Find the gradient fields of the functions in Exercises 1−4
g(x,y,z)=ez−ln(x2+y2)

Answer:

Step-by-step explanation:

DONT distribute the exponent

Instead, expand it to (x-2)*(x-2)

Multiply the First terms, Outer terms, Inner terms, then Last terms (FOIL)

Writing it out: (x*x) + (x*-2) + (-2*x) + (-2*-2)

Simplify: x^2 - 2x - 2x + 4

Answer: x^2 - 4x + 4

The variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.


To find the variance of a random variable X, you need to follow these steps:
1. Calculate the mean (average) of X.
2. Calculate the squared difference between each value of X and the mean.
3. Calculate the expected value of the squared differences.
4. The result obtained in step 3 is the variance of X.
Let’s apply these steps to the given values of X: 28, 46, 73, and 73.
Step 1: Calculate the mean (average) of X.
Mean(X) = (28 + 46 + 73 + 73) / 4 = 220 / 4 = 55
Step 2: Calculate the squared difference between each value of X and the mean.
(28 – 55)^2 = 27^2 = 729
(46 – 55)^2 = 9^2 = 81
(73 – 55)^2 = 18^2 = 324
(73 – 55)^2 = 18^2 = 324
Step 3: Calculate the expected value of the squared differences.
Expected value = (729 + 81 + 324 + 324) / 4 = 1458 / 4 = 364.5
Step 4: The result obtained in step 3 is the variance of X.
Variance(X) = 364.5
Therefore, the variance of X, where X takes the values 28, 46, 73, and 73 with equal probability, is 364.5.

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Answer:

\( \huge{= \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} }} \)

Step-by-step explanation:

\(\huge{ \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} } \div \frac{ {a}^{2b} - {ab}^{2} }{ {a}^{2b} - {ab}^{2} }} \)

\( \huge{\frac{ {x}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} } \div 1}\)

\( \huge{\boxed{\green{= \frac{ {a}^{2} - {b}^{2} }{ {a}^{2b} + {ab}^{2} }}}} \)

Answer:

Step-by-step explanation:

8x+14=2x=50

6X+14=50

6X=36

X=6

2(6)+50

12+50

Angle B equals 62

The narrator suggests that she now lives her life by striving to find optimism in even the worst circumstances when she adds, "I too have planted marigolds," at the conclusion of the story.

Because the narrator characterized the marigolds in the story as "Dazzling strips of bright petals bunch together in gigantic mounds warm and passionate in sun golden," the narrator's description of and response to seeing the marigolds is rather favorable.

The ability to comprehend and appreciate others as fully human beings serves as the story's central subject and marks the start of adulthood. Lizabeth felt ashamed when she realized she had wronged a genuine human being instead of a "witch" when she vented her anger at the marigolds and turned to look at Miss Lottie.

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Answer:the answer is app u welcome text me back if i got it wrong armstrongtamarion

Step-by-step explanation:

Answer:

D, 36/8

Step-by-step explanation:

12*3/8

Since all the answers are in a fraction, we can leave our answer in one.

12x3 = 36

36/8

The solution to the equation is x = 17/30.

To solve the equation, start by combining like terms on both sides.

On the left side, we have the fraction 2/3 and the term -4x.

On the right side, we have the fraction 7/2 and the term -9x.

To combine the fractions, we need a common denominator.

The least common multiple of 3 and 2 is 6.

So, we can rewrite 2/3 as 4/6 and 7/2 as 21/6.

Now, the equation becomes:

4/6 - 4x = 21/6 - 9x

Next, let's get rid of the fractions by multiplying both sides of the equation by 6:

6 * (4/6 - 4x) = 6 * (21/6 - 9x)

This simplifies to:

4 - 24x = 21 - 54x

Now, we can combine the x terms on one side and the constant terms on the other side.

Adding 24x to both sides gives:

4 + 24x - 24x = 21 - 54x + 24x

This simplifies to:

4 = 21 - 30x

Next, subtract 21 from both sides:

4 - 21 = 21 - 30x - 21

This simplifies to:

-17 = -30x

Finally, divide both sides by -30 to solve for x:

-17 / -30 = -30x / -30

This simplifies to:

x = 17/30

So the solution to the equation is x = 17/30.

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Answer: If you take out the price of the golf clinic with a local pro, you could buy 6 buckets.

Step-by-step explanation:

Answer:

r = -8

Step-by-step explanation:

Since we're given two points and the slope (m), we'll have to use the slope formula, which is

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

Step 1:  Since we know that m = 2, we can allow (2, r) to be our (x1, y1) point and (5, -2) to be our (x2, y2) point.  We can then solve for r:

2 = (-2 - r) / (5 - 2)

2 = (-2 - r) / 3

6 = -2 - r

8 = -r

-8 = r

Optional Step 2:  We can check that r is the right coordinate by plugging it into the slope formula and seeing whether we get 2:

2 = (-2 - (-8)) / (5 - 2)

2 = (-2 + 8) / 3

2 = 6 / 3

2 = 2

Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer:

someone else had same question before you did https://brainly.com/question/11677565Step-by-step explanation:

a) Domain of the function 0 ≤ d ≤ 21 (0,21)

Range of the function 0 ≤ B ≤ 400 (0,400)

b) Estimate to the nearest hundreds for B(0) is 200

c) Ebony's bank balance first reached $0 on day 12 can be shown as functional notation as - we can add the number 12 below the first point reaching the horizontal axis.

d) Ebony's bank balance remained $0 from day 12 through day 15. The segment which represents the information is - segment 4.

(a) Domain: the collection of values used as input or arguments for the function.

Range: Either the codomain or the function's image is mentioned.

For three weeks, Ebony's bank account was active (21 days). then the domain is 0 ≤ d ≤ 21 (here 'd' refers to day)

Her highest balance was $400 and her lowest was zero, so the range is  0 ≤ B ≤ 400. (Here, 'B' refers to Balance)

(b) When d = 0, the graph's highest point, which represents her highest balance of $400, is displayed. This means that on the first day, the point will probably only be half as high as the highest point. Therefore, we may calculate the nearest hundred for B(0) is about equal to 0.5 * 400 = 200.

(c) In other words, the line of the function first touches the horizontal axis at d = 12; the balance first reached $0 on day 12. Below the first point that reaches the horizontal axis, we can add the number 12.

(d) From day 12 through day 15, the bank balance stayed at zero dollars; this is shown by the vertical axis of segment 4 of graph 4.

COMPLETE QUESTION:

The amount in Ebony's bank account B(d)  is a function of the number of days(d) since she opened the account. The graph shows segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions. (Score for Question 1;_ of 4 points) 1. Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that time, her greatest balance was $400.

(a) Give the domain and range of the function. 0 ≤ d ≤ 21  domain; 0 ≤ B ≤ 400  

(b) Give an estimate to the nearest hundreds for B(0). Explain how you determined your estimate and tell what B(0) means in the context of the situation.

(c) Ebony's bank balance first reached $0 on Day 12. How would you show that information in function notation? B(12) = 0  

(d) Ebony's bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know. 4th segment

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Answer: 112i + 85.8j

Step-by-step explanation:

Answer:

\(\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}\)

Step-by-step explanation:

To find the components of a vector given its magnitude and direction, use the following formula:

\(\large\boxed{\vec{u}=\left(||\vec{u}|| \cos(\theta),|| \vec{u}|| \sin(\theta)\right)}\)

where:

Given:

Substitute the given values into the formula:

\(\vec{H}=\left(85.8 \cos(112^{\circ}),85.8 \sin(112^{\circ})\right)\)

\(\vec{H}=\left(-32.1, 79.6\right)\)

Therefore:

\(\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}\)

Answer:Example 1.

2x2 - 5x - 12 = 0.

(2x + 3)(x - 4) = 0.

2x + 3 = 0 or x - 4 = 0.

x = -3/2, or x = 4.

Step-by-step explanation:

Answer:

Third Choice: a = 2, b = -3, c = -27

Step-by-step explanation:

The equation to be solved with the quadratic formula must be written in the form

ax^2 + bx + c = 0

2x^2 = 27 + 3x

Subtract 3x from both sides. Subtract 27 from both sides.

2x^2 - 3x - 27 = 0

Now we see we have

a = 2, b = -3, c = -27

Answer: Third Choice

Turbidity is a physical wastewater quality parameter and refers to the turbidity of water caused by suspended solids. It is generated from sources such as soil erosion, industrial waste, and wastewater itself.

When turbidity increases, it affects the environment by reducing the amount of solar radiation, impairing the growth of aquatic plants, and impairing the respiratory and feeding mechanisms of aquatic organisms. affects In addition, reduced heat dissipation can lead to higher water temperatures, further impacting aquatic life.

Biological oxygen demand (BOD), a water quality parameter for biological wastewater, measures the amount of dissolved oxygen consumed by microorganisms when breaking down organic matter. Elevated BOD levels cause oxygen starvation, harming fish and other aquatic organisms and unbalancing aquatic ecosystems. 

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The linear function f Eve can use to determine her pay would be; D. f(x) = 14x + 12

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is the form Ax + B = 0.

Given that Eve earns $14 per hour for yard work and an extra amount for dog walking on Saturdays.

The table shows the data;

Hours 1 2 3 4 5

Pay 26 40 54 68 82

Thus, the linear function f Eve can use to determine her pay is;

f(x) = 14x + 12

To check;

f(x) = 14x + 12

f(x) = 14(1) + 12

f(x) = 14 + 12 = 26

Hence, The linear function f Eve can use to determine her pay would be; D. f(x) = 14x + 12

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Answer:

-4?

Hope I helped

Answer:

4

Step-by-step explanation:

Answer:

the answer is -72-41

Step-by-step explanation:

Answer:

12th Customer

Step-by-step explanation:

We have to find the lcm (lowest common multiple) of the number.

We do that by taking their multiples. Watch down below

3 x 1 = 3                4 x 1 = 4

3 x 2 = 6               4 x 2 = 8

3 x 3 = 9               4 x 3 = 12

3 x 4 = 12

See how they both have a 12 as their first lcm.

So the 12th customer gets both items.

Glad to help!

The proof of the congruent sides RU and TS is given below.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given figure is a rectangle RSTU.

Since the all four angles of rectangle are of 90 degree.

So, each angle of rectangle RSTU is 90 degree.

Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.

Both the triangles having same measure of angles and sides.

⇒  ΔSRU ≅ ΔSTU

As the triangles are congruent so their sides are congruent.

Hence, RU is congruent to TS.

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The supplied differential equation by variable separation is y(x) = sin(x²/2+c), as stated in the statement.

Any equation containing one or more terms and first or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f (x) In this case, the variables "x" and "y" are isolated and dependent, respectively. For illustration, dy/dx = 5x. Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

With respect to that differential equation \(\frac{d y}{d x}=x \sqrt{1-y^2}\)

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

By implementing integration across both sides,

\(\begin{aligned}& \int \frac{d y}{\sqrt{1-y^2}}=\int x d x \\& \sin ^{-1}(y)=\frac{x^2}{2}+c \quad\left[\int \frac{d y}{\sqrt{a^2-y^2}}=\sin ^{-1}\left(\frac{y}{a}\right)\right]\end{aligned}\)

\(y(x)=\sin \left[\frac{x^2}{2}+c\right]\)

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Answer:

45 degree line

Step-by-step explanation:

A distinguishing characteristic of a Keynesian cross diagram is the 45-degree line.

The Keynesian cross diagram is a simple graphical representation of the relationship between aggregate expenditure and real GDP in an economy. It shows the equilibrium level of real GDP where aggregate expenditure equals real GDP, and helps to illustrate the effects of changes in aggregate expenditure or other factors on the economy.

The 45-degree line in the Keynesian cross diagram represents the level of real GDP where aggregate expenditure equals real GDP, or where there is equilibrium in the economy. Points below the 45-degree line indicate that aggregate expenditure is less than real GDP, while points above the 45-degree line indicate that aggregate expenditure is greater than real GDP. The slope of the aggregate expenditure function determines the sensitivity of real GDP to changes in aggregate expenditure.

The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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Answer: The index of refraction for the unknown wavelength is approximately 1.355.

Step-by-step explanation:

We can use Snell's law to relate the incident angle and refracted angle to the indices of refraction:

n1 sinθ1 = n2 sinθ2

where n1 and θ1 are the index of refraction and incident angle of the light in air, and n2 and θ2 are the index of refraction and refracted angle of the light in glass. Since the incident angle is 45.00 degrees, we have:

sinθ1 = sin(45.00) = √2/2

Since we know the index of refraction for the 450.0 nm light is 1.482, we can solve for the refracted angle θ2:

1.000 * √2/2 = 1.482 * sinθ2

sinθ2 = 1.000 * √2/2 / 1.482 = 0.4951

θ2 = sin^(-1)(0.4951) = 29.07 degrees

Now, we can use Snell's law again to relate the index of refraction to the refracted angle for the unknown wavelength:

n1 sinθ1 = n3 sinθ3

where n3 is the index of refraction for the unknown wavelength, and θ3 is the refracted angle for the unknown wavelength. We know that θ3 is 0.8000 degrees greater than θ2:

θ3 = θ2 + 0.8000 = 29.87 degrees

Substituting all the known values into Snell's law, we get:

1.000 * √2/2 = n3 * sin(29.87)

n3 = 1.000 * √2/2 / sin(29.87) = 1.355

Therefore, the index of refraction for the unknown wavelength is approximately 1.355.

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Answer:

50

Step-by-step explanation:

Answer:

x = 30

y = 5

Step-by-step explanation:

Because the top triangle shows 3 congruent angles, we know it's an equilateral.

Therefore 8y = 40

y = 5

______________

Now we have two sides of the triangle: 40 and 80.

The lower left angle of the whole triangle must be 90 degrees because if the hypotenuse is twice the adjacent side, it must be a 30-60-90 triangle.

So, the larger angle containing angle x must be 90 degrees. And because we know that the adjacent angle (equilateral triangle) is 60 degrees, angle x must be 30.