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
The garden itself is 5 yards by 8 yards. The total area need to build this landscape
design is 60.9525 square yards. What is the width of the walkway?
O a) 0.725 yards
b) 2.9 yards
C) 1.45 yards
d) 4.58 yards
Answers
Answer: 1.45
Step-by-step explanation:
Sea ice is frozen ocean water, which freezes at a temperture of about -1.8 degress celsius. What is the temperture in fahrenheit use the formula F=(c) (9/5)+32
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
the equation y=7× represents a proportional relationship. What is the constant of proportionality
Answers
The answer is the number 7
PLEASE ANSWER NUMBER 2 3 AND 4 THANK YOU
Answers
simplify
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.
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Solve each triangle using the information provided. If necessary, round to the
nearest tenth.
Answers
Answer:
1) B = 66.5° c = 10.9
Step-by-step explanation:
I will do question one as an example. In general, for these questions you want to use the appropriate trigonometric ratios to solve for the variables and/or apply logic using rules regarding triangles. See attached image for all solving steps.
For side c, we can use Cosine of angle A for a ratio between 10 and c. When we write out the equation, we can solve for side c. So when we write it out, we get the equation:
cos23.5 = ¹⁰⁄c
c = ¹⁰⁄cos₂₃.₅
c = 10.9044 (make sure to round to the nearest tenth, which is one decimal place)
For angle B, since they have given two angles, you can solve for B since all angles of a triangle add up to 180 degrees.
So b = 180 - (90 + 23.5) = 180 - 113.5
b = 66.5
It is also possible to solve this using sine of angle B and solve it from there, but applying the theory this way is much simpler. (this is on the image if you're curious about it)I hope this helps you with the other 3 questions.
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]
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Answer:
I cant see the problems
Step-by-step explanation:
PLEASE HELP ME. due in a few minutes!!
Answers
Answer:
slove is 1
Step-by-step explanation:
if you distribute you get g(x)= x+4
the number invisivble in front of x is 1
4 - 0.34
show your work
Answers
Answer:
5
Step-by-step explanation:
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Step-by-step explanation:
18.....................
A 5-foot piece of aluminium wire costs $21.00. What is the price per inch?
Answers
The answer would be .35 cent.
Answer:
The price per inch is $0.35
Step-by-step explanation:
First you have to convert 5 feet into inches.
5·12= 60.
Then, divide the 21 by 60.
21/60 = 0.35
In conclusion, it costs $0.35 per inch.
Carrie and Alex are playing hiding and seek
Answers
Answer:
Ok.
Step-by-step explanation:
What is your question?
Answer: YESS
Step-by-step explanation:
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Y=??? Answer pls I will try to answer one of urs if u do
Answers
Answer:
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Step-by-step explanation:
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
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)
2. (4,6,) and (-11, -4)
3. (-8, -6) and (-5, -6)
4. (-2, -7) and (10, -16)
5. (-8, 5) and (-20, 13)
6. (18, 14) and (0, 5)
7. (6, -2,) and (6,0)
8. (-5, 14) and (-3,11)
9. (-18, 16) and (2, -9)
10. ( 4, 6) and (1,2)
Answers
Answer:
1. Slope = -4/5
2. Slope = 2/3
3. Slope = 0
4. Slope = 3/-4
5. Slope = 7/-12
6. Slope = 1/2
7. Slope = -2/0 --> Undefined
8. Slope = 3/-2
9. Slope = 5/-4
10. Slope = 4/3
Step-by-step explanation:
Ok so I'm assuming that you want the slope for all the two points. Basically, the formula for slope is rise/run, or y2-y1/x2-x1. Solve using that. For example, for number 1, it would be:
10-2/1-11 = 8/-10 = -4/5
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.
PLEASE HELP ME ASAP DUE IN A FEW MINUTES
Answers
Answer:
B
Step-by-step explanation:
the answer is b because the graph will shift to the left by 1 :D
13 points answer this asappppp
Find the value of the function below for the given x-value
F{x} = -5x-1 when x=-3
A.15
B 14
C-16
D-14
Answers
3) A cookie recipe calls for 9 cups of flour for 4
batches of cookies. How many cups of flour
per 1 batch of cookies? How many cups of
flour are needed for 11 batches of cookies?
Answers
Will give brainliest if correct.
Answers
Answer:
slope is 5, y intercept is -7
Step-by-step explanation:
In the form y=mx+c, m is the slope and c is the y-intercept.
Rearrange the formula to fit this form:
5x-y=7
-y=7-5x
y=5x-7
∴m(slope)=5
∴c(y-intercept)=-7
diffrentiate between save and save as
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.
Danny charges $40 for 4 hours of swimming lessons, Martin charges $85 for 5 hours of swimming lessons. Who offers a better deal?
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.
Please I need help with that, I am desperate. Brainliest for someone who gets it right
Answers
What is the solution to the linear equation? 2/5+p=4/5+3/5p
p=1
p=2
p=8
p=10
Answers
Answer:
p = 1
Step-by-step explanation:
Multiply both sides of the equation by 5
2 + 5p = 3 + 3p
reraange for p
p = 1
Will mark brainliest - GEOMETRY, show work plz
Answers
Answer:
1. Slope is 3/2
2. Slope is -2/3
3. Slope is 3/2
Step-by-step explanation:
Plz mark as Brainliest!
Answer:
Step-by-step explanation:
(-8-4)/(5+3)= -12/8= -3/2
perp. 2/3
y - 4 = 2/3(x + 3)
y - 4 = 2/3x + 2
y = 2/3x + 6
y - 4 = -3/2(x + 3)
y - 8/2 = -3/2x - 9/2
y = -3/2x - 1/2
If you go on this question at all you are a republican and that is good
Answers
Answer: hahshejehdbddndb
Step-by-step explanation:
Answer:
you chose poison thanks for the points payback
Step-by-step explanation:
don't do this to people
its rude and people actualy need help not free points
PLEASE HELP !! 10 POINTS AND BRAINLIEST !!!:)
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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
Answers
Answer:
C
Step-by-step explanation:
Mr. Jordan plans to leave the total of his savings to his four children. If they all are to receive the same amount of inheritance and the total savings that he has is $501,052.40, how much will each of them receive?
Answers
Answer:
$125,263.10
Step-by-step explanation:
In order to calculate the total amount that each one of the children will receive we simply need to divide Mr. Jordan's total savings by the total amount of children that he has. This will evenly divide his savings to the children so that each one has the exact same amount.
501,052.40 / 4 = 125,263.10
Therefore, each of the four children will receive a grand total of $125,263.10
If you roll a number cube 60 times and use the results to calculate the experimental probability of rolling a 1, the experimental probability of rolling a 1 will _____ be less than the theoretical probability of rolling a 1.
Answers
Answer:
sometimes
Step-by-step explanation:
Theoretical probability is fixed/remains the same because it is based on theory which is calculated, while the experimental probability is based on data that is gained from actually doing it. According to the law of large numbers, the average experimental probability always approaches the theoretical probability.