If x^2+y^2=1, what is the largest possible value of |x|+|y|?
Answers
If x² + y² = 1, then y = ±√(1 - x²).
Let f(x) = |x| + |±√(1 - x²)| = |x| + √(1 - x²).
If x < 0, we have |x| = -x ; otherwise, if x ≥ 0, then |x| = x.
• Case 1: suppose x < 0. Then
f(x) = -x + √(1 - x²)
f'(x) = -1 - x/√(1 - x²) = 0 → x = -1/√2 → y = ±1/√2
• Case 2: suppose x ≥ 0. Then
f(x) = x + √(1 - x²)
f'(x) = 1 - x/√(1 - x²) = 0 → x = 1/√2 → y = ±1/√2
In either case, |x| = |y| = 1/√2, so the maximum value of their sum is 2/√2 = √2.
An equation is formed of two equal expressions. The largest possible value of |x|+|y|=1.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the value of x²+y²=1. Therefore, The largest possible value of |x|+|y|=1.
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Related Questions
(1) In an investigation of toxins produced by molds that infect corn crops, a biochemist prepares extracts of the mold culture with organic solvents and then measures the amount of the toxic substance per gram of solution. From 6 preparations of the mold culture, the following measurements of the toxic substance (in milligrams) are obtained:1.4, 1.5, 1.8, 1.9, 2.5, 2.2Find a 99% confidence interval for the mean weight (in milligrams) of toxic substance per gram of mold culture in the sampled population.(2) Which of the following statements is true regarding part (a)?(A) The population mean must be inside the confidence interval. (B) The population does not need to be normal. (C) The population must be normal. (D) The population standard deviation ? must be known. (E) The population must follow a t-distribution.
Answers
Answer:
Following arew the solution to this question:
Step-by-step explanation:
Build the 99% trust period of harmful chemicals for both the community, because no information is provided mostly on population standard, they just use t-test procedure to find the necessary trust period.
The confidence interval of 99 percent for both the mean community is provided by,
[tex](\bar{x} \pm t_{\frac{\alpha}{2}} \frac{s}{\sqrt{n}})[/tex]
Use Minitab as seen below to get the necessary result:
T study one: weight
Variable N Mean stDev SE Mean 99% CI
weight 6 1.883 0.417 0.170 (1.197, 2.569)
The overall population weight of a toxic material in the above output is 99 percent (1.197, 2.569).
They may say of the 99% trust interval, the 99% trust between about 1.197 mg and 2.569 mg will lie throughout the average population.
Therefore, the option (A) is valid
One of conditions would be that the overall population should be standard in attempt to discover the standard deviation. This is the true option (C).
I do not understand the process/steps to do this.
Answers
Answer:
Step-by-step explanation:
Remark
An angle bisector sets up a triangle ratio that looks like the following proportion.
3x - 3 5x
====== = ====== Cross multiply
24 44
44*(3x-3) = 24*5x Remove the brackets on the left
132x - 132 = 24*5x Combine the right side
132x - 132 = 120x Add 132 to both sides
132x = 120x + 132 Subtract 120x from both sides
132x- 120x = 132 Combine
12x = 132 Divide by 12
x = 11
Jamal planted 53 fewer flowers than Heidi. Write an expression to show how many flowers Heidi planted.
Answers
Answer:
y = x + 53
Step-by-step explanation:
Let x be the number of flowers Jamal planted and y the number of flowers Heidi planted.
Jamal planted 53 fewer flowers than Heidi:
x = y - 53
Isolate the y.
x + 53 = y (Change the - sign to + sign when switching from different sides of an equation)
y = x + 53
Answer:[tex]j=h-53[/tex]
Step-by-step explanation:
Let h be the number of flowers Heidi planted, and j the number for Jamal.
[tex]j=h-53[/tex]
Find the Slope of the line through each pair of points: (-4,11),(1,-9)
Answers
Answer:
rise/run= -20/5= -4/1=-4 slope
or you sound use the slope formula (y2-y1)/(x2-x1)
(-9-11)/(1+4)
-20/5
-4
Step-by-step explanation:
0.00007547 in standard form
Answers
Answer:
it already is in standard form
Step-by-step explanation:
Answer:
7.5X10^5, I may be wrong.
Step-by-step explanation:
Pls help my brain hurt
Answers
Answer:
-15,-10,25
-1,-2,-2,-2,-6
3,2,-2,1,
Step-by-step explanation:
why do we use newton's
Answers
depends. for example: we use his telescopes to see farther. we use his laws of motion to understand certain events that are mostly on said motion
help me plz this is my first doing slopes
Answers
SOMEONE PLEASE ANSER THIS QUESTION ASAP!!!
Answers
Answer: 28
Step-by-step explanation:
Find the missing number of the unit rate--What is "x"?
205=x1
Answers
Is it not 205? because when you put the numbers in calculator it shows up 205 so I believe that is your answer.
I WILL GIVE YOU 30 POINTS!! ASAP PLZ
You use a line best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is -0.833. How confident can you be that your predicted value will be reasonably close to the actual value? Why or why not?
Answers
Answer:
no
Step-by-step explanation:
Write the following statement as a mathematical expression.
Let x be a number.
The quotient of two and a number, subtracted from seventeen
Answers
Answer:
17 - (2 / x)
Step-by-step explanation:
because it is being subtracted from 17. that goes first, and then x is being divided by 2.
Hope this helps!
Answer:
17 - (2 / x)
Step-by-step explanation:
i just did it and got a 100%
100 POINTS!!!!!
5x + 1 over 2 y2
What is the value of the expression above when x = 3 and y = 2? You must show all work and calculations to receive full credit.
Answers
Answer:
Step-by-step explanation:
5(3)+1=
15+1
16
2(2)^2=
2(4)
8
16 over 8 = 2
Answer:
2
Step-by-step explanation:
2
The cost of tickets to a local amusement park are $45 per adult and $25 per child. What would be the total cost for 5 adults and 8 children?
Answers
45x5=225
25x5=200
name of the each shape below
Answers
In a survey, 46 people, which was 20% of those surveyed chose red as their favorite color how many people were surveyed
Answers
Answer:
answer: 230
Step-by-step explanation:
20% is 1/5 of 100 so you multiply 46 by 5 and you get 230 people
hope this helps!!
Marta walked at 4.9 mile per hour for 0.89 miles. How fa did she walk?
Answers
Answer:
2.808 hope this helps :)
Answer:
I think it would be .89 miles because it says that she walked that distance.
Step-by-step explanation:
If it gives you the distance she walked, the speed won't change the distance traveled, only the amount of time paired with speed would change the distance.
The expression 2y + 2.6 is equal to ? for y = 1.4
Answers
Answer:
5.4 :))
Step-by-step explanation:
ok so first you take 2*1.4=2.8 (you replace the Y with the number)
so now you have 2.8+2.6 which is equal to 5.4
Answer:
5.4
Step-by-step explanation:
2*1.4 is 2.8. Now the expression is y2+2.6=. Now, that we figured out what 2y is, which is 2.8, we need to add on 2.6. 2.6 + 2.8 is equal to 5.4. Now, to write out the whole equation, it would look like this.
2y+2.6=?
y2+2.6=?
2.8+2.6=?
5.4
So in the end:
2y+(2.6)= 5.4
Real easy probability problem please help!
Answers
if u know that y=30 then what is y=4x-2
Answers
Answer:
x = 8
Step-by-step explanation:
y = 4x - 2
30 = 4x - 2
+ 2 + 2
32 = 4x
/ 4 / 4
8 = x
the foundation of a building is in the shape of a rectangle WITH THE LENGTH OF 20 METERS AND A WIDTH OF 18 METERS. TO THE NEAREST METER, WHAT IS THE DISTANCE FROM THE TOP LEFT CORNER OF THE FOUNDATION TO THE BOTTOM RIGHT CORNER
Answers
Answer:
Pythagoras theorem. 20^2 times 18^2 = distance^2
Jayden used the multiplication table below to determine that 8:14 is equivalent to 24:42.
Which statement explains why Jayden’s reasoning is correct?
a. The ratio 8:14 is 4:7 times 2, and the ratio 24:42 is 4:7 times 6.
b. The terms 8 and 14 are multiples of 2, and the terms 24 and 42 are also multiples of 2 when the table is extended.
c. The term 24 is a multiple of the term 8, and the terms 14 and 42 are multiples of 7.
d. The ratio 8:14 is equivalent to 2:7, and the ratio 24:42 is also equivalent to 2:
Answers
Answer:
A please give me brainlest im sorry if its wrong i tried
Step-by-step explanation:
Answer:
the answer is D
Step-by-step explanation:
Just trust me
A linear function models the height of a burning candle. Candle A comes out of the mold at 217 mm, and is expected to be at 193 mm after 3 hours of burning. The model for Candle B is h=260-5t, where h is the height in millimeters and t is the time in hours. What are the initial values for each candle? What do the initial values for each candle tell you?
Answers
Answer:222
Step-by-step explanation:
find the slope and y-intercept of the line in the graph. Express the answers as simplified fractions, if necessary.
Answers
Answer:
y=1 3/5x+-5
Step-by-step explanation:
So the y intercept is where your slope meets the middle, basically the y. So it hit the y on -5. And the rise and run 8/5 rise is 8 and run is 5. 8/5= 1 3/5. in equation it is y=1 3/5x+-5.
99x-99y=99 how to graph it
Answers
Answer:
Hope this helped!
Divide all sides by 99 so that you have
x-y=1
Take x to the other side as a negative
-y=x-1
Divide all sides by negative one
y=-x+1
So basically it will look like a straight line that has a negative slope and a y intercept of (0,1)
What is the area of a triangle whose vertices are D(3, 3), E(3, −1), and F(−2, −5)?
Answers
Answer:
10 units²
Step-by-step explanation:
5/8 m
Calculate the perimeter of a square with side length 5/8m
Give your answer as a mixed number.
Answers
Answer:
2.5 m
Step-by-step explanation:
perimeter of a square=side *4
5/8*4
5/2
2 1/2
Answer:
[tex]\boxed{2\frac{4}{8} }[/tex]
Step-by-step explanation:
Perimeter of a square = All 4 sides added up together
[tex]\frac{5}{8}+\frac{5}{8} +\frac{5}{8} +\frac{5}{8} = \frac{20}{8} =2\frac{4}{8}[/tex]
Help me plz I need lots of help
Answers
Answer:
18x + 16
Step-by-step explanation:
(Not simplest form) 9x + 9x + 8 + 8
To get simplest form, just add the terms and integers together, which in this case would give you 18x + 16.
Which equation does this graph represent?
Answers
Michael spends 3 hours cleaning his house. He spends equal amounts of time cleaning each room. If he spends 1/2 hour cleaning each room, how many rooms does his house have
Answers
Answer:
6 rooms
Step-by-step explanation:
3 hours= 60min*3= 180 min
180/30 min each room= 6 rooms
