Suppose
f(x,y,z)=xyz 3
+e (y−x 2
)
(a) At the point
(−1,1,2)
, find the direction in which the maximum rate of change of
f(x,y,z)
occurs. (b) What is the maximum rate of change of the function at the point
(−1,1,2)
? Enter your answer in the blank blow. Round your answer to two decimal places. Your Answer:

Answer:

Susan and 4 quests

5 people

Step-by-step explanation:

Take 9/10 and divide by 1/6

9/10 ÷1/6

Copy dot flip

9/10 * 6/1

54/10

50/10 + 4/10

5 4/10

We can only serve whole numbers

5 people

Susan and 4 quests

Answer:

\((\frac{12}{-4n^{2}})\)

Step-by-step explanation:

\((\frac{3}{-2n})(\frac{4}{2n})=(\frac{3*4}{-2n*2n})=(\frac{12}{-4n^{2}})\)

Answer:

\( -\dfrac{3}{n^2} \)

Step-by-step explanation:

\( \dfrac{3}{-2n} \times \dfrac{4}{+2n} = \)

\( = \dfrac{3 \times 4}{-2n \times 2n} \)

\( = \dfrac{12}{-4n^2} \)

\( = -\dfrac{3}{n^2} \)

Answer:

This equation has two solutions.

1 solution is: x - 1

Solution #2 is : x - 7

Step-by-step explanation:

1. Move the constant to the left. We end up with x^2 - 8x +7 = 0

2. Rewrite the expression: x^2 - x - 7x + 7 = 0

3. Factor the expressions: x * (x-1) -7(x-1) = 0

4. Separate into possible cases : (x-1) * (x-7) = 0

5. Solve the equation(s): x-1 = 0

                                         x-7 = 0

6. Possible solutions are as follows: x-1 OR x-7

Answer:

x = 40

Step-by-step explanation:

We have to find,

→ the value of x in the equation.

The equation is,

→ (x/2) + 3 = 23

Now the value of x will be,

→ (x/2) + 3 = 23

→ x/2 = 23 - 3

→ x/2 = 20

→ x = 20 × 2

→ [ x = 40 ]

Hence, the value of x is 40.

Answer:

f[g(x)] = 10x + 105

Step-by-step explanation:

f(x) = 10x + 25 and g(x) = x + 8

\(f[g(x)] = 10(x + 8) + 25 \\ \\ f[g(x)] = 10x + 80 + 25\\ \\ f[g(x)] = 10x + 105\)

Answer:

I hope I've finally done justice to it.

Step-by-step explanation:

\(y=-5x^2 \sqrt{x}\)

\(y=-5x^2(x)^\frac{1}{2}\)

\(y=-5( {x}^{2 + \frac{1}{2} }) = - 5 {x}^{ \frac{5}{2} } \)

\( \frac{dy}{dx} = - 5( \frac{5}{2}) {x}^{ \frac{5}{2} - 1 } \)

\(\frac{dy}{dx} = ( \frac{ - 25}{2}) {x}^{ \frac{3}{2} } \)

\(\frac{dy}{dx} = ( \frac{ - 25}{2}) \sqrt[3]{ {x}^{2} } \)

\(\boxed{\underline{\bf \: ANSWER}}\)

\((2 + 3)(1 + x) = 25 \\ 5(1 + x) = 25 \\ 1 + x = 25 \div 5 \\ 1 + x = 5 \\ x = 5 - 1 \\ \boxed{x = 4}\)

Note :-

Image is attached.

Hope it helps!

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂

Answer:

4

Step-by-step explanation:

2+3=5

5*(1+4)

1+4=5

5*5=25

The value of cot(B) in a right triangle with angle B equal to 60 degrees can be found by taking the reciprocal of the tangent of angle B. In this case, the tangent of angle B is √3, so the cotangent of angle B is 1/√3.

The cotangent of an angle in a right triangle is defined as the ratio of the adjacent side to the opposite side. In this case, since we are given the measures of the sides and angle B, we can use the values to find the cotangent.

Let's label the sides of the right triangle as follows: the longest side (hypotenuse) as c, the shortest side (opposite side to angle B) as a, and the remaining side (adjacent side to angle B) as b.

In the given triangle, the shortest side (a) has a length of 1 inch and the longest side (c) has a length of 2 inches. We need to find the value of cot(B), where B is the angle equal to 60 degrees.

Using the trigonometric relationship of tangent, we know that tan(B) = opposite/adjacent = a/b. Therefore, b/a = 1/tan(B).

Since the tangent of 60 degrees is √3, we have b/a = 1/√3. To find cot(B), we take the reciprocal of b/a:

cot(B) = 1/(b/a) = 1/(1/√3) = √3/1 = √3.

So, the value of cot(B) in this right triangle is √3, which means the ratio of the adjacent side to the opposite side is √3/1 or simply √3.

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Answer:

∠A = 20°

Step-by-step explanation:

Given:

Line AB equal to line AC

So, we can say that;

∠B = ∠C

So

∠B = ∠C = 80°

Using angle sum rule

∠A + ∠B + ∠C = 180°

∠A + 80° + 80° = 180°

∠A = 20°

Step-by-step explanation:

RQT=4x-20°+3x+14°=

7x-6°=155°

7x=161°

x=23°

4x-20°=72°=RQS

Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

Answer:

27

Step-by-step explanation:

Let's call boys and girls 3x and x respectively. Since 3x + x = 36, x = 9. Boys = 3x = 3 * 9 = 27.

HEYA FRIEND..

.

.

.

YOUR ANSWER IS 27

.

.

HOPE IT WILL HELP YOU UP.

.

HAVE A GREAT DAY

ĶÁŤÉ

Answer:

I think that Ishaan is 6

Step-by-step explanation:

I am very sorry if it is wrong

Answer:

inequality

Step-by-step explanation:

Emphasis on in because that is the part that negates the equality.

Inequalities fit the description of all of the following.

1) 2 Linear Expressions: 2x ? 5y (EXAMPLE)

Linear expressions are expressions that have a variable to the first power.

2) OR Linear Expression and a Constant: 2x ? 5

A constant is a fixed value. For example, a variable is NOT a constant because if the variable changes, the value changes.

3) Are not equal: >, <, \(\geq\), \(\leq\)

Greater than, less than, greater than or equal to, and less than or equal to, are NOT equality.

Mean= 5.1 (Sum of all the terms/number of terms)

‭( 6   +   7   +   2   +   4   +   6   +   6   +   9   +   5   +   3   +   3 )   ÷   10 =‬  5.1

Median= 5.5 (The middle term when you order them from lowest to highest)

2 3 3 4 5 6 6 6 7 9

Step-by-step explanation: The mean of a data set is equal tot he sum of the set of numbers divided by however many numbers are in the set.

So to find the mean of the data set shown here,

let's begin by adding the numbers.

So we have 6 + 7 + 2 + 4 + 6 + 6 + 9 + 5 + 3 + 3.

Adding the numbers, we get 51.

Now, 51 will be divided by the number

of numbers in the set which is 10.

So 51 divided by 10 gives us 5.1.

So the mean of the data set is 5.1.

Now, the median is the middle number in the data set

when the data set is written from least to greatest.

So let's write our data set from least to greatest.

So we have 2, 3, 3, 4, 5, 6, 6, 6, 7, 9.

Notice that there are two numbers in the middle, 5 and 6.

In this situation, add the numbers and divide by 2.

So 5 + 6 is 11 and 11 divided by 2 is 5.5.

So the median is 5.5.

To draw 2-chloro-4-isopropyl-octandioic acid, we'll start by breaking down the name of the compound.

The "2-chloro" part indicates that there is a chlorine (Cl) atom attached to the second carbon atom in the chain. The "4-isopropyl" part means that there is an isopropyl group attached to the fourth carbon atom. An isopropyl group is a branched chain of three carbon atoms with a methyl (CH3) group attached to the middle carbon atom. Finally, "octandioic acid" tells us that there are eight carbon atoms in the chain and that the compound is an acid.

Now, let's begin drawing the structure step by step:

1. Start by drawing a straight chain of eight carbon atoms. Each carbon atom should have a single bond to the next carbon atom in the chain.
2. Place a chlorine atom (Cl) on the second carbon atom in the chain.
3. On the fourth carbon atom, draw a branch for the isopropyl group. The isopropyl group consists of three carbon atoms, with a methyl (CH3) group attached to the middle carbon atom. This branch should be connected to the fourth carbon atom in the main chain.
4. Finally, add two carboxyl (COOH) groups to the ends of the carbon chain. These groups represent the acid part of the compound.

Your final structure should have eight carbon atoms in a chain, with a chlorine atom on the second carbon and an isopropyl group branching off the fourth carbon. Each end of the chain should have a carboxyl group (COOH). Remember to label the carbon atoms and include any lone pairs or formal charges if necessary.

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Answer:

3/20 I think

Step-by-step explanation:

Answer:

A. (-1, -16)

Step-by-step explanation:

The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:  θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.

First, we find the derivative of g(θ) using the chain rule and quotient rule:

g'(θ) = 4 - sec²(θ)

To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:

4 - sec²(θ) = 0

sec²(θ) = 4

Taking the square root of both sides, we get:

sec(θ) = ±2

Since sec(θ) = 1/cos(θ), we can rewrite this as:

cos(θ) = ±1/2

We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.

For cos(θ) = 1/2, we have:

θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant

For cos(θ) = -1/2, we have:

θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant

Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:

θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

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Answer:

Step-by-step explanation:

surface area = 2( LW + LH + WH)

where L = Length = 9

          W = Width = 2

          H = Height = 9

plugin values into the formula:

surface area = 2 ( LW + LH + WH)

                     = 2 ( 9*2  + 9*9  + 2*9 )

                     = 2 ( 18 + 81 + 18 )  

                     =  2 (117)

                     = 234

Answer:

162

Step-by-step explanation:

9x9x2=162

Answer:

d = 13

Step-by-step explanation:

First, the distance formula is needed:

\(d = \sqrt{(x_{2} - x_{1} )^{2} +(y_{2} - y_{1 })^{2} }\)

Next we assign the points

(2,-4) is point 1, (7,8) is point 2

\(d = \sqrt{(7 - 2 )^{2} +(8 - (-4))^{2} } \\d = \sqrt{5^{2} +12^{2} } \\d = \sqrt{25 + 144}\\ d = \sqrt{169} \\d = 13\)

Given two points (2,-4) and (7,8)

To find - The distance between given points.

We know the formula that is used to find the distance is given as

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We let P = (2,-4)

and Q = (7,8)

\(x_1=2, y_1=-4\\x_2=7,y_2=8\)

on substituting we get

\(d=\sqrt{(7-2)^2+(8+4)^2}\\ d=\sqrt{(5)^2+(12)^2} \\d=\sqrt{25+144} \\d=\sqrt{169}\\ d=13\)

Hence we get the distance between (2,-4) and (7,8) is 13.

Final answer - The distance is 13.

The constant c which produces a solution that also satisfies the initial condition y(6) = 7 is c = -1044.

Given the function y = x^2 + c/x^2 and the equation xy' + 2y = 4x^2 with the initial condition y(6) = 7, we will first find the derivative of y with respect to x and then substitute the function and its derivative into the equation to find the constant c.

The derivative of y with respect to x is:
y' = d/dx (x^2 + c/x^2) = 2x - 2c/x^3

Now, substitute the function y and its derivative y' into the equation:
x(2x - 2c/x^3) + 2(x^2 + c/x^2) = 4x^2

Simplify the equation:
2x^2 - 2cx + 2x^2 + 2c = 4x^2

Combine like terms:
4x^2 - 2cx + 2c = 4x^2

Now, we can cancel out the 4x^2 terms:
-2cx + 2c = 0

Factor out 2c:
2c(-x + 1) = 0

Since c cannot be zero, we can divide by 2c on both sides:
-x + 1 = 0

Solving for x, we get x = 1. Now we can use the initial condition y(6) = 7:
7 = 6^2 + c/6^2

Simplify and solve for c:
7 = 36 + c/36
c/36 = -29
c = -29 * 36

Therefore, the constant c which produces a solution that also satisfies the initial condition y(6) = 7 is c = -1044.

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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In order to calculate the slope in between the given points, use the following formula:

m = (y2 - y1)/(x2 - x1)

where (x1,y1) and (x2,y2) are the given points.

Replace the values of all coordinates:

m = (3 - 1)/(-2 - 7)

m = 2/(-9)

m = -2/9

Hence, the slope is -2/9

Answer:

10

Step-by-step explanation:

x-1 = 0

x = 1

f(x) = 3x⁵+2x⁴+5

f(1) = 3(1)⁵+2(1)⁴+5

= 3+2+5

= 10

I hope this helps

The area of the 8-sided shape is 27.5 square centimeters. having a width of 0.875cm and a length of 7.875cm.

Let us assume that Wdth of rectangle= w

Length of rectangle = Width + 7cm

The perimeter of a rectangle is calculated by using the formula,

The perimeter of rectangle = 2(w + w + 7) = 4w + 14

It is given that there are 4 rectangles, which means there are 8 sides. Therefore, the Total perimeter of the area is 4 times that single rectangle.

Total perimeter = 4(4w + 14) = 16w + 56

16w + 56 = 70

16w = 14

w = 0.875

The width of the rectangle = 0.875cm

Length of rectangle = 7cm + 0.875cm =  7.875cm

The area of a triangle is calculated as:

The area of triangle = (1/2) x base x height

The area of triangle = (1/2) x 0.875 x 7.875 = 3.4375

The area of the triangle for an 8-sided shape = 8 x 3.4375 = 27.5 \(cm^2\)

Therefore we can conclude that the area of the 8-sided shape is approximately 27.5    \(cm^{2}\)

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Answer:

1. 1hour 10minutes = 70 minutes

2. 190 miles

Step-by-step explanation:

1.
*Fraction*

Feet/minutes

- Divide

4/1 - 4feet over 1minute

4/1 = 280/x

4x70=280

1x70= 70

70 minutes = 1 hour 10 minutes

2.
1 hour = 65 miles

65x2hours=130miles

2hours= 130 miles

65x3hours= 195miles

3hours = 195miles

Answer:

either use substitution or elimination

Step-by-step explanation:

eg for substitution

make 7x+3y=18 into

7x = 18-3y,

x = (18 - 3y)/7

then input into 2nd equation to find y

ie 3[(18 - 3y)/7] +7y =18

solve to find y

then use ans in y to find x using either equation