Evaluate the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1)

Therefore , the solution of the given problem of expression comes out to be 794.0481.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

• 3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Here,

Given : 5 + [tex](5.3)^{4}[/tex]

=> 5 + (5.3)*(5.3)*(5.3)*(5.3)

=> 789.0481 + 5

=> 794.0481

Therefore , the solution of the given problem of expression comes out to be 794.0481.

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The answer of the equation "2x^2 -  4x - 6 =  0" is -1 and 3.

The equation is solved using factorization:

2x^2 -  4x - 6 =  0        , given equation

2x^2 -  6x + 2x - 6 =  0     , factorizing

2x(x - 3) + 2 ( x - 3 ) = 0    , taking 2x common from the first two terms and 2 common from the last two terms

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

now solving further

( 2x + 2 ) = 0   &   ( x - 3 ) =0

2x = (0 - 2)    ,          x  = (0 +  3)

2x = (-2)        ,         x = 3

x = (-2/2)

x = -1

Thus, the equation gives the solution as x = -1 and x = 3.

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Answer:

Step-by-step explanation:

Converting 0.632 to a fraction, Step-by-Step

Step 1:

The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.

Step 2:

Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:

\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}

1×1000

0.632×1000

​

=

1000

632

​

Step 3:

Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:

\frac{632}{1000} = \frac{79}{125}

1000

632

​

=

125

79

​

Using the formula for the volume of cuboid that is the product of length, breadth and height, The answer is 7cm.

A cuboid is a three-dimensional shape with six rectangular faces, three of which are pairs of congruent squares and the other three are rectangles. It is also known as a rectangular prism. The opposite sides of a cuboid are parallel and equal in area. The length, width, and height of a cuboid are three of its measures of size.

The volume of a three-dimensional object is a measure of the amount of space it occupies. It is typically measured in units of cubic units, such as cubic centimeters (cm^3) or cubic meters (m^3). The formula for the volume of a cuboid is length x width x height. For example, if a cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm, its volume would be 5 x 3 x 2 = 30 cubic centimeters. In general, the volume of a three-dimensional object can be found by multiplying the area of its base by its height.

length = 2cm

breadth =3cm

volume = 42 cm³

volume = l*b*h

42 = 2*3*h

h= 42/6 =7cm

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We can determine sin an in the above triangle using the available information without applying the Pythagorean theorem since the length of BC is required because it is the side opposite A.

We are told that we must calculate sin(a) without utilizing the Pythagorean theorem.

Now, we can see from the abbreviation SOHCAHTOA that if we wish to determine Sin a, it will be; sin a = opposite/adjacent

We must now locate a side opposing the angle A or the hypotenuse.

As a result, since the triangle is ABC, the required side is BC because it is the side opposite to A.

Finally, the length of BC is required because it is the side opposite A.

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The complete question should be like:

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.

If pesos had it would be so pesos have 169.25 dollars left 200-30.75=169.25

Plotting a graph step by step is mentioned below.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

There are a few steps to follow when plotting a graph:

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Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:

x² = y² + z²

where x is the hypothenuse and y, z are the legs of the right angle triangle.

To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.

x² = y² + z²

15² = 2² + z²

z² = 15² - 2²

z² = 221

z = √221

z = 14.87 feet

The height is 14.87 feet

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The upper and lower bounds of the parameter h is found to be 0 and 1 respectively.

What is upper and lower bound of a function?

A number U serves as an upper bound for a function f, meaning that for any x, f(x) ≤ U. A number L serves as a function's lower bound, ensuring that for all x, f(x) ≥ L.

Given,

 [tex]f(h) = \frac{48-h}{48}[/tex]

where    f(h) = Percentage of battery left

              h = Hours of cell phone use

Lower Bound of parameter h,

h = 0 ( When percentage is 100%)

f(h) = [tex]\frac{48 - 0}{48}[/tex] = 1

Upper bound of parameter h,

h = 48 (When percentage is 0%)

f(h) = [tex]\frac{48-48}{48}[/tex] = 0

Therefore the upper bound of h is 0 and lower bound of h is 1.

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Answer:16,777,216

Step-by-step explanation:

This is a symbol in mathematics that represents "to the power of" or "exponent".

It is used to indicate that a number or expression is being multiplied by itself a certain number of times. For example, if the expression 2aˆ3 is written, it means that 2 is being multiplied by itself 3 times, or 2x2x2. In other words, 2aˆ3 = 2x2x2 = 8.

The number to the right of the aˆ symbol is called the "exponent". The number or expression to the left of the aˆ symbol is called the "base". When a number is raised to the power of one, it is equal to itself. Any number to the power of zero is equal to one. The exponent can be a positive, negative, or fractional number.

Exponents are used to simplifying calculations and can be used to represent large numbers in a more concise form.

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Therefore , the solution of the given problem of equation comes out to be  each diagonal measures 8.4 units in length..

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

Given: 16x + 2 = 36x - 6

8 = 20x

x = 8/20,

simplifying to 2/5, or 0.4

You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.

Re-enter the value of x into a single of the equations.

=>16(0.4) + 2

=>6.4 + 2

=>8.4

To make sure, confirm with the other diagonal.

=>36(0.4) - 6

=>14.4 - 6

=>8.4

Each diagonal measures 8.4 units in length..

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The complete question is "To find the diagonal  x value by the given equation  16x + 2 = 36x - 6 "

The equation becomes true if we put brackets in the following way:

7x(5 - 2 + 3) = 42

Here we have the expression:

7x5 - 2 + 3 = 42

And we want to find where we need to put brackets in such a way that the equation becomes true.

If we solve the equation as it is, we will get:

7x5 - 2 + 3 = 42

35 - 2 + 3 = 42

36 = 42

Now, let's return to the equation:

7x5 - 2 + 3 = 42

If we put one pair of brackets that includes from the 5 to the 3, we will get:

7x(5 - 2 + 3) = 42

7x(4) = 42

42 = 42

So the equation becomes true.

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Answer: 4k^7

Step-by-step explanation:

The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].

An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:

[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]

Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.

[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]

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Answer:

Sales = 20

Step-by-step explanation:

Simply make the equation "1300 = 65s" to solve the problem

1300 = 65s

Divide both sides by 65.

1300/65 = 65s/65

Divide 1300 by 65 to get 20.

20=s

Swap sides so that all variable terms are on the left-hand side.

s=20

Answer:

Step-by-step explanation:

put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8

b^3=8/125

b=2/5

then the answer is 125*(2/5)^x

Answer:

453

Step-by-step explanation:

To perform long division of 11,778 by 26, we follow these steps:

452

_____

26 ) 11,778

-104

------

157

156

----

21

Therefore, 11,778 divided by 26 is equal to 452 with a remainder of 21.

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In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.

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Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.

Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.

We are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.

When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.

Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate

Successes anticipated: np= 300(0.45) = 135 10

Failures predicted: n(1p)=300 (10.45)=165 10

Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.

Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.

As a result, the sample distribution has a roughly normal shape.

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The constant of proportionality is 9 and equation of the proportion.

is y= 10x.

If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.

Given:

As, we know using the Constant of Proportionality

y = kx

or,  k = y/x  where k is Constant of Proportionality.

Then, from the table we have

k = 90/9

k= 10

Thus, y = kx

or, y= 10x

Hence, the equation of the proportion is y= 10x.

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22/154=11/77=1/7

1/7 is the lowest form

Answer:

The total cost of the science class trip to the zoo is $1200

Step-by-step explanation:

The cost of the science class trip to the zoo is $1200, and the cost of Mr. Sexton's class trip to the state park is $1000.

The probabilities for the game of roulette that involves spinning a wheel with 38 slots, for a and b, are 0.4737, or 18/38, or 47.37%.

The following are the rationales:

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The expression is x + 9.Generally speaking, an expression is at its simplest form when it is most usable.

Explanation:

8x + 6+5 - x - 6x - 2

= x + 9.

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0.71 percentage points greater is wyatt’s effective interest rate than his nominal interest rate.

Interest is a fee paid by a borrower to a lender for the use of borrowed money. It is calculated as a percentage of the amount borrowed, and is usually paid periodically at intervals. Interest is generally considered to be a form of compensation for the time and risk taken by the lender in providing a loan or other form of credit.

The effective interest rate is calculated by taking the (1 + nominal interest rate/number of compounding periods per year) to the number of compounding periods per year power minus 1. In this case, the effective interest rate would be 0.1362 x (1 + 0.1362/4)^4 - 1, which is 0.1439 or 14.39%. The difference between the nominal interest rate of 13.62% and the effective interest rate of 14.39% is 0.71 percentage points.

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When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.

The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.

When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.

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The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]

To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.

When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:

[tex]$x = ky^3$[/tex]

where k is the constant of proportionality.

Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:

[tex]$y = \frac{m}{\sqrt{z}}$[/tex]

where m is the constant of proportionality.

Substituting the second equation into the first equation gives:

[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Since the value of x is 3 when z is 12, the equation can be written as:

[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]

Rearranging gives:

[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]

Substituting this value of k into the original equation gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]

Substituting z as 75 gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]

Simplifying gives:

[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]

Therefore, the value of x  when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].

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Answer:  To solve this problem, we can use the fact that a cubic centimeter of osmium has a mass of about 23 grams and the information provided about the chemist's amount of osmium.

First, we can divide the total mass of osmium by the mass of a cubic centimeter of osmium to find out how many cubic centimeters of osmium the chemist has. The equation would look like this:

2,530 grams / 23 grams/cubic centimeter = 110 cubic centimeters

So, the chemist has approximately 110 cubic centimeters of osmium.

It's worth mentioning that an exact value would require additional information as 23 grams per cc is an approximate value and also any impurities or loss of material in the sample also effect the total mass.

Step-by-step explanation: