First check for the critical points of f by checking where the first-order derivatives vanish.
[tex]\dfrac{\partial f}{\partial x}=4x-4=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=2y-4=0\implies y=2[/tex]
Notice how the point (1, 2) lies on the line y = 2x ; at this point, we get a value of f(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find f(0, 0) = 1 (MAX) and f(0, 2) = -3.
Now check on the boundary lines themselves. If x = 0, then
[tex]f(0,y)=y^2-4y+1=(y-2)^2-3[/tex]
which has a maximum value of -3 when y = 2 (so we get the same critical point as before).
If y = 2, then
[tex]f(x, 2)=2x^2-4x-3=2(x-1)^2-5[/tex]
with a maximum of -5 when x = 1.
If y = 2x, then
[tex]f(x,2x)=6x^2-12x+1=6(x-1)^2-5[/tex]
with the same maximum of -5 when x = 1.
This question is based on the absolute maximum and absolute minimum.
We get this by differentiating the terms.
Given:
f(x,y) = [tex]2x^{2} - 4x + y^2 - 4y +1[/tex], bounded by the lines x=0,y=2,y=2x in the first quadrant,bounded by the lines x=0,y=2,y=2x in the first quadrant.
We need to determined the absolute maximum and absolute minimum of the function.
Now, partial differentiating wrt x and y.
[tex]\dfrac{\partial f}{ \partial x} = 4x -4 = 0 \Rightarrow x= 1 \\\dfrac{\partial f}{ \partial y} = 2y - 4 = 0 \Rightarrow y = 2[/tex]
Now, point (1, 2) lies on the line y = 2x ; at this point, we get a value of
f(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2).
Now, find f(0, 0) = 1 (MAX) and f(0, 2) = -3.
Now check on the boundary lines themselves.
If x = 0, then we get,
[tex]f(0,y) = y^2 - 4y +1 = ( y-2)^2 -3\\[/tex]
which has a maximum value of -3 when y = 2 (so we get the same critical point as before).
If y = 2, then we get,
f(x,2) = [tex]2x^2-4x -3 = 2(x-1)^2 -5[/tex] with a maximum of -5 when x = 1.
If y = 2x, then we get,
f(x,2x) = [tex]6x^2 -12x +1 = 6(x-1)^2 -5[/tex] with the same maximum of -5 when x = 1.
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Set C is the set of two-digit even numbers greater than 34 that are divisible by 5
C=
NEED GEOMETRY HELP ASAP PLEASE (11 POINTS)
Answer:
d = 2[tex]\sqrt{17}[/tex]
Step-by-step explanation:
P1 (-5, 4) P2 (-3, -4)
Use the distance formula: d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
Plug in the values and simplify
d = [tex]\sqrt{(-3 + 5)^{2} + (-4 -4)^{2} }[/tex]
d = [tex]\sqrt{(2)^{2} + (-8)^{2} }[/tex]
d = [tex]\sqrt{4 + 64 }[/tex]
d = [tex]\sqrt{68}[/tex]
d = 2[tex]\sqrt{17}[/tex]
I hope this helps :)
simplify : 3/5x+x , find the answer ?
Answer:
8x/5
There’s a 1 in front of the x also remember to always simplify
3/5x + 1x
Answer:8x/5
Step-by-step explanation:
Which ordered pair is a solution of the equation? y=-6x+1y=−6x+1y, equals, minus, 6, x, plus, 1 Choose 1 answer: Choose 1 answer:Only (-2,13)(−2,13)left parenthesis, minus, 2, comma, 13, right parenthesis (Choice B) B Only (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis (Choice C) C Both (-2,13)(−2,13)left parenthesis, minus, 2, comma, 13, right parenthesis and (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis (Choice D) D Neither
Answer:
C Both (-2,13) and (-1,7)
Step-by-step explanation:
Try the offered points in the equation and see if they work
y = -6x +1
For (-2, 13):
13 = -6(-2) +1 = 12 +1 . . . . true
For (-1. 7):
7 = -6(-1) +1 = 6 +1 . . . . true
Both ordered pairs are solutions.
To ______ a function, you need to stretch or compress it
Answer: It’s to change the shape of a function
Step-by-step explanation:
To change the shape of a function, you need to stretch or compress it.
How to stretch or compress a function?In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
Is there a function for every shape?By definition, a function has one possible output for any given input. So if you want your function defined as some y=f(x), then not every shape can be written as a function. Any shape that has two points directly above each other (relative to the x-axis) cannot be written as a function, even a piecewise one.
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At a football game, a vender sold a combined total of 152 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
38 hot dogs114 sodasStep-by-step explanation:
Sometimes problems of this nature are easily worked by considering groups of items. Here, it is convenient to consider a group as 1 hot dog and 3 sodas, so the number of sodas in the group is 3 times the number of hotdogs in the group.
Each group is 4 items, so 152/4 = 38 groups were sold.
In the 38 groups, there were 38 hot dogs and 3×38 = 114 sodas.
114 sodas and 38 hot dogs were sold.
5.2 times a number is 46.8
Answer:
9
Step-by-step explanation:
"5.2 times a number is 46.8" as an equation is:
[tex]5.2*n=46.8[/tex]
Solve for 'n':
[tex]5.2*n=46.8\\5.2/5.2*n=46.8/5.2 \leftarrow \text {Division Property of Equality} \\\boxed {n=9}[/tex]
128 less than a number is 452
Answer:
580
Step-by-step explanation:
"128 less than a number is 452" is represented by:
n - 128 = 452
Solve for 'n':
n - 128 + 128 = 452 + 128 (Addition Property of Equality)
n = 580
my last question and im done, please help!
Answer:
2 acute and one right.
Step-by-step explanation:
plz mark brainliest!
Answer:
2 acute 1 right, you asked for ASAP so theres no explanation
You cant mix right and obtuse, and you cant have more than 1 obtuse in a triangle. There has to be at least 2 acute angles.
Define a function sinc(x) (pronounced "sink of x") by: text(sinc)(x)={(sin(x)/x text(if)\ x != 0, 1 text(if)\ x = 0.) (This function is used frequently in electrical engineering and signal processing.) Use this list of Basic Taylor Series to find the Taylor Series for f(x) = sinc(x) based at 0. Give your answer using summation notation and give the largest open interval on which the series converges. (If you need to enter [infinity] , use the [infinity] button in CalcPad or type "infinity" in all lower-case.)
Answer:
Step-by-step explanation:
To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that
[tex]\sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}[/tex]
which is the taylor series expansion based at 0. Then for [tex]x\neq 0[/tex], by dividing both sidex by x, we have that
[tex]\text{sinc}(x) = \frac{\sin(x)}{x}= \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n+1)!}[/tex]
which is the taylor series expansion for the sinc function. Since the series of sine converges for every value of x. Then the taylor series of sinc converges for every value of x, but 0.
How do you solve this?
Answer:
.75 teaspoons per ounce
Step-by-step explanation:
Take the number of teaspoons and divide by the number of ounces
10.5 / 14
.75 teaspoons per ounce
In two sample surveys 125 people were asked about their favorite fruit in the survey 40 people chose apples 64 choose oranges and 21 chose bananas in the second 34 chose apples 63 chose oranges 19 Joe’s banana marine inferred before is this a French trooper by us on the data explain
Answer:
Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.
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perimeter.
6) A quadrilateral can have 2
reflex angles.
Answer:
False
Step-by-step explanation:
Answer:
A quadrilateral can't have 2 reflex angles
Step-by-step explanation:
A quadrilateral can't have 2 reflex angles because reflex angles > 180° so if you add two together, it is > 360°
A flexible cable always hangs in the shape of a catenary curve y = c + a cosh(x/a), where cand a are constants, a > 0. Suppose a telephone line hangs between two poles 18 meters apart, in the shape of the catenary y = 30 cosh(x/15) - 4, where x and y are measured in meters. a. (3 pts.) Find the slope of this curve where it meets the right pole. (Round to 3 decimal places.] b. (3 pts.) Find the angle between the line and the right pole. [Give your answer in degrees, rounded to the nearest hundredth.) Expert Answer
Answer:
The slope of this curve where it meets the right pole is 1.130
The angle between the line and the right pole is 41.51 °
Step-by-step explanation:
Given that ;
[tex]y = 30 \ cos h (\dfrac{x}{15} - 4)[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{30}{15} sinh(\dfrac{x}{15})[/tex]
[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{x}{15})[/tex]
x = 9 m;( i.e half of the distance of the two poles at 18 meters apart.
[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{9}{15})[/tex]
= 1.130
The slope of this curve where it meets the right pole is 1.130
The angle between the line an the right rope can be determined by using the tangent of the slope .
tan ∝ = 1.130
∝ = tan⁻¹ (1.130)
∝ = 48.49°
The angle is θ; so
θ = 90 - ∝
θ = 90 - 48.49°
θ = 41.51 °
Thus; the angle between the line and the right pole is 41.51 °
HELP PLEASE!!
NEED ANSWER ASAP!!!
A farmer in China discovers a mammal
hide that contains 54% of its original
Find age of the mammal hide to the nearest year.
amount of C-14
N=N0e^-kt
N = Noe
No = inital amount of C-14 (at time t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
6163.2 years
Step-by-step explanation:
A_t=A_0e^{-kt}
Where
A_t=Amount of C 14 after “t” year
A_0= Initial Amount
t= No. of years
k=constant
In our problem we are given that A_t is 54% that is if A_0=1 , A_t=0.54
Also , k=0.0001
We have to find t=?
Let us substitute these values in the formula
0.54=1* e^{-0.0001t}
Taking log on both sides to the base 10 we get
log 0.54=log e^{-0.0001t}
-0.267606 = -0.0001t*log e
-0.267606 = -0.0001t*0.4342
t=\frac{-0.267606}{-0.0001*0.4342}
t=6163.20
t=6163.20 years
PLEASE MARK BRAINLY
Express the following in usual form
Answer:
52300
Step-by-step explanation:
When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300
The mean of 6 numbers is 32.If one of the numbers is excluded, the mean reduces by 2.Find the excluded number.
Answer:
42
Step-by-step explanation:
Mean = Sum of numbers/ Total numbers
Sum of 6 numbers = 32 x 6
= 192
If one number is excluded the mean reduce by 2 . so it becomes 30
Sum of 5 Numbers = 5 x 30
=150
Therefore the excluded number is
= 192 - 150
= 42.
What is the simplified value of the exponential expression 27 1/3
1/3
1/9
3
9
Answer:
I think its 1/9
Answer:
B
Step-by-step explanation:
Find f(g(−1)), f(g(−1))=___
Answer:
Find g(f(−1)).
g(f(−1)) = 64
Find f(g(−1)).
f(g(−1)) = -6
f(g(−1)) is - 8.
What is a composite function ?A composite functions is a function where two or more than two functions are combined.The output of the previous function is the input of the next function.
According to the given question we have to find a composite function.
Assuming f(x) = x² + 9x and g(x) = x³.
To find f(g(-1)) first we have to put x = -1 for g(x) which is
= g(-1) = (-1)³ = -1.
Now we put this value of g(-1) in f(x).
∴ f(g(-1))
= f(-1)
= (-1)² + 9(-1)
= 1 - 9
= - 8.
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Formula to find the number of subsets of a set that has "n" number of elements. 2 raise 1)to the nth power 2)n squared 3)2 times n 4)All of these
Answer:
(A)[tex]2^n[/tex]
Step-by-step explanation:
Given a set with "n" number of elements, the collection of all subsets of the set is referred to as the Power set of the given set.
To find the number of possible subsets of any set, we use the formula: [tex]2^n[/tex]
Take for example the set: A={2,3,4)
A has 3 elements, therefore n=3
The number of possible subsets of A is: [tex]2^3=8$ subsets[/tex]
A college basketball player makes 80% of his freethrows. Over the course of the season he will attempt 100 freethrows. Assuming free throw attempts are independent, the probability that the number of free throws he makes exceeds 80 is approximately:____________.
A) 0.2000
B) 0.2266
C) 0.5000
D) 0.7734
Answer:
The probability that the number of free throws he makes exceeds 80 is approximately 0.50
Step-by-step explanation:
According to the given data we have the following:
P(Make a Throw) = 0.80%
n=100
Binomial distribution:
mean: np = 0.80*100= 80
hence, standard deviation=√np(1-p)=√80*0.20=4
Therefore, to calculate the probability that the number of free throws he makes exceeds 80 we would have to make the following calculation:
P(X>80)= 1- P(X<80)
You could calculate this value via a normal distributionapproximation:
P(Z<(80-80)/4)=1-P(Z<0)=1-50=0.50
The probability that the number of free throws he makes exceeds 80 is approximately 0.50
The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.
Given that,
A college basketball player makes 80% of his free throws.
Over the course of the season, he will attempt 100 free throws.
Assuming free throw attempts are independent.
We have to determine,
The probability that the number of free throws he makes exceeds 80 is.
According to the question,
P(Make a Throw) = 80% = 0.80
number of free throws n = 100
Binomial distribution:
Mean: [tex]n \times p = 0.80 \times 100 = 80[/tex]
Then, The standard deviation is determined by using the formula;
[tex]= \sqrt{np(1-p)} \\\\=\sqrt{80\times (1-0.80)}\\\\= \sqrt{80 \times 0.20 } \\\\= \sqrt{16} \\\\= 4[/tex]
Therefore,
To calculate the probability that the number of free throws he makes exceeds 80 we would have to make the following calculation:
[tex]P(X>80)= 1- P(X<80)[/tex]
To calculate this value via a normal distribution approximation:
[tex]P(Z<\dfrac{80-80}{4})=1-P(Z<0)=1-0.50=0.5000[/tex]
Hence, The probability that the number of free throws he makes exceeds 80 is approximately 0.5000.
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please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
a. 3
b. 5
c. 4
d. 4
e. 10
Step-by-step explanation:
Answer:
read below
Step-by-step explanation:
a.3
b.5
c.2
d.2
6. 8p
Express (In 35+ln(1/7))/ In 25 in terms of In 5 and In 7
Properties of the logarithm: for any base of logarithm,
log(a*b) = log(a) + log(b)
If we replace b with 1/b, or b^-1, we have
log(a/b) = log(a) + log(1/b) = log(a) - log(b)
since
log(1/b) = log(b^-1) = - log(b)
using the power property of logarithms,
log(b^n) = n log(b)
Now,
ln35 = ln(5*7) = ln5 + ln7
ln(1/7) = - ln7
ln25 = ln(5^2) = 2 ln5
Putting everything together, we have
(ln35 + ln(1/7))/ln25 = (ln5 + ln7 - ln7)/(2 ln5) = ln5/(2 ln5) = 1/2
If sin(θ -π/2) = 0.73.. find cos (-θ) plz explain how to solve
Answer:
[tex]cos(-\theta) = -0.73[/tex]
Step-by-step explanation:
It is given that:
[tex]sin(\theta -\dfrac{\pi}{2}) = 0.73[/tex]
Formula to be used:
[tex]1.\ sin(-x) = -sinx\\2.\ sin(\dfrac{\pi}{2}-x) = cosx\\3.\ cos(-x) = cosx[/tex]
Using Formula (1) written above:
[tex]\Rightarrow sin (\theta - \dfrac{\pi}{2})=sin(-(\dfrac{\pi}{2}-\theta ))\\\Rightarrow -sin(\dfrac{\pi}{2}-\theta)[/tex]
Now, using Formula (2) written above:
[tex]\Rightarrow -sin(\dfrac{\pi}{2}-\theta) = -cos \theta[/tex]
So, we can say that:
[tex]sin(\theta -\dfrac{\pi}{2}) = -cos\theta = 0.73 ...... (1)[/tex]
We have to find the value of [tex]cos(-\theta)[/tex].
Using Formula (3) written above:
[tex]cos(-\theta) = cos\theta[/tex]
So, ultimately we need to find the value of [tex]cos\theta[/tex]
Using equation (1):
[tex]-cos\theta = 0.73\\\Rightarrow cos\theta = -0.73[/tex]
So, the answer is [tex]cos(-\theta) = -0.73[/tex].
What is the result of adding these two equations? 2x+3y=-5 5x-y=-12
Answer:
[tex]x = \frac{-41}{17} , y = \frac{-1}{17}[/tex]
Step-by-step explanation:
Step(i):-
Given equations are 2 x+3 y=-5 ...(i)
5 x-y=-12 ...(ii)
Multiply equation (ii) by '3'
2 x + 3 y = -5
15 x - 3 y = - 36
17 x = - 41
[tex]x = \frac{-41}{17}[/tex]
Step(ii):-
Substitute [tex]x = \frac{-41}{17}[/tex] in equation (i)
2 ([tex]\frac{-41}{17}[/tex]+3 y=-5
3 y = - 5 + [tex]\frac{82}{17}[/tex]
[tex]3 y = \frac{-85 + 82}{17} = \frac{-3}{17}[/tex]
[tex]y = \frac{-1}{17}[/tex]
The solution of the two equations
( x, y ) = [tex](\frac{-41}{17} , \frac{-1}{17})[/tex]
In a random sample of six cell phones, the mean full retail price was $538.00 and the standard deviation was $184.00. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean mu. Interpret the results. Identify the margin of error. Construct a 90% confidence interval for the population mean. Interpret the results. Select the correct choice below and fill in the answer box to complete your choice.
Answer:
The margin of error is 370.8.
The 90% confidence interval for the population mean is between $167.2 and $908.8
The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0150
The margin of error is:
M = T*s = 2.0150*184 = 370.8.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 538 - 370.8 = $167.2
The upper end of the interval is the sample mean added to M. So it is 538 + 370.8 = $908.8
The 90% confidence interval for the population mean is between $167.2 and $908.8
The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
V=
Answer: V=4778.4 cm³
Step-by-step explanation:
[tex]V=\pi r^2\frac{h}{3}[/tex] is the formula for volume. Since we are given the height and radius, we can directly plug it into the equation
[tex]V=\pi (13)^2(\frac{27}{3})[/tex]
[tex]V=169\pi (9)[/tex]
[tex]V=1521\pi[/tex]
[tex]V=4778.4cm^3[/tex]
If Romeo earns 8% more than Juliet, Romeo’s salary is how many times Juliets salary?
A) 1.08
B) 0.92
C) 80
D) 108
Answer:
1.08
Step-by-step explanation:
If Romeo earns 8% more than Juliet,
Example?
If Juliet earns $80
80x8% = 6.40 So his pay would be 80 + 6.40
If you times 80 by 1.08 (this would also be 108%) you would get $86.40
Math Is TU parallel to VW explain
Answer: C ( yes, both lines have a slope of 2/3. )
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Aakash has a liability of 6000 due in four years. This liability will be met with payments of A in two years and B in six years. Aakash is employing a full immunization strategy using an annual effective interest rate of 5%.Calculate |A-B|
Answer:
|A-B|= 586.411565Step-by-step explanation:
We know that = Liability
[tex]PLiability= \frac{6000}{1.05^{4} }[/tex]
[tex]\frac{6000}{1.05^{4} }=\frac{A}{1.05^{2} }+\frac{B}{1.05^{6} }\\\\6000(1.05^{2} ) = (1.05^{4} ) +B\\B= 6000(1.05^{2} )-(1.05^{4} )----------(1)\\\\[/tex]
dAssets =dLiability
[tex]4=2*\frac{\frac{A}{1.05^2} }{\frac{6000}{1.05^4} } +6*\frac{\frac{B}{1.05^6} }{\frac{6000}{1.05^4} } \\4={\frac{6000}{1.05^4}= 2*\frac{A}{1.05^2} +6*\frac{B}{1.05^6}\\\\4[6000(1.05^2)]= 2*A(1.05^4)+6*B[/tex]
From equation 1 we have
[tex]4[6000(1.05^2)]= 2*A(1.05^4)+6*6000(1.05^2)-6*A(1.05^4)\\4*A(1.05^4)=2*6000(1.05^2)\\A=\frac{2*6000(1.05^2)}{4*(1.05^4)} \\A=272.088435\\[/tex]
Going back to equation 1 we have
[tex]B= 6000(1.05^2)-A(1.05^4)\\B= 3307.5\\|A-B|= |2721.088435-3307.5|= 586.411565[/tex]
