Find point
on the x-axis so that AC + BC is a minimum.
A(4,-5), B(12,3)
Answers
Answer:-3
Step-by-step explanation:
The minimum value of a function can be obtained from its derivative
The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]
Reason:
Let (d, 0) represent the coordinate of the point, on the x-axis, we have;
[tex]\overline{AC}[/tex]² = (4 - d)² + (-5)²
[tex]\overline{AC}[/tex] = √((4 - d)² + (-5)²)
[tex]\overline{BC}[/tex]² = (12 - d)² + 3²
[tex]\overline{BC}[/tex] = √((12 - d)² + 3²)
[tex]\overline{AC}[/tex]² + [tex]\overline{BC}[/tex]² = L = 4² + (-5 - d)² + 12² + (3 - d)²
When [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] is minimum, we have;
[tex]\lim_{n \to \infty} a_n \dfrac{d}{dd} (\overline{AC} + \overline{BC}) = \dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = 0[/tex]
Which gives;
[tex]\dfrac{d}{dd} \left(\sqrt{ (4 - d)^2 + (-5)^2)} + \sqrt{ (12 - d)^2 + 3 ^2)} \right) = \dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8\cdot d + 41} }[/tex]
Therefore;
[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } + \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} } = 0[/tex]
[tex]\dfrac{2 \cdot d - 24}{2 \cdot \sqrt{d^2-24 \cdot d + 153} } =- \dfrac{2 \cdot d - 8}{2 \cdot \sqrt{d^2 - 8 \cdot d + 41} }[/tex]
Squaring both sides and cross multiplying gives;
16·d² - 528·d + 3456 = 0
Which gives;
16·(d - 24)·(d - 9) = 0
Therefore, d = 24, and d = 9
The point (9, 0), is closer to the given points than the point (24, 0), therefore;
The point on the x-axis that makes [tex]\overline{AC}[/tex] + [tex]\overline{BC}[/tex] minimum is the point [tex]\underline{(9, \, 0)}[/tex]
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Related Questions
Troy is chasing his little brother Kyle, but Kyle got a 30 second head start. If Kyle is traveling at 2 feet per second on his tri cycle and Troy is traveling at 5 feet per second on his skateboard, how many seconds will it be before Troy catches Kyle?
Answers
Answer:
20!
Step-by-step explanation:
when you add how far kyle's already traveled you get sixty, the rest of the tt lecture explains the rest, leaving you with 20 seconds
The table list the profits of some of the worlds largest corporations in 2013. List the companies in order from greatest to least amount of profit
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Answer:
C
Step-by-step explanation:
6. When rounded to the nearest hundredth, log, 7 =1.77. Which of the following represents the value of
log, 63 to the nearest hundredth? Hint: write 63 as a product involving 7.
Answers
Note: Consider the base of all is 3 instead of comma.
Given:
Consider the given value is [tex]\log_37=1.77[/tex].
To find:
The value of [tex]\log_363[/tex].
Solution:
Using properties of logarithm, we get
[tex]\log_363=\log_3(9\times 7)[/tex]
[tex]\log_363=\log_3(3^2\times 7)[/tex]
[tex]\log_363=\log_3(3^2)+\log_3(7)[/tex] [tex][\because \log ab=\log a+\log b][/tex]
[tex]\log_363=2+ \log_3(7)[/tex] [tex][\because \log_aa^x=x][/tex]
[tex]\log_363=2+1.77[/tex] [tex][\because \log_37=1.77][/tex]
[tex]\log_363=3.77[/tex]
Therefore, the value of [tex]\log_363[/tex] is 3.77.
Applying logarithm properties, it is found that:
[tex]\log_3{63} = 3.77[/tex]
We want to find [tex]\log_3{63}[/tex], considering that [tex]63 = 7 \times 9 = 7 \times 3^2[/tex], we have that:
[tex]\log_3{63} = \log_3{(7 \times 3^2)}[/tex]
The first property applied is:
[tex]\log{a \times b} = \log{a} + \log{b}[/tex]
Hence:
[tex]\log_3{63} = \log_3{(7 \times 3^2)} = \log_3{7} + \log_3{3^2}[/tex]
The next property is:
[tex]\log_a{a^b} = b[/tex]
Hence:
[tex]\log_3{7} + \log_3{3^2} = 1.77 + 2 = 3.77[/tex]
A similar problem is given at https://brainly.com/question/2620660
If f(x) = 2x – 1 and g(x) = f(x + 1), how does the graph of g compare with the graph of f?
O
A. g is a horizontal translation of f by 0 units.
B. g is a horizontal translation off by 1 unit.
C. g is a horizontal translation of f by 2 units.
D. g is a horizontal translation off by 3 units.
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Answers
Answer:
B
Step-by-step explanation:
the answer is b because the graph will shift to the left by 1 :D
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Answers
Answer:
28.76 °F
Step-by-step explanation:
The temperture of sea ice frozen ocean water is about -1.8 °C .
We are to convert to a temperture in fahrenheit using the formula F=(c) (9/5)+32
°C = -1.8°C
°F=(c) (9/5)+32
= [(-1.8°C × 9/5) + 32]°F
= [-16.2/5 + 32]°F
= [-3.24 + 32]°F
= 28.76°F
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Answers
Answer:
Danny does
Step-by-step explanation: 40 / 4 = 10
85 / 5 = 17
10 is less than 17 meaning that Danny is offering a better deal.
Hope this helps!
Answer:
Danny
Step-by-step explanation:
Danny offers $40 for four hours and Martin has a deal of $85 for five hours of swimming lessons so i know that Danny has the beater deal.
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4m+2mn+m^2+m+3m^2
Answers
Answer:
4m^2+ 5m +2mn
Step-by-step explanation:
The simplified value of 4m + 2mn + m² + m + 3m² is equal to 4m²+ 5m + 2mn.
The expression given is 4m + 2mn + m² + m + 3m².
We have to simplify the above expression.
What are the variables ?
A variable is a term which represents an unknown number or unknown value or unknown quantity.
As per the question ;
The expression given is 4m + 2mn + m² + m + 3m²
Let's simplify this by adding similar variables ;
4m , m are same variables
i.e., 4m + m = 5m
Similarly ,
m² and 3m² are same variables
i.e., m² + 3m² = 4m²
So ,
The value after simplification will be ;
4m + 2mn + m² + m + 3m²
= 4m²+ 5m + 2mn
Thus , simplified value of 4m + 2mn + m² + m + 3m² is equal to 4m²+ 5m + 2mn.
To learn more about variables click here ;
https://brainly.com/question/22965573
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
Hello everyone I need help with this worksheet it's ten problems answer the ones you know for me please it's homework.
I need help with finding the of two points.
1. (1,10) and (11,2)
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3. (-8, -6) and (-5, -6)
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Multiply both sides of the equation by 5
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reraange for p
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Step-by-step explanation:
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13 points answer this asappppp
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Answers
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Answer:
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Step-by-step explanation:
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Answers
Answer:
sometimes
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Step-by-step explanation:
The main difference between Save and Save As is that Save helps to update the lastly preserved file with the latest content while Save As helps to store a new file or to store an existing file to a new location with the same name or a different name.mark me brainlist if i help
Answer:
difference between save and save as is that save helps to update lastly preserved file with least content while save as to store a new file or to store an existing file to a new location with the same name or different name.
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Answers
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Answers
Answer:
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Step-by-step explanation:
if you distribute you get g(x)= x+4
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