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Related Questions
Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. The idea is to save on the cost of the cable by arranging the cable in a Y-shaped configuation. Centerville is located at ( 10 , 0 ) in the x y -plane, Springfield is at ( 0 , 5 ) , and Shelbyville is at ( 0 , − 5 ) . The cable runs from Centerville to some point ( x , 0 ) on the x -axis where it splits into two branches going to Springfield and Shelbyville. Find the location ( x , 0 ) that will minimize the amount of cable between the 3 towns and compute the amount of cable needed. Justify your answer.
To solve this problem we need to minimize the following function of x : f ( x ) =
We find that f ( x ) has a critical number at x =
To verify that f ( x ) has a minimum at this critical number we compute the second derivative f ' ' ( x ) and find that its value at the critical number is ,
a positive number. Thus the minimum length of cable needed is
Answers
Answer:
hi i dont understand this
Step-by-step explanation:
sorry
The function will be
[tex]f(x) = 9 - x + \sqrt[2]{ {x}^{2} + 9} [/tex]
and minimum value required will be
[tex]9 + \sqrt[3]{3} [/tex]
How to solve this problem?The steps are as follow:
[tex]f(x) = (9 - x) + \sqrt[2]{ (x^2 + 3^2) } \\ =(9 - x) + \sqrt[2]{ (x^2 +9)} \\ f(x) = \frac{2x}{ \sqrt{ {x}^{2} + 9} } - 1 \\ f(x) = 0 \\ \frac{2x}{ \sqrt{ {x}^{2} + 9} } - 1 = 0 \\ \frac{2x}{ \sqrt{ {x}^{2} + 9}} = 1 \\ 2x = \sqrt{ {x}^{2} + 9} \\ 4{x}^{2} = { x}^{2} + 9 \\ 3 {x}^{2} = 9 \\ {x} = \sqrt{3} [/tex]
so putting value of in f(x) we will get
[tex]f( \sqrt{3} ) = 9 - \sqrt{3} + \sqrt[2]{ { (\sqrt{3} )}^{2} + 9} \\ = 9 + 2 \sqrt{3} [/tex]
So The function will be
[tex]f(x) = 9 + \sqrt[2]{ {x}^{2} + 9}[/tex]
and minimum value required will be
[tex]9 + \sqrt[3]{3} [/tex]
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HELPP!! I report wrong answers!!
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19.214÷13
pls someone help me
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Answer:
1.478
Step-by-step explanation:
12. What is the perimeter of triangle ABC to
the nearest whole number?
A
19.5
49°
B
40°
C
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Step-by-step explanation:
61.945
62the perimeter of triangle ABC to
the nearest whole number
Please help, will give brainliest! Which is NOT equivalent to this expression? 4(3x^2+6x)
Answers
a triangle has angles that measure 50 degrees and 50 degrees what is the measure lf the third angle?
Answers
Answer:
80
Step-by-step explanation:
the combined angles of any triangle equal 180 degrees. take the known angles ( 50 and 50) and subtract their sum from 180. 180-100=80
During a competition, numismatist Aditi has been given Rs. 200 in Rs.1 denominations. The judge asks Aditi to allocate the Rs. 1 denominations into a number of pouches such that any amount required between Rs.1 & Rs. 200 can be given by giving out a certain number of pouches without opening them. Aditi thinks and asks the judge to give her 'x' number of pouches to keep the money, where 'x' is the minimum number of bags required to keep the total money. Can you guess the value of 'x'?
Answers
9514 1404 393
Answer:
8
Step-by-step explanation:
If the bags can either be given or not, each bag can assume one of two states. In order for there to be 200 possible combinations of items in one of two states, there must be at least log2(200) = 7.64 items. The minimum number of bags is x = 8.
_____
The contents of the 8 bags will be Rs. 1, 2, 4, 8, 16, 32, 64, 73.
Compute the discriminant D(x,y)D(x,y) of the function. f(x,y)=x3+y4−6x−2y2+3 f(x,y)=x3+y4−6x−2y2+3 (Express numbers in exact form. Use symbolic notation and fractions where needed.) D(x,y)=D(x,y)= Which of these points are saddle points? (2⎯⎯√,0)(2,0) (2⎯⎯√,1)(2,1) (−2⎯⎯√,1)(−2,1) (2⎯⎯√,−1)(2,−1) (−2⎯⎯√,−1)(−2,−1) (−2⎯⎯√,0)(−2,0) Which of these points are local minima?
Answers
The discriminant of function [tex]f(x,y)=x^3 + y^4 - 6x-2y^2+3[/tex] is 72xy³ – 24x and points (√2,0), (-√2, 1) and (-√2, -1) are saddle point, and points (√2, 1) and (√2, -1) are local minima.
A function is an expression in terms of one or more variable.
If f(x, y) is a two-dimensional function that has a local extremum at a point ([tex]x_o, y_o[/tex]) and has continuous partial derivatives at this point, then [tex]f_x (x_o, y_o)=0[/tex] and [tex]f_y (x_o, y_o)=0[/tex]. The second partial derivatives test classifies the point as a local maximum or local minimum.
Then
1. If D > 0 and [tex]f_{xx}(x_o, y_o) > 0[/tex] , the point is a local minimum.
2. If D > 0 and [tex]f_x_x (x_o, y_o) < 0[/tex], the point is a local maximum.
3. If D < 0, the point is a saddle point.
4. If D = 0, higher order tests must be used.
Given that
[tex]f(x,y)=x^3 + y^4 - 6x-2y^2+3[/tex]
[tex]f_x = 3x^2-6[/tex]
[tex]f_x = 0[/tex] implies that [tex]x = \pm\sqrt2[/tex]
[tex]f_y= 4y^3-4y[/tex]
[tex]f_y= 0[/tex] implies that y = 0; y = [tex]\pm[/tex]1.
Thus, the critical points are (√2,0), (√2,1), (√2, -1);(-√2,0), (-√2,1); (√2, -1).
[tex]f_{xx} = 6x[/tex]; [tex]f_y_y = 12y^3 - 4[/tex], [tex]f_{xy}= 0[/tex]
D(x, y) = [tex]f_{xx}f_{yy} - f_{xy}^2[/tex]
= 6x × (12y³ – 4)
D(√2, 0) = -24√2 < 0 implies (√2,0) is a saddle point.
D(√2, 1) = 48√2 > 0 ; [tex]f_{xx}(2, 1) = 6\sqrt2 > 0[/tex] implies (√2, 1) is local minimum.
D(√2, -1) = 48√2 > 0; [tex]f_{xx}(2, -1) = 6\sqrt2 > 0[/tex] implies (√2, -1) is local minimum.
D(-√2, 0) = 24√2 > 0; [tex]f_{xx}(-2,0) = -6\sqrt2 < 0[/tex] implies (-√2, 0) is local maximum.
D(-√2, 1) = -48√2 < 0 implies (-√2, 1) is a saddle point.
D(-√2, -1) = -48√2 < 0 implies (-√2, -1) is a saddle point.
Thus, (√2,0), (-√2, 1) and (-√2, -1) are saddle point, and (√2, 1) and (√2, -1) are local minima.
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Marlis has 765 songs on her ipod she deletes 153 of the songs what is the percent of decreasse in the number of songs on her ipod
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Answer:
20%
Step-by-step explanation:
Answer:
20%
Step-by-step explanation:
WO-Step Equations Pra
Solve each equation.
1) 3+ 5r=-47
Answers
Answer:
r=-10 Hope this helps! If I could have brainliest I'm trying to level to level up.
Step-by-step explanation:
Let's solve your equation step-by-step.
3+5r=−47
Step 1: Simplify both sides of the equation.
5r+3=−47
Step 2: Subtract 3 from both sides.
5r+3−3=−47−3
5r=−50
Step 3: Divide both sides by 5.
5r/5=-50/5
r=−10
Answer:
r=−10
Please help me with the question
Answers
Answer:
4(7+y) and 4·7+4·y
Step-by-step explanation:
4(7+y)= 28+4y
4·7+4·y= 28+4y
-3/4 ( 8y - 12 ) + 1/5 ( 15y - 30 )
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-3(y-1)
5th grade math. correct answer will be marked brainliest.
Answers
Answer:
common denominator: 48
Step-by-step explanation:
common denominator: 8x6=48
1/8 = 6/48
1/6= 8/48
13) A certain radioactive isotope decays at a rate of 0.1% annually. Determine the half-life of this isotope, to the
nearest year.
C) 301 yr
D) 500 yr
A) 7 yr
B) 693 yr
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Answer:
se__xxxx cha_t
Step-by-step explanation:
aaah aaaah
Complete the comparison : 17>?
Answers
Answer:
17>16
Step-by-step explanation:
Answer:
17 is greater than or (>) than any number lower than 17 :)
Step-by-step explanation:
For example, 17>16.. 17> 15, or 17> 14...ect.
Hope this helps! :)
Have a nice day <3
Periodic grab some phase shifts
Answers
Answer:
The sine function is:
[tex]y(x)=\frac{2}{3}sin[3\pi (x-\frac{2\pi}{3})]-2[/tex]
Step-by-step explanation:
We need to recall that a sine function can write as:
[tex]y(x)=Asin[B(x+C)]+D[/tex]
Where:
A is the amplitude of the functionB is the periodC is the phase shift leftD is the vertical shiftSo we just need to use the listed attributes
Therefore, the sine function is:
[tex]y(x)=\frac{2}{3}sin[3\pi (x-\frac{2\pi}{3})]-2[/tex]
I hope it helps you!
Frank can paint houses at the rate of 2/3 houses per week.
The value of the ratio is (colon form)
Frank paints for 12 weeks, he will paint houses.
Frank paints 10 houses, it will take him weeks.
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Answer:
0.25
Step-by-step explanation:
. Use 3.14
plss help
Answers
Answer:
A≈494.13
R = 12.54
D = 25.08
Step-by-step explanation:
Here is all the answers.
PLZZZZ give me brainliest!!!
Pls help this so hard
Answers
Answer:
616 cm²
Step-by-step explanation:
small cube (4 sides) = 8 x 3 x 4 = 96
large cube (4 sides) = 7 x 10 x 4 = 280
top and bottom of large cube = 12 x 10 x 2 = 240
(we would deduct the 3 x 3 area from the top of the large cube and add a 3 x 3 area for the top of the small cube. So that cancels each other out.)
total surface area = 96 + 280 + 240 = 616 cm²
A triangle has a base of (x+9) feet and a height of (4x+4). The expression below represents the area of the triangle.
12(x+9)(4x+4)
Which of the following choices represents the simplified form of the expression above?
Select one:
A. 4x2+36x+36
B. 2x2+80x+18
C. 2x2+18x−18
D. 2x2+20x+18
Answers
Answer:
I think the answer would be B
Step-by-step explanation:
Because we multiply, distribute and combine like terms
A Japanese bullet train travels 558 miles per 3 hours A. What is the rate B. How far does the train travel in 1 hour WHO EVER ANSWERS I WILL MARK BRAINLIEST
Answers
Answer:
Step-by-step explanation:
Remark
The rate is going to be the same as the distance travelled in 1 hour. The units will be different.
Formula
d = r * t
Givens
d = 558 miles
t = 3 hours
Problem A
r = d / t
r = 558/ 3 = 186 miles / hr
Problem B
Givens
r = 186 miles / hour
t = 1 hour
d = ?
Solution
d = 186 mi/hr * 1 hr
d = 186 miles
Note
This looks really trivial, but it's not. You have to learn to see the difference between a number and its units. It's not very often that the numbers will be the same, but if the units differ, then it is an entirely different question.
Pls help I’m failing I need a good grade
Answers
The answer is B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Find the area of the figure.
= m
(simplify your answer)
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What’s the answer to 7x when x=8 I need help please
Answers
Answer:
56
Step-by-step explanation:
7x8=56
Step-by-step explanation:
7(8)
= 56
use tye substitution property
Help me out thanks u !!!
Answers
Answer:
116
Step-by-step explanation:
All angles will add up to 360°
So just do 360 -55 -79 -110 = 116
Answer:
The answer is 116 because the sum of angles in a quadrilateral is 360 degrees.
5÷(4-3).3 evaluat'te
Answers
Answer:
1.5 thats the answer
Step-by-step explanation:
1.5
You score an 83 on the first of two exams. Write and solve an
equation to find the score x that you need on the second exam to
have a mean score of 85.
Answers
Answer: The mean is the same as the average. In order to find the mean, or average score of the two tests, you need to take the sum of the two tests, and then divide by the number of tests, which is two.
We don't know the score of the second exam. Let it = x
Then we have the following equation:
(88 + x)/2 = 93
88 + x = 2 * 93
88 + x = 186
x = 186 - 88 = 98
You need to score a 98 on the second test
Tamar surveyed six friends, asking each how many times he or she had ridden in a helicopter. The numbers of times she recorded were 0, 0, 0, 1, 3, and 8.
What is the mean absolute deviation of the number of times?
Round to the nearest tenth, if needed.
a. 0
b. 2
c. 2.3
d. 2.5
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well, to do this we first need to find the mean of all values.
we need to find the distance of each value from that mean (subtract the mean from each value, ignore minus signs)
Then find the mean of those distances.
so, after we do all of that with the given numbers, our final result would be 2.333333333..... (It goes on) we round it up to 2.3, and viola! the answer is C.
Answer: the answer is c
Step-by-step explanation: i took the test
Write an equation or inequality.
A number times three increased by seven is 25.
Answers
(n represents the unknown number)
I hope this helps
HELPP ASAP PLSS I’ll mark brainliest!!!