The minimum and maximum values are (16/9)√3 and -(16/9)√3.
According to the statement
we have given that the function
First of all, since the constraint's graph is a circle, which is a closed loop, and f is continuous in [tex]R^2[/tex], there must exist a constrained global maximum and minimum value.
Lagrange Multipliers:
f(x,y) = xy^2
g(x,y) = x^2 + y^2
We want ∇f = λ∇g so we get the following system of equations
1. y^2 = 2λx
2. 2xy = 2λy
3. x^2 + y^2 = 4 ← The constraint.
Equation 2 implies that y = 0 or λ = x
We can ignore y = 0, since that will make f(x,y) = 0 and clearly f(x,y) takes on both positive and negative values subject to the constraint.
Plugging in the alternative, λ = x to equation 1 gives y^2 = 2x^2.
Plugging this into the constraint gives 3x^2 = 4 so that x^2 = 4/3 and y^2 = 8/3
Taking square roots gives
x = ±√(4/3) = ±(2/3)√3
y = ±√(8/3) = ±(2/3)√6
At the points < (2/3)√3 , ±(2/3)√6 >, f(x,y) = (16/9)√3 ← Maximum
At the points < -(2/3)√3 , ±(2/3)√6 >, f(x,y) = -(16/9)√3 ← Minimum
So, The minimum and maximum values are (16/9)√3 and -(16/9)√3.
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give the answer please
The inverse of a function is given as √x - 1
Inverse of a functionTo get the inverse of any function f(x) we need to ensure that it passes the horizontal line test.
Given the following function
f(x) = (x+1)^2
Let y= f(x) to have:
y = (x+1)^2
Replace y with x to have:
x = (y+1)^2
Make y the subject of the formula
√x =y + 1
Subtract 1 from both sides
√x - 1 = y
Swap
y = √x - 1
Hence the inverse of a function is given as √x - 1
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A tailor needs meters of cloth to make a poncho. How many meters does he need to make 15 ponchos of the same size?
Answer:
15 mister of cloths are needed to make 15 m if 1 puchu is 1 miter
Answer:15 meters
step by step explanation
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representation of the inequality is -6x + 15 < 10 - 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
What is inequality?In mathematical concept, an inequality is a representation of an order linking two numbers or algebraic expressions together. These orders are called inequality signs such as greater than (>), less than (<), greater than or equal to(≥), or less than or equal to(≤). Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.
From the given information, we are given the inequality:
= -3(2x - 5) < 5(2 -x)
Open brackets, we get:
= -6x + 15 < 10 - 5x
Subtract 15 from both sides, we have:
= -6x + 15 - 15 < 10 - 5x - 15
= -6x < -5x - 5
Add 5 to both sides
= -6x + 5 < -5x - 5 + 5
= -6x + 5 < -5x
= -x < - 5
= x < 5
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A regular decagon with exterior angle 1 is shown.
In the regular decagon shown, what is the measure of angle 1?
°
Answer:
∠1 = 36°
Step-by-step explanation:
All angles of a regular polygon are congruent, as are the sides. A regular decagon will have 10 congruent angles.
Exterior anglesThe sum of the measures of the exterior angles of a convex polygon is always 360°. This decagon has 10 congruent exterior angles, so the measure of each is given by ...
10(∠1) = 360°
∠1 = 36° . . . . . . . . divide by 10
Answer: 36°
Step-by-step explanation: Trust Me!
Answer is correct on Edge. Good Luck! :)
In the regular decagon shown, what is the measure of angle 1?
36°360° is always the sum of all measures of all exterior angles of a convex polygon. A decagon have 10 sides.
Since ∠1 = 36°, then each other angle should measure the same, 36°.
In order to know whether the sum of all the angles equal 360°,
we need to multiply: 36° x 10.
36° x 10= 360°.
And sure enough the answer is correct.
Hank is currently reading a book that is 250 pages long. if he can read 10 pages every 15 minutes, how many hours will it take him to read the book?
Answer:
The answer is B, 2.78 hours
Step-by-step explanation:
Answer:
6 hours 15 minutes, or 6.25 hours
Step-by-step explanation:
We assume Hank reads at a constant rate. His reading time will be proportional to the number of pages.
ProportionWe know that 15 minutes is 1/4 hour, so the proportion can be written ...
hours/pages = (book hours)/(250 pages) = (1/4 hour)/(10 pages)
Multiplying by 250 pages gives ...
book hours = 250(1/4 hour)/10 = 25/4 hour = 6 1/4 hour
It will take Hank 6 1/4 hours to read the book.
Rohan was planning a party and needed to provide 35 lunches. the cost for each plate 5$ and each plate was 6$. how many of each could he buy and spend $198 total?
for 5 bucks a plate its 39 for 6 bucks its 33
Step-by-step explanation:
Subtract.
(3x²+2x9) - (4x² - 6x + 3)
4
Answer:
-13x²+24x+6
Hope this helps:)
When a graphed line is vertical it indicates that the relation:
1. is a function and begins with y =
2. is not a function and begins with x =
3. is a function and begins with x =
4. is not a function and begins with y =
Answer:
y does not depend on x - it is not a function
That leaves (2) or (4)
Since one does not need y in the equation (4) is eliminated
(2) is the only possible result
For example: x = 5
Consider this absolute value function. how can function f be written as a piecewise function?
The absolute value exists its distance from zero on the number line.
⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0
⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8
⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8
How to estimate the absolute value?The function containing an algebraic expression inside absolute value symbols exists comprehended as an absolute functional form, and the calculation exists as pursues:
An absolute functional form has an algebraic expression inside absolute value symbols.
Remember that a number's absolute value exists its distance from zero on the number line.
⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0
⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8
⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8
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Please help im bad at math!
Answer:
answer is 3 ft
Step-by-step explanation:
area of circle= 3*(1)^2
PLEASE HELP, I THINK IT’S EITHER B OR C.
(09.01 LC)
A function is shown in the table.
x g(x)
-2 2
-10
02
1 8
Which of the following is a true statement for this function? (5 points)
The function is decreasing from x = 0 to x = 1.
The function is decreasing from x = -1 to x = 0.
The function is increasing from x = 0 to x = 1.
The function is increasing from x = -2 to x = -1.
its c! there isnt a decrease between x = -1 and x = 0, as when x = -1 y = 0 and when x = 0 y = 2, showing an increase of +2.
pls help asap screenshot also posted- Which expression is equivalent to the given expression? 180‾‾‾‾√⋅230‾‾
The expression √180 * 2√30 is equivalent to the expression 60√6
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The square root is a factor of a number that, when multiplied by itself, gives the original number.
Given the expression √180 * 2√30
Collecting like terms give:
= 2√(180 * 30)
Simplifying:
= 60√6
The expression √180 * 2√30 is equivalent to the expression 60√6
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Use the root test to determine the convergence or divergence of the series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] 1 nn n = 1
The root test is Divergent, for given [infinity] 1 nn n = 1.
The foundation take a look at to research the restrict of the nth root of the nth time period of your collection. Like with the ratio check, if the restrict is less than 1, the series converges; if it is extra than 1 (together with infinity), the series diverges; and if the restrict equals 1, you analyze not anything.
The root check this collection is divergent. again, there is not too much to this series. therefore, with the aid of the root take a look at this collection converges clearly and hence converges. notice that we needed to maintain the absolute cost bars at the fraction until we would taken the limit to get the sign accurate
Root test requires you to calculate the value of R the usage of the components under. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent.
explanation:
If tan is series
if Lim n root (1) = l
if l =<1 than it is convergent
if l = > 1 than it is divergent
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x^2-15x+54=0 solve for x
Answer: x = 9 and x = 6
Step-by-step explanation:
[tex]x^2-15x+54=0\\(x-9)(x-6)\\x-9=0\\x=9\\x-6=0\\x=6[/tex]
Therefore, x = 9 and x = 6
Q. An ornithologist wants to estimate the number of parrots in a large field. She uses a net to catch some, and catches 32 parrots, which she rings and sets free. The following week she manages to net 40 parrots, of which 8 are ringed.
(1) What fraction of her second catch is ringed?
(2) Find an estimate of the total number of parrots in the field.
Need help! Urgent!
Total parrot=40
Caught=8
Fraction
8/401/5#2
Out of 40 parrots 8 are ringed
Parrots per one ringed=40/8=5
Total ringed before=32
Total no of parrots
32(5)160There are 160 parrots
Answer:
[tex]\sf 1) \quad \dfrac{1}{5}[/tex]
[tex]\sf 2) \quad 160\:parrots[/tex]
Step-by-step explanation:
Question 1Given information:
Second catch = 40 parrotsRinged = 8 parrotsTherefore, the fraction of ringed parrots from the second catch is:
[tex]\implies \sf \dfrac{ringed\:parrots}{total\:caught\:parrots}= \dfrac{8}{40}=\dfrac{1 \times 8}{5 \times 8}=\dfrac{1}{5}[/tex]
Question 2If she caught and ringed 32 parrots in her first catch, but only 1/5 of the parrots caught in the second catch were ringed, then 32 parrots represents 1/5 of the total number of parrots. To find the total number of parrots, simply multiply the total number of ringed parrots by 5:
[tex]\implies \sf \textsf{Total number of parrots}=32 \times 5 = 160[/tex]
____________ 15. What is m∠A? Select all that apply.
The angle m∠A can be represented as follows:
m∠A = 47°m∠A = 164 - 70 / 2How to find the angle in a circle?The above circle, a secant and a tangent intersect outside the circle.
A secant is a straight line that intersects a circle in two points.
A tangent is a line that never enters the circle's interior.
Therefore, when a secant and a tangent intersect, the following rules applies:
m∠A = 1 / 2 (BD - BC)
m∠A = 1 / 2 (164 - 70)
m∠A = 1 / 2 (94)
m∠A = 47 degrees.
Therefore, the angle m∠A can be represented as follows:
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You conduct a quasi-experiment to assess the impact of raising the speed limit from 55 to 65 miles per hour. You find that there are more accidents in the 6-month period following the speed limit change than in the 6-month period before the speed limit change. Although it is tempting to say that raising the speed limit caused higher accident rates, you must be careful because
It's tempting to say that increasing the speed limit has led to higher accident rates, but you have to be careful because other variables (e.g. cheaper gas or time of year the change was introduced) can also affect accident rates. The option C is correct.
Given the impact of the speed limit increase from 55 to 65 mph, there are more crashes in the 6 months after the speed limit change than in the 6 months before the speed limit change. speed.
The dependent variable is the variable that is attempted and expected in a survey and is "dependent" on the free aspect. In a survey, the scientist tries to find the conceivable influence on the reliable variable, which can be approximated by changing the free thing. The free aspect is the variable that the experimenter adjusts or controls, and should directly affect the dependent variable. Therefore, increasing the speed limit from 55 to 65 mph resulted in higher accident rates, you have to be careful with other variables.
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Rearrange the equation so q is the independent variable.
9q-43r-6
R =
Answer:q = 6+43r/9
Step-by-step explanation:
Assuming R=9q-43r-6 is what you meant
R+6 = 9q - 43r
R + 6 + 43r = 9q
q = 6+43r/9
I have one try left on this problem
Answer:
632
Step-by-step explanation:
So we can define decreasing x% in two ways: we can define 20% off as 80% of the original value, or we can define subtracting 20% from the original value, and both representations are useful.
In this case it's more useful to define 20% as subtracting 20%, from the original value. The reason for this, is because since we're subtracting 20% of the original value, we then know that 126.40 is 20% the original value.
So to find x% of some value, you generally use the following equation: [tex]A*\frac{x}{100}[/tex] where A=original amount, and x is the percent. This equation is simply converting the x% to a decimal value. Since 126.40 is 20%, we can derive the following equation.
[tex]0.20A = 126.40[/tex]
We can solve for A, by dividing by 0.20
[tex]A=632\\[/tex]
It's also important to note, you didn't really have to set up this entire equation, since you know that the 126.40 is 20%, you simply could've multiplied by 5, since 20% is really just 1/5 of the entire value, so get the entire value, or original value you multiply by 5
I need this answer now please!!
Last option, (-2,6) where the lines intercept / cross over each other.
Hope this helps!
Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 4x 2, [0, 9], f(c) = 23 c =
The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.
Especially, he has been credited with proving the following five theorems: a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same; the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.
In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.
In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a theorem and is maximum extensively used in the domain of science.
2-1and interval = [4]
since function text is continuous in a given interval. And also
+(4) = 42+4 = 4-1
20 = 6667
$(5/4) = ($145/2
stone-1
= 5.833
simple, f(4) > $(5/2), hence Intermediate
Theorem & applies to the indicated proved.
Now,
= 6 C-1
C-5c +6 = 0
C=2 or c=3
1=3 or
C= 2, 3
<= 2
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Mrs. wright made 92 cups of fruit punch for a party. how many gallons of punch did she make?
Answer:
5.75 - 5 3/4
Step-by-step explanation:
1 Cup = 0.0625 gallons
92 cups = 5.75 gallons
Twelve education students, in groups of four, are taking part in a student-teacher program. Mark cannot be in the first group because he will be arriving late. How many ways can the instructor choose the first group of four education students?.
330 ways can the instructor choose the first group of four education students.
What is probability in math?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.Given:
12 students
3 groups consisting of 4 students.
Mark can't be in the first group.
The combination formula that I used is = n! / r!(n-r)!
where: n = number of choices ; r = number of people to be chosen.
This is the formula I used because the order is not important and repetition is not allowed.
Since Mark can't be considered in the first group, the value of n would be 11 instead of 12. value of r is 4.
numerator: n! = 11! = 39,916,800
denominator: r!(n-r)! = 4!(11-4)! = 4!*7! = 120,960
Combination = 39,916,800 / 120,960 = 330
Therefore, There are 330 ways that the instructor can choose 4 students for the first group.
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A trapezoid has bases with lengths of 1.5 yards and 4 yards. The height is 12 yards. What is the area of the trapezoid?
A) 24 square yards
B) 27 square yards
C) 33 square yards
D) 66 square yards
When mutex lock is implemented as a binary semaphore, what should its value be initialized to be?
a) 0
b) 1
c) -1
d) none of the above
Find sin() and cos(), tan() and cot(), and sec() and csc(). webassign plot (a) sin() and cos() (b) tan() and cot() (c) sec() and
The values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
How to evaluate the trigonometry functions?The figure that completes the question is added as an attachment
From the figure, we have the third side of the triangle to be
Third = √(7^2 - 4^2)
Evaluate
Third = √33
The sin(α) is calculated as:
sin(α) = Opposite/Hypotenuse
This gives
sin(α) = 4/7
The cos(β) is calculated as:
cos(β) = Adjacent/Hypotenuse
This gives
cos(β) = 4/7
The tan(α) is calculated as:
tan(α) = Opposite/Adjacent
This gives
tan(α) = 4/√33
The cot(β) is calculated as:
cot(β) = Adjacent/Opposite
This gives
cot(β) = 4/√33
The sec(α) is calculated as:
sec(α) = Hypotenuse/Adjacent
This gives
sec(α) = 7/√33
The csc(β) is calculated as:
sec(β) = Hypotenuse/Opposite
This gives
sec(β) = 7/√4
Hence, the values of the trigonometry functions are sin(α) = 4/7, cos(β) = 4/7, tan(α) = 4/√33, cot(β) = 4/√33, sec(α) = 7/√33 and sec(β) = 7/√4
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Determine the size of the unknown angle to the nearest tenth of a degree.
tan Y : 0.2334
Also, two different questions down below.
Answer:
shown below
Step-by-step explanation:
1) tanY = 0.2334
Y = arctan(0.2334)
Y = 13.14 degrees
2) X = 12 / tan(40)
X = 14.3km
3) x = arctan(5/8)
x = 32°
Is Figure B a scale copy of Figure A?
A regular-size box of crackers measures 214 inches by 912 inches by 14 inches. The manufacturer also sells a snack-size box that has a volume that is 15 of the volume of the regular-size box. What is the volume of the snack-size box of crackers
Answer:
182,156.8
Step-by-step explanation:
214 x 912 x 14 = 2,732,352
1/15 of that Volume is 182,156.8
P.S. I'm assuming you meant 1/15, when you said the volume was 15 of
Follow my gram it's Greyhasnoshame
In regression, the difference between the confidence interval and prediction interval formulas is ________
In regression, the difference between the confidence interval and the prediction interval formula is "The addition of 1 to the quantity under the radical sign i.e., standard error".
What are the formulas for the confidence interval and prediction interval?
The formula for the confidence interval is
[tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE([tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))
The formula for prediction interval is
Prediction interval = Sample estimate ± (t multiplier × standard error)
[tex]y_{new}[/tex] = [tex]y_h[/tex] ± [tex]t_{(1-\alpha /2,n-2)[/tex] × √(MSE(1 + [tex]\frac{1}{n}[/tex] + ([tex]x_h[/tex] - μ)²/∑([tex]x_i[/tex] - μ)²))
Where μ = x bar.
What is the difference between the confidence interval and the prediction interval?From the above, the prediction interval has one additional MSE term in the standard error calculation. But in the confidence interval, only one term is used.
So, the difference between them occurs in the standard error value.
The formula shows it by adding 1 to the quantity under the radical sign.
Thus, the difference is in the standard error.
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