A thin metal plate, located in the xy-plane, has temperature T(x, y) at the point (x, y). Sketch some level curves (isothermals) if the temperature function is given by
T(x, y)= 100/1+x^2+2y^2
Answers
Answer:
Step-by-step explanation:
Given that:
[tex]T(x,y) = \dfrac{100}{1+x^2+y^2}[/tex]
This implies that the level curves of a function(f) of two variables relates with the curves with equation f(x,y) = c
here c is the constant.
[tex]c = \dfrac{100}{1+x^2+2y^2} \ \ \--- (1)[/tex]
By cross multiply
[tex]c({1+x^2+2y^2}) = 100[/tex]
[tex]1+x^2+2y^2 = \dfrac{100}{c}[/tex]
[tex]x^2+2y^2 = \dfrac{100}{c} - 1 \ \ -- (2)[/tex]
From (2); let assume that the values of c > 0 likewise c < 100, then the interval can be expressed as 0 < c <100.
Now,
[tex]\dfrac{(x)^2}{\dfrac{100}{c}-1 } + \dfrac{(y)^2}{\dfrac{50}{c}-\dfrac{1}{2} }=1[/tex]
This is the equation for the family of the eclipses centred at (0,0) is :
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
[tex]a^2 = \dfrac{100}{c} -1 \ \ and \ \ b^2 = \dfrac{50}{c}- \dfrac{1}{2}[/tex]
Therefore; the level of the curves are all the eclipses with the major axis:
[tex]a = \sqrt{\dfrac{100 }{c}-1}[/tex] and a minor axis [tex]b = \sqrt{\dfrac{50 }{c}-\dfrac{1}{2}}[/tex] which satisfies the values for which 0< c < 100.
The sketch of the level curves can be see in the attached image below.
Related Questions
Use parenthesis to make each number sentence true.
124 - 6 x 0 + 15 = 34
Answers
Answer:
12 - 6 x (0 + 15) = 34
How I got my answer
First, how i got my answer was that I had to solve the equation first, ignoring the answer. I got 0 x 6 = 0, then I did 124 - 0 = 124, then I did 124 - 15 = 109, which clearly isn't 34. I figured that we have to put the parentheses around the zero because if we don't, we are going have to multiply something by zero, which always gets zero. After that, I decided that I should put the parentheses around either the 6, or the 15. I did both, and saw which one was correct. If we put it around the 6, we get, 124 - (6 x 0) + 15 = 124 - 0 - 15 = 124 - 15 = 109, which isn't 34. Then I checked 124 - 6 x (0 + 15) = 124 - 6 x 15 = 124 - 90 = 34, and we just got the answer.
P.S. Sorry if it was confusing, I didn't really know how to explain it
2. Use the diagram and given information to answer the questions and prove the statement.
a. Re-draw the diagram of the overlapping triangles so that the two triangles are separated.
b. What additional information would be necessary to prove that the two triangles, XBY and ZAY , are congruent? What congruency would be applied?
c. Prove (AZ) is congruent to (BX) using a flow chart proof. ( ):both have a line over them
Answers
[tex] \huge{ \underline{ \tt{ \purple{Solution:}}}}[/tex]
2) a)⚘ Refer to the attachment....
After separating, we will get two triangles △XYB and △ZYA where ∠Y is common to both the triangles, hence their measure is equal. This will be use in further proof.
b) We have,
∠X = ∠Z (Given, ATQ)∠Y = common to both triangles. XY = ZYSo, here
Two pairs of corresponding angles are equal along the side contained between them. So, The above triangles are congurent by ASA criterion.
✤ No more additional information Required to prove the above triangles be congurent.
➝ △XYB ≅ △ZYA (By ASA Criterion)
c) By using flow chart proof:
[tex] \boxed{ \sf{ \angle X = \angle Z}} \searrow[/tex]
[tex] \boxed{ \sf{\small{ \angle Y = com.}}} \rightarrow \boxed{\small{ \sf{ \triangle XYB \cong \triangle ZYA}}}\rightarrow \small{\boxed{ \sf{AZ= XB}}}[/tex]
[tex] \boxed{ \sf{XY = ZY}} \nearrow[/tex]
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Step-by-step explanation:
Hey mate ut answer is in the given attachment.
hope i help u
Solve the equation using square roots x^2+20=4
Answers
Answer:
Step-by-step explanation:
x^2+20=4 first isolate the variable by subtracting 20 on both sides.
x^2=-16 again isolate the variable but this time you square root both sides.
[tex]\sqrt{x}^2[/tex]=[tex]\sqrt{-16[/tex] then simplify
x= ±4
Y * 3 = 81 please i need it for today
Answers
Answer:
Y = 27
Step-by-step explanation:
Y * 3 = 81
Divide each side by 3
Y * 3/3 = 81/3
Y = 27
Hello people, please if you can give me a Hint with this, l only get half of the marks, what i am doing wrong here? thanks
Answers
Errors: Both of your upper bounds are wrong
You subtracted the upper bound from the upper bound
Step-by-step explanation:
605 kg to the nearest 5 kg
lower bound is 602.5 (because it rounds up to 605)
upper bound is 607.4 (because it rounds down to 605)
Note: 607.5 would round up to 610
78 kg rounded to the nearest 1 kg
lower bound is 77.5 (because it rounds up to 78)
upper bound is 78.4 (because it rounds down to 78)
Note: 78.5 would round up to 79
Upper Bound - Lower bound is the maximum weight remaining on the elevator
607.4 - 77.5 = 529.9
529.9 ≤ 530 so YES the elevator is safe.
Solve for 2 in the diagram below.
45°
150
42°
ea
Stuck? Watch a video or use a hint.
Answers
Step-by-step explanation:
Hi, there!!!
It's so simple..
Let me clear you, alright.
Here, On the fig line, OE is just a confusing line. If you look it in simple way,
AB and CD are interested at a point O.
so, angle AOD and angle COB are equal.{ because they are vertically opposite angle}
so, angle AOD= angle COB
or, 4x°=45°+15°
or, 4x°= 60°
or, x= 60°/4
Therefore, x= 15°.
Hope it helps....
How many solutions does the following equation have ?
−3x+9−2x=−12−5x
Answers
[tex]\text{Solve for x:}\\\\-3x+9-2x=-12-5x\\\\\text{Combine like terms}\\\\-5x+9=-12-5x\\\\\text{Add 5x to both sides}\\\\9=-12\\\\\text{Since that's not valid, there would be no solutions}\\\\\boxed{\text{No solutions}}[/tex]
Factor of
x2 – 14x + 24
A. (x - 6)(x - 4)
B. (x - 8)(x - 3)
C. (x - 12)(x - 2)
D. (x - 24)(x - 1)
Answers
Answer: The answer is C.
Step-by-step explanation:
Hi, there!!!
The answer is option C.
The solution is in picture.
I hope it helps....
line m in the xy-plane above is to be reflected through the x-axis. if the slope of line m is 2/3,whats is the slope of the image of line m under the reflection.
Answers
Answer: The new slope is -(2/3)
Step-by-step explanation:
Ok, we know that our line can be written as:
y = (2/3)*x + b
where b is the y-intercept, and here does not really matter.
Ok, remember that if we have a point (x, y) and we reflect it over the x-axis, the new point will be (x, -y).
For our linear equation, the point (x, y) can be written as:
(x, y = (2/3)*x + b) = (x, (2/3)*x + b)
Now, after the reflection, our point is:
(x, - ( (2/3)*x + b)) = (x, -(2/3)*x - b)
Then our new line is y = -(2/3)*x - b
The new slope is -(2/3)
Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 3 .10 11 .30 19 .20 27 .40
Answers
Answer:
69.76
Step-by-step explanation:
The mean is the average of the numbers. It can be gotten by adding all the numbers, then divide by how many numbers available.
Variance (σ2) measure the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean .
mean value can be computed using below expression
= ∑x(i)P(x(i))
= 3(0.10)+11(0.30)+19(0.20)+27(0.40)
= 18.2
Therefore, the mean value is 18.2
The variance can be calculated using below expression
variance
= ∑(x(i)-mean)^2 P(x(i))
= (3-18.2)^2 (.10) + (11-18.2)^2 (.30) + (19-18.2)^2 (.20)+(27-18.2)^2(0.40)
= 69.76
Therefore, the variance Vale is 69.76
Jill works at a cell phone store. Jill earns $175 every week plus $45 for every phone p that she sells. if Jill makes $445 at the end of the week how many phones did she sell?
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
6 phones
▹ Step-by-Step Explanation
$445 - $175 = $270
$270 ÷ $45 = 6
6 phones
Hope this helps!
CloutAnswers ❁
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In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. Group of answer choices may have different df values but they all have the same denominator all have the same df values and they all have the same denominator may have different df values and may have different denominators all have the same df values but they may have different denominators
Answers
Answer:
may have different df values but they all have the same denominator
Step-by-step explanation:
In a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction _____. may have different df values but they all have the same denominator
In two--factor analysis of variance, the estimates of the variance can be obtained by partitioning the total sum of squares into three components corresponding to the three possible sources of variation , viz; Between Rows, Between Columns, and Within Samples or error.
As the number of rows and columns may differ the degrees of freedom differ with them.
In other words
Total df= Rows df + Columns df + Error df
Since the variance is identically the same for each row of the c values and variance is the same for each observation in the jth column of r values the sum of squares becomes an identity.
Therefore it may have different df values but they all have the same denominator.
I need help badly best answer gets BRAINLIEST:)
Answers
Answer:
a = 55°, b = 65°, c = 65°, d = 60°, e = 120°, f = 60°
Step-by-step explanation:
Vertical angles are congruent. Since a and 55° are vertical angles, we know that a = 55°. Since b and 65° are vertical angles, we know that b = 65°. Alternate interior angles are congruent. Since b and c are alternate interior angles and b = 65°, we know that c = 65° as well. Since 60° and d are alternate interior angles, we know that d = 60°. Supplementary angles add up to 180°. Since d and e are supplementary and d = 60°, we know that e = 180 - 60 = 120°. Since vertical angles are congruent, we see that d and f are vertical angles and we know d = 60°, we also know that f = 60°.
Assuming that the loss of ability to recall learned material is a first-order process with a halflife of 35 days. Compute the number of days required to forget 90% of the material that you have learned today. Report to 1 decimal place.
Answers
Answer:
5.3 days
Step-by-step explanation:
Let us assume the loss of ability to recall a learned material = 100%
Formula to calculate number of days = time(t) =
t = t½ × Log½(Nt/No)
Nt = Ending Amount
No = Beginning Amount
t½ = Half life
t = Time elapsed
Therefore, we have the following values from the questions:
Half life (t½)= 35 days
Initial or beginning amount = 100%
Ending amount = 90%
t = t½ × Log½ (Nt/No)
t = 35 × Log ½(90/100)
t = 5.3201082705768 days
Approximately = 5.3 days
A diameter that is perpendicular to a chord bisects the chord. True False
Answers
Answer:
[tex]\Large \boxed{\sf True}[/tex]
Step-by-step explanation:
[tex]\sf A \ diameter \ that \ is \ perpendicular \ to \ a \ chord \ bisects \ the \ chord.[/tex]
Answer:
True!!
I just did the assignment and got it right
Diana paints 150 fence posts and chuck paints 130 fence posts. Diana paints 10 more fence posts than chuck. How many fence posts does chuck paint per hour?
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
Step-by-step explanation:
From the question we are told that
The relationship is [tex]\frac{150 }{d} = \frac{130}{c}[/tex]
The number of fence post painted by chuck is [tex]l = 130[/tex]
The number of fence post painted by Diana is [tex]k = 150[/tex]
can paint 10 fences more than chuck so let say the of fence painted in an hour by chuck is [tex]g[/tex]
Then the number of fence post painted by Diana in one hour is
[tex]f = g+ 10[/tex]
So
[tex]\frac{150 }{ g + 10 } = \frac{130}{g}[/tex]
[tex]130 g + 1300 = 150g[/tex]
[tex]g = 65 \ m[/tex]
A deli sandwich shop is offering either a ham or turkey sandwich, either tomato or vegetable soup, and either coffee or milk for their lunch special. What is the probability that a customer will choose vegetable soup as part of the chosen combination?
Answers
Answer:
Ok, the first step is to count all the possible selections that we have and the number of options in each selection:
1) Sandwich: 2 options, ham or turkey.
2) Soup, 2 options, tomato or vegetable.
3) Drink, 2 options, coffee or milk.
(i assume that the sandwich and the soup are separated selections)
Now, if the customer chooses at random, the probability that in one given selection he selects a given outcome is equal to the number of options that match the outcome divided by the total number of options for that selection.
Then in the soup selection we have: options that match the outcome (one, is the vegetable soup). Total number of options = 2.
Then the probability is:
P = 1/2 = 0.5
or 0.5*100% = 50% in percentage form.
Answer:
1/2
Step-by-step explanation:
Using Normal Distribution, what is the area to the right of 0.72 under the
standard normal curve?
Answers
Answer: 0.2358
Step-by-step explanation:
Using Normal Distribution, under the standard normal curve
The area to the right of z is given by P(Z>z)=1-P(Z<z)
So, the area to the right of z= 0.72 under the standard normal curve would be:
P(Z>0.72)=1-P(z<0.72)
=1-0.7642 [By using p-value table]
= 0.2358
Hence, the area to the right of z= 0.72 under the standard normal curve is 0.2358 .
What is the value of 1/3x-3/4 when x =1/4
Answers
Answer:
The value of 1/3x-3/4 when x=1/4 is 0.08333 repeated.
Step-by-step explanation:
Compare the line passing through the points (–2, –9) and (4, 6) to the line given by the equation y = 25x – 4.
A. They have the same slope.
B. They have the same x-intercept.
C. The two lines are perpendicular.
D. They have the same y-intercept.
Answers
Answer:
D. They have the same y-intercep
Step-by-step explanation:
Before the comparison will be efficient, let's determine the equation of the two points and the x intercept .
(–2, –9) and (4, 6)
Gradient= (6--9)/(4--2)
Gradient= (6+9)/(4+2)
Gradient= 15/6
Gradient= 5/2
Choosing (–2, –9)
The equation of the line
(Y+9)= 5/2(x+2)
2(y+9)= 5(x+2)
2y +18 = 5x +10
2y =5x -8
Y= 5/2x -4
Choosing (4, 6)
The equation of line
(Y-6)= 5/2(x-4)
2(y-6) = 5(x-4)
2y -12 = 5x -20
2y = 5x-8
Y= 5/2x -4
From the above solution it's clear that the only thing the both equation have in common to the given equation is -4 which is the y intercept
3 divided by 6 it hard
Answers
Answer:
3/6 = 1/2 = 0.5
Step-by-step explanation:
3 / 6 = 1/2 = 0.5
GIVING OUT BRAINLIEST TO THE FIRST PERSON TO ANSWER!!
One circle has a diameter of 6 inches. A second, larger circle has a diameter that is four times the diameter of the first circle. What is the ratio of the area of the smaller circle to the larger circle?
A. 2:3
B. 1:6:4
C. 1:16
D. 1:64
Please include ALL work! <3
Answers
Answer:
The answer is option CStep-by-step explanation:
To find the ratio first find the diameter of the larger circle
Diameter of first circle = 6 inches
Diameter of second circle = 4 × diameter of the first circle
Which is
Diameter of second circle
= 4 × 6 = 24 inches
Area of a circle = πr²
r is the radius
Area of smaller circle
Diameter = 6 inches
Radius = 6 / 2 = 3 inches
Area = (3)² π = 9π in²
Area of larger circle
Diameter = 24 inches
Radius = 24 / 2 = 12 inches
Area = (12)²π = 144π in²
The ratio of the smaller circle to the larger circle is
[tex] \frac{9\pi}{144\pi} [/tex]
Reduce the fraction by 9π
That's
[tex] \frac{1}{16} [/tex]
We have the final answer as
1 : 16Hope this helps you
Answer:
C. 1:16
Step-by-step explanation:
Area of a circle is:
[tex]\pi \times {r}^{2} [/tex]
Small circle Area:
radius = diameter/2
radius = 6/2 = 3
[tex]area \: of \: a \: circle \: = \pi {3}^{2} [/tex]
a = 28.27
Large circle 4 times larger diameter
6*4 = 24
diameter = 24
r = 24/2
r = 12
[tex]a \: = \pi {12}^{2} [/tex]
a = 452.39
area of large circle/ area of small circle
452.39/28.27 = 16.00
ratio is 1:16
Fiona wrote the linear equation y = y equals StartFraction 2 over 5 EndFraction x minus 5.x – 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s? x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 2 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 2 EndFraction.y =
Answers
Answer:
D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{2}{5}x - 5[/tex]
Required
Determine its equivalent
From the list of given options, the correct answer is
[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]
This is shown as follows;
[tex]y = \frac{2}{5}x - 5[/tex]
Multiply both sides by [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]
Open Bracket
[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]
[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]
Subtract x from both sides
[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]
[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]
Multiply both sides by -1
[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]
[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]
Reorder
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Hence, the correct option is D
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Answer:
The 4th option
Step-by-step explanation:
g a video game claims that the drop rate for a certain item is 5% according to the game publisher. in online forums, a number of players are complaining that the drop rate seems to be low. in order to test the drop rate claim, 100 players agree to attempt to get the drop, each attempting 10 times. of the 1000 tries, the item only drops 40 times state the null hypothesis needed to test this claim group of answer choices
Answers
Answer:
p0 = 0.05
Step-by-step explanation:
A researcher wants to determine the impact of soil type on the growth of a certain type of plant. She grows three plants in each of four different types of soil and measures the growth in inches for each plant after one month resulting in the data below.
Soil 1 Soil 2 Soil 3 Soil 4
12.6 12.2 12.2 11.1
12.6 12 10.6 11.7
14.3 13 9.1 9.6
1. What null hypothesis is the researcher testing if she runs an ANOVA with this data?
a.The mean growth of the plant in each type of soil is the same.
b. One type of soil has a higher mean growth for the plant than the others.
c. The variability in growth of the plant in each type of soil is the same.
d. Oil 3 provides a lower mean growth for the plant than the other types of soil.
e. The mean growth of the plant is different in each type of soil.
2. What is the SStrt for the ANOVA? Give your answer to at least three decimal places.
3. What is DFerr for the ANOVA?
4. What is the value of the F statistic for the ANOVA? Give your answer to at least three decimal places.
5. Using a 0.05 level of significance, what conclusion should the researcher reach?
a. There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.
b. Soil 1 has a higher mean growth for the plant than the other types of soil.
c. The mean growth of the plant is not the same for all soil types .
d. Soil 3 has a lower mean growth for the plant than the other types of soil.
Answers
Answer:
(1) Option a
(2) 13.737
(3) 8
(4) 3.803
(5) Option a
Step-by-step explanation:
In this case, we need to determine whether the soil type effects the growth of a certain type of plant.
Perform the ANOVA test for the provided data on Excel.
Go to Data - Data Analysis - Anova: Single factor
Select the data for the growth.
Press OK.
The output is attached below.
(1)
The hypothesis for the study can be defined as follows:
H₀: The mean growth of the plant in each type of soil is the same.
Hₐ: The mean growth of the plant is different in each type of soil.
Correct option a.
(2)
The sum of square for treatment is:
[tex]\text{SS}_{trt}=\text{SS}_{BG}=13.737[/tex]
(3)
The degrees of freedom of error is:
[tex]\text{DF}_{err}=\text{DF}_{WG}=8[/tex]
(4)
The F statistic for the ANOVA is:
[tex]F=3.803[/tex]
(5)
The p-value of the test is:
[tex]p-value=0.058[/tex]
Decision Rule:
Reject H₀ if the p-value of the test is less than the level of significance.
[tex]\text{p-value}=0.058>\alpha=0.05[/tex]
The null hypothesis was failed to be rejected.
Conclusion:
There is not enough evidence to reject the claim that the mean growth of the plant is the same in each type of soil.
Correct option a.
Which rule describes this transformation? (Zoom in to see it clearly)
Answers
Answer:
(x,y) -> (x+6, y-3)
Step-by-step explanation:
I followed c and it translated like the last ans choice.
Find the area of the shaded regions:
Answers
area of Arc subtending [tex]360^{\circ}[/tex] (i.e. the whole circle) is $\pi r^2$
so area of Arc subtending $\theta^{\circ}$ is, $\frac{ \pi r^2}{360^{\circ}}\times \theta^{\circ}$
$\theta =72^{\circ}$ so the area enclosed by one such arc is $\frac{\pi (10)^272}{360}$
abd there are 2 such arcs, so double the area.
[tex] \LARGE{ \underline{ \boxed{ \rm{ \purple{Solution}}}}}[/tex]
Given:-Radius of the circle = 10 inchesAngle of each sector = 72°Number of sectors = 2To FinD:-Find the area of the shaded regions....?How to solve?For solving this question, Let's know how to find the area of a sector in a circle?
[tex] \large{ \boxed{ \rm{area \: of \: sector = \frac{\theta}{360} \times \pi {r}^{2} }}}[/tex]
Here, Θ is the angle of sector and r is the radius of the circle. So, let's solve this question.
Solution:-We have,
No. of sectors = 2Angle of sector = 72°By using formula,
⇛ Area of shaded region = 2 × Area of each sector
⇛ Area of shaded region = 2 × Θ/360° × πr²
⇛ Area of shaded region = 2 × 72°/360° × 22/7 × 10²
⇛ Area of shaded region = 2/5 × 100 × 22/7
⇛ Area of shaded region = 40 × 22/7
⇛ Area of shaded region = 880/7 inch. sq.
⇛ Area of shaded region = 125.71 inch. sq.
☄ Your Required answer is 125.71 inch. sq(approx.)
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Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answers
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
PLEASE HELP !! (2/5) -50 POINTS-
Answers
Answer:
3 -1 -2
5 1 6
Step-by-step explanation:
An augmented system has the coefficients for the variables and then the solution going across
Rewriting the equations to get them in the form
ax + by = c
-3x+y =2
3x-y =-2
5x+y = 6
The matrix is
3 -1 -2
5 1 6
The first equation becomes 3x-y=-2.
The second becomes 5x+y=6.
Using the coefficients of x and y, and separating the constants results in the first augmented matrix.
he sum of two nonnegative numbers is 300. What is the maximum value of the product of these two numbers?
Answers
Answer:
[tex]\boxed{22,500}[/tex]
Step-by-step explanation:
Hey there!
Well, half of 300 is 150, and 150•150 = 22500
So 150 and 150 are it's highest numbers.
Hope this helps :)
