find the differential of f(x,y)= sqrt(x^3 + y^2) at the point (1,2)

The difference written in scientific notation is:

1.1×10⁴ - 5.6×10² = 1.044×10⁴

Here we have two numbers in scientific notation, and we want to find the difference between them, it is:

1.1×10⁴ - 5.6×10²

To find that difference, we need to find a common factor between the two numbers, we can write the first one as:

1.1×10⁴ = 110×10²

Then we can take the difference:

1.1×10⁴ - 5.6×10²

110×10² - 5.6×10² = (110 - 5.6)×10² = 104.4×10²

104.4×10² = 1.044×10⁴

That is the difference in scientific notation.

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Answer:

\(m=-\frac{1}{6} \approx -0.1667\)

\(M=(1,\frac{17}{2} )=(1,8.5)\)

\(d=\sqrt{37} \approx 6.083\)

Step-by-step explanation:

(i) For two different points on a line, the slope m is defined as the difference on the y-axis divided by the difference on the x-axis:

\(m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}\)

Where:

\((x_1,y_1)=(-2,9)\\\\(x_2 , y_2)=(4,8)\)

So:

\(m=\frac{8-9}{4-(-2)} =\frac{-1}{6} \approx -0.1667\)

(ii)

To find the coordinates of the midpoint, you can use the following formula:

\(M=(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\)

Therefore:

\(M=(\frac{-2+4}{2} , \frac{9+8}{2} )=(\frac{2}{2} , \frac{17}{2} ) =(1,8.5 )\)

(iii) The distance between two points is given by the following formula:

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

Hence:

\(d=\sqrt{(4-(-2))^{2}+(8-9)^{2} } =\sqrt{(6)^{2}+(-1)^{2} } =\sqrt{36+1} =\sqrt{37} \\\\d\approx 6.083\)

Answer:

120

Step-by-step explanation:

Don't know if this is a joke, but have a great day regardless!

The pattern in y = x² exhibits a nonlinear increase in y as x increases, forming a U-shaped curve, while the pattern in y = 15 + x shows a linear increase in y as x increases at a constant rate.

The patterns in the equations y = x² and y = 15 + x differ in terms of the direction of change. In the equation y = x², the pattern shows an increase in y as x increases.

As x increases from negative to positive values, the corresponding y values also increase, forming a symmetric U-shaped curve. The rate of increase for y becomes steeper as x moves further away from zero.

On the other hand, in the equation y = 15 + x, the pattern shows a linear increase in y as x increases. As x increases, the corresponding y values increase in a straight line.

The rate of increase for y remains constant at one unit per increase in x. This linear pattern reflects a constant upward shift of the graph as x increases.

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The subsets of s with one or two elements are:

{1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4} and the intersection graph is drawn below.

To draw the intersection graph of the nonempty subsets of set s = {1, 2, 3, 4} that have at most two elements, we need to consider all possible subsets of s with one or two elements and draw edges between subsets that have a non-empty intersection.

The subsets of s with one or two elements are:

{1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}

Now, let's draw the intersection graph:

Start by representing each subset as a vertex.

Draw edges between vertices if the corresponding subsets have a non-empty intersection.

The intersection graph of the nonempty subsets of s with at most two elements is as follows:

 {1} --- {1, 2}

  |      /   \

 {2}   /     {1, 3}

  |   /       /  

 {3} --- {1, 4}

  |      

 {4} --- {2, 3}

  |

 {3, 4} --- {2, 4}

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Environmental Errors and Instrumental Errors are two possible systematic errors that can occur in measurements.

In scientific experiments, a systematic error can occur due to equipment or procedure, resulting in measurements being off by a fixed amount each time they are measured. Here are two possible systematic errors that can occur in measurements:

1. Instrumental Errors: These are systematic errors that occur as a result of the tools used for measuring. Instrumental errors can arise due to a variety of factors, including the following:

Non-linear scales, where the scale is not linear and there is an error in measurement due to the reading being too high or too low.

Parity error, which occurs when a device displays a value that is higher or lower than the actual value in a proportionate manner.

Zero errors, in which a device consistently provides a reading of zero when it should not be providing such readings.

2. Environmental Errors: Environmental errors occur when environmental factors cause systematic errors in measurements. These types of errors may be difficult to detect, but they can have a significant impact on the results of an experiment. Environmental errors can be caused by a variety of factors, including the following: Temperature changes can cause expansion or contraction of materials, affecting the size of the object being measured. Changes in humidity can cause materials to warp or expand, affecting the size of the object being measured. Changes in atmospheric pressure can cause changes in the behavior of liquids and gases, affecting the readings.

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The value of the quadratic equation is given by the formula. Then the value of x is 0.8968 and negative 2.23.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The equation for the expression is given below.

3x² + 4x = 6

3x² + 4x - 6 = 0

we know that the formula

\(\rm x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\)

Then we have

\(x = \dfrac{-4 \pm \sqrt{4^2-4*4*(-6)}}{2*3}\\\\x = \dfrac{-4 \pm \sqrt{112}}{6}\\\\x = 0.8968, \ -2.23\)

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Answer:

3n + 14 = 83n = 8 - 14 = -63n/3 = -6/3n = -2The value of n is -2.

Step-by-step explanation:

Answer:

8.

a) f'x means you find the derivative.

2 * d/dx x^2 -b * d/dx x + d/dx c

use power rule x^2 = 2x^1

2*2x = 4x.  the derivative of the differentiation variable, x is 1 and the derivative of a constant, c is 0

4x-b+0

4x-b is our derivative

(I am still figuring out b and c, I will edit this answer and put the solution for b and c.)

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The degree of a polynomial is the highest degree of a monomial contained within the polynomial. The degree of the monomial is the sum of the exponents on the variables. Example, the degree of -4x^6y is 6+1=7.

Example, the degree of 4x^8 is 8.

So the degree of 5x^4 is 4.

The degree of 3x^2 is 2.

The degree of 1 is 0 since there is no variable in this expression.

So the degree of 5 x^4 + 3 x^2 + 1 is 4.

Answer:

1/5=0.2

0.3=3/10

1/2=0.5

7/10=0.7

3/4=0.75

Answer:

children = 87 ; adults = 366

Step-by-step explanation:

a + c = 453

2.25a + 1.25c = 932.25

a = 453 - c

2.25(453 - c) + 1.25c = 932.25

1019.25 - 2.25c + 1.25c = 932.25

-c = 932.25 - 1019.25

-c = -87

c = 87

a = 453 - 87

a = 366

The common set of values shared by citizens in a society that determines what is socially acceptable behavior is known as culture.

Culture is a broad term that encompasses the beliefs, customs, traditions, art, and way of life of a group of people. It shapes the way individuals perceive the world and interact with one another. Culture is transmitted from one generation to the next through various means such as education, family, and socialization. It provides a framework for behavior and helps individuals make sense of the world around them.

Cultural values determine what is considered appropriate or inappropriate, moral or immoral, and acceptable or unacceptable behavior in a given society. These values vary across different cultures and may change over time. Understanding and respecting cultural differences is essential for promoting social harmony and building a more inclusive and tolerant society.

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On solving the provided question, we can say that the equation that can be used to find the lengths of the congruent sides of an isosceles triangle, given the base and the perimeter, is: 2x + 12 = P

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric form. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.

Let's call the length of each congruent side of the isosceles triangle "x".

Since the triangle has two congruent sides and a base, we know that the perimeter, P, is given by:

\(P = x + x + 12\\P = 2x + 12\\2x + 12 = 60\\2x = 48\\x = 24\)

Therefore, the lengths of the two congruent sides of the isosceles triangle are both 24 feet.

To summarize, the equation that can be used to find the lengths of the congruent sides of an isosceles triangle, given the base and the perimeter, is:

2x + 12 = P

where P is the perimeter and x is the length of each congruent side.

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Answer:

c is your answers,...,. s s s s s s s s s s w

The size of angle x is \(61.2^{o\\}\)

Trigonometry is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

From the diagram,

Using SOHCAHTOA which stands for:

SINE= OPPOSITE SIDE / HYPOTHENUSE SIDE

COS= ADJACENT SIDE/HYPOTHENUSE SIDE

TAN=OPPOSSITE SIDE/ ADJACENT SIDE

By applying the tangent trigonometric ratio

Tangent = Opposite side/ Adjacent side

\(tan(x) = \frac{20}{11} \\\)

\(tan(x) = 1.82\)

To find the size of angle x,

x =  \(tan^{-1}\)(1.82)

x = \(61.2^{o}\)

Using the tangent trigonometry, the size of angle x  is \(61.2^{o}\)

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Answer:

Step-by-step explanation:

not sure if we're supposed to be dividing, adding or what

Answer:

y = 20 \(4^{x}\)

Step-by-step explanation:

Use the points to find the values of a and b

Using (0, 20 ) , then

20 = a\(b^{0}\) [ \(b^{0}\) = 1 ] , then

20 = a

y = 20\(b^{x}\)

Using (3, 1280 ) , then

1280 = 20 b³ ( divide both sides by 20 )

64 = b³ ( take the cube root of both sides )

\(\sqrt[3]{64}\) = b , that is

4 = b

Then exponential function is

y = 20. \(4^{x}\)

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

1/25 to get both correct

Step-by-step explanation:

So the probability of getting one choice correct is 1/5

Since 5 choices 1 is correct

now we have to get 2 in a row correct so

1/5*1/5=1/25

Answer:

∠ 1 = 50°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the 4 angles of the polygon and equate to 540°

let the unknown interior angle be x

x + 100° + 120° + 100° + 90° = 540° , that is

x + 410° = 130°

∠ 1 and x are adjacent angles on a straight line and sum to 180° , so

∠ 1 = 180° - 130° = 50°

Answer:

B. 1-third

Step-by-step explanation:

The formula for probability = Number of favorable outcomes/ Total number of outcomes

From the question, we are told that:

Owen knows he only has three pencils in his backpack, and they are all yellow. Hence, total number of outcomes = 3

He reaches into his backpack without looking and takes out a pencil.

Hence, total number of favorable outcomes = 1

What is the probability that the pencil was yellow?

Probability ( That the pencil is yellow) =

Number of favorable outcomes/ Total number of outcomes

= 1/3

Therefore, the probability that the pencil was yellow is 1/3 or one - thirds

a) The standard error of the mean is 0.90

b) The marginal error is 1.76

Given,

Number of samples in the population, n = 60

Sample mean of the population, μ = 25

Standard deviation of the population, σ = 7

We have to find the standard error of the mean and the margin of error at 95% confidence.

Here,

a) The standard error of the mean = Standard deviation / root of sample

= σ / √n

= 7/√60

= 0.90

b) The margin error;

Zₐ/₂ ×  σ / √n

= Zₐ/₂ × 7/√60

= 1.96 × 0.90

= 1.76

Therefore,

a) The standard error of the mean is 0.90

b) The marginal error is 1.76

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Answer:

120$ 60$

Step-by-step explanation:

The total cost 161+19=180

180X150%=180×1.5

=                 = 120  

150%=15, the rule of multiplication

" Stefan spend originally $120. 180-120=60

He make $60 by selling the bicycle and helmet to Jin.

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em}\textit{we know that} \begin{cases} y=-4\\ x=10 \end{cases}\implies -4=k(10) \\\\\\ \cfrac{-4}{10}=k\implies -\cfrac{2}{5}=k\hspace{10em}\boxed{y=-\cfrac{2}{5}x} \\\\\\ \textit{when x = 2, what is "y"?}\qquad y=-\cfrac{2}{5}(2)\implies y=-\cfrac{4}{5}\)

Answer:

c

Step-by-step explanation:

By using the unit conversion method, 2 million seconds converted to days are equal to 23 days.

A unit conversion expresses the same aspect as another unit of measurement. For example, time can be expressed in minutes rather than hours, and distance can be represented from miles to kilometers, feet, or any other unit of measurement.

In this situation, you need to convert between seconds and days:

A day consists of 24 hours. Therefore, the fraction 24 hours/day is equal to 1. There is no value change when multiplying a number by 1. The same holds true for the conversion factors 1 hour/60 minutes and 1 minute/60 seconds.

If you multiply 2,000,000 seconds (2 million seconds) by these conversion factors, you will change the seconds to days:

2,000,000 sec. x (1 min/60 sec.) x (1 hour/60 min) x (1 day / 24 hours)

Therefore, all that is required is to divide 2,000,000 by the product of 60, 60, and 24.

(2,000,000) / (60*60*24) = 2,000,000 / 86,400 = 23.148 days ≈ 23 days

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The solution to the inequality is x ≤ 14/3, which means option C) x ≤ 2 is the correct answer.

To solve the inequality 3x/4 - 2/3 ≤ 5/6, we can follow these steps:

First, let's simplify the left side of the inequality:

3x/4 - 2/3 = (3x - 8)/4 - 2/3

To combine the fractions, we need to find a common denominator, which in this case is 12. We can multiply the first fraction by 3/3 and the second fraction by 4/4:(3x - 8)/4 - 2/3 = (9x - 24)/12 - 8/12

Now, we can rewrite the inequality as:

(9x - 24)/12 - 8/12 ≤ 5/6

Next, we can combine the fractions on the left side:

(9x - 24 - 8)/12 ≤ 5/6

Simplifying the numerator:

(9x - 32)/12 ≤ 5/6

To get rid of the fraction, we can multiply both sides of the inequality by the least common denominator, which is 12:

12 * (9x - 32)/12 ≤ 12 * 5/6

This simplifies to:

9x - 32 ≤ 10

Next, let's isolate the x term by adding 32 to both sides:

9x ≤ 10 + 32

9x ≤ 42

Finally, divide both sides of the inequality by 9 to solve for x:

x ≤ 42/9

Simplifying the fraction:

x ≤ 14/3.

Option C

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