natural
numbers is greater than 6 and less than
11. The greater of the two numbers is 14.
How many possible values for the
unknown number are there?
Answers
Answer:
y = unknown number
3 < y < 8
Step-by-step explanation:
Let x and y be the two natural numbers
x - y > 6 and x - y < 11
6 < x - y < 11
x is still positive after y amount is taken away from it. Since y is part of x, x is the greater value.
Hence, x=14:
6 < 14 - y < 11 ==> solve for y, the missing value
-8 < -y < -3 ==> subtract 14 on all sides
8 > y > 3 ==> Since each side is being divided by -1, switch the inequality
signs since the numbers are being divided by a negative number
3 < y < 8 ==> rearrange the inequality
x/a+b=c. solve for x
Answers
what type of transformation is it
Answers
Answer:
Translation
Step-by-step explanation:
You're moving down 5 units, and left 1 unit, so therefore it's a translation 5 units down and 1 unit to the left.
Write an equation of the direct variation that includes the point (9, -12).
A. y = -1/2 x
B. y=-1½ x
C. y=1/3x
D. y=-3x
Answers
Answer:
none of these
Step-by-step explanation:
An equation in the form of direct variation is in the form
y = kx
Checking each equation and substituting the point
-12 = -1/2 (9)
-12 = -4.5 not true
-12 = -1 1/2 (9) = -3/2 *9 = -27/2 - 13.5
-12 = -13/5 not true
-12 = 1/3 (9)
-12 = 3 not true
-12 = -3(9)
-12 = -27 not true
A Sumer job pays $5 per hour
b. After working 24 hours, do you have enough money to buy an MP3
player that costs $100? Explain your reasoning.
Answers
Answer:
Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
Step-by-step explanation:
hourly pay: $5/hour
number of hours: 24 hours
total pay = hourly pay × number of hours
total pay = $5/hour × 24 hours
total pay = $120
MP3 player costs $100.
Total pay is $120.
Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
Please hurry need answer right away.
Usain can run 100 yards (yd.) in
seconds (s.). If there are 1,760 yards in
a mile (mi.), which of the following shows
Usain's speed in miles
per hour
(hr.)?
100 yd.
mi.
9 s.
1,760 yd.
3,600 s.
1 hr.
K
100 yd.
1,760 yd.
1 hr.
9 s.
mi.
3,600 s.
9 s.
1,760 yd.
100 yd.
1 mi.
3,600 s.
1 hr.
9 s. • 100 yd.
M
3,600 s. 1,760 yd.
N
3,600 s. • 1,760 yd.
9 s. • 100 yd.
Answers
Answer: To find Usain's speed in miles per hour, we need to convert the distance from yards to miles and the time from seconds to hours. To convert yards to miles, we divide the number of yards by the number of yards in a mile (1,760). To convert seconds to hours, we divide the number of seconds by the number of seconds in an hour (3,600).
So, to find Usain's speed, we use the formula:
Speed = Distance / Time
In this case, we have:
Speed = (100 yd) / (9 s)
We need to convert yards to miles and seconds to hours, so we can use the following conversion factors:
1 yd = 1/1,760 mi
1 s = 1/3,600 hr
By applying this conversion factor we get the speed in miles/hour.
Speed = (100 yd) / (9 s) * (1/1,760 mi/yd) * (1/3,600 hr/s)
So the final answer will be:
Speed = (100/9) * (1/1,760) * (1/3,600) miles/hour
Hence, option M: 3,600 s is the final answer.
Step-by-step explanation:
Winnie the witch just got a new spell book- Quick and Easy Spells for the Overworked Witch. It contains 3 different spells that take 20 minutes each to complete, 5 spells that take 9 minutes each, and 3 spells that take 4 minutes each. She performed 8 spells for 95 minutes. Which spells did she do? (She didn't repeat any spells.)
Answers
Answer:
The three spells that take 20 minutes to complete and the five spells that take 9 minutes each
Complete the statement about how you could solve the equation 2c−3=2(6−c)+ 7c .
Distribute and collect like terms on each side, , 1 of 3.
Select Choice
12 from each side, , 2 of 3.
Select Choice
2c from each side, then , 3 of 3.
Select Choice
each side by 3.
Answers
To solve the equation 2c - 3 = 2(6 - c) + 7c, option 1: Distribute and collect like terms on each side is done.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given equation is 2c−3=2(6−c)+ 7c.
To solve the equation first use the distributive property to multiply 2 by 6-c.
2c - 3 = 12 - 2c + 7c
Next, combine the like terms -2c and 7c to get 5c.
2c - 3 = 12 + 5c
Now, subtract 5c from both left-hand side and right-hand side.
2c - 3 - 5c = 12 - 5c
Next, combine the like terms 2c and -5c to get -3c.
- 3 - 3c = 12
Now, add 3 to both left-hand side and right-hand side.
- 3 - 3c + 3 = 12 + 3
Next, on right-hand side add 12 and 3 to get 15.
- 3c = 15
Now, divide both left-hand side and right-hand side by -3.
(-3c)/-3 = 15/-3
The result is obtained as -
c = -5
Therefore, the solution for the equation is c = -5.
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IM BEGGING HELPPPPPPPPPPP
Answers
Answer: 20
Step-by-step explanation: 12 divided by 3 is 4 multiply the 2 by 4 12 + 8 = 20
is f(x)=3/7+7x^2 polynomial
Answers
You must first formulate a polynomial equation in standard form before you can solve it. Factor it, then set the values of each variable factor to zero after it reaches zero.
How do you calculate a polynomial?The original equations' answers are the answers to the derived equations. Factoring cannot be used to resolve all polynomial equations.
The sum of terms with the pattern kxn, where k is any number and n is a positive integer, is what we call a polynomial.
It is impossible to classify an expression as a polynomial if it contains a variable with exponents that are negative or fractional, divides by a variable, or is included inside a radical.
Solving Equations : f(x)=3/7+7x^2
Domain of 3/7 + 7x²
Solution : -∝ < x <∝
Interval Notation : ( - ∝,∝)
Rage of 3 / 7+ 7x²
Solution : 0 < f(x) ≤ 3/7
Interval Notation : ( 0 , 3/7)
Axis interception Points of (3 / 7+7x²;
Y Intercepts : (0,3/7)
Asymptotes of 3 / 7 + 7x² ;
Horizontal : y = 0
Extremes Points of 3 / 7 - 7x²;
Maximum(0 , 3 / 7).
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Kayla is 3/4 of the way from New York to Boston. She began with 4/5 of a full tank of gas. She has 1/5` of a tank of gas left. Does she have enough gas to reach Boston?
Answers
Yes, Kayla has enough gas to reach her destination which is Boston.
What is ratios?Ratios can be defined as the expression that shows the relationship between two variables that are of the same unit.
The present location of Kayla = 3/4 of the way to new York.
The remaining distance = 1/4
The quantity of fuel that took her to that present location = 4/5 of full tanks
Therefore if 3/4 distance = 4/5 fuel
1/4 distance = 1/5 fuel
It can be concluded that Kayla has enough gas to reach her destination which is Boston.
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It has not been shown that _____. The triangles ____ congruent because ______.
Answers
A triangle only has 3 sides and 3 angles. If we know 4 distinct side measures or 4 distinct angle measures, then we know the two triangles cannot be congruent.
what is congruent triangles?
SSS: When all three sides are equal to each other on both triangles, the triangle is congruent. AAS: If two angles and a non-included (you can think of it as outside) side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal. For example, draw two circles of the same radius, then cut them out and place them on one another.To learn more about triangle refers to:
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Malinda took a bag of apples on her trip to mars. The apples weighed 5 pounds on earth. How much will the bag of apples weigh on mats?
Answers
The bag of apples weighs 1.89 pounds on Mars.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Malinda took a bag of apples on her trip to Mars.
The apples weighed 5 pounds on earth.
The formula is Weight on Mars,
= (Weight on Earth/9.81 m/s²) x 3.711 m/s²
= (5 / 9.81) x 3.711
= 1.89 pounds.
Therefore, the apple weighs 1.89 pounds on Mars.
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I need help on These I’ll give you brainliest
Answers
Answer:
its b
Step-by-step explanation: if your doing lcm it would be 40 please comment on this if its not lcm or if I'm just wrong
Am actually in the same math
The LCM of 12 and 15 is 60. To find the least common multiple (LCM) of 12 and 15, we need to find the multiples of 12 and 15 (multiples of 12 = 12, 24, 36, 48 . . . . 60; multiples of 15 = 15, 30, 45, 60) and choose the smallest multiple that is exactly divisible by 12 and 15, i.e., 60.
1. ANSWER .60
2. Maybe C or D
Because Juan is fast but Joe is slow so am not really sure
Graph the solution of |2x-1|=3 on the number line.
Answers
The graph of the solutions of the absolute value equation can be seen on the image at the end.
How to graph the solution of the equation?Here we have the absolute value equation:
|2x - 1| = 3
We can "break" that absolute value equation into two simpler ones, we will get:
(2x - 1) = 3
(2x - 1) = -3
Now we can solve these two, we will get for the first one.
2x - 1 = 3
2x = 3 + 1
x = 4/2
x = 2
The other gives.
2x - 1 = -3
2x = -3 + 1
2x = -2
x = -2/2 = -1
The solutions are 2 and -1, then the graph is the one below.
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If f(1) = 8 and f(n) = F(n - 1)-4 then find the value of f(4)
Answers
Answer:
Step-by-step explanation:
f(2)=f(1)-4=8-4=4;
f(3)=f(2)-4=0
f(4)=f(3)-4=-4;
92 people had lunch in the cafeteria. 9 people had soup, a sandwich, and a drink. 33
people had soup, 45 had a sandwich, and 52 had a drink. 5 people had soup and a sandwich. 10 people had a sandwich and a drink. 5 people had soup and a drink. How many people had only a drink?
14 people
21 people
28 people
93 people
Answers
Answer:
28
Step-by-step explanation:
52 in toatal had a drink
10 had a drink and a sandwich
5 had drink and soup
9 had all
so in total out of the 52 drinks, 24 had a drink and something
52 - 24 = 28
Three people swim a total of 2125 laps john swam 3 times more than rita and mathew swam 25 more than jhon how many laps did they each swim
Answers
Answer:
let x to be john
y to be Rita and z to be Mathews
Step-by-step explanation:
x+y+z=2125....,..........i
x=3y............................ii
y+25=z......................iii
from Qnii substitute in qn i
3y+y+z=2125
4y+z=2125
-y+z=25 by eliminate z
5y=2100 by 5 both sides
y=420
z=445
x=1260
John swam about 2128 laps
Matthew swam about 2150 laps
A
Bob discovers gold in the hills, and suddenly the area is full of people mining for gold. What impact might this have on the land of the
region?
B
7th Grade Geography (CoS) / Physical Sy
[G.11] Natural Resources 3-Strategic Thinki:
The farms will increase production immediately in order to feed all the people.
Sh
The land will be significantly changed as people dig mines, clear land, and use up natural resources.
C
Air pollution will increase as equipment is used to make the gold mines more efficient.
D The water supply will decrease as more people use it to bathe.
4 of 25
11:37
E
E
C
F
Next
Answers
Answer: Gold mining can contaminate drinking water and destroy pristine environments, endangering the health of people and ecosystems.
Thus the answer is d
Step-by-step explanation:
who needs special prayer
Answers
Answer: ok
Step-by-step explanation: :D
please help me with math i’ll give you brainlist
Answers
Answer: y = -1.6x + 4
Step-by-step explanation:
I used the y = mx + b method, m is your slope and b is your intercept.
Lmk if this answer was useful towards you!
Which statement best explains the paradox that occurs to Alexia at the end of the
passage?
A.Alexia realizes that the reward is not worth the cost.
B. Alexia discovers that the prize for being first is misleading.
C. Alexia learns that winning by cheating is not as satisfying as an honest victory.
D.Alexia believes that winning the competition is more important than anything
else.
Answers
A statement that best explains the paradox that occurs to Alexia at the end of the passage is she realizes that the reward is not worth the cost. The Option A is correct.
The Excerpt from the Passage of "Virtual Reality":“Hey, Sis,” Eric answered after two rings, shouting over loud music in the background. “Where’ve you been? Why didn’t you return my calls?”
“Sorry, Eric,” Alexia bit her lip guiltily. “I’ve been really busy.”
“Well, I’m sorry too,” Eric replied, “because my old band just asked me to sit in on their weekend shows and I won’t be able to see you at all now.”
Alexia’s heart plummeted. “Oh, Eric, can’t I come see you?”
“No, we’re traveling around the state,” Eric said. “I won’t be back home from school again until spring. I hope whatever was keeping you so busy was worth it. I miss you, Lex.”
As Alexia said goodbye, she noticed that her likes had topped 5,000. She had won, but somehow, she didn’t feel victorious at all.
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Solve for x.
x2.5<10
x
Answers
Answer:
[tex]-2\sqrt{5} < x < 2\sqrt{5}[/tex]
Step-by-step explanation:
f(x) = 4 - 3x
g(x) = 2x^2 - 3x +1
Answers
Answer:
[tex]x = \frac{4}{f - 3} [/tex]
Step-by-step explanation:
add 3x to both sides
[tex]fx + 3x = - 3x + 4 + 3x \\ fx + 3x = 4[/tex]
factor out variable x
[tex]x(f + 3) = 4[/tex]
divide both sides by f+3
[tex]x = \frac{4}{f - 3} [/tex]
Meg has 10 feet of ribbon that she wants to divide into of foot pieces. How many foot pieces are there in 10 feet?
Answers
Answer:
20
Step-by-step explanation:
A person has 2 feet (1 is a foot)
Meg has 10 feet of ribbon
therefore 10 × 2 = 20
in 10 feet there are 20 "foot"
Amanda joins a health club with a one time membership fee of $40 and $25 for each month. So far, Amanda has paid a total of $240. Find the number of months Amanda has been a member of the club.
Answers
Answer:
She has been there for 8 months
Step-by-step explanation:
Add 40 and keep adding $25
until you get to $240 and then count how many times you added 25 and you should get the answer
Stacy read a book with 106 pages, her friend read a book with 164 pages, look at the 6 digit in both of the page numbers, what is similar and different about the 6's
Answers
The difference is one 6 is at ones place and another 6 is at tens place.
What is Place Value?In mathematics, place value refers to the relative importance of each digit in a number. These locations begin at the unit's location (ones place). The place values of a number's digits are expressed in the following order: ones/units, tens, hundreds, thousands, ten thousands, and so on.
Given:
Stacy read a book with 106 pages.
and, her friend read a book with 164 pages.
In case of stacy the place value of 6 is at ones place.
and, in Stacy's friend case the place value of 6 is at tens place.
So, the difference is one 6 is at ones place and another 6 is at tens place.
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Please show me how to work out these math problems. Only the ones with stairs next them please. Thank you. Don’t understand how to work it out. Try to give me a good and simple step by of how to do this. Thanks .
Answers
Answer:just add them all together!!
Step-by-step explanation:
Answer: Solving the first one. Feel free to ask questions!
Step-by-step explanation:
Area - number of units inside a given shape (Your using this one)
Perimeter - number of units to cover the outside
Step 1: Determine the needed formulas. In this case, there are 2 rectangles, so we will use Width X Height to solve
Step 2: Break the shape into simple shapes to solve
Step 3: Solve
Solving purple rectangle: 8 is the width, and the height is 2
8 x 2 = 16
Solving pink rectangle: 4 is the height, and 5 is the width
4 x 5 = 20
Step 4: Once all areas are found, add them together
16 + 20 = 36 36 is the total Area
_______________________________________________________
Problem 2
Again there are 2 rectangles, so we will use Width X Height to solve
Step 2: Break the shape apart
Step 3: Solve
Solving blue rectangle: 2 is the width, 3 is the height
2 x 3 = 6
Solving green rectangle: 7 is the width, 3 is the height
7 x 3 = 21
Step 4: Add
6 + 21 = 27 27 is the total Area
* Remember, Every shape has a given formula to find the area*
Here are some that you will need for the worksheet:
-The formula for finding the area of a rectangle is length x width.
-The formula for finding the area of a square is side x side.
-The formula for finding the area of a triangle is base x height 1/2.
-The formula for finding the area of a circle is π x radius x radius.