The sum of two positive numbers is 120. The product of those numbers will be maximum if both numbers are equal to 60 and the maximum value is 3600.
Suppose we have a function f(x). At the extreme point (maximum/minimum), it holds:
f ' (x) = 0
In the given problem, let the two numbers be a and b. Then,
a + b = 120 or
a = 120 - b (equation 1)
f(b) = a x b = (120 - b) x b
f(b) = -b² + 120b
At the maximum point, the derivative with respect to b is zero,
f ' (b) = 0
-2b + 120 = 0
b = 120 / 2 = 60
Substitute b = 60 to equation 1,
a = 120 - 60 = 60
Hence, the two numbers that give maximal value of the product is 60 and 60. The product is 60 x 60 = 3600.
We can conclude that the maximum value of the product of those two numbers is 3600.
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A solution to a system of linear equations in two variables is an ordered pair that.
The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.
What ordered pair is a solution to the system of linear equations?
An equation is said to linear when it is in ax+ by = c form where a , b and c are real numbers . System of linear equation consist of a set of two or more equation with same variables. such as ,
a₁ x + b₁ y = c₁
a₂ x + b₂ y = c₂
A solution to a linear system is an ordered pair (x ,y) that solves both the equations .
To check that an ordered pair is a solution ,we have to substitute the corresponding values of our variables (x ,y) into our equations and see if they satisfy both the equations.
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Solve the equation [tex]\frac{1}{x+9} +\frac{1}{5}=\frac{1}{4}[/tex]
[tex]\boldsymbol{\sf{Your\:exersice \to \dfrac{1}{x+9}+\dfrac{1}{5}=\dfrac{1}{4} }}[/tex]
Variable x cannot be equal to −9 as division by zero is undefined. Multiply both sides of the equation by 20(x+9), the lowest common denominator of x+9,5,4.
[tex]\boldsymbol{\sf{20+20(x+9)\times\left(\dfrac{1}{5}\right)=5(x+9) }}[/tex]
Multiply 5 and 1/5 to get 4.
[tex]\boldsymbol{\sf{20+4(x+9)=5(x+9)}}[/tex]
Use the distributive property to multiply 4 by x+9.
[tex]\boldsymbol{\sf{20+4x+36=5(x+9)}}[/tex]
Add 20 and 36 to get 56.
[tex]\boldsymbol{\sf{56+4x=5(x+9)}}[/tex]
Use the distributive property to multiply 5 by x+9.
[tex]\boldsymbol{\sf{56+4x=5x+45}}[/tex]
Subtract 5x on both sides.
[tex]\boldsymbol{\sf{56+4x-5x=45}}[/tex]
Combine 4x and −5x to get −x.
[tex]\boldsymbol{\sf{56-x=45}}[/tex]
Subtract 56 from both sides.
[tex]\boldsymbol{\sf{-x=45-56}}[/tex]
Subtract 56 from 45 to get −11.
[tex]\boldsymbol{\sf{-x=-11}}[/tex]
Multiply both sides by −1.
[tex]\boldsymbol{\sf{x=11}}[/tex]
Between which two integers does √84 lie?
Answer:
Step-by-step explanation:
Between 9 and 10.
Why?
Because sq of 9 is 81 and sq of 10 is 100 which gives us the gesture that sq.rt of 84 is between 9&10.
Hence, Two integers are 9 and 10.
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Which postulate should be used to show that the
triangles are congruent?
SSS should be used to show that the triangles are congruent.
What is the congruent triangle?
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them. Two triangles must have the same angles and, as a result, must be congruent if their sides are the same.
From the given images of the triangles, it is clear that the the legs of the triangles are equal to each other.
If two legs of two triangles are equal, then the bases are equal to each other.
Thus to prove that the triangles are congruent to each other, apply SSS postulate.
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How do you solve this problem?
Given the ordered pairs A(1,4) and B(0,-4), create a sine and cosine equation
The sine and cosine functions with the ordered pairs A(1,4) and B(0,-4) are given as follows:
Sine: f(x) = 4sin(π(x + π/2)).Cosine: g(x) = -4cos(πx).What is the definition of the trigonometric functions?Both the sine and the cosine functions have similar definitions, given as follows:
f(x) = asin(b(x+c))+d.g(x) = acos(b(x+c))+d.The meaning of the coefficients of the functions are presented as follows:
a is the amplitude of the trigonometric function.b: The period of the trigonometric function is of 2π/b.c is the phase shift of the trigonometric function.d is the vertical shift of the trigonometric function.The functions vary between -4 and 4, hence the amplitude is given as follows:
a = 4.
This is the standard oscillation for a trigonometric function with amplitude 4, between -4 and 4, hence the vertical shift is of:
d = 0.
The difference between the x-coordinates of the maximum and the minimum value is half the period, hence the period is of 2 x 1 = 2, and the coefficient b is:
2π/b = 2
b = π.
The cosine function has no phase shift, it just is inverted, as it should assume a value of 4 at x = 0, hence the definition is:
g(x) = -4cos(πx).
The sine function has a phase shift, as it should assume a value of -4 at -π/2, not π/2, hence it is shifted shift π/2 units, hence the definition is:
f(x) = 4sin(π(x + π/2)).
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Help! Im being timed
What statment about the graph is true?
The graph is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.as stated
Describe range.The term "range" refers to every potential value in a graph's output.
The result of range is seen in the y coordinate, and the range of potential values is given here.
0 ≤ y ≤ 5
Describe domain.The term "domain" refers to every conceivable value in a graph's input.
The x coordinate is the input, and the extent of potential values is
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Work out the lengths of sides a and b give your answer to the 1st decimal
The length of the side a = 9.43 cm and b = 12.04 cm
Consider the first triangle
The hypotenuse of the triangle = a
The base of the triangle = 5 cm
The length of the vertical side = 8 cm
Apply the Pythagorean theorem here
[tex]a= \sqrt{8^2+5^2}[/tex]
Find the square of the terms
a = [tex]\sqrt{64+25}[/tex]
a = [tex]\sqrt{89}[/tex]
a = 9.43 cm
Consider the second triangle
The hypotenuse of the triangle = 17 cm
The base of the triangle = 12 cm
The length of vertical side = y cm
Apply the Pythagorean theorem
b = [tex]\sqrt{17^2-12^2}[/tex]
b = [tex]\sqrt{289-144}[/tex]
b = [tex]\sqrt{145}[/tex]
b = 12.04 cm
Hence, the length of the side a = 9.43 cm and b = 12.04 cm
The complete question is
Work out the lengths of sides a and b give your answer to the 1st decimal
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find the annual salary of a person who is paid $3,800.00 per month
The number of books in Hannah's home library can be described by n(x) = 4x + 2, where x is the number of months that have passed since she began expanding her library. Describe how n(x) is related to its parent function and interpret the function in the context of the situation.
n(x) is a vertical dilation of scale factor 4 followed by a translation of 2 units upwards of the parent linear function.
How is n(x) related to the parent function?
The parent linear function is:
f(x)= x
And the function n(x) is:
n(x) = 4x + 2
If first we apply a vertical dilation of scale factor 4 to the parent linear function, we will get:
n(x) = 4*f(x)
And if now we apply a translation of 2 units upwards, then we get:
n(x) =4*f(x) + 2
Replacing f(x) by x we get:
n(x) = 4*x + 2
And we returned to n(x), so these are the transformations that define our function in terms to the parent function.
And the slope 4 means that each month 4 books are added, the y-intercept 2 means that she starts with 2 books.
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If you cross 2 parrots that are heterozygous for color and barring, what is the possibility, in the form of a ratio, of a blue and unbarred parrot as offspring? green parakeets dominant (g) blue are recessive (g) barred wing pattern dominant (b) unbarred recessive (b).
1/16 is the ratio of a blue and unbarred parrot as offspring
Dihybrid cross:
Dihybrid cross is a cross between two individuals with two observed traits that are controlled by two distinct genes. The idea of a dihybrid cross came from Gregor Mendel when he observed pea plants that were either yellow or green and either round or wrinkled. Crossing of two heterozygous individuals will result in predictable ratios for both genotype and phenotype in the offspring. The expected phenotypic ratio of crossing heterozygous parents would be Deviations from these expected ratios may indicate that the two traits are linked or that one or both traits has a non-Mendelian mode of inheritance.
When two heterozygous parents for color (Gg) and barring (Bb) are crossed, each parent's genotype is GgBb. Each parent produces four gametes, such as GB, Gb, gB, and gb. As a result, the total number of offspring will be 16, as each parent produces four gametes. Nine will be G B_, three will be G bb, three will be ggB_, and one will be ggbb.
Therefore, 1/16 is the ratio of a blue and unbarred parrot as offspring
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How to solve and find derivative of y at 1
After differentiation of function with respect to y, the value of y'(1) is 0.225.
In the given question we have to find the value of derivative of y at 1.
The given function is [tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]
To find the derivative of y at 1 we have to firstly derivate the given function with respect to y.
Now writing the given function in the y form
[tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]
Subtract x^2/36 on both side, we get
[tex]\frac{y^2}{64}=1-\frac{x^2}{36}[/tex]
Multiply by 64 on both side, we get
[tex]y^2=64-64\times\frac{x^2}{36}[/tex]
[tex]y^2=64-\frac{16x^2}{9}[/tex]
Differentiating with respect to y on both side
[tex]2y\frac{dy}{dx}=0-\frac{16\times2x}{9}[/tex]
[tex]2y\frac{dy}{dx}=\frac{32x}{9}[/tex]
Simplifying
dy/dx = 16x/9y
We can write dy/dx as y' so
y' = 16x/9y
We have to find the value of y'(1).
Since the y is the function of x so we put x=1 and we know y(1)=7.89, so
y'(1) = 16*1/9*7.89
y'(1) = 16/71.01
y'(1) = 0.225
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Rafi has $6,629 in an account that earns 10% interest compounded annually. To the nearest cent, how much interest will he earn in 4 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6629\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A=6629\left(1+\frac{0.1}{1}\right)^{1\cdot 4} \implies A \approx 9705.52~\hfill \underset{earned~interest}{\stackrel{9705.52~~ - ~~6629}{\approx\text{\LARGE 3076.52 }}}[/tex]
when the lengths of two opposite sides of a square garden were increased by x meters each and the lengths of the other two sides were decreased by x meters each, the area of the new garden was 64 square meters. what was the area of the original square garden?
the area of the original square garden is 80 square meters.
Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.
We want to find the area of the original square, so the value of a².
(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.
(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.
the area is the quantity that expresses the quantity of a location on the aircraft or on a curved surface. The place of an aircraft region or plane vicinity refers back to the location of a form or planar lamina, at the same time as floor area refers to the place of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of fabric with a given thickness that might be vital to style a model of the form, or the amount of paint necessary to cowl the surface with an unmarried coat. it's by far the two-dimensional analog of the duration of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).
place plays a vital position in current mathematics. further to its apparent importance in geometry and calculus, the place is associated with the definition of determinants in linear algebra and is a simple asset of surfaces in differential geometry. In analysis, the vicinity of a subset of the plane has defined the use of the Lebesgue measure, though no longer every subset is measurable. In the trendy, region in better mathematics is visible as a unique case of quantity for two-dimensional regions.
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Find the solution for this system of equations. 12x 15y = 34 -6x 5y = 3 x = y =
The solution for this system of equations. 12x+ 15y = 34 -6x+ 5y = 3
is (x,y) =(2/3, 8/5)
Given a system of equations,
12x + 15y = 34 ------(1)
-6x + 5y = 3 ------(2),
To solve this we use the elimination method
In the elimination method, you either add or subtract the equations to get an equation in one variable.
Equation (1) + 2 × Equation (2),
We get,
(12x+15y=34)+(-12x+10y=6)
⇒ 15y+10y=34+6
⇒ 25y=40
⇒ y=40/25
⇒ y=8/5
From equation (2),
⇒ -6x+5(y)=6
⇒ -6x+5(8/5)=6
⇒ -6x+8=6
⇒ -6x=-2
⇒ x=2/3
Hence the solution for this system of equations. 12x 15y = 34 -6x 5y = 3
is (x,y =(2/3, 8/5)
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Effie and Kristen live 23.6 km apart. They decided to cycle to the pool at the park, which is located between their homes. If Jennifer lives 5.2 km closer to the park, how far did they each cycle?
Answer:
I think 28.6
Step-by-step explanation:
Form a polynomial with real coefficients having the given degree and zeros. Degree 4; zeros: multiplicity 2 Question content area bottom Part 1 Let a represent the leading coefficient. The polynomial is . (Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.)
The equation of the polynomial equation P(x) = (x + 3)²(x - 5)²
How to determine the polynomial equation?The given parameters are
Degree of polynomial = 4-3 is a zero of multiplicity 25 is the only other zeroThe sum of multiplicities of the polynomial equation must be equal to the degree.
This means that the multiplicity of the zero 5 is 2
The equation of the polynomial is then calculated as
P(x) = (x - zero)^multiplicity
So, we have
P(x) = (x - (-3))² * (x - 5)²
This gives
P(x) = (x + 3)²(x - 5)²
Hence, the equation is P(x) = (x + 3)²(x - 5)²
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Possible question
Form a polynomial with real coefficients having the given degree and zeros.
Degree 4;
Zeros: -3 and 5 with multiplicity 2
What is the value of -7 + (-12) + 81? Pls help asap
A: -100
B: -76
C: 62
D: 86
Answer: C: 62
Step-by-step explanation: -7 + -12 = -19
-19 + 81 = 62
twenty tiles are numbered through and are placed into box . twenty other tiles numbered through are placed into box . one tile is randomly drawn from each box. what is the probability that the tile from box is less than and the tile from box is either even or greater than ? express your answer as a common fraction.
The probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.
In the given question we have to find the probability of first tile is less than 15 and the second tile is even or greater than 25.
Tiles numbered 1 through 20 are placed in a box.
Tiles numbered 11 through 30 are placed in a second box.
One tile is randomly drawn from each box.
Now finding the probability of first tile is less than 15.
Since in first box tile is numbered as 1 to 20.
So the outcomes of less than 15 = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
So favourable outcome = 14
Total number of tile = 20
So the probability = 14/20 = 70%
Now finding the probability of second tile is even or greater than 25.
Since in second box tile is numbered as 11 to 30.
So the outcomes of even or greater than 25 = 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 29, 30
So favourable outcome = 12
Total number of tile = 20
So the probability = 12/20 = 60%
Hence, the probability of first tile is less than 15, is 70% and the second tile is even or greater than 25, is 60%.
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The right question
"Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30 are placed in a second box. One tile is randomly drawn from each box. Find each probability. The first tile is less than 15 and the second tile is even or greater than 25."
Solve five and five-sixths minus three and three-fourths plus two and one-half equals blank line.
Step-by-step explanation:
55/12
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In triangle XYZ, m∠Y = 62.45° and m∠Z = 41.8°. Determine the measure of the exterior angle to ∠X.
Answer:
m∠X=75.75
Step-by-step explanation:
A triangle's angles combine to 180 degrees. Subtract 62.45+41.8 from 180.
The measure of the exterior angle of the triangle is given by ∠A = 104.25°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ΔXYZ
Let the measure of the exterior angle be m∠A
Now , the measures of the angles of the triangle are
The measure of angle ∠Y = 62.45°
The measure of angle ∠Z = 41.8°
The measure of angle ∠X = m∠X
Now , for a triangle , the sum of the interior angles = 180°
So ,
m∠X + m∠Y + m∠Z = 180°
Substituting the values in the equation , we get
m∠X + 62.45° + 41.8° = 180°
Subtracting 104.25 on both sides of the equation , we get
m∠X = 75.75°
Now , the measure of angle exterior to m∠X be ∠A = 180° - m∠X
The measure of m∠A = 180° - 75.75°
The measure of m∠A = 104.25°
Therefore , the measure of ∠A = 104.25°
Hence , the exterior angle of the triangle is ∠A = 104.25°
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A manatee can swim an average of 10 miles every 2 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.
The distance Manatee will swim in 5 hours is 25 miles.
What is distance?Distance can be defined as the length between two points.
To calculate the distance manatee can swim in 16 hours, we use the equation below
y₁/x₁ = y₂/x₂............ Equation 1Make y₂ the subject of the equation
y₂ = (y₁×x₂)/x₁............ Equation 2Where:
y₁ = 10 milesx₁ = 2 hoursx₂ = 5 hoursSubstitute these values into equation 2
y₂ = (10×5)/2y₂ = 25 mile.Hence, manatee can swim a distance of 25 miles.
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Complete question: A manatee can swim an average of 10 miles every 2 hours how far can it swim in 5 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.
Please help me please
Find the circumcenter of the triangle formed by the vertices (4 2) (3 3) and (2 2)
Coordinate of circumcenter of the given triangle = (3, 2)
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of circumcenter be (x , y)
Distance of Circumcenter from (4,2) =
[tex]\sqrt{(x - 4)^2 + (y-2)^2[/tex]
Distance of Circumcenter from (3, 3) =
[tex]\sqrt{(x - 3)^2 + (y-3)^2[/tex]
Distance of Circumcenter from (2,2) =
[tex]\sqrt{(x - 2)^2 + (y-2)^2[/tex]
By the problem,
[tex]\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\[/tex]..... (1)
Again,
[tex]\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\[/tex]...... (2)
Adding (1) and (2)
[tex]2x = 6\\x = \frac{6}{2}\\x = 3[/tex]
Putting the value of x in (1),
3 + y = 5
y = 5 - 3
y = 2
Coordinate of circumcenter = (3, 2)
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in rational expression what is the answer of 7n-7 divide n-1
The area of a triangle i 247 inche. If the width i 19 inche find the height of the triangle
[tex]\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh ~~ \begin{cases} b=\stackrel{width}{base}\\ h=height\\[-0.5em] \hrulefill\\ A=247\\ b=19 \end{cases}\implies 247=\cfrac{1}{2}(19)h \\\\\\ 494=19h\implies \cfrac{494}{19}=h\implies 26=h[/tex]
PLEASE HELP 15 POINTS!!
AND WILL MARK BRAINLIEST
The data in the table describes the preferred type of exercise of student athletes.
Cycling. Running Row Totals
Male 0.22 0.32 0.54
Female. 0.15 0.31 0.46
Column Totals 0.37 0.63. 1.00
What is the conditional relative frequency that a male prefers cycling? Round your answer to two decimal places.
0.41
0.58
0.59
0.62
Step-by-step explanation:
you take the specific number (males prefer cycling = 0.22) and the fitting total.
note there are 2 possibilities for that total :
all males
all people preferring cycling
the way it was phrased I would say the reference is all males.
the conditional relative frequency is then
0.22 / 0.54 = 0.407407407... ≈ 0.41
but if the meaning would be rather about how many of all people preferring cycling are male, then we would have
0.22 / 0.37 = 0.594594595... ≈ 0.59
both results are in your answer options.
I think the intended result is 0.41, because I understand the problem that way :
find the conditional relative frequency that a student athlete surveyed prefers cycling, given that the student is male.
the other should be phrased like
find the conditional relative frequency that a student athlete surveyed is male, given that the student prefers cycling.
PLEASE HURRY WILL GIVE BRAINILY Find the area of this triangle.
155
175
260
Area = [?] units²
Answer:
Area = 1/2 * base * height
Area = 1/2 * 155 * 175
Area = 13,563.75
(PLEASE HELP FAST) A 9-member team plans to run a 4-mile relay race. Distance markers are placed on the racecourse every 0.25 mile. a. Place an X on the number line at the approximate locations where the relay exchanges will take place. b. Will any of the relay exchanges take place at any of the 0.25-mile markers? If so, which one(s)? List the locations of all of the exchanges in decimal form.
Answer:
D or C
Step-by-step explanation:
The area of a parallelogram i 12 quare unit. One ide of the parallelogram i 18 unit long. The other ide i 6 unit long. Determine whether each dimenion could be the height of the parallelogram. Pick all correct. A. 2/3 unit
B. 3/2 unit
C. 2 unit
D. 3 unit
The possible heights of the parallelogram are 2/3 and 3
So, the correct option is A and C
The given expression:
area of a parallelogram, A = 12 square unit
a side of the parallelogram, = 18 units
another side of the parallelogram = 6 units
let,
the height of the parallelogram, h
The area of a parallelogram is given as;
Area = base (b) x height (h)
height (h) = Area/base(b)
From the given sides, the possible heights of the parallelogram are calculated as follows;
if the base, b = 18 units
height(h) = 12/18
= 2/3
Also, if the base, b = 6 units
height(h) = 12/6
= 2
Therefore, the possible heights of the parallelogram are 2/3 and 2
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Greg and Max left Ottawa for Toronto in their old jalopy to see the Grey Cup football game
The mileage gauge on the car was not working but the speedometer was. Their jalopy
averaged 40 mph from Ottawa to Toronto and 35 mph on the return trip. The total
traveling time for the round trip was 15 hours. Being good mathematics students, Greg and
Max were able to determine the distance between the two cities. What is this distance?
The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.
What is a Speedometer?
The instrument on a car that measures and shows speed is called a speedometer, and it is crucial for safety on roads and highways all over the world.By instantly sensing the speed on the ground, the speedometer on a car, truck, or motorbike can instantly notify the driver how fast the vehicle is travelling at any given moment.The instrument currently appears in many forms as a motorcycle speedometer or a bike speedometer and is digital in many modern automobiles.What is Distance?
The measurement of the distance between two objects or locations can be quantitative or occasionally qualitative.Distance in physics or common language can refer to a physical length or an assumption based on other factors. The term is also frequently used metaphorically to denote a measurement of the degree of separation or difference between two related objects.A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.How is Distance Calculated?
The distance between two locations can be calculated using the formula,
d = s x t,------ (1)
where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.
In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.
So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].
The total travelling time for the round trip, T = 15h ------(2)
Let the distance from Ottawa to Toronto be x.
From (1), we get that, the formula for the time taken is,
[tex]t=\frac{d}{s}[/tex]
So, the time taken to travel from Ottawa to Toronto,
[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex] ------- (3)
And, the time taken for the return trip (back from Toronto to Ottawa),
[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex] --------(4)
Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.
T = t_1 + t_2------(5)
Substituting the values of (2), (3), and (4) in (5), we get
15 = x/40 + x/35
--> 15 = 0.0535x
Simplifying,
x = 15/0.0535
--> x = 280.37 miles
Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.
To learn more about distance from the given link
https://brainly.com/question/26046491
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