find and sketch the domain of the function. f(x, y, z) = ln(36 − 4x2 − 9y2 − z2)

Answer:

a = 22

AB = 50

Step-by-step explanation:

\(a-5=17\)

\(a=17+5\)

\(a=22\)

Line AB=2a+6

\(2(22)+6=44+6=50\)

\(AB=50\)

Hope this helps

To find the absolute maximum and minimum of a function, determine the critical points and evaluate the function at those points and the endpoints of the interval.

To find the absolute maximum and minimum of a function, you need to follow these steps:

1. Determine the critical points of the function by finding where its derivative equals zero or is undefined. These points can be potential candidates for the maximum or minimum values.

2. Evaluate the function at the critical points and at the endpoints of the interval you are considering. The highest value among these points will be the absolute maximum, while the lowest value will be the absolute minimum.

Let's illustrate this with an example:

Consider the function f(x) = x^2 - 4x + 5 on the interval [0, 5].

1. To find the critical points, we need to find where the derivative is equal to zero or undefined. Taking the derivative of f(x),

we get f'(x) = 2x - 4.

Setting this equal to zero gives us 2x - 4 = 0, which implies x = 2. So, x = 2 is the only critical point.

2. Now, we evaluate the function at the critical point and the endpoints of the interval:
f(0) = 0^2 - 4(0) + 5 = 5
f(2) = 2^2 - 4(2) + 5 = 1
f(5) = 5^2 - 4(5) + 5 = -5

From these evaluations, we see that f(0) = 5 is the absolute maximum and f(5) = -5 is the absolute minimum.

To know more about absolute maximum visit:

https://brainly.com/question/31585619

#SPJ11

Answer:

b) y = -x2 + 6x + 2

Step-by-step explanation:

Step-by-step explanation:

Area of the cube : 6a²

6 ( 3/5)²

6 (9/25)

54/25

54/25 = 2.16

Answer:

The magnetic is stronger when it is closer to the wires. the magnets rotates around the wire. she can determine the directions by telling if it is repelling or attracting objects that contain iron.

A magnet is stronger when closer to the wires It rotates around the wire. she can determine the directions by telling if it is repelling or the attracting objects have contained iron.

An electromagnetic is a type of magnet that makes a magnet field that is produced by the electric current. They consist of a wire placed around a coil.  

The current in the wire creates the magnetic effect and the wire turn of the magnetic core which consists of the magnetic flux. this makes the magnet is more powerful.

They are widely used for motors and electrical devices.  As the magnet rotates closer to the wire as she can determine the repelling force of the object that is containing the iron.

Find out more information about the demonstration.

brainly.com/question/11164829.

Answer:

Set1 = 1/12

Set2 = 1/12

Set3 = -12

Step-by-step explanation:

Substitute, use Keep-Change-Flip to handle division when there's fractions involved. See image.

Also to multiply fractions, multiply

top×top and bottom×bottom straight across. Also negative times a negative is a positive and negative is like opposite so -(-6) is 6 and -(-1/2) is 1/2.

see image.

A linear equation is the equation of a line.The equation which is passing through the point (-1,6) and parallel to the line -2x+y=9 is -2x + y = 8.

A straight line on the coordinate plane is represented by a linear function.

A linear function is a function that varies linearly with respect to the changing variable.

A linear equation in slope y-intercept form is written as,

y = mx + c where m is the slope while c is the y-intercept.

Given equation is -2x+y=9

y = 2x + 9 so slope m is 2.

Since parallel lines have the same slope so equation will be,

y = 2x + c

Substitute,(-1,6)

6 = 2(-1) + c → c = 8

So,

y = 2x + 8 → -2x + y = 8.

Hence "A linear equation is the equation of a line. The equation which is passing through the point (-1,6) and parallels to the line -2x+y=9 is -2x + y = 8".

For more about the linear function,

brainly.com/question/21107621

#SPJ1

The given question is incorrect correct question follows ;

Find the equation of the line passing through the point (-1,6) and parallel to the line -2x+y=9

Answer:

Step-by-step explanation:

the answer is 7 hours not 4 hours

Answer:

Yes, 4 hours

Step-by-step explanation:

\(\frac{x + 56}{3} = 5x\)  Multiple both sides by 3

x + 56 = 15x  Subtract x from both sides

56 = 14x  Divide both sides by 14

4 = x

Answer:Points, Lines, and Ang. A midpoint is a point that bisects, or divides, a line segment into two congruent pi. Point B is the midpoint of AC

Step-by-step explanation:

The tree has 11 vertices with degree 1.

To find the number of vertices with degree 1 in a tree with degree sequence (6,6,6,6,4,...), we can use the Handshaking Lemma. This lemma states that the sum of all vertex degrees in a graph is twice the number of edges. In a tree, the number of edges is one less than the number of vertices, so we can write:

6+6+6+6+4+...+2+2+1+1 = 2n-1

where n is the number of vertices. Simplifying this equation gives:

n = (6+6+6+6+4+...+2+2+1+1+1)/2 + 1

The term inside the parentheses is the sum of all vertex degrees, which we know from the degree sequence. Plugging in the values and simplifying, we get:

n = 18

So the tree has 18 vertices. Since we know that the rest of the vertex degrees are either 2 or 1, we can subtract the six vertices with degree 6 and the one vertex with degree 4 to get:

18 - 6 - 1 = 11

For more about vertices:

https://brainly.com/question/31502059

#SPJ11

Answer:

a

Step-by-step explanation:

a

Answer:

D

Step-by-step explanation:

For a circle, the equation of the circumference is c = π * 2r (radius). Since in this case, the circumference is 15.3, that means π * 2r = 15.3. I'm going to assume that pi is 3.14 because the four answers aren't particularly close to each other. This means that 2r = approx. 4.872. If you then divide both sides by 2 you get r = approx. 2.436, which is closest to answer D.

Answer:

9 and 13/15 or 148/15

Step-by-step explanation:

Hope this helps!

The price of one adult ticket is $15 and the price of one child ticket is $8.

Two sets of equations can be derived from this question:

14a + 14c = 322 equation 1

12a + c = 188 equation 2

These equations are known as simultaneous equations and they can be solved to determine the cost of each ticket using the elimination method.

In order to determine the cost of the adult's ticket multiply equation 2 by 14

168a + 14c = 2632 equation 3

Subtract equation 1 from 3

2310 = 154a

Divide both sides by 154

a = $15

To determine the cost of the children's ticket substitute for a in equation 1

14(15) + 14c = 322

210 + 14c = 322

322 - 210 = 14c

112 = 14c

c = $8

To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults

The probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

Total number of outcomes = C(25, 2) = 300

Total number of favorable outcomes = C(20, 2) = 190

Probability = 190/300 = 19/30 or

= 0.63

Thus, the probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

The area of the parallelogram, that have a base length of 22 and one-half feet, and a height of 19 and one-fourth feet is 433 and one-eight square feet. The correct option is therefore;

Four hundred thirty-three and one-eighth ft²

A parallelogram is a quadrilateral that has a pair of opposite sides that are parallel. The area of a parallelogram, A, of base length, b, and height, h can be presented as ; A = b·h

The base length of the parallelogram = 22 1/2 feet

Height of the parallelogram = 19 1/4 feet

Area of a parallelogram = Base length × Height

Therefore; The area of the parallelogram = 22 1/2 × 19 1/4 = 433 1/8

The area of the parallelogram = 433 1/8 square feet

The third option is correct;

Learn more on parallelograms here: https://brainly.com/question/29130284

#SPJ1

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

Step-by-step explanation:

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Answer:$6.50

Step-by-step explanation:

if you divide 91 by 14 you get 6.5 which makes one candle $6.50

Answer:

a

Step-by-step explanation:

to find a proportion they must equal each other

8/4 in its simplest form is just 2

to make r/3 = 2 r must be 6

6/3 is 2

Answer:

x=3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

I did this on a quiz and I got it right :)

The volume of the steel barrel with the given diameter and depth is 138.474ft³.

Hence, option C) 138.474 cubic feet is the correct answer.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given the data in the question;

Volume of the steel barrel V = ?

We substitute our values into the expression above.

V = π × r² × h

V = 3.14 × (3ft)² × 4.9ft

V = 3.14 × 9ft² × 4.9ft

V = 138.474ft³

The volume of the steel barrel with the given diameter and depth is 138.474ft³.

Hence, option C) 138.474 cubic feet is the correct answer.

Learn more about volume of cylinder here: brainly.com/question/16788902

#SPJ1

Answer:

-36

Step-by-step explanation:

Answer:

6561

Step-by-step explanation:

For Morgan to make one cabinet by alone, it will take 12 hours.

Assuming Donna takes "x" hours to make one cabinet.

Morgan takes 8 more hours

Then , Donna = "x + 8" hours to make one cabinet.

Working together , time taken = 3 hours.

We can set up an equation based on their rates of work:

1/(x + 8) + 1/x = 1/3

(1 * x + 1 * (x + 8)) / ((x + 8) * x) = 1/3

(x + x + 8) / (x² + 8x) = 1/3

(2x + 8) / (x² + 8x) = 1/3

3(2x + 8) = x² + 8x

6x + 24 = x² + 8x

Rearranging the equation:

x² + 2x - 24 = 0

Now we can factor or use the quadratic formula to solve for "x." Factoring the equation:

(x + 6)(x - 4) = 0

x + 6 = 0 or x - 4 = 0

x = -6 or x = 4

Since we are considering time, the solution cannot be negative. Therefore, x = 4, which means it takes Donna 4 hours to make one cabinet.

Morgan's time = 4 + 8 = 12 hours

Therefore, it takes Morgan 12 hours to make one cabinet by herself.

Learn more on equations: https://brainly.com/question/29133548

#SPJ1

Answer:

y>-2

y<-4x+2

Step-by-step explanation:

A. y>-2

The reason is because the line is horizontal which means the slope is 0 and your "y" value equals a number (0,#) so your line starts on -2 so it would just be -2 and since it is shaded above then "y" is greater than -2.

B. y<-4x+2

The reason is because you start with your slope (2) and go done to where the line crosses another point (in your case the other point is -2) and then you go over to the right where that specific point is plotted (so your coordinate that is plotted is (1,-2)). So, however many units you go down is the slope (in your problem (-4)) and however many you go over is also part of the slope but it can be either a whole number or fraction but for you it is just (-4) because you only go over to the right once. So now you have your equation -4x+2. And since the lines shading is below that means "y" is less than your equation.

And the reason why both lines are less than and greater than is because they are dotted lines if they were solid they would be "less than or equal" to or "greater than or equal to"

I hope this helped!

\({\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}\)

\( \sf \dfrac{2}{15} \div \dfrac{3}{20} = \dfrac{2 \times 20}{15 \times 3} = \dfrac{40}{45} = \dfrac{8}{9} \)

Answer :-

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \Rrightarrow \dfrac{8}{9} \)

I hope I've helped : )

\(\dfrac{1}{50}\)

\( \cfrac{2}{15} \times \cfrac{3}{20} \)

\( \cfrac{2 \times 3}{15 \times 20} \)

\( \cfrac{6}{15 \times 20} \)

\( \cfrac{6}{300} \)

\( \cfrac{1}{50} \)

-------------------------------------------------------------------------------------------------------

Learn more about solving fractions here:

https://brainly.com/question/16627508

https://brainly.com/question/29121733

Answer:

What is the y-value of the vertex of the function f(x)=â’(xâ’3)(x 11) 1060 by cata

Answer:

xy=1.5

-7x=1.75

x+2y=-12.25

(1/3)y=-2

Step-by-step explanation: