The figure illustrates the apparatus for a tightrope walker. Two poles are set y = 50 feet apart, but the point of attachment P for the rope is yet to be determined. (a) Express the length L of the rope as a function of the distance x from P to the ground.
Answers
Equation for the length L of the rope as a function of the distance x from P to the ground is,
⇒ L = √((x-2)²+50²)
Since L is to the second pole, not x, we can't simply say that;
⇒ x² + y²= L² using the Pythagorean Theorem.
Since, due to that we simply increase the original height by 2, decreasing x by 2.
We can, however, say that ;
⇒ (x-2)² + y² = L²
Plugging 50 as y in, we get ;
⇒ (x-2)² + 50² = L².
Square rooting both sides, we get;
⇒ L = √((x-2)²+50²)
Thus, Equation for the length L of the rope as a function of the distance x from P to the ground is,
⇒ L = √((x-2)²+50²)
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Related Questions
2) Mr. Somers had twenty pieces of metal that were all the same length. If each piece of metal was 3 1/5 inches long and he put them side by side, what would be the total length of all the pieces together?
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Which of the following is not an isometry?
rotation
dilation
translation
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Answer:
B. Dilation.
Step-by-step explanation:
We are asked to find which transformation is not isometric.
We know that isometry preserves length.
We know that the length of a figure remains unchanged after rotation and dilation as they preserves length.
We also know that dilation either enlarges length or shrinks length of a figure, therefore, the correct choice is dilation.
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 4 h. Train B reaches station B after 312 h. Station A and Station B are 562.5 mi apart. What is the rate of the trains? Enter your answer in the box.
Answers
the answer is 75 mph i took the test and it said 75 not 1.78
Answer:
its 75 i did the math a calaculator
Step-by-step explanation:
A couple has 4 children. what is the probability they would have four boys
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Find parametric equations for the line through the point ( 0,3,2 ) that is perpendicular to the line ! ! x =1+t , ! ! ! y = 3−t , ! ! z = 4t , and intersects this line. (use the parameter t ).
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An oil storage tank is a cylinder 30 feet high. The base of the tank is a circle with a diameter of 50 feet. When full, how many gallons are in the tank? 1 gallon equals approximately 0.13 cubic feet.How many gallons are in the tank?
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suppose you wanted the tank to hold 100 gallons of water and it was 50 gallons per cubic feet. How many cubic feet would you need? Obviously, 2 cubic feet. How did you get that?? Well, you divided 100 by 50 to get 2.
O.K., now, let's try YOUR problem. 225000 gallons and 7.5 gallons per cubic feet. How many cubic feet do you need? Must be 225,000/7.5 = 30,000 cubic feet
O.K., now we're half way there. we (should) know that the volume of a prism is
l x w x h. We now know the volume must also be 30,000
so l x w x h = 30000
100 x 20 x h = 30000
you should be able to take it from there.
Problem #2
We approach it the exact same way.
It's too hard as stated. Let's make up an easier problem.
suppose 1 gallon took up 5 cubic feet. If you had 10 cubic feet, how many gallons would you have?
well, clearly, you would have 2 gallons. How did you get it?
Now, how many cubic feet in the cylinder? Well you (should) know that the volume of a cylinder is:
Pi r^2h = 3.14 x 25^2 h = 1962.5 h
Now we have a bit of a problem. You didn't tell me how high the tank is. Let us say it is 10 feet.
So, the tank had 19,625 cubic feet.
Go back to the start of this problem and you will know what to do next.
Answer: 7653.75 gallons
Step-by-step explanation:
Given : Height of cylinder = 30 feet
Diameter : d= 50 feet
Radius : [tex]r=\dfrac{d}{2}=\dfrac{50}{2}=25\text{ feet}[/tex]
The volume of a cylinder is given by :-
[tex]V=\pi r^2 h\\\\\Rightarrow\ V=(3.14)(25)^2(30)\text{ cubic feet}[/tex]
Also, 1 gallon equals approximately 0.13 cubic feet.
Then , the number of gallons of water in the tank :-
[tex]V=(3.14)(25)^2(30)(0.13)=7653.75\text{ gallons}[/tex]
Evaluate. 7^2 - 3 + 9 × 8 ÷ 2
w =
Answers
49 - 3 + 9 x 8 / 2
49 - 3 + 72/2
49 - 3 + 36
46 + 36
82
w = 82
Starting from the same place, Sara walks due west and Ammad walks due east. On the number line, 0 represents their starting point, negative values represent the distance traveled west and positive values represent the distance traveled east. A number line with a point for Ammad at coordinate 480 and a point for Sara at coordinate -240. How many feet apart are Sara and Ammad on the number line? Enter your answer in the box.
Answers
It's 720, because all you need to do is 240 + 480 = 720.
Hope it helps,
347,456 round to the place value of the underlined digit. The four being in the ten thousand places
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A line passes through the point (d, d) and has a slope of k. Which equation models the line?
Answers
is 11:17 equivalent to 17:11
Answers
Answer:
No
Step-by-step explanation:
If these are time values, ...
11:17 is about 5 hours 54 minutes earlier than 17:11.
___
If these are ratios, ...
11/17 is less than 1, whereas 17/11 is greater than 1
Each is the inverse of the other.
A bear, awakening from winter hibernation, staggers directly northeast for 15 m and then due east for 15 m. Show each displacement graphically and graphically determine the single displacement that will take the bear back to her cave to continue her hibernation.
Answers
The total displacement east is:
15 cos(45) + 15
= 25.607 m
The total displacement north is:
15 sin(45)
= 10.607 m
The magnitude of the total displacement is:
sqrt(25.607^2 + 10.607^2)
= 27.717 m = 27.7 m
Its direction is N x E where:
tan(x) = 25.607 / 10.607
x = 67.5 deg
The return displacement is therefore of the same magnitude
but in the opposite direction.
Displacement 27.7 m, direction S 67.5 deg W
So is the answer - least is the negative first, them zero, them the positive?
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-0.6, -5/8, -7/12, -0.72 least to greatest
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Find an equation for the line with the given properties. Express the equation in slope-intercept form. Containing the points Upper P equals (-1, 3) and Upper Q equals (1, 0)
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[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-3=-\cfrac{3}{2}[x-(-1)] \\\\\\ y-3=-\cfrac{3}{2}(x+1)\implies y-3=-\cfrac{3}{2}x-\cfrac{3}{2}\implies y=-\cfrac{3}{2}x-\cfrac{3}{2}+3 \\\\\\ y=-\cfrac{3}{2}x+\cfrac{3}{2}[/tex]
Find the mean of the data set. If necessary round to nearest tenth. 18.1,17.9,16.8,18.7,15.1
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[tex]\frac{18.1+17.9+16.8+18.7+15.1}{5} = 17.32[/tex]
And if we round to the nearest tenth it would be 17.3
what is The cost per unit?
Answers
To figure your total manufacturing cost per unit, divide your total costs by the total number of units produced. For example, say for the year your company made 1 million units and incurred production costs of $3 million. Divide your $3 million costs by the 1 million units to find your cost per unit: $3.
358=15n+85 what does n equal
Answers
Ms. Ache is paid $1250 per week but it's fined $100 each day she is late to work Ms.A che wants to make at least $3,000 over the next three weeks so she can take a vacation. over the next three weeks, what is the maximum number of days she can be late to work and still reach her goal of making at least $3000?
Answers
Answer:
7 days
Step-by-step explanation:
Given: Ms. Ache is paid $1250 per week but it's fined $100 each day she is late to work.
To Find: maximum number of days she can be late to work and still reach her goal of making at least $3000?
Solution:
per week payment of Ms. Ache =[tex]\$[/tex] [tex]1250[/tex]
Fine for getting late a day = [tex]\$[/tex] [tex]100[/tex]
let number of days Ms. Ache gets late = [tex]\text{x}[/tex]
Amount Ms. Ache wants to make in three weeks = [tex]\$[/tex] [tex]3000[/tex]
maximum earning potential of Ms. Ache in 3 weeks = [tex]1250\times3[/tex]= [tex]\$[/tex] [tex]3750[/tex]
Net earning = maximum earning potential of Ms. Ache in 3 weeks - total fine
=[tex]\$ 3750 - 100\text{x}[/tex]
To reach a goal of [tex]\$[/tex] [tex]3000[/tex]
[tex]\$ 3750 - 100\text{x}[/tex] ≥ [tex]3000[/tex]
[tex]100\text{x}[/tex]≤[tex]750[/tex]
[tex]\text{x}\leq 7[/tex]
Maximum number of days she can be late to work and still reach her goal of making at least $3000 is [tex]7[/tex] [tex]\text{days}[/tex]
june is working on an addition problem and starts with 17,985. after she adds, she still has 17,985. which property od addition did june use
Answers
Find the determinant of the n×n matrix a with 's on the diagonal, 's above the diagonal, and 's below the diagonal
Answers
Find a parametric representation of the solution set of the linear equation. (enter your answer as a comma-separated list of equations. use s and t as your parameters.) x + y + z = 2
Answers
The parametric representation of the solution set for the equation x + y + z = 2 is x = t, y = 2 - s - t, z = s, with 's' and 't' as the parameters.
Explanation:To find the parametric representation of the solution set of the linear equation x + y + z = 2, we first need to express two variables in terms of the third. Let's use 's' and 't' as parameters.
We can express x and y in terms of z. Let's express z as 's'. So, z = s.
The equation x + y + z = 2 thus becomes x + y = 2 - s. We can choose x = t and y = 2 - s - t.
So, the parametric representation of the solution set for the given linear equation is (x = t, y = 2 - s - t, z = s), where 's' and 't' are parameters that can assume any real value.
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5 minus the product of V and 7
Answers
5 - 7V <== ur expression
ymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is
C(x) = 3250 + 5x + 0.1x2 (0 ≤ x ≤ 500).
Gymnast Clothing sells the cleats at $110 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?
Answers
Profit = Revenue - Total Cost
Since the cost is given as a function, the equation will be substituted as
Profit = Revenue - (3,250 + 5x + 0.1x²)
Now, the revenue is a linear graph because it is the number of pairs multiplied the fixed rate. So, the slope is constant.
Revenue = 110x --> this is the function for revenue
Thus, the equation for profit would be
Profit = 110x - 3,250 - 5x - 0.1x²
P = -0.1x²+105x-3,250 --> this is the function for profit
Now, to find the minimum value of x to make profit, differentiate P with respect to x and equate to 0.
dP/dx = 0 = -0.2x + 105
x = 525
Thus, the Gymnast Clothing should manufacture at least 525 pairs in order to make profit.
Solve the equation 6x + 3y = 15 for y. What does y equal if x = 2? If x = 5?
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3y = 15 -6x
y = 5 - 2x
Part b. y = 1
Part c. y = -5
3/5 of 40 dollar restaurant
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120/5
24
Hope this helps!
One positive number is 1/5 of another number. The difference between the two numbers is 60. Find the numbers.
Answers
Answer:
15 and 75Step-by-step explanation:
[tex]n-second\ number\\\\\dfrac{1}{5}n-first\ number\\\\n-\dfrac{1}{5}n=\dfrac{4}{5}n-difference\ between\ the\ two\ numbers\\\\\text{Equation:}\\\\\dfrac{4}{5}n=60\qquad\text{multiply both sides ny 5}\\\\\not5\cdot\dfrac{4}{\not5}n=(5)(60)\\\\4n=300\qquad\text{divide both sides by 4}\\\\\dfrac{4\!\!\!\!\diagup n}{4\!\!\!\!\diagup}=\dfrac{300}{4}\\\\n=75\\\\\dfrac{1}{5}n=\left(\dfrac{1}{5}\right)(75)=\dfrac{75}{5}=15[/tex]
The two positive numbers are 15 and 75 respectively.
What is an expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let the two numbers be x and y respectively. Now let corelate the statement given in question :
One positive number is 1/5 of another number which means x=(1/5) y
and, it is also given that the difference between the two numbers is 60 which means y -x = 60. Now solving these question by substitution method.
y-x = 60
5x-x= 60
4x = 60
x = 15
y = 75
Therefore, the two positive numbers are 15 and 75 respectively.
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Country A produces about eight times the amount of diamonds in carats produced in country B. If the total produced in both countries is 9,000,000 carats, find the amount produced in each country
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Then A + B = 8B + B = 9000000 9B = 9000000
B = 1000000
A = 8xB = 8000000
Compound interest £2000 for 3 years 5.5% annum
Answers
The ordered pair (–2, –4) is a solution of which system?
Answers
y < = x + 2....(-2,-4)....x = -2 and y = -4
-4 < = -2 + 2
-4 < = 0 (true)
y > = x - 3.....(-2,-4)...x = -2 and y = -4
-4 > = -2 - 3
-4 > = -5 (true)
ur answer is the last one
The given ordered pair is the solution of y ≤ x + 2 and y ≥ x - 3. Option E is correct.
As of the given numeral, The ordered pair (–2, –4) is a solution of which system is to be determined.
What is inequality?Inequality is defined as the relationship of an equation containing the symbol ( ≤, ≥, <, >) instead of the equal sign.
here,
(–2, –4) is a solution of y ≤ x + 2 and y ≥ x - 3,
Proof,
Substitute this ordered paired in the inequality,
-4 ≤ -2 + 2
-4 < 0
and
-4 ≥ -2 - 3
-4 > -5
Thus, the ordered pair supplied is the solution of y x + 2 and y x - 3. Option E is the right answer.
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