Answer:
2.97m
Step-by-step explanation:
1% of 3m =1/100×3=0.03
0.03m of cloth was shrunk,
So, New lenght : 3-0.03=2.97m
if x+y=2 and x=4 then x+2y
If the white rod is 1/3, what color is the whole??
Answer:
brown
Step-by-step explanation:
it might be brown because it compelled
(b) An economy has an agricultural industry and a textile industry. Each unit of agricultural output requires 0.4 unit of agricultural input and 0.1 unit of textiles input. Each unit of textiles output requires 0.1 unit of agricultural input and 0.2 unit of textiles input.
(i) Write the technology matrix for this economy. [2 marks]
(ii) If surpluses of 5 units of agricultural products and 195 units of textiles are desired, find the gross production of each industry
Leontief input output model (technology matrix) is an economic model that shows the quantitative relationship and sectorial interdependency in a national economy
The responses with regards to the question are;
(i) The technology matrix for the economy is presented as follows;
[tex]\mathbf{ A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) The required gross production of each industry to meet the desired surplus are;
50 units of agriculture and 250 units of textile
The reason the above values are correct is as follows:
(i) The given parameters are;
The industries in the economy = Agricultural industry and textile industry
Units of agricultural input required per unit of agricultural output = 0.4
Units of textile input required per unit of agricultural output = 0.1
Units of agricultural input required per unit of textile output = 0.1
Units of textile input required per unit of textile output = 0.2
Let X represent agriculture, and let Y represent textile, we have;
[tex]Agric \ for \ agric = \dfrac{0.4 \ units \ of \ agriculture}{1\ unit \ of \ agric \ produced} \times X \ Agric \ produced= 0.4 \cdot X[/tex]
[tex]Agric \ for \ textile = \dfrac{0.1 \ units \ of \ agriculture}{1\ unit \ of \ textile \ produced} \times Y \ textile \ produced= 0.1 \cdot Y[/tex]
We also have;
Textile for agriculture = 0.1·X
Textile for textile = 0.2·Y
Therefore;
X = 0.4·X + 0.1·Y
Y = 0.1·X + 0.2·Y
Therefore;
The technology matrix for the economy is presented as follows;
[tex]\mathbf{Technology \ matrix, A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) Let P represent the production vector, and let d represent the demand vector, we have;
[tex]P = \left[\begin{array}{c}X \\Y\end{array}\right][/tex], [tex]d = \left[\begin{array}{c}5 \\195\end{array}\right][/tex]
P = A·P + d
∴ P - A·P = d
Therefore;
[tex]P = \mathbf{ \dfrac{d}{(I - A)}}[/tex]
Where I = The 2 by 2 identity matrix
We get;
[tex]I - A =\left[\begin{array}{ccc}1&&0\\&&\\0&&1\end{array}\right] - \left[\begin{array}{ccc}0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] = \mathbf{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]}[/tex]
With the use of a graphing calculator, we have;
[tex]P =\left[\begin{array}{c}X \\Y\end{array}\right] = \dfrac{\left[\begin{array}{c}5 \\195\end{array}\right]}{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]} = \left[\begin{array}{ccc}50\\\\\ 250\end{array}\right][/tex]
The required gross product of agriculture, X = 50 units
The required gross product of textile, Y = 250 units
Learn more about the Leontief input output model here:
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We have that he technology matrix for this economy and the the gross production of each industry are
a) [tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b) [tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
From the Question we have told that
Each unit of agricultural output requires 0.4 unit of agricultural input
Each unit of agricultural output requires 0.1 unit of textiles input.
Each unit of textiles output requires 0.1 unit of agricultural input
Each unit of textiles output requires 0.2 unit of textiles input.
Generally the technology matrix for this economy is given below
With
X =Agricultural industry Gross output
Y= Textile industry Gross Output
Therefore
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b)
From the Question we are told that
Surpluses of 5 units of agricultural products and 195 units of textiles are desired.
Therefore, we have Desired surplus matrix of
[tex]D= \begin{vmatrix}5\\195\end{vmatrix}[/tex]
Generally the Technology equation is mathematically given as
[tex](I-X)\phi=D[/tex]
Where
X =Agricultural industry Gross output
I=A Unit matrix
\phi=Matrix of gross production
Therefore
[tex]\begin{vmatrix}1 & 0\\0 & 1\end{vmatrix}-(\begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}))\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}5\\195\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
In conclusion
The technology matrix for this economy and the the gross production of each industry are
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex] Respectively
In conclusion
https://brainly.com/question/16863924
The HCF of two numbers is 175. The LCM of these two numbers is 12600. Both numbers are greater than their HCF. Find the two numbers
Answer:
Hello,
Answer : 1400 and 1575
Step-by-step explanation:
Let's say a and b the ywo numbers
[tex]HCF(a,b)=a\vee b=175=5^2*7\\LCM(a,b)=a\wedge b=12600\\\\a*b=(a\vee b)*(a\wedge b)=(2^3*3^2*5^2*7)*(5^2*7)=2^3*3^2*(5^2*7^2)^2\\\\Both\ numbers\ are\ greater\ than\ their HCF\\a=175*k_1\\b=175*k_2\\\\k_1=2^3\ and\ k_2=3^2\\\\a=175*2^3=1400\\b=175*3^2=1575\\\\[/tex]
if a stone is dropped from a cliff that is 122.5m high then its height in meters after t seconds is h=122.5-4.9t^2. find its velocity after 2s
Answer:
Step-by-step explanation:
Let t = 2
h = 122.5 - 4.9·2² = 122.5-19.6 = 102.9
factorise m^2 - 12 m + 24
Answer:
(m-6+2root3)(m-6-2root3)
Step-by-step explanation:
m^2 - 12m +36 -12
= (m-6)^2 - 12
= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]
Find the length of FT
Step-by-step explanation:
Hey there!
From the given figure;
Angle FVT = 43°
VT = 53
Taking Angle FVT as reference angle we get;
Perpendicular (p) = FT = ?
Base (b) = VT = 53
Taking the of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep all values and simplify it;
[tex] \tan(43) = \frac{ft}{53} [/tex]
0.932515*53 = FT
Therefore, FT= 49.423.
Hope it helps!
Answer:
A. 49.42
Step-by-step explanation:
tan 43 = FT ÷ VT
0.932515086 = FT ÷ 53
49.42 = FT
please help! thanks!
find y.
Answer:
y = 4
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : √3 : 2
The sides in this triangle are in the order:
y : 4√3 : x
y/1 = 4√3/√3
y = 4
Please helps fill in the charts
A and b
With order of pairs
Answer:
...
Step-by-step explanation:
seeee the above picture
1. Ewa has 20 balls of four colors: yellow, green, blue, and black. 17 of them are not green, 5 are black, and 12 are not yellow. How many blue balls does Ewa have? (Use Gaussian elimination method).
Answer:
In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?
There are 4 colours of balls - green, blue, yellow and white.
Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.
Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.
Check: Total number of balls = 12+6+4+26 = 48
Answer: 6 balls are blue....
the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age
We have,
[tex]a:b=3:6,a+b=96[/tex]
Introduce variable [tex]x[/tex] such that [tex]a=3x,b=6x[/tex]
The sum [tex]a+b=96[/tex] is therefore [tex]9x=96\implies x=10.\overline{6}[/tex]
So,
[tex]a=3\cdot10.\overline{6}=\boxed{32}[/tex] (sadia's age)
[tex]b=6\cdot10.\overline{6}=\boxed{64}[/tex] (father's age)
Hope this helps :)
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis.
Using the shell method, the volume integral would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]
That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].
The volume itself would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]
Using the disk method, the integral for volume would be
[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]
where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.
The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
[tex]\rm y = x^8[/tex] or
[tex]x = \sqrt[8]{y}[/tex]
And y = 256
By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.
[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]
Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]
[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]
After solving definite integration, we will get:
[tex]\rm V = \pi(\frac{4096}{5} )[/tex] or
[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit
Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
Learn more about integration here:
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Find the output, hhh, when the input, ttt, is 353535.
h = 50 - \dfrac{t}{5}h=50−
5
t
h, equals, 50, minus, start fraction, t, divided by, 5, end fraction
h=
9514 1404 393
Answer:
43
Step-by-step explanation:
Put the value where t is and do the arithmetic.
h = 50 -t/5
h = 50 -35/5 = 50 -7 = 43
The output, h, is 43 when the input is 35.
Answer:
43
Step-by-step explanation:
The answer is 43 on Khan :)
△DOG ~△?
Complete the similarity statement and select the theorem that justifies your answer.
**If they are not similar, select "none" for both parts
9514 1404 393
Answer:
nonenoneStep-by-step explanation:
The reduced side ratios, shortest to longest are ...
AC : AT : CT = 8 : 9 : 15
OD : OG : DG = 5 : 6 : 10
These are different ratios, so the triangles are not similar.
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
You're looking for a number w such that the numbers
{1 + w, 7 + w, 15 + w}
form a geometric sequence, which in turn means there is a constant r for which
7 + w = r (1 + w)
15 + w = r (7 + w)
Solving for r, we get
r = (7 + w) / (1 + w) = (15 + w) / (7 + w)
Solve this for w :
(7 + w)² = (15 + w) (1 + w)
49 + 14w + w ² = 15 + 16w + w ²
2w = 34
w = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
I need help completing this problem ASAP
Answer:
D. [tex]3x\sqrt{2x}[/tex]
Step-by-step explanation:
The problem gives on the following equation:
[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]
Alongside the information that ([tex]x\geq0[/tex]).
One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,
[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]
Now remove the duplicate factors from underneath the radical,
[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]
Simplify,
[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]
[tex]3x\sqrt{2x}[/tex]
In a study on the time that
a student required to obtain a college degree is randomly selected to 80
students and it is discovered that they have an average of 4.8 years (according to data from the National
Center for Education Statistics). Assuming s 2.2 years, construct an estimate of a confidence interval of the population mean. The confidence interval
the result contradicts the fact that 39% of students get their college degree in four years?
The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.
-----------------------------
To solve this question, we need to find the confidence interval for the amount of time it takes the students to get the degree.
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
-----------------------------
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 80 - 1 = 79
-----------------------------
95% confidence interval
Standard level of confidence, we have to find a value of T, which is found looking at the t table, with 79 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9905.
-----------------------------
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.9905\frac{2.2}{\sqrt{80}} = 0.5[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
-----------------------------
The lower end of the interval is the sample mean subtracted by M. So it is 4.8 - 0.3 = 4.3 years.
The upper end of the interval is the sample mean added to M. So it is 4.8 + 0.3 = 5.3 years.
-----------------------------
The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.
A similar question is given at https://brainly.com/question/24278748
–21:(–2 – 5) + ( –14) + 6.(8 – 4.3)
work out missing angle following polygons
Answer:
x = 150°
Step-by-step explanation:
Interior angle of a hexagon = 120° and interior angle of a square = 90°
so remaining angle, 360-120-90 = 150°
If ‘BOXES’ is OBXSE, then BOARD is
9514 1404 393
Answer:
OBADR
Step-by-step explanation:
The first two letters are swapped, and the last two letters are swapped.
BOARD . . . becomes
OBADR
In a high school graduating class of 300, 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year.
a. These are mutually exclusive events.
b. These are not mutually exclusive events.
c. You should add their individual probabilities.
d. None of the above are true.
The answer pl shhaoksngausinxbbs pls
Answer:
D. 3
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.
Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.
Why wouldn't you use division to find an equivalent fraction for 7/15
Answer:
This depends whether you want to make the fraction bigger or smaller.
Step-by-step explanation:
If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.
However, if you want to make the fraction bigger, then you would multiply.
Hope this helps! :)
Answer:
Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.
Step-by-step explanation:
Rotation 90° counterclockwise around the origin of the point (-8,1)
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
The probability distribution of a random variable X is given. x 1 2 3 4 P(X = x) 0.4 0.1 0.3 0.2 Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean variance standard deviation
Mean:
[tex]E(X) = \displaystyle \sum_{x\in\{1,2,3,4\}}x\,P(X=x) = 1\times0.4 + 2\times0.1 + 3\times0.3 + 4\times0.2 = \boxed{2.3}[/tex]
Variance:
[tex]\displaystyle V(X) = E\left((X-E(X))^2\right) = E(X^2) - E(X)^2 \\\\ E(X^2) = \sum_{x\in\{1,2,3,4\}}x^2\,P(X=x) = 1^2\times0.4 + 2^2\times0.1 + 3^2\times0.3 + 4^2\times0.2 = 6.7 \\\\ \implies V(X) = 6.7 - 2.3^2 = \boxed{1.41}[/tex]
Standard deviation:
[tex]\sigma_X = \sqrt{V(X)} = \sqrt{1.41} \approx \boxed{1.19}[/tex]
Hello Pls help and thanks
Answer:
c.) in the correct answer
A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A.M. and he leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
(d) Find the length of time above which we find the slowest 10% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.
Answer:
Step-by-step explanation:
a) Probability-Above 30 min = 5.72% = .0572
b) Probability-Above 15 min = 99.11% = .9911
c) *Probability-Between 1 - 59.49% = .4051
d) 19.136 minutes z = -1.28
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
What do you mean by normal distribution ?
A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.
Let assume the time taken for a one way trip be x .
x ⇒ N( μ , σ ²)
x ⇒ N( 24 , 3.8 ²)
a)
The probability that trip will take at least 1/2 hour or 30 minutes will be :
P ( x ≥ 30)
= P [ (x - μ) / σ ≥ (30 - μ) / σ ]
We know that , (x - μ) / σ = z.
= P [ z ≥ (30 - 24) / 3.8)]
= P [ z ≥ 1.578 ]
= 1 - P [ z ≤ 1.578 ]
Now , using the standard normal table :
P ( x ≥ 30)
= 1 - 0.9394
= 0.0606
b)
The percentage of the time the lawyer is late for work will be :
P ( x ≥ 15)
= P [ z ≥ -2.368 ]
= P [ z ≤ 2.368]
= 0.9918
or
99.18%
c)
The probability that lawyer misses coffee :
P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)
= P [ z < 0.263] - P ( z < -2.368)
or
= 0.3659
d)
The length of time above which we find the slowest 10% of trips :
P( x ≥ X ) ≤ 0.10
= 0.5438
e)
Let's assume that y represents the number of trips that takes at least half hour.
y ⇒ B ( n , p)
y ⇒ B ( 3 , 0.0606)
So , the probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is :
P ( Y = 2 )
= 3C2 × (0.0606)² × ( 1 - 0.0606)
= 0.0103
Therefore , the answers are :
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
Learn more about normal distribution here :
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find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
Cos C = a/h
= 21/35
Step-by-step explanation:
since cos is equal to adjacent angle over hypotenuse angle, so from the question we conclude Cos C = 21/35
Help me plz 20 points to who ever gets it right
Step-by-step explanation:
2., 3., 4., 5.
yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.
you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).
2.
(-4, 6) to (10, -10)
in x the distance is 10 - -4 = 14. half is 7.
in y the distance is |-10 - 6| = |-16| = 16. half is 8.
so the midpoint is
(-4 + 7, 6 - 8) = (3, -2)
remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).
3.
(-3, -8) to (-6.5, -4.5)
in x distance : -3 - -6.5 = 3.5. half is 1.75
in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75
midpoint is
(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)
4.
(3, 7) to (-8, -10)
x : 3 - -8 = 11. half is 5.5
y : 7 - -10 = 17. half is 8.5
midpoint is
(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)
5.
(-6, -13) to (-6.4, -3.8)
x : -6 - -6.4 = 0.4. half is 0.2
y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6
midpoint is
(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)
6.
(-1, 7) to (5, 1)
x : -1 - 5 = |-6| = 6. 1/3 is 2.
y : 7 - 1 = 6. 1/3 is 2.
1/3 from C to D
(-1 + 2, 7 - 2) = (1, 5)
7.
2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).
again
(1, 5)
8.
2/3 of the way from C to D.
so, we need to double what we added in 6.
(-1 + 4, 7 - 4) = (3, 3)
9.
1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).
again
(3, 3)
10.
exactly. Pythagoras.
the square root of the sum of the squares of the coordinate differences.
distance = sqrt((x1 - x2)² + (y1 - y2)²)
11.
(6, 8) to (-1, 8)
distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7
12.
(5, -6) to (5, 6)
sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12
13.
(-2, 0) to (11, 0)
sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13
14.
(1, -5) to (9, 1)
sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10
15.
ST and MT are basically the same equation.
MT is half of ST.
ST equation based on 2 points :
y – yS={(yT – yS)/(xT – xS)}(x – xS)
M = (xS + (xT - xS)/2, yS +(yT - yS)/2)
so, let's put that into the general equation :
y - yM={(yT - yM)/(xT - xM)}(x - xM)
y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))
16.
the two corners farthest away are (5, 10) and (9, 6).
what distance from (0, 0) is now bigger ?
since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.
5² + 10² = 125
9² + 6² = 117
so, the corner (5, 10) is the farthest away.