The equation of parabola is expressed as: y² = -20x
What is the equation of the parabola?
A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.
The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
Given, vertex = (0, 0)
Focus = (-5, 0)
We have to find the equation of the parabola.
The equation is of the form y = -ax²
Directrix x = 5.
As every point on parabola is equidistant from focus and directrix, the equation will be
y² + (x + 5)² = (x - 5)²
y² + x² + 10x + 25 = x² - 10x + 25
y² = - 10x - 10x
y² = -20x
Therefore, the equation of parabola is y² = -20x
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its a b and c they all equal 45
Answer:
1 * 45
5 * 9
3 * 15
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A lazy high school senior types up application and envelopes to and different colleges, but puts the applications randomly into the envelopes. What is the expected number of applications that went to the right college?
To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. The expected number of applications that went to the right college is 1.
Explanation:To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. Let's say there are n applications and n colleges.
The probability of a specific application going to the right college is 1/n. Therefore, the expected number of applications that went to the right college can be calculated as:
Expected number = Total number of applications * Probability of an application going to the right college
Expected number = n * (1/n)
Expected number = 1
The expected number of applications that went to the right college is 1. This means that, on average, one application will go to the right college.
At the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork. When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork. What is the market demand at $5?
Answer:
Market demand at $5 is 12 pork.
Step-by-step explanation:
In a market, the sum of individual demand for a product from buyers is known as market demand.
It is give that the at the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork.
So, market demand at $3 is
8 + 10 = 18
When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork.
So, market demand at $5 is
5 + 7 = 12
Therefore, the market demand at $5 is 12 pork.
Consider the rational expression (IMAGE ATTACHED)
3x^2−3/
3x^2+2x−1
Which statements are true?
Answer:
3x² is a term in the numeratorx + 1 is a common factorThe denominator has 3 termsStep-by-step explanation:
You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.
When you factor the expression, you get ...
[tex]\dfrac{3x^2-3}{3x^2+2x-1}=\dfrac{3(x^2-1)}{(3x-1)(x+1)}=\dfrac{3(x-1)(x+1)}{(3x-1)(x+1)}[/tex]
This reveals a common factor of x+1.
So, the above three observations are true of this rational expression.
State the postulate or theorem you would use to prove each pair of triangles congruent.
If the triangles cannot be proved congruent, choose "Not Possible."
Answer:
Not possible
Step-by-step explanation:
The only information we are given are the pairs of angles that are congruent which is not enough information to prove that they are congruent
The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The two triangles are congruent if two sides are as well and the angle (angle between any of these two sides) among one triangle is congruent to the comparable two sides as well as the angle of a second triangle.
The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.
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Calculate the simple interest paid on a loan of $544 at 3% for three months.
$48.96
$4.80
$4.90
$4.08
Answer:
Step-by-step explanation:
Answer: interest at the end of 3 months is $4.08
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 3 months = 3/12 = 0.25 years
P = $544
R = 3%
Therefore
I = (544 × 3 × 0.25)/100
I = 408/100
I = 4.08
Ron walks 0.5 mile on a track in 10 minutes. Stevie walks 0.25 mile on the track in 6 minutes find the unit rate for each walker in miles per hour. Who is faster?
Answer:
Ron's speed = 3 miles/hour
Stevie's speed = 2.5 miles/hour
On comparing we see Ron is walking faster than Stevie.
Step-by-step explanation:
Given:
Ron takes 10 minutes to walk on a track to cover a distance of 0.5 miles
Stevie takes 6 minutes to walk on a track to cover a distance of 0.25 miles
To find their unit rates in mile per hour and choose the faster one.
Solution:
Unit rate in miles per hour signifies their speeds. Thus, we will find out their speeds.
Ron:
Distance= 0.5 miles
Time = 10 minutes = [tex]10\ min\times \frac{1\ hr}{60\ min}=\frac{1}{6}[/tex] hours
Speed = [tex]\frac{Distance}{Time}=\frac{0.5}{\frac{1}{6}}=0.5\times6=3\ miles/hour[/tex]
Stevie
Distance = 0.25 miles
Time = 6 minutes = [tex]6\ min\times \frac{1\ hr}{60\ min}=\frac{1}{10}[/tex] hours
Speed = [tex]\frac{Distance}{Time}=\frac{0.25}{\frac{1}{10}}=0.25\times10=2.5\ miles/hour[/tex]
Thus, we have
Ron's speed = 3 miles/hour
Stevie's speed = 2.5 miles/hour
On comparing we see Ron is walking faster than Stevie.
Ten spheres each with radius of 2 cm are fully immersed in a cylinder of water with radius 10 cm. find the rise in water level
Answer:
no. of spjeres=10
radius of those cylinders =2cm
radius of the cylinder in which water is poured=10
rise in water water level =10×2÷10 = 2cm
The rise in water level will be 2 centimeters when spheres are fully immersed in a cylinder.
What is the volume of a cylinder?The volume of a cylinder is defined as the space occupied by the cylinder and the volume of any three-dimensional shape is the space occupied by it.
Ten spheres, each with a radius of 2 cm, are fully immersed in a 10 cm cylinder of water.
As per the given question, we have
The number of spheres = 10
The radius of those cylinders = 2cm
The radius of the cylinder in which water is poured = 10
According to the condition, the required solution would be as:
The rise in water level = 10 × 2 ÷ 10
The rise in water level = 20/10
Apply the division operation, and we get
The rise in water level = 2 cm
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Office Furniture Makers, Inc. uses machines to produce high quality office chairs for other firms. The initial cost of one customized machine is $750,000. This machine costs $12,000 a year to operate. Each machine has a life of 3 years before it is replaced. What is the equivalent annual cost of this machine if the required return is 10 percent? (Round your answer to whole dollars.)
The equivalent annual cost of the machine, considering a 10% return, is approximately $309,535 per year.
Explanation:First, accumulate the total cost over the lifespan of the machine which is $750,000 (initial cost) + ($12,000 * 3 years) = $786,000. The equivalent annual cost can be calculated using the formula for the present value of an annuity: PV = PMT [(1 - (1 + r)^-n ) / r], where 'PMT' is the payment per period, 'r' is the rate of return, and 'n' is the number of periods. Rearrange to calculate PMT: PMT = PV * r / (1 - (1 + r)^-n). Substituting in given values gives us, PMT = $786,000 * 0.1 / [1 - (1 + 0.1)^-3] = $309,535/year.
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Carol puts some green cubes and red cubes in a box. The ratio is 2:1. She adds 12 more cubes to the red cubes in the box and the ratio becomes 4:5. How many green cubes were in the box?
Answer:
16 green cubes are in the box.
Step-by-step explanation:
No. of red cubes at first (x):
4(x + 12) = 5(2x)
4x + 48 = 10x
6x = 48
x = 8
No. of green cubes:
= 8 * 2
= 16
Answer: 16 green cubes are in the box.
20 red cubes are in the box in the end.
Proof (the ratio in the end is 4:5):
= 16 is to 20
= 16/4 is to 20/4
= 4 is to 5
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If (x − 5) is a factor of the polynomial function f(x) = 3x^2 − 23x + 40, which of the following is another factor?
A. (3x − 8)
B. (3x + 8)
C. (8x − 3)
D. (8x + 3)
Answer:
option a is correct , watch explanation
Answer:
There are two factors of the function. You already said the first one, x-5. The second factor is Option A
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State if the triangles in each pair of similar. If so, State how you know they are similar and complete the similarity statement.
Answer:
Step-by-step explanation:
They are not similar. If they were, ∠LMF and ∠GHF would both have the same angle measure and they do not.
Final answer:
Mathematics question on similar triangles; triangles are similar if they have congruent corresponding angles and proportional sides obtained through AA, SSS, or SAS criterion. A similarity statement describes the correspondence of the vertices.
Explanation:
The question provided falls within the subject of Mathematics, specifically within the study of geometry and the concept of similar triangles. To determine if two triangles are similar, we must check if they have the same shape, which implies that their corresponding angles are equal and their corresponding sides are in proportion. In other words, two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. This can be verified by angle-angle similarity (AA), side-side-side similarity (SSS), or side-angle-side similarity (SAS). The similarity statement provides the order of correspondence of vertices between similar triangles.
When evaluating if triangles BAO and B1A1O are similar, we must compare their corresponding angles and sides. If the given information indicates that at least two angles of one triangle are congruent to two angles of another triangle (AA criterion), or that the sides are proportional (SSS or SAS criterion), then the triangles are similar. For instance, if ∠BAO ≅ ∠B1A1O and ∠BOA ≅ ∠B1O1A1, then by the AA criterion, the triangles are similar, and we could write the similarity statement as triangle BAO ∼ triangle B1A1O.
Complete the statement to describe the expression (a+b)(d+e)(a+b)(d+e)left parenthesis, a, plus, b, right parenthesis, left parenthesis, d, plus, e, right parenthesis. The expression consists of factors, and each factor contains 4 terms.
Final answer:
To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we expand it by multiplying each term. Simplifying the expression, we get a²*d² + 2a²de + 2abde + b²e².
Explanation:
To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we need to expand it. This can be done by multiplying each term in the first factor by each term in the second factor and then multiplying the result by the third factor. So the expression becomes:
(a+b)(d+e)(a+b)(d+e) = (a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e)
We can simplify this further by combining like terms:
(a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e) = a²*d² + 2a²de + 2abde + b²e²
The cost of a peanut butter bar is $0.07 more than the cost of a chocolate bar. If you buy 5 peanut butter bars and 6 chocolate bars, the total cost is $6.40. How much does the chocolate bar cost?
$0.61
$0.55
$0.54
$0.62
Hello!
To be quick and simple, your answer would be $0.55
The cost of the chocolate bar in the given scenario is $0.55. This was determined by solving a two-variable system of linear equations from the information provided.
Explanation:This problem is a classic example of a system of linear equations, specifically two-variable linear equations. Here, we need to find the cost of one chocolate bar and one peanut butter bar, and we have two pieces of information that can be translated into equations. The first information is that a peanut butter bar costs $0.07 more than a chocolate bar. The second is that 5 peanut butter bars and 6 chocolate bars total $6.40. We'll use these equations to solve for the variables.
Let's denote the cost of the chocolate bar as x and the cost of the peanut butter bar as y. Then, from the information given, we can form two equations:
y = x + $0.075y + 6x = $6.40Substitute the first equation into the second to solve for x:
5(x + $0.07) + 6x = $6.405x + $0.35 + 6x = $6.4011x + $0.35 = $6.4011x = $6.05x = $0.55So the cost of the chocolate bar is $0.55.
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if I'm in a plane flying at 512 miles per hour and a plane flies below me in the opposite direction, will it appear to fly slow or fast
Answer:
It appears to fly faster than its actual speed.
Step-by-step explanation:
In general, if talking about velocities, the direction of the movement should also be taken into account. For example, if two objects move in opposite directions, a person inside one object observes that the other one moving in the opposite goes faster than its actual speed (because the velocities are summed up). If they are moving in the same direction the opposite phenomenon is true (the velocities are subtracted).
Finally, in this example the planes move in opposite direction, therefore, a plane flying in the opposite direction will appear to fly faster.
An egg farm packages 264 total cartons of eggs each month.The farm has three different sizes of cartons.The small carton holds 8 eggs,and 1/6 of the total cartons are small.TThe medium carton holds 12 eggs and 2/3 of the total Cardinals are medium to large carton holds 18 eggs and the rest of the total clients are large determine how many of each size of the curtain is needed each month then determine how many eggs are needed to fill the 264 cartons show your work or explain your answers
I don't know.. can you please explain it?
Find a formula C(x,y,z) that gives the cost of materials for a closed rectangular box, with dimensions in feet. Assume that the material for the top and bottom costs $3 per square foot and the material for the sides costs $5 per square foot. Show all work in steps clearly.
Answer:
C(x,y,z)=6*x*y+10*x*z+10*y*z
Step-by-step explanation:
Lets assume that x is width, y is length and z is height. To find the area of the top and bottom surfaces we need to simply multiply length and width.
x*y
There is a 2 surface exist (top and bottom) we need to multiply this value with 2 again.
2*x*y
and the cost is 3$ for per square foot and the cost for top and bottom is:
6*x*y$
Surface areas of side surfaces are multiply of width, height and length, height:
x*z+y*z
There are 4 side surfaces exist. Therefore the are need to be multiply with 2.
2*x*z+2*y*z
and the cost is 5$ for per square foot and the cost for side surfaces is:
10*x*z+10*y*z
Total equality for cost is C(x,y,z)=6*x*y+10*x*z+10*y*z
To calculate the cost of materials for a closed rectangular box, use the formulas C(x,y) = 2 * (3xy) for the top and bottom and C(z,y) = 2 * (5zy) for the sides. Then, find the total cost by adding the costs together.
Explanation:To calculate the cost of materials for a closed rectangular box, we need to consider the dimensions of the box. Let's assume the dimensions are given as x, y, and z in feet.
The cost for the top and bottom parts of the box can be calculated using the formula C(x,y) = 2 * (3xy), where 3 is the cost per square foot and xy is the area of the top and bottom.
The cost for the side parts of the box can be calculated using the formula C(z,y) = 2 * (5zy), where 5 is the cost per square foot and zy is the area of the sides.
Finally, the total cost of materials for the box can be found by adding the costs for the top and bottom parts to the cost of the side parts: C(x,y,z) = C(x,y) + C(z,y).
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demochares has ived a fourth of his life as a boy, a fifth as a youth, a third as a man, and has spend 13 years in his dotage. how old is he?
Answer: 60 years
Step-by-step explanation:
Let x denotes the age of Demochares .
Time he spent as a boy = [tex]\dfrac{x}{4}[/tex]
Time he spent as a youth = [tex]\dfrac{x}{5}[/tex]
Time he spent as a man= [tex]\dfrac{x}{3}[/tex]
Time he spent in dotage= 13 years
As per given , we have the following equation:
[tex]x=\dfrac{x}{4}+\dfrac{x}{5}+\dfrac{x}{3}+13[/tex]
[tex]x=\dfrac{15x+12x+20x}{60}+13[/tex] [Take LCM]
[tex]x=\dfrac{47x}{60}+13[/tex]
[tex]x-\dfrac{47x}{60}=13[/tex]
[tex]\dfrac{60x-47x}{60}=13[/tex]
[tex]\dfrac{13x}{60}=13[/tex]
[tex]x=13\times\dfrac{60}{13}=60[/tex]
Hence, he is 60 years old.
Maggie can paint a fence in 9 hours, but Tom needs 12 hours to paint the same fence. How long does it take them to paint the fence if they work together? Round to the nearest tenth.
Working together, Maggie and Tom can paint the fence in 5.1 hours
Solution:Given that,
Maggie can paint a fence in 9 hours
So in 1 hour maggie paints, [tex]\frac{1}{9}[/tex] of the house
Tom needs 12 hours to paint the same fence
So in 1 hour, tom can paint [tex]\frac{1}{12}[/tex] of the house
To find: time taken to paint the fence if they work together
Let "a" be the time taken to paint the fence if they work together
So working together, in 1 hour, they can paint [tex]\frac{1}{a}[/tex] of the house
We can frame a equation as:
To see how much of the fence they can paint together in one hour, we add these together.
[tex]\frac{1}{9} + \frac{1}{12} = \frac{1}{a}[/tex]
[tex]\frac{1}{a}[/tex] is how much of the fence they can paint together in one hour. Therefore "a" is the number of hours it will take them both to paint the fence
On solving,
[tex]\frac{12 + 9}{12 \times 9} = \frac{1}{a}\\\\\frac{1}{a} = \frac{21}{108}\\\\a = \frac{108}{21} = 5.1428[/tex]
So working together, Maggie and Tom can paint the fence in 5.1 hours
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book
Answer: 120 pages
Step-by-step explanation:
42 p on Monday
2/5x on Tuesday
1/4x rest of book
---------------------------------------------------
42+2/5x+1/4x=x
42*20 +8x+5x=20x
840=20x-8x-5x
840=7x
x=840/7
x=120
The required number of pages in the book is given as 120 pages.
Given that,
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
let the number of pages in the book be x,
According to the question,
x - 42 - 2/5x = 1/4x
x - 2/5x - 1/4x = 42
x[1 - 2/5 - 1/4] = 42
x[20 - 8 - 5] / 20 = 42
x [7] / 20 = 42
x = 6 × 20
x = 120 pages
Thus, the required number of pages in the book is given as 120 pages.
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What is the total interest earned in two years on an account containing $500 at 3.5% interest, compounded annually?
$35.61
$35.16
$35.00
$36.51
Answer: Compound interest is $36.61
Step-by-step explanation:
Initial amount deposited into the account is $500 This means that the principal,
P = 500
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 3.5%. So
r = 3.5/100 = 0.035
It was compounded for 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.035/1)^1×2
A = 500(1.035)^2 = $535.61
Compound interest = 535.6 - 500 = $35.61
A man flies a kite at a height of 15 ft. The wind is carrying the kite horizontally from the man at a rate of 5 ft./s. How fast must he let out the string when the kite is flying on 32 ft. of string?
Answer:
4.4 ft/s
Step-by-step explanation:
Height = 15ft
Rate= 5 ft/s
Distance from the man to the kite= 32ft
dh/dt = 5 ft/s
h = √32^2 - 15^2
h = √ 1025 - 225
h = √800
h = 28.28ft
D = √15^2 + h^2
dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt
= h(225 + h^2)^-1/2 dh/dt
= (h / √225 + h^2)5
= (28.28 / √225 + 28.28^2)5
= (28.28 / √1024.7584)5
= (28.28/32)5
= 0.88*5
= 4.4 ft/s
If the function b(t) gives the number of boats it takes t people to cross a river, what is the appropriate domain?
Answer:
whole numbers
Step-by-step explanation:
The domain is the number of people. The smallest number of people you could have would be 0 people so the appropriate domain is whole numbers.
Make me the brainliest
Answer:
whole numbers
Step-by-step explanation:
A circle has its center at (0,0) and passes through the point (0,9). What is the standard equation of the circle?
x² + y² = 0
x² + y² = 9
x² + y² = 9²
Answer:
Step-by-step explanation:
I believe the answer is x² + y² = 9²
Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}. Find alpha.
Final answer:
To find the value of alpha given that alpha and beta are conjugate complex numbers, and alpha/beta^2 is real, we can use the equation |alpha - beta| = 2√3. We can substitute alpha = a + bi and beta = a - bi, and solve for a and b to find the value of alpha.
Explanation:
Let α and β be conjugate complex numbers such that α/β² is a real number and |α - β| = 2√3. We need to find the value of α.
Since α and β are conjugate complex numbers, they have the form α = a + bi and β = a - bi, where a and b are real numbers. Substituting these values into the given equation, we get:
|α - β| = |(a + bi) - (a - bi)| = |2bi| = 2|b| = 2√3
From this, we can conclude that |b| = √3. Since |b| is the absolute value of b, it is always positive. Therefore, we have two options: b = √3 or b = -√3.
If b = √3, then α = a + √3i. We can substitute this into the equation α/β² to check whether it is a real number.
α/β² = (a + √3i)/(a - √3i)² = (a + √3i)/(a² - 2a√3i - 3) = [(a(a² - 3) + √3i(3a - a²)] / (a² - 2a√3i - 3)
This expression is not a real number, so b ≠ √3.
If b = -√3, then α = a - √3i. We can substitute this into the equation α/β² to check whether it is a real number.
α/β² = (a - √3i)/(a + √3i)² = (a - √3i)/(a² + 2a√3i + 3) = [(a(a² + 3) - √3i(3a + a²)] / (a² + 2a√3i + 3)
This expression simplifies to (a(a² + 3) - √3(3a + a²))/ (a² + 3) = a - √3(2a + 1)/ (a² + 3)
For this expression to be a real number, the imaginary term √3(2a + 1) must be equal to 0. So, we have √3(2a + 1) = 0.
Solving this equation, we get 2a + 1 = 0, which implies a = -0.5.
Therefore, the value of α is α = -0.5 - √3i.
A bicycle moves approximately 7 feet with each revolution of the wheels. If the bicycle wheels are making 30 revolutions per minute, approximately how many feet will the bicycle travel in 1 hour?
Answer:
[tex]12,600\ ft[/tex]
Step-by-step explanation:
step 1
Find out the number of revolutions in one hour
we know that
The bicycle wheels are making 30 revolutions per minute
One hour are 60 minutes
so
using proportion
[tex]\frac{30}{1}\ \frac{rev}{min}=\frac{x}{60}\ \frac{rev}{min}\\\\x=60(30)\\\\x=1,800\ rev[/tex]
step 2
Find out how many feet the bicycle will travel in one hour
we know that
A bicycle moves approximately 7 feet with each revolution and the number of revolutions in one hour is 1,800
so
Multiply the number of revolutions in one hour (1,800 rev) by 7 feet
[tex](1,800)7=12,600\ ft[/tex]
Assume that a surveyor stands at the top of a mountain that is "h" feet tall. If the distance (in feet) that he can see is defined by d = 3200.2 SQRT(h), then answer the following. (a) How far can the surveyor see from the top of a 2000-foot mountain? (b) How tall is the mountain, if the surveyor can see 15 miles? (Note: 1 mile equals 5280 feet.)
Answer:
a) d = 143,117 ft
b) h = 612.45 ft
Step-by-step explanation:
If height of the mountain = h
And distance till the surveyor can see = d = 3200.2 SQRT (h)
Refer to attached file for graphical representation
Then;
A) If h=2000 ft
Then d =3200.2 √ (2000)
d = 3200.2 (44.72)
d = 143,117 ft
B) If d = 15 miles
1mile = 5280 ft
15 mile = 15*5280
15 mile = 79,200 ft
Therefore;
d = 79,200 ft
Since,
d =3200.2 √ (h)
79,200 = 3200.2 √ (h)
79200/3200.2 =√ (h)
√ (h) = 24.75
{√ (h)} ² = (24.75) ²
h = 612.45 ft
A right triangle has a hypotenuse of 70 feet and a leg of 35 feet. What is the length of the other leg? A. 51 feet B. 61 feet C. 78 feet D. 80 feet
URGENT!!!!!
Answer: the answers b i think
Good evening ,
Answer:
The right answer is B.
Step-by-step explanation:
If we apply the Pythagorean theorem we get
the length of the other leg is :
√(70^2-35^2)
= √(3 675)
= 60,621778264911.
:)
The total cost of producing a type of car is given by C(x)=12000−40x+0.04x2, where x is the number of cars produced. How many cars should be produced to incur minimum cost?
Answer:
Step-by-step explanation:
C'(x)=-40+0.08 x
C'(x)=0 gives
-40+0.08 x=0
x=40/0.08=500
C"(x)=0.08>0 at x=500
so C(x) is minimum if x=500
so 500 cars need to be produced for minimum cost.
or we can solve by completing the squares.
c(x)=12000+0.04(x²-1000 x+250000-250000)
=12000+0.04(x-500)²-0.04×250000
=0.04 (x-500)²+12000-10000
=0.04(x-500)²+2000
c(x) is minimum if x=500
To minimize the cost based on the provided quadratic cost function, 500 cars should be produced.
Explanation:This a problem of optimization in the arena of Calculus. The cost function C(x) = 12000-40x+0.04x2 is a quadratic function, and the minimum cost occurs at the vertex of the parabola described by this function.
For any quadratic function f(x)=ax2 +bx + c, minimum or maximum value occurs at x = -b/2a.
In this case, a = 0.04 and b = -40.
So minimum cost occurs when x = -(-40) / 2*0.04 = 500.
So, to incur minimum cost, 500 cars should be produced.
Learn more about Optimization in Calculus here:https://brainly.com/question/35182200
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why is it that when you take the squre root of a function that is squared you get an absolute value?
Answer and explanation :
When we square any number then its gives absolute value for example even when we square the negative numbers it will given positive , that is absolute value
So we can conclude that square of any number is absolute number
And then is we take square root of that absolute number it will always positive and absolute