Answer:
critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0
and it local minimum.
Step-by-step explanation:
Let the given function be;
f(x,y) = x²+y²+2xy
From above function, we can locate relative minima, maxima and the saddle point
f(x,y) = x²+y²+2xy = (x+y)²
df/dx = 2x+2y = 0 ---- (1)
df/dy =2y+2x = 0 ---- (2)
From eqn 1 and 2 above,
The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0
Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:115:115, colon, 1. He currently has 404040 grams of the spice blend, and he can go buy more if necessary. He wants to make 101010 servings, where each serving has 757575 grams of rice. Overall, David spends 4.504.504, point, 50 dollars on rice.
Answer:
.006
:)
Step-by-step explanation:
8 servings can David make with the current amount of spice.
What is Ratio?Ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
The rice-to-spice ratio = 15:1
The 75 grams of rice in one serving will require
⇒75/15
⇒5 gram of spice.
David's inventory of 40 gram of spice is enough for
40 g/(5 g/serving) = 8 servings
Hence, 8 servings can David make with the current amount of spice.
Learn more about Ratio
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Can you help me with this.
Answer:
You would basically expand all the equations!
1. 7(4z+8b) is equal to 28z+56b.
2. 8(2x+3^2) is equal to 16x+72
3. 4(r+r+r+r) is equal to 4r+4r+4r+4r
4. 9(3+8x) is equal to 27+72x
5. 4^2(3+6f) is equal to 48+96t
6. (t+t+t)/4 is equal to t/4+t/4+t/4
7. 2(4s^3+2) is equal to 8s^3+4
8. 30(3x+4) is equal to 90x+120
9. 6(5a+9b) is equal to 30a+54b
10. 9(3x+5^4) is equal to 27x+5625
11. 7(c+c+c) is equal to 7c+7c+7c
12. 9(2+7f) is equal to 18+63f
13. 7^5(4g-8d) is equal to 67228g-134456d
Step-by-step explanation:
find the area under (sin x) bounded by x= 0 and x = 2π and x-axis
You probably want the unsigned area, which means you don't compute the integral
[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]
but rather, the integral of the absolute value,
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]
[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]
The marked price of a mobile set is Rs3500 and the shopkeeper allows of 10%discount? (I) find the amount of discount. (ii)How much should a customer pay for it after discount.
Step-by-step explanation:
3500 × 10/100
rs. 350 is the discount
and to find the amnt the customer should pay subtract 350 from 3500
which is,
3150 Rupees
Use the cubic model y = 6x3 - 5x2 + 4x – 3 to estimate the value of y when x = 2.
a 25
(b 33
c 48
d 79
Done
Try Again
-
Answer:
The answer is B.
Step-by-step explanation:
You have to substitute x = 2, into the equation of y :
[tex]y = 6 {x}^{3} - 5 {x}^{2} + 4x - 3[/tex]
[tex]let \: x = 2[/tex]
[tex]y = 6 {( 2)}^{3} - 5 {(2)}^{2} + 4(2) - 3[/tex]
[tex]y = 48 - 20 + 8 - 3[/tex]
[tex]y = 33[/tex]
How many solutions does the following equation have? −5(z+1)=−2z+10
Answer:
One solution, z=-5
Step-by-step explanation:
First, We simplify the right side.
Distribute -5, -5z-5=-2z+10
Now add +2z to both sides, −3z−5=10
Add 5 to both sides, now the equation stands as -3z=15
We can simplify this by dividing -3 to both sides, z=-5.
Now we know there is only one solution to this equation!
How does the frequency of f(x) = cos(2x) relate to the frequency of the parent function cos x?
Answer:
The frequency of f(x) is two times the frequency of the parent function.
Step-by-step explanation:
We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.
Then, for the parent function, we get:
[tex]1 = 2\pi f_1[/tex]
or solving for [tex]f_1[/tex]:
[tex]f_1=\frac{1}{2\pi }[/tex]
At the same way, for f(x), we get:
[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]
But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:
[tex]f_2=2f_1[/tex]
It means that the frequency of f(x) is two times the frequency of the parent function.
Divide $36 between Vincent and Francis giving Francis $8 more than Vincent. What does Francis gets?
Solve the question and post.
Answer:
$22
Step-by-step explanation:
Let Vincent = v, Francis= f
Equations to reflect given:
v+f= 36and
f= v+8Replacing f with v+8:
v+v+8= 362v= 28v= $14Now finding f:
f= 14+8= $22Francis gets $22
Write these numbers in standard form 0.000 05
Answer:
5x 10 ^-5
Step-by-step explanation:
UHM that would be
NaN × [tex]10^{0}[/tex]
I hope this helps!
so my reasoning... Any number that can be written in the decimal form between 1.0 to 10.0 multiplied by the power of 10.
Write each ratio as a fraction in simplest form.
a) 9 miles to 15 miles
b) 6 1/3 ounces to 9 1/2 ounces
5.-10. 20.-40.... determine if arithmetic,geometrical or neither
Answer:
It is a geometrical progression
Step-by-step explanation:
Geometric progressions have a constant number that they are multiplied by
To find that number you divide the 2nd term by the 1st term and also the 4th term by the 3rd term. ie,
[tex]\frac{-40}{20} = \frac{-10}{5} \\[/tex]
[tex]-2 = -2[/tex]
since they are both equal it is a G.P
Because they have a constant ratio.
Answer:
Geometric progression.
Step-by-step explanation:
I suppose you mean this equation:
5, -10, 20, -40, ...
For a geometric progression, an n^th term is given by:
[tex]a_{n}[/tex] = [tex]a_{n - 1}[/tex] × r
Where a is the first time, n is the term and r is the common ratio.
The common ratio here is -2 .
For instance to check the forth term;
[tex]a_{4}[/tex] = [tex]5_{4 - 1}[/tex] × -2 = 20 × -2 = -40
A = 100(1+r)^4
Expand the right of this formula.
appreciate your help with an explanation
Answer:
100r^4 + 400r^3 + 600r^2 + 400r + 100
Step-by-step explanation:
Expanding ( r + 1 )^4 gives :-
r^4 + 4r^3 + 6r^2 + 4r + 1
So multiplying 100 with r^4 + 4r^3 + 6r^2 + 4r + 1 gives :-
100r^4 + 400r^3 + 600r^2 + 400r + 100
Solve:
3/x -4>0
A.) x<4
B.) x>-4
C.) x>4
D.) x<-4
Answer:
x > 4
Step-by-step explanation:
2. A survey is being conducted of students’ residences. Data is gathered from a random sample of 1000 students. The data is summarized in the table below. Gender and Residence of Students Males Females Apartment off campus 50 90 Dorm room 150 210 With Parent(s) 100 50 Sorority/ Fraternity House 200 150 a) What is the probability that a student is female and lives in a dorm? ____________________ b) What is the probability that a student is female given that she lives in a dorm? __________
Answer:
Gender and Residence of Students
a) What is the probability that a student is female and lives in a dorm?
= 58.33%
b) What is the probability that a student is female given that she lives in a dorm?
= 21%
Step-by-step explanation:
a) Data and Calculations:
Gender and Residence of Students
Males Females Total
Apartment off campus 50 90 140
Dorm room 150 210 360
With Parent(s) 100 50 150
Sorority/ Fraternity House 200 150 350
Total 500 500 1,000
a) Probability that a student is female and lives in a dorm:
= number of females who live in a dorm divided by total number of students who live in a dorm * 100
= 210/360 * 100
= 58.33%
b) Probability that a student is female given that she lives in a dorm
= number of female students who live in a dorm divided by the total number of students * 100
= 210/1,000 * 100
= 21%
Consider the inequality x3 + 4x2 - 5x < 0.
Select all intervals for which the statement is true.
There may be more than one correct answer. Select all correct answers.
Answer:
Interval notation is
[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]
Solutions:
[tex]\left(-\infty, -5\right)[/tex]
[tex]\left(0,1)[/tex]
Step-by-step explanation:
[tex]x^3 + 4x^2 - 5x < 0[/tex]
In this inequality, luckly we can easily factor it.
[tex]x^3 + 4x^2 - 5x[/tex]
[tex]x(x^2+4x-5)[/tex]
[tex]x(x-1)(x+5)[/tex]
So we have
[tex]x(x-1)(x+5)<0[/tex]
In exercises of this kind I usually do in my mind, but just to make it clear, let's do a table to organize. This table represents the x-intercepts in order to evaluate the inequality.
Consider [tex]x(x-1)(x+5)=0[/tex]. Here, those are the possible values for [tex]x[/tex] for each factor to be 0:
The first step to complete the table is the x value where the factor will be equal to zero.
[tex]x<-5[/tex] [tex]x=5[/tex] [tex]-5<x<0[/tex] [tex]x=0[/tex] [tex]0<x<1[/tex] [tex]x=1[/tex] [tex]x>1[/tex]
[tex]x[/tex] 0
[tex]x-1[/tex] 0
[tex]x+5[/tex] 0
Then, just consider the signal:
[tex]x<-5[/tex] [tex]x=5[/tex] [tex]-5<x<0[/tex] [tex]x=0[/tex] [tex]0<x<1[/tex] [tex]x=1[/tex] [tex]x>1[/tex]
[tex]x[/tex] - - - 0 + + +
[tex]x-1[/tex] - - - - - 0 +
[tex]x+5[/tex] - 0 + + + + +
[tex]x(x-1)(x+5)[/tex] - 0 + 0 - 0 +
When [tex]x(x-1)(x+5)<0[/tex] ?
It happens when [tex]x<-5[/tex] and when [tex]0<x<1[/tex]
The solution is
[tex]\{x \in \mathbb{R} | x<-5 \text{ or } 0<x<1 \}[/tex]
[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]
Find the value of y.
Answer:
[tex] \sqrt{55} [/tex]Step-by-step explanation:
∆ BCD ~ ∆ DCA
[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]
Plug the values:
[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]
[tex] \frac{5}{y} = \frac{ y}{11} [/tex]
Apply cross product property
[tex]y \times y = 11 \times 5[/tex]
Calculate the product
[tex] {y}^{2} = 55[/tex]
[tex]y = \sqrt{55} [/tex]
Hope this helps...
Good luck on your assignment..
Raina, Justin, and cho have $79 in their wallets. Raina has $5 leas than Justin. Cho has 2 times what Justin has. How much does each have?
Hey there! I'm happy to help!
Let's represent everybody with variables. Raina is R, Justin is J, and Cho is C. Let's write down this information as a system of equations.
R+J+C=79 (they all have 79 total dollars in their wallets combined)
R=J-5 (Raina has five less than Justin.)
C= 2J (Cho has twice that of Justin)
Since we know what R and C equal, we can plug in their values in terms of J into the first equation to solve for J.
J-5+J+2J=79
We combine like terms.
4J-5=79
We add 5 to both sides.
4J=84
We divide both sides by 4.
J=21
This means that Justin has $21. If Raina has 5 less, she has $16 and since Cho has twice that of Justin he has $42. These added up equal 79.
I hope that this helps! Have a wonderful day!
The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − (x − π/2) + 1/6 (x − π/2)3 + R3(x). Using this, estimate cos(86°) correct to five decimal places.
Answer:
The cosine of 86º is approximately 0.06976.
Step-by-step explanation:
The third degree Taylor polynomial for the cosine function centered at [tex]a = \frac{\pi}{2}[/tex] is:
[tex]\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}[/tex]
The value of 86º in radians is:
[tex]86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi[/tex]
[tex]86^{\circ} = \frac{43}{90}\pi\,rad[/tex]
Then, the cosine of 86º is:
[tex]\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}[/tex]
[tex]\cos 86^{\circ} \approx 0.06976[/tex]
The cosine of 86º is approximately 0.06976.
HELP PLEASE ANYONE !!!!!
Answer:
B. -3x
Step-by-step explanation:
A term is defined as either a constant or a variable with a coefficient.
-3 is incorrect because there is no constant -3 in the expression.
-3x is correct because there is a -3x in the expression
(x + 4) is incorrect because that is a linear binomial and has yet to be distributed.
-7 is incorrect because it has to be distributed.
Please help. I’ll mark you as brainliest if correct!
Answer:
y=10000 at rate 0.12 or 12%
x=8500 at rate 0.14 0r 14 %
Step-by-step explanation:
x+y=18500 ⇒ x=18500-y
0.14x+0.12y=2390 ( solve by substitution)
0.14(18500-y)+0.12y=2390
2590-0.14y+0.12y=2390
-0.02y=2390-2590
-0.02y=-200
y=-200/0.02
y=10000 at rate 0.12
x=18500-y
x=18500-10000=8500
x=8500 at rate 0.14
check : 0.14(8500)+0.12(10000)=2390 ( correct)
Answer:
Amount invested at 14% = 8500
Amount invested at 12% = 10000
Step-by-step explanation:
Assume money was invested for one year.
18500 at 14% = 18500*0.14 = 2590
18500 at 12% = 18500*0.12 = 2220
actual interest earned = 2390
Let
x = ratio of money invested at 14%
1-x = ratio of money invested at 12%
Then
18500*x * 0.14 + 18500 * (1-x)*0.12 = 2390
0.14x - 0.12x = 2390/18500-0.12
0.02x = 0.1291892-0.12 = 0.0091892
x = 0.0091892/0.02 = 0.4594595
Amount invested in 14% = 18500 * x = 8500
Amount invested in 12% = 18500 * (1-x) = 10000
Help with inequality
Answer:
1. x>20 2. x≤1 3.x<4 4.x>9 5.x≥-13
In the last year, the population of Japan had a decay rate of 0.17% and decreased to 127,484,450. If this rate continues, what will be the population in 7 more years? Round your answer to the nearest whole number.
Answer:
125975100 the population in 7 years
Step-by-step explanation:
the population in 7 more years : 127,484450(1-0.0017)^7=125975100.1919 close to 125975100
Answer: 125,976,376 IN 7 YEARS
Step-by-step explanation:
A=127,484,450
R=-0.0017/YEAR
T=7/YEARS
[tex]A=127,484,450E ^{-0.0017.7}[/tex]a=125,976,375.88a=125,976,376 in 7yearsSelect all the correct answers. Which of these pairs of functions are inverse functions?
Answer:
D
Step-by-step explanation:
an inverse function is a function that reverses another function for ex. if f(x)=y and g(y)=x.
Answer:
A and C
Step-by-step explanation:
The school district uses the Hamilton method to apportion its 22 board members to the 4 towns. How many board members are assigned to each town, using this method? 2. The following year, 900 people move out of Town D. Two hundred of these people move Town C, and 700 of them move to Town B. Now, how many board members does each town have? (Be careful. Make sure you assign a total of 22 board members). 3. Compare the results from the 2 years. Do you think they make sense? How do you think each town would react? Are they fair? Why or Why not?
Answer:
(A, B, C, D) = (2, 2, 6, 12)(A, B, C, D) = (2, 2, 6, 12)identical results; yes, they make senseyes they are fairStep-by-step explanation:
1. The Hamilton method has you compute the number represented by each board member (total population/# members). Using this factor, the number of board members for each district are computed. This raw value is rounded down.
Because this total does not allocate all board members, the remaining members of the board are allocated to the districts based on the size of the fraction that was truncated when rounding down. Allocations start with the largest fraction and work down until all board members have been allocated.
The attached spreadsheet implements this algorithm using a "threshold" that is adjusted to a value between 0 and 1, signifying the cutoff point between a fraction value that gets an additional member and one that doesn't. (Often, that threshold can be set at 0.5, equivalent to rounding the raw board member value to the nearest integer.)
The resulting allocations are ...
Town A: 2
Town B: 2
Town C: 6
Town D: 12
__
2. The second attachment shows the result after the population move. The allocations of board members are identical.
__
3. The "factor" (persons per board member) is about 4500, so we don't expect a move of 900 people to make any difference in the allocation. These results make complete sense.
__
4. Of course each town will consider its own interest at the expense of everyone else, so they may or may not consider the results fair. The towns have population ratio of about 9 : 9 : 25 : 56, so the ratios 2 : 2 : 6 : 12 are quite in line. Even in the second year, when the ratios are closer to 9 : 10 : 26 : 56, the changes are small enough that the allocation of board members still makes sense. The results are fair.
_____
Comment on "fair"
The reason there are different methods of allocation is that each seeks to rectify some perceived flaw in one or more of the others. The reason there is not a general agreement on the method to be used is that some benefit more from one method than from another. "Fair" is in the eye of the beholder. I believe in this case it would be very difficult to justify any other allocations than the ones computed here.
Which of the following theorems verifies that CRV BYU?
A.
AA
B.
HL
C.
LL
D.
HA
Answer:
LL
Step-by-step explanation:
We have two right triangles
The two legs are congruent
We can use the LL congruence theorem
A rectangular parking lot has an area of 7/10 km 2.The width is 1/3 km 2 .What is the length of the parking lot written as a improper fraction ,in kilometers
Answer:
[tex]\dfrac{21}{10}\text{ km}[/tex].
Step-by-step explanation:
It is given that,
Area of rectangular plot [tex]=\dfrac{7}{10}\text{ km}^2[/tex]
Width of rectangular plot [tex]=\dfrac{1}{3}\text{ km}[/tex]
We need to find the length of the parking lot.
We know that,
[tex]\text{Area of rectangle}=length\times width[/tex]
[tex]\dfrac{7}{10}=length\times \dfrac{1}{3}[/tex]
[tex]\dfrac{7\times 3}{10}=length[/tex]
[tex]length=\dfrac{21}{10}[/tex]
Therefore, length of the parking lot is [tex]\dfrac{21}{10}\text{ km}[/tex].
Simplify the rate:
46 cans of Soda / 8 people
Only enter the numeric amount:
Answer: 23 cans of soda/4 people.
or (23/4) cans of soda per person.
Step-by-step explanation:
So we have the rate:
46 cans of soda/ 8 people
First, 46 and 8 are multiples of 2, so we can divide both numerator and denominator by 2:
46/2 = 23
8/2 = 4
Then the rate can be:
23 cans of soda/4 people.
Now 23 is a prime number, so we can not simplify it furthermore
6. Find x. (2 pt)
48°
X
Answer:
x = 96
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
48 = 1/2 ( x)
Multiply by 2
96 = x
Answer:
[tex]\boxed{x=96}[/tex]
Step-by-step explanation:
Apply the inscribed angle theorem, where the measure of an inscribed angle is half the measure of the intercepted arc.
[tex]48=\frac{1}{2}x[/tex]
Multiply both sides by 2.
[tex]48(2)=\frac{1}{2}x(2)[/tex]
[tex]96=x[/tex]
Which is the graph of f(x) = 3/7?
Answer:
Rewrite the function as an equation. y= 3/7 Use the slope-intercept form to find the slope and y-intercept. Slope: 0 Y-intercept: 3/7 Hope this can help
Step-by-step explanation:
Solve 2x^2 + x - 4 = 0
X2 +
Answer:
[tex]\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }[/tex]
Step-by-step explanation:
Hello, please find below my work.
[tex]2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0[/tex]
[tex]\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you