A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven")
Polygon Formula
The important polygon formulas are: The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n.
with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended
This polygon has 7 sides
heptagon is a seven sided polygon
decagon is a ten sided polygon
dodecagon is a 12 sided polygon
hexagon is a six sided polygon
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What is the value of x?. round to the nearest tenth, if necessary. responses x = 6 x, = 6 x = 6.3 x, = 6.3 x = 7 x, = 7 x = 9.2
Round to the nearest tenth , if necessary the value of x is 6.3.
What is right triangle ?
A right triangle is a type of triangle in which one angle is equal to 90 degrees. The side opposite this 90-degree angle is known as the hypotenuse, and the other two sides are known as the legs. The Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, applies to all right triangles.
To find the value of x ,
⇒ [tex]\frac{10}{x}=\frac{x}{4}[/tex]
⇒ [tex]x^{2} = 40[/tex]
⇒ x = 6.3
Hence , Round to the nearest tenth , if necessary the value of x is 6.3.
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help me pleaseeeeeeee dont guess
The inequalities given are 9) "And inequality, 10) "Or" inequality.
What are Compound Inequalities?Compound inequalities are inequalities which consist of two or more simple inequalities.
"And" compound inequality has both the inequalities true.
"Or" compound inequalities have any one of them as true.
9. |5 + m| < 13
This can be written as,
-13 < 5 + m < 13
-13 - 5 < m < 13 - 5
-18 < m < 8
This is an "and" inequality. Because m can lie between -18 and 8.
10. 4 |y + 6| ≥ 3
|y + 6| ≥ 3/4
-3/4 ≥ y + 6 ≥ 3/4
-3/4 - 6 ≥ y ≥ 3/4 - 6
-6.75 ≥ y ≥ -5.25
The value of y can be either ≤ -6.75 or y ≥ -5.25. y cannot be both.
So this is an "or" inequality.
Hence the first one is and inequality and the second one is or inequality.
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Find the length of the indicated
side of the similar figure.
12
X
x = [?]
X
8
4
The length of the side indicated in the similar figure can be found using the concept of similarity.
Find the length of the indicated side?The length of the side indicated in the similar figure can be found using the concept of similarity.When two figures are similar, the corresponding sides are proportional.In this case, the side indicated in the figure is 8, and the side we are looking for is X.To find the length of X, we can set up a proportion and solve for X. The proportion would be 8/X = 12/8, which simplifies to X = 12.Therefore, the length of the side indicated in the similar figure is 12.The length of the indicated side of the similar figure is 4.This is because the two figures are similar, meaning they have the same shape and ratio of sides.This means that if one side is 8, the other will be 4, since 8/4 = 2.This theory is called the Proportionality Rule and states that if two figures are similar, the corresponding sides are proportional.To learn more about Proportionality Rule refer to:
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3. A skydiver started his jump from the airplane. He fell 4.9 m in the 1st second, 14.7 m
in the 2nd second, 24,5 m in the 3rd second. How far did he fall between the 7th and the
10th seconds?
Arithmetic or geometric
The distance between the 7th seconds and the 10th seconds is 29.4 m.
It is arithmetic.
How to determine how far did he fall between the 7th and the 10th seconds?An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is always the same, called the common difference.
Since the height in the 1st second, 2nd second and 3rd second are 4.9m, 14.7 and 24.5 respectively.
They have a common difference (d) of 9.8. That is:
d = 14.7 - 4.9 = 9.8
Thus, it is arithmetic
The formula for determining nth of an AP is given by:
nth = a + (n-1)d
where a is the first term, d is the common difference and n is the number of terms
7th seconds:
nth = a + (n-1)d
nth = 4.9 + (7-1)9.8 = 63.7 m
10th seconds:
nth = a + (n-1)d
nth = 4.9 + (10-1)9.8 = 93.1 m
distance between the 7th and the 10th seconds:
10th seconds - 7th seconds = 93.1 - 63.7 = 29.4 m
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Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct ? Why or why not
It is possible that Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct
The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example the little "2" says to use 8 two times in a multiplication: 82 = 8 × 8 = 64.
What are powers?
A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.
Since 2376÷10
It will give us
237.6
So to convert to standard form it will be
2376×10^-1
How
Since the point has been shifted to the right side
And it will definitely give us 2376.0
But the point zero is not necessary
10^1 also means 0.1
So it is possible
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Show that the quadrilateral with the given vertices is a trapezoid. Then decide whether it is isosceles.
The quadrilateral MNPQ is trapezoid but not an isosceles trapezoid .
What is a trapezoid?A trapezoid, as well known as a trapezium, is a closed, flat shape with four straight sides and one pair of parallel sides.
Here given points,
M(-2,0), N(0,4), P(5,4), and Q(8,0) are given.
We are familiar with the slope formula,
Slope = y2 - y1 / x2 - x1
So here,
Slope of MN = 4 - 0 / 0 - (-2)
= 4/2
= 2
Slope of NP = 4 - 4 / 5 - 0
= 0/5
= 0
Slope of PQ = 0 - 4 / 8 - 5
= -4/3
Slope of QM = 0 - 0 / -2 -(-8)
= 0/10
= 0
Therefore we can see, NP||QM and MN∦PQ.
Therefore MNPQ is a trapezoid because it has two parallel sides.
By using distance formula,
MN = [tex]\sqrt{0-(-2)^{2} +(4-0)^{2} }[/tex]
= √20
= 2√5 units
PQ = [tex]\sqrt{(8-5)^{2} +(0-4)^{2} }[/tex]
= √25
= 5 units
Here MN ≠ PQ , MN and PQ are not congruent to each other.
Therefore MNPQ not is a isosceles trapezoid.
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A 1. 50-kilogram ball is attached to the end of a 0. 520-meter string and swung in a circle. The velocity of the ball is 9. 78 m/s. What is the tension in the string? do not round your answer during any of your calculations until the end and then round to the nearest whole number. 3. 39 n 28. 2 n 276 n 74. 6 n.
The the tension in the string is 276 N. Thus, the correct answer is B.
The tension in the string provides the centripetal force needed to keep the ball moving in a circular motion. As the tension in the string increases, the centripetal force increases as well, and the ball will move in a smaller circle (the radius will decrease). Therefore, if the tension increases, the radius decreases and the velocity increases, and if the tension decreases, the radius increases and the velocity decreases.
To determine the tension in the string, we can use the equation:
Tension = m * v^2 / rWhere m is the mass of the ball, v is the velocity of the ball, and r is the radius of the circle.
In this problem:
m = 1.50 kgv = 9.78 m/sr = 0.520 mSo, tension:
= (1.50 kg) * (9.78 m/s)^2 / (0.520 m) = (1.50 kg) * 96.0864 m^2/s^2 / (0.520 m)= 276 NThe tension in the string is 276 N. Hence, the correct answer is B.
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What is an exponential function called?
An exponential function is a function in which the variable appears in an exponent.
The most common form of an exponential function is f(x) = aˣ, where a is a positive constant, known as the base of the function, and x is the variable. The variable x is called the exponent of the function.
The base, a, determines the growth rate of the function. If the base is greater than 1, the function will increase rapidly as x increases. If the base is between 0 and 1, the function will decrease rapidly as x increases.
Exponential functions can also be written in the form y = a×bˣ, where a and b are constants, b is the base and x is the exponent. In this form, a represents the y-intercept of the function, which is the point where the function crosses the y-axis.
An exponential function can be recognize by the presence of the variable in an exponent and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.
In conclusion, an exponential function is a function in which the variable appears in an exponent and is defined as f(x) = aˣ or y = a×bˣ, where a is the base of the function and x is the exponent.
The base determines the growth rate of the function and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.
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Shawn has 22 boxes of golf balls. Each box has three golf balls.
Look at each equation below. Decide if it can be used to find the total number of golf balls?
(SCREENSHOT BELOW)
Answer:
1) can 2) can’t 3) can’t 4) can
Step-by-step explanation:
There are 66 golf balls in total 1 and 4 are the only equations that equal 66
Find the measure of angle “x” in degrees. Round to two decimals places as necessary!! HELPP PLS
The value of x is 0.01
What is the measure of a degrees?Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees. We'll just take into account angles between 0° and 360° for the time being; however, we'll take into account angles higher than 360° and negative angles later, in the section on trigonometric functions.
Minutes and seconds can be used to further split degrees, but this separation is less common than it once was. Minutes are the 60 equal pieces that make up each degree. Thus, seven and a half degrees can also be written as seven degrees and thirty minutes, or seven°30'. Additionally, each minute is divided into 60 equal seconds.
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1. Which polygon or polygons are regular? (2 points)
Answer:
the first and the third
Step-by-step explanation:
How do you convert base 10 to base E?
To convert from base 10 to base e, we need to split down a number in base e into the powers of e.
When we convert from base 10 to base e, the pattern will be exactly the same. It will be just with e instead of 10.
For example, to see how many digits (before the decimal point) of ln(12) = 2.4849...
It means that the first digit will be on the e^2 position. Now lets find:
12 / e^2 = 1.624…
So, there will only be a 1 in the e^2 position. The remaining is 12 – e^2. The next position is e^1 position. To find out what’s on this position, we need to do the following calculation:
(12 – e^2) / e = 1.696…
The next digit will also be a 1.
Now we do the 1’s position:
(12 – e^2 – e) / 1 = 1.892…
Next digit’s a 1.
We can continue for a few more decimal places:
(12 – e^2 – e – 1) / e – 1 = 2.426…
Next digit’s a 2.
(12 – e^2 – e – 1 – 2 * e – 1) / e – 2 = 1.159…
Next’s digit a 1.
So, 12 in base e is 111.21…
Since e is irrational and 12 is not, this will be never ending. But there will only can be 0’s, 1’s, and 2’s, since e is less than 3.
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what is the measure of the length of a rectangle with a perimeter of 10 inches and a width of 2 inches?
Answer:
3 inches
Step-by-step explanation:
The perimeter is the sum of all the sides of a shape. A rectangle has 4 sides.
2 * 2 = 4
One side is 2 in., so the parallel side is also 2 in.
10 - 4 = 6
Subtract the sum from the perimeter.
6 / 2 = 3
Since there are two sides left, divide by 2.
SOMEONE HELP ME PLEASE DUE TONIGHT
HI is 7 because all sides are equal. K is 100 because J is 40 and L is also 40 because they are equal. All triangles are equal to 180. 40+40+100=180
i cant figure this out
Answer:
4^2 or 16
Step by step explanation:
4^5 = 4x4x4x4x4
4^3 = 4x4x4
4^5 ÷ 4^3 = 4x4x4x4x4 ÷ 4x4x4 = 4x4
4x4 = 4^2 = 16
PLSSS HELP ME LAST ONE AND I PASS PLEASEEEEEE HELP
Answer: D
Step-by-step explanation:
Answer:
D) 320 pi
Step-by-step explanation:
pi*r^2*h is the equation for the volume of a cylinder.
If you plug in the given values, then you get 320pi.
The answer is D) 320 pi.
Hope this helped! :)
Which graph represents the inequality y is less than negative one-third times x plus 1?
A graph which represents the inequality y is less than negative one-third times x plus 1 is shown in the image below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).How to determine the graph which represents the inequality?In order to determine and plot the graph which represents the inequality, we would first of all translate the word problem into an algebraic equation as follows;
y is less than or equal to one-third times x plus 1 ⇒ y < x/3 + 1.
Next, we would use an online graphing calculator to graphically solve the given inequality.
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Answer:
B
Step-by-step explanation:
The graph shows the answer accurately
What is the solution to the system that is created by the equation y = negative x + 6 and the graph shown below?
On a coordinate plane, a line goes through (0, 0) and (4, 2).
What is the solution to the system that is created by the equation y = negative x + 6 and the graph shown below?
On a coordinate plane, a line goes through (0, 0) and (4, 2).
(4, 2)
(–4, –2)
(–8, –4)
(6, 3)
The solution of system of equations are (4, 2). Therefore, option A is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given equation is y=-x+6 ---------(I)
On a coordinate plane, a line goes through (0, 0) and (4, 2).
Here, slope m=(2-0)/(4-0)
= 1/2
Substitute m=1/2 and (4, 2) in y=mx+c, we get
2=1/2 (4)+c
c=0
y=1/2 x ---------(II)
Substitute equation (II) in equation (I), we get
1/2 x=-x+6
x=-2x+12
x+2x=12
3x=12
x=4
Substitute x=4 in equation (II), we get
y=2
Then, solution of system of equations is (4, 2)
Therefore, option A is the correct answer.
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Your math teacher tells you that the next week's test is worth 100 points and contains 28 problems. Each problem is worth either 5 or 3 points. How many of each type of problem are on the test?
Therefore , equation problem answer is there will be six 5 mark problem and twenty two 3 mark problem.
How do you quickly solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.
Here,
Given :
Since the total number of points is 28, we can create the Let Statements:
Let x= one type of question
Let 28-x= the other type of questions
Create an equation to relate the number of questions to the price
100=5x+3(28-x) Distribute
100=5x+82-3x Subtract 76 from both sides of the equation
100-82=5x-3x Combine like terms
18=3x Divide both sides by 3
x=6
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There are 8 squares and 2 triangles. What is the simplest ratio of triangles to total shapes?
Answer:
2:10 or 1:5
Step-by-step explanation:
Answer: 4 squares to 1 triangle
Step-by-step explanation: both can be divided by two and that is the largest number they can be divided into
I'LL GIVE BRAINIEST TO WHOEVER ANSWERS THIS CORRECTLY
3. The function represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.
(a) During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
(c) When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
Answer:
The correct answer is A
I hope that helped.
Step-by-step explanation:
Select the reason why these triangles are
similar. If they are not, select "Not similar."
A. AA
C. SAS
60°
/60°
B. SSS
D. Not similar
The reason why these triangles are similar is A. AA.
What is similar triangle?A similar triangle is a triangle in which the corresponding angles are congruent (equal in measure) and the corresponding sides are in proportion. This means that the corresponding sides of two similar triangles are in the same ratio, but the triangles may be different sizes.
What is triangle?A triangle is a three-sided polygon. It is defined by three points in a plane, called its vertices, and the straight lines connecting each pair of these points, called its sides. The three angles of a triangle always add up to 180 degrees.
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in 1988, I paid$8450 brand new car, but boy, did that car depreciate. by 1993, it was only worth $2200
write an equation that will model this situation. round your rate the nearest 4 places
y = 8450(0.7640)ˣ is the equation that will model this situation
How to write an equation that will model this situation?The general form of exponential equation is given by:
y = abˣ
Where a is the initial value of the car, b is the depreciation rate and x is the number of years
When x = 0, y = $8450:
y = abˣ
8450 = ab⁰
a = 8450
In 1993, x = 1993 - 1988 = 5 years and y = $2200:
y = abˣ
2200 = 8450b⁵
b⁵ = 2200/8450
b = [tex]\sqrt[5]{}[/tex](2200/8450)
b = 0.7640
Thus, the equation that model the situation is y = 8450(0.7640)ˣ
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if each quadrilateral below is a kite, find the missing measures
please hurry
A quadrilateral shape called a trapezoid that has exactly one set of parallel sides. Isosceles Trapezoid: A trapezoid with congruent non-parallel sides.
What are angles in a quadrilateral?A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed by two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle.
With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. A quadrilateral's internal angles add up to 360 degrees in all cases. The four angles found at each vertex of a four-sided form are referred to as the interior angles of a quadrilateral and are the only angles in a quadrilateral. Every quadrilateral's internal angles add up to 360 degrees.
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Five Smithtown High School students are saving up to buy their first cars. They all have after-school jobs, and their weekly sala-ries are listed in the table. (Table: Emily $110, Sam $145, Danielle $130, Katie $160, Stephanie $400)
a. What is the mean weekly salary for these students?
b. What is the median salary?
c. Whose salary would you consider to be an outlier?
d. Which number do you think is better representative of the data, the mean or the median?
e. Explain your answer to part d.
Answer:
A. $189.
B. $130.
C. Stephanie's.
D. The Mean.
E. The mean is the average of the data. The Median is just the middle number which doesn't reveal all that much about the data.
Answer:
A.) $189
B.) $145✔️ | *(not $130❌)*
C.) Stephanie's
D.) Median✔️ | *(not "mean"❌)
E.) Because there is an outlier, the median is better representative than the mean.
Which description best compares the graphs of the two functions below?
A description which best compares the graphs of the two functions above include the following: B. The line for function A is steeper.
How to compare the two functions?In order to compare the two functions, we would have to find the slope of function B based on the data points contained in the table by using the slope formula.
Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Substituting the given points into the slope formula, we have the following;
Slope, m = (-1 - (-2))/(3 - 0)
Slope, m = (-1 + 2)/3
Slope, m =1/3
From function A y = 3x - 2, the slope is equal to 3. Consequently, we can logically deduce that the line representing function A is steeper than the line representing function B because its slope is bigger i.e 3 > 1/3.
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The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
If the equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books. The number of books is 4.
How to find the number of books?Given data:
Equation: 3.95m + 8.95b = 47.65
Where:
Magazine, m = 3
Now let find the number of book by using the equation to solve for b
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
Collect like terms
8.95b = 35.8
Divide both side by 8.95b
b = 35.8/8.95
b = 4 books
Therefore we can conclude that the number of books is 4.
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The complete question is;
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
How do you find the sides of a triangle given the vertices?
So on solving the provided question we can say that - all angles of triangle - 180; x = 60
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
all angles of 180
x +90+30 = 180
x = 60
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Reggie made a cale drawing of a houe. In real life, the garage i 3 meter wide. It i 6 millimeter wide in the drawing. What i the drawing' cale factor?
The scale factor of Reggie's drawing is 1/500.
The scale factor of a drawing is the ratio of the size of the drawing to the size of the real object.
To find the scale factor of Reggie's drawing, we can use the information given: in real life, the garage is 3 meters wide, and in the drawing, it is 6 millimetres wide.
We know that:
Scale factor = size of drawing/size of the real object
We can use this equation to find the scale factor of Reggie's drawing:
Scale factor = 6 millimetres / 3 meters
To make the units consistent, we need to convert 3 meters to millimetres.
1 meter = 1000 millimeters
So, 3 meters = 3 * 1000 millimeters = 3000 millimeters
Now we can substitute this value into the scale factor equation:
Scale factor = 6 millimetres / 3000 millimetres
Simplifying the fraction: Scale factor = 1/500
Therefore, the scale factor of Reggie's drawing is 1/500. This means that every 1 millimetre on the drawing represents 500 millimetres (or 0.5 meters) in real life.
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42 POINTS!!!
Better Cable Company must provide service to a customer whose house is located 2 miles from the main highway. The nearest connection box for the cable is located 5 miles down the highway from the customer's driveway. The installation cost is $14/mile for any cable that is laid from the house to the highway. (The cable must be laid along the driveway to the house or across the field). The cost is $10/mile when the cable is laid along the highway. Determine where the cable should be laid so that the installation cost is as low as possible.
Please show work!
The required point is 0.25 miles away from the nearest point on the shore.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = lim h--> 0 (f(x + h) - f(x)) /(x + h - x).
here, we have,
It can be applied to minimize or maximize a function.
The given problem can be shown in the form of a diagram as follows
Suppose the underwater cable meet the shore at a distance x from the nearest point.
Then, the distance of cable in water is x² + 3.5² = x² + 12.25
And, the distance of cable in the ground is 10 - x.
As per the question, the cost of the laying cable can be represented as follows,
C(x) = 1200(10 - x) + 2400(x² + 12.25)
In order to minimize the cost the above function can be differentiated and equated to zero as,
C'(x) = -1200 + 4800x = 0
=> x = 1200/4800
= 1/4
= 0.25
Hence, in order to minimize the cost of the entire project the underwater cable should meet the shore at 0.25 miles away from the nearest point.
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