8. A chair lift at a ski resort travels along the
cable as shown.
AY
6
4
O
U
w
w
2
t
0
0 2
4 6 8 10 12 14 16 18
1 unit = 10 ft
How long is the cable? Round your answer
to the nearest whole foot.
Answers
This value is approximate.
==========================================================
Explanation:
The cable is connected by these key points
A = (0,3)B = (6,5)C = (12,4)D = (18,2)Let's use the distance formula to find the length of segment AB.
[tex]A = (x_1,y_1) = (0,3)\\\\B = (x_2,y_2) = (6,5)\\\\d = \text{Distance from A to B} = \text{length of segment AB}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-6)^2 + (3-5)^2}\\\\d = \sqrt{(-6)^2 + (-2)^2}\\\\d = \sqrt{36 + 4}\\\\d = \sqrt{40}\\\\d \approx 6.325\\\\[/tex]
Segment AB is roughly 6.325 units long. You could use the pythagorean theorem as an alternative route instead of the distance formula.
If you repeated this process for the other segment lengths, then you should get these other approximate lengths.
BC = 6.083CD = 6.325Add up those three results:
AB+BC+CD = 6.325+6.083+6.325 = 18.733
The entire cable is roughly 18.733 units long.
Since 1 unit = 10 feet, we'll multiply that result by 10.
18.733*10 = 187.33 feet
This rounds to 187 feet which is the approximate length of the cable.
The length of the cable will be 187.2 feet long.
What is the distance between two points?Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
From the diagram, the length between (0, 3) and (6, 5), (6, 5) and (12, 4), and (12, 4) and (18, 2) will be the length of the cable (L).
[tex]\rm L = \sqrt{(6 - 0)^2 + (5-3)^2} + \sqrt{(12 - 6)^2 + (4 - 5)^2} + \sqrt{(18 - 12)^2 + (2 - 4)^2}\\[/tex]
Simplify the equation, then we have
L = √40 + √37 + √40
L = 6.32 + 6.08 + 6.32
L = 18.72 units
L = 18.72 x 10
L = 187.2 ft
The length of the cable will be 187.2 feet long.
Learn more about the distance between two points here:
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Related Questions
Please answer this
Answer choice
A. Subtraction Property Of Equality
B.Associative Property Of Equality
C.Division Property Of Equality
D.Addition Property Of Equality
Answers
Answer:
step 1. Subtraction Property Of Equality
step 2.Associative Property Of Equality
step 3.Division Property Of Equality
3 6/12 rounded to the nearest whole number
Answers
Answer:
4
Step-by-step explanation:
6/12= .5
3.5≈4
Throughout Singapore it has been estimated that about a billion (1 000 million) cubic meters of water are used each day. If we assume a population of 3 million, what is the rate of consumption of water per person?
Answers
Answer:
333 cubic meters of water are used each day by one person
Step-by-step explanation:
Xavier buys a two-quart bottle of juice for $5.12. What is the unit rate of the cost of the juice per fluid ounce?
Before you try that problem, answer the question below.
How many fluid ounces of juice did Xavier buy?
Answers
Answer:
2.56
Step-by-step explanation:
2 divided by 512
2 lol
Answer:
Q1. $2.56
Q2. 2 fluid ounces
Step-by-step explanation:
Q1. $5.12÷2=$2.56
Q2. 2 fluid ounces (inferred from qn)
2. The ratio of chocolate to vanilla ice cream is 3 scoops to 7 scoops. If there
are 147 scoops of vanilla ice cream, how many total scoops are there?
Answers
write down 1/y-2/x as a single fraction in its lowest terms
Answers
Answer:
It is (x - 2y)/xy
Step-by-step explanation:
[tex] \frac{1}{y} - \frac{2}{x} [/tex]
carry out LCM method:
LCM of y and x is xy
[tex] = \frac{x - 2y}{xy} [/tex]
Solve the equation-
200=16(6t-3)
Answers
Hi ;-)
200 = 16(6t - 3)
16 · 6t - 16 · 3 = 200
96t - 48 = 200 / + 48
96t = 248 / : 96
t = ²⁴⁸/₉₆ = ³¹/₁₂ = 2 ⁷/₁₂
The solution of the linear equation 200 = 16 (6t - 3) will be 2.58.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
200 = 16 (6t - 3)
Simplify the equation, then the value of the variable t will be
200 = 16 (6t - 3)
12.5 = 6t - 3
6t = 15.5
t = 2.58
The solution of the linear equation 200 = 16 (6t - 3) will be 2.58.
More about the solution of the equation link is given below.
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Find a polynomial f(x) of degree 4 that has the following zeros. 2, 5, 0, -7
Answers
Answer:
Step-by-step explanation:
f(x) = (x - 2)(x - 5)x(x+ 7)
f(x) = (x^2 - 7x + 10)*x * (x + 7)
f(x) = x(x^3 - 39x + 70)
f(x) = x^4 - 39x^2 + 70x
To show that this is correct, I've made a graph with these points labeled. The graph is just around the x axis. The local maximums and minimums are just too large a value.
Find the coordinates of the image of M (−3, −4) after the translation (x, y) → (x + 4, y).
A. (−3, 0)
B. (−1, −4)
C. (1, −8)
D. (1, −4)
Answers
Answer:
d
Step-by-step explanation:
cause x becomes x+4 to get 1
and y remains y.
Which numbers are a distance of 3.5 units from −4 on a number line?
A number line with increments of .5 with a range of 0 to negative 7.5
Select the two correct answers.
−7
−7.5
−6.5
−4.5
−3.5
−0.5
(help)
Answers
-4 - 3.5 = -7.5
-4 + 3.5 = -0.5
The mean age of 6 women in an office is 23 years old.
The mean age of 3 men in an office is 23 years old.
What is the mean age (nearest year) of all the people in the office?
Answers
the mean for both mean and women are 23 so the mean of all the people would be the same.
Answer:23
Is 17 a interger or a counting number
Answers
PLS HELP ASAP PLS
A net of a triangular prism is show. What is the surface area, in square feet, of the triangular prism?
44 square feet
96 square feet
108 square feet
120 square feet
Answers
To find surface area, all you need to do is add up the areas of all the faces of the prism. Let’s start by remembering some basic area formulas:
Area of a triangle= 1/2*base*height
Area of a rectangle= length*width
First, find the area of each of the little triangles on the sides of the net. The base is 3 ft, and the height is 4 ft. So:
1/2*3*4= 6 ft
There are two triangles of the same size, so multiply that number by 2.
6*2=12
Now, find the area of the top rectangle:
3*8= 24
And the area of the bottom rectangle:
5*8= 40
Finally, add all of those numbers together:
12+24+40= 76 ft^2
That should be your answer!
(-4, 6) and (3,-7)
Find the distance between each pair of points
Answers
Answer:
14.76482306
Step-by-step explanation:
distance equals the square root of (x2-x1)^2 + (y2-y1)^2.
think of your ordered pairs as set 1 and set 2. (-4, 6) would be set 1 and (3, -7) would be set 2. so your equation will look similar to: (3- -4)^2 + (-7-6)^2 then you square root the whole thing and you will have your answer.
Select all expressions that are equivalent to x2 - 4x – 32.
0 (x – 16)(x + 2)
(x + 2)(x – 16)
(2 – )(x + 4)
(x + 8)(x – 4)
(x + 4)(x – 8)
(x – 4)(x+8)
Answers
Answer:
(x + 4)(x – 8)
Step-by-step explanation:
1. (x – 16)(x + 2)
x² - 2x - 16x - 32
x² - 18x - 32
2. (x + 2)(x – 16)
x² - 16x + 2x - 32
x² - 14x - 32
3. (2 – )(x + 4)
2x + 8
4. (x + 8)(x – 4)
x² - 4x + 8x - 32
x² + 4x - 32
5. (x + 4)(x – 8)
x² - 8x + 4x - 32
x² - 4x - 32
6. (x – 4)(x+8)
x² + 8x - 4x - 32
x² + 4x - 32
How do you solve this?
Answers
Answer:
Its minus 70 every time
Step-by-step explanation:
n=32
Answer:
it will take 36 months to completely pay the loan
Step-by-step explanation:
see that if the number of months paid is 1 and the amount owed is 2450 and that on number of months paid is 2 and then the amount owed is 2380
every month we have to substract 70
so we can make a pattern
0 months = 2520
1 month = 2450 that is 2520 - 70
2 months = 2380 that is 2520 - (2 × 70)
3 months = 2310 that is 2520 - (3 × 70)
.....
then it continues till n months
so
n months = 2520 - (n ×70)
n months = 2520 - (36 × 70)
36 months = 2520 - 2520
Rewrite in simplest terms: -10f – 6(-9f +2)
Answers
Answer:
-44f - 12
Step-by-step explanation:
Here's the method :
-10f - 6 (-9f + 2 )
-10f + 54f - 12
-44f - 12
Answer:
[tex]44f - 12[/tex]
Step-by-step explanation:
[tex] - 10f - 6( - 9f + 2)[/tex]
[tex] - 6( - 9 + 2)[/tex]
[tex] - 6 \times ( - 9f) - 6 \times 2[/tex]
[tex]6 \times 9f - 6 \times 2[/tex]
[tex]54f - 6 \times 2[/tex]
[tex]54f - 12[/tex]
[tex] - 10f + 54f[/tex]
[tex]( - 10 + 54)f[/tex]
[tex] = 44f - 12[/tex]
4 A curve has equation y=x^3 - 2x² +5. Find the coordinates of its two stationary points.
Answers
Answer:
Stationary points are (0, 5) and (4/3, 103/27)
Step-by-step explanation:
At stationary point (turning point), dy/dx :
[tex]y = {x}^{3} - 2 {x}^{2} + 5 \\ \frac{dy}{dx} = 3 {x}^{2} - 4x \\ \\ \frac{dy}{dx} = x(3x - 4)[/tex]
but dy/dx = 0:
[tex]x(3x - 4) = 0 \\ either \: x \: is \: 0 \: and \: (3x - 4) = 0 \\ x = 0 \\ and \\ 3x - 4 = 0 \\ x = \frac{4}{3} [/tex]
let y = x³ - 2x² + 5:
[tex]when \: x \: is \: 0 \\ y = 5 \\ when \: x \: is \: \frac{4}{3} \\ \\ y = {( \frac{4}{3}) }^{3} - 2 {( \frac{4}{3} )}^{2} + 5 \\ \\ y = \frac{103}{27} [/tex]
What is the least positive integer by which 1922 should be divided so that the resultant integer is a
perfect square?
Answers
Answer:
1922 = 2× 31 × 31
Therefore, 1922 should be divided by 2 to get 961 which is a square of 31.
I hope this helped!
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she went down 23.9 feet. How many feet had she been below sea level, if she was 82.2 feet below sea level after she went down?
Answers
Answer:
58.3
Explanation:
x is the depth that the scientist started at. The asked equation is
x + 23.9 = 82.2
To find x, all we have to do is reverse the equation by doing
82.2 - 23.9 = x
This gives us x = 58.3
At a school camp there is enough food for 150 students for 5 days.
a How long would the food last if there were only 100
students?
Answers
Answer:
If there were only 100 students, there would be enough food for 3 days.
Step-by-step explanation:
Set up an equation:
Variable x = number of days
150/5 = 100/x
Cross multiply:
150 × x = 5 × 100
150x = 500
x = 3.3333...
Round down to a whole number which represents a full day of food.
x = 3
round 856.321 nearest 1 decimal place
Answers
Answer:
856.3
Step-by-step explanation:
Can anyone help me find w
Answers
The goal of a benefit concert is to collect 50,000 cans of food. Food is collected at each entrance to the concert.
Entrance A, 15,682 cans
Entrance B, 18,940 cans
Entrance C, 16,114 cans
Entrance D, 12,468 cans
Did they collect more or fewer cans than desired? How many more or fewer?
Answers
Answer:
they collected altogether 63204 cans
so,they collected 13204 cans more than desired
Heelp ez question, just answer no steps needed
Answers
Answer:
i think 16 is the correct answer
Step-by-step explanation:
a
The following 5 keys are for the following 5 locked padlocks. Each key opens one and only one padlock. Different keys open different padlocks. What is the least number of trials needed to guarantee that you will open all 5 padlocks?
Answers
[tex] {5}^{5} [/tex]
is the answer.
if a set of 14 pens is 12.44 then what is the cost of each pen
Answers
Answer:
Convert to a decimal by dividing the numerator by the denominator.
$1.15 = Estimate.
pens per then .
Step-by-step explanation:
14 Divided 12.44
I’ve been stuck on this for days I just need a simple answer
Answers
Answer:
408
Step-by-step explanation:
Surface area formula is A=2(wl+hl+hw)
Substituting these values into the formula you would get
2·(3·8+4·8+4·3)=136
136 accounts for one rectangular prism.
Since you have 3 multiply 136 by 3 which would leave you with 408
Answer:
280 in²
Step-by-step explanation:
The opposite faces are congruent , then surface area (SA ) is
SA = top/ base + front/ back + 2 sides
note for the front/ back and 2 sides we have 3 + 3 + 3 = 9 in
SA = 2(8 × 4) + 2(8 × 9) + 2(4 × 9)
= 2 × 32 + 2 × 72 + 2 × 36
= 64 + 144 + 72
= 280 in²
Please helppp!!! I have this question for geometry and I can’t figure it out.
Answers
Answer: shoot proofs
Step-by-step explanation:
A flea which is 8 x 10^-3 can jump 3.5 10^2 times of its own
length. How far can it jump?
meters
Answers
Answer:
(8 × 10 ^-3) (3.5× 10 ^2)
= 2.8 meters