Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = x³y + 24x²- 8y local maximum value(s) local minimum value(s). saddle point(s) (x, y, ) =

Answers

Answer 1

Answer:

Answer:

DNE.) f(x, y) = x³y + 24x²-

Step-by-step explanation:

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enterDNE.) f(x, y) = x³y + 24x²- 8y local maximum value(s) local minimum value(s). saddle point(s) (x, y, ) =

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Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at the rate of 4 mph, she reaches the station 5 minutes before the arrival of the train. Find the distance Gilda walks to the station.David knew he made a mistake when he calculated that Gilda walks 123 miles to the station. Read through David's calculations:Using d = rt, the distance is the same, but the rate and time are different.If Gilda misses the train, it means the time t needs 7 more minutes so d = 3(t + 7).If she gets to the station 5 minutes early means the time t can be 5 minutes less so d = 4(t - 5).3(t + 7) = 4(t - 5)3t + 21 = 4t - 20t = 41d = rt, so d = 3(41) = 123Find David's mistake in his calculations. In two or more complete sentences, explain his mistake. Include the correct calculations and solutions in your answer.

Answers

We'll represent the distance as d and the time as t.
d= 3(t+7) because Gilda is 7 minutes late when travelling 3 mph
d= 4(t-5) because Gilda is 5 minutes early at 4 mph

d= 3t + 21
d= 4t -20
3t +21 =4t -20
41=t
d= 3(41) +21= 144
The distance is 144 miles.

$d=3(t + 7)\ \ \ if\ Gilda\ walks\ of\ 3mph\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ she\ is\ 7\ minutes\ after\ departure\ of\ the\ train\n\n d= 4(t - 5)\ \ \ if\ Gilda\ walks\ of\ 4mph\ \n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ she\ is\ 5\ minutes\ before\ the\ train\ \n\n3(t+7)=4(t-5)\n\n3t + 21 = 4t - 20 \n\nt = 41\ \ \ \Rightarrow\ \ \ d=3(t+7)=3\cdot(41+7)=3\cdot48=144\n\nAns.\ The\ distance\ to\ the\ station\ is\ 144\ miles.$

Which of the following relations is a function? {(-6, 4), (-6, 2), (2, 9), (1, 4)}

{(8, 2), (9, -2), (7, 0), (-3, 6)}

{(1, 2), (4, -1), (1, 2), (-3, 4)}

{(8, -2), (-4, 3), (8, 4), (-2, 3)}

Answers

The formal definition of a function states that: "A function relates each element of a set with exactly one element of another set (possibly the same set)."

The part "..with exactly one element.." means that for every input (x-coordinate), it cannot give back 2 or more return values (y-coordinates). With that rule alone, we can look at the different groups of coordinate points, and find which of the groups don't have repeating x-coordinates.

Let us look at each group:
{(-6, 4), (-6, 2), (2, 9), (1, 4)} contains 2 pairs with the -6 x-coordinate, so this is not a function.

{(1, 2), (4, -1), (1, 2), (-3, 4)} contains 2 pairs with the 1 x-coordinate so this is not a function.

{(8, -2), (-4, 3), (8, 4), (-2, 3)} contains 2 pairs with the 8 x-coordinate so this is not a function.

{(8, 2), (9, -2), (7, 0), (-3, 6)} does not have any repeating x-coordinates, so this relation is a function.

I am confused on this , I’ve tried twice and got it wrong.

Answers

Answer:

$f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$

Step-by-step explanation:

Consider the function $f(x)=√(4-x)+3$ for the domain $(- \infty, 4]$ .

Find $f^-^1(x)$ , where f^(-1) is the inverse of f.

Also state the domain of f^(-1) in interval notation.

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We can start solving this problem by finding the inverse of f(x). This is done by switching the x- and y- variables, and solving for y.

$y=√(4-x)+3 \rightarrow x=√(4-y)+3$
$x=√(4-y)+3$

We can start solving for y by subtracting 3 from both sides of the equation.

$x-3=√(4-y)$

Get rid of the radical by squaring both sides of the equation.

$(x-3)^2=(√(4-y))^2$
$(x-3)(x-3)=4-y$

Use FOIL to multiply the binomial (x-3) together.

$x^2-3x-3x+9=4-y$

Combine like terms.

$x^2-6x+9=4-y$

Subtract 4 from both sides of the equation.

$x^2-6x+5=-y$

Divide both sides of the equation by -1.

$-x^2+6x-5=y$
$f^-^1(x)=-x^2+6x-5$

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The domain and range of a function are flipped for its inverse, meaning that to find the domain of the inverse function, you can find the range of the original function f(x), and that will be your inverse function's domain.

The range of $f(x)=√(4-x) +3$ is $y \geq 3$ , since the vertical shift of the graph is at k = 3. You can also graph this function on a calculator to see that the graph does indeed start at y = 3.

Now that we know the domain and range of the original function, we know that these are flipped for the inverse function.

Original function:

Domain: $x\leq 4$
Range: $y\geq 3$

Inverse function:

Domain: $x\geq 3$
Range: $y\leq 4$

The final answer is:

The inverse $f^-^1(x)=-x^2+6x-5 \ \text{for the domain}\ [3, \infty)$ .

You can also write the domain as: $x\geq 3$ .

If the population of an ant hill doubles every 20 days and there are currently 30 ants living in the hill, what will the population be after 60 days?

Answers

The number of ants after 60 days is 240.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The population of ants doubles every 20 days.

Current number of ants = 30

Now,

The number of ants after 20 days.

= 30 x 2

= 60

The number of ants after 40 days.

= 60 x 2

= 120

The number of ants after 60 days.

= 120 x 2

= 240

Thus,

The number of ants is 240.

Learn more about expressions here:

brainly.com/question/3118662

#SPJ2

after 20 days , ants will be double so 60 ants
again after 20 days, there will be 120 ants

and at last

after total of 60 days, ants will be 240 in number ! .....answer !

The difference of a number and thirty-six is seven. Algebraic expression

Answers

Answer:

x-36=7

Step-by-step explanation:

x-36=7

x=36+7

x=43

Determine the volume of a sphere with a diameter of 5 inches.Use 3.14 for Pi, and round your answer to the nearest inch. a. 65 cu. in c. 60 cu. in b. 75 cu. in d. 11 cu. in Please select the best answer from the choices provided

Answers

Answer:

Step-by-step explanation:

r = 2.5 in

V = 4(3.14) $(2.5 in)^(3)$ /3 = $65 in^(3)$

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