3.6 as a mixed number and improper fraction

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

In a two-dimensional space, a point is defined by two coordinates, typically denoted by (x, y), where x represents the horizontal position, and y represents the vertical position. In a three-dimensional space, a point is defined by three coordinates, typically denoted by (x, y, z), where x, y, and z represent the horizontal, vertical, and depth positions, respectively.

We want to minimize the distance between the point (14, 8, 0) and the surface of the cone defined by the equation z² = x² + y², subject to the constraint that we stay on the surface of the cone.

Let f(x,y,z) = (x-14)² + (y-8)² + z² be the function we want to minimize subject to the constraint g(x,y,z) = z² - x² - y² = 0.

The Lagrange multiplier method involves finding the critical points of the function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z), where λ is the Lagrange multiplier.

So we have:

L(x,y,z,λ) = (x-14)² + (y-8)² + z² - λ(z² - x² - y²)

Taking the partial derivatives with respect to x, y, z, and λ, and setting them equal to zero, we get the following system of equations:

2(x-14) + 2λx = 0

2(y-8) + 2λy = 0

2z - 2λz = 0

z² - x² - y² = 0

The third equation simplifies to z(1-λ) = 0, which gives us two possibilities:

Case 1: z = 0

In this case, the fourth equation becomes -x² - y² = 0, which implies that x = y = 0. But this point does not lie on the surface of the cone, so it is not a valid critical point.

Case 2: λ = 1

In this case, the first two equations become x-14 = -xλ and y-8 = -yλ, which imply that x = -7λ and y = -4λ. Substituting into the fourth equation gives:

z² = x² + y² = 65λ²

To minimize the distance between the point (14, 8, 0) and the surface of the cone, we want to find the value of λ that minimizes the function f(x,y,z) subject to the constraint g(x,y,z) = 0. Substituting x = -7λ, y = -4λ, and z = √(65λ²) into f(x,y,z), we get:

f(λ) = (7λ-14)² + (4λ-8)² + 65λ²

To minimize this function, we take its derivative with respect to λ and set it equal to zero:

f'(λ) = 30λ - 80 = 0

Solving for λ, we get λ = 8/3. Substituting this back into x = -7λ, y = -4λ, and z = √(65λ²), we get:

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

To know more about points visit:

https://brainly.com/question/16907812

#SPJ1

Since Sour Drops, Chocolate Chews and Tangy Twists are in the ratio 2:3:4, respectively, it follows that Sour Drops account for 2/9 and Tangy Twists account for 4/9 of the candy mixture. So, Sour Drops make up (2/9)(45) = 2 × 5 = 10 pounds, while Tangy Twists make up (4/9)(45) = 4 × 5 = 20 pounds of the 45-pound candy mixture. Therefore, there are 20 – 10 = 10 pounds more Tangy Twists than Sour Drops. Alternatively, the given ratio means that Tangy Twists account for 4/9 – 2/9 = 2/9 more of the candy mixture than Sour Drops do. So, in a 45-pound batch of the candy mixture, there would be (2/9)(45) = 2 × 5 = 10 pounds more Tangy Twists than Sour Drops.

Nyelle purchases some Sour Drops, Chocolate Chews and Tangy Twists to combine into her personal batch of the Sugar Shack’s signature candy mixture using the same proportions as the previous problem. If the prices per pound for the candies are $6.00 for Sour Drops, $3.50 for Chocolate Chews and $4.25 for Tangy Twists, what is the total cost (not including tax) to purchase the exact amounts of all three candies required to make 4.5 pounds of this signature candy mixture?

Again, since Sour Drops, Chocolate Chews and Tangy Twists are in the ratio 2:3:4, respectively, it follows that Sour Drops, Chocolate Chews and Tangy Twists account for 2/9, 3/9 = 1/3 and 4/9 of the candy mixture, respectively. So, to make 4.5 pounds of this candy mixture, Nyelle needs (2/9)(4.5) = 2 × 0.5 = 1 pound of Sour Drops, (1/3)(4.5) = 1.5 pounds of Chocolate Chews and (4/9)(4.5) = 4 × 0.5 = 2 pounds of Tangy Twists. At the given prices per pound, we calculate Nyelle’s total cost to be 1(6.00) + 1.5(3.50) + 2(4.25) = 6 + 5.25 + 8.50 = $19.75.

Rae purchases 4.5 pounds of the signature candy mixture when it goes on sale at the Sugar Shack for $4.00 per pound. What is the absolute difference between Nyelle’s and Rae’s total costs (not including tax) to get 4.5 pounds of the signature candy mixture?

At a sale price of $4.00 per pound, 4.5 pounds of the candy mixture would cost Rae 4.5(4.00) = $18.00. From the previous problem, we know that Nyelle’s total cost was $19.75. Therefore, the absolute difference between Nyelle’s and Rae’s total costs is 19.75 – 18.00 = $1.75.

Answer:

No, is not a right triangle

Step-by-step explanation:

If it is a right triangle Pythagoras theorem do apply.

Since the hypotenuse is the side with 16in, sides are 7 and 14 inches

notice

[tex]\sqrt{7^{2} +16^{2} } = \sqrt{245} \neq 16[/tex]

Answer:

Step-by-step explanation:

i assume the figure he needs to "make" is the turnover and not the marginal profit - no indication of the cost of the toys he sells is given so it is impossible to work out the marginal profit of the each toy sold. (Though how the toymaker worked out the turnover required without knowing the cost of the toy is beyond me - though that didn't stop British Leyland pricing their best selling Mini in the 1970s.)

In this case divide the income required by the price of each toy, but as the income must be at least the required amount, any fractional part of a toy must be rounded *UP* to the next whole number.

17,235 ÷ 45 = 383 (so no rounding is needed).

He needs to sell 383 toys (made at zero marginal cost).

Step-by-step explanation:

Area of a square = s x s   and this equals  10 x s

 this is :  

     s^2 = 10 s    divide both sides of the equation by 's'

  s = 10   units    ( or zero....but that makes no sense)

The area of the given shape is 109.25 ft² .

What is Area?

Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is the size of the surface of the shape, and it is measured in square units, such as square meters, square centimeters, or square inches.The area of a shape can be found by multiplying the length and width of a rectangle or the base and height of a triangle, or by using specific formulas for other shapes such as circles, trapezoids, or parallelograms

Given : height of triangle = diameter of semicircle = 10 ft

            radius of semicircle = 5 ft

           base of triangle = 14 ft

we know that, The area of given shape :

= area of given triangle + area of semi circle

=  1/2 × base × height  +   πr²/2

= 1/2 × 14 × 10 + (3.14 × 5²)/2

= 70 + 39.25

= 109.25 ft²                                  

To learn more about Area, visit the link:

https://brainly.com/question/25292087

#SPJ1

Answer:

Length = 53 feet

Width = 22 feet

Step-by-step explanation:

Perimeter = 2(length + width)

Then:

a = 2w + 9            Ec. 1

150 = 2(a + w)       Ec. 2

a = length

w = width

From Eq. 1:

a - 9 = 2w            Eq. 3

From Eq. 2:

150 = 2*a + 2*w

150 = 2a + 2w

150 - 2a = 2w        Eq. 4

Equalizing Eq. 3 and Eq. 4

a - 9 = 150 - 2a

a + 2a = 150 + 9

3a = 159

a = 159/3

a = 53

From Eq. 1:

a = 2w + 9

53 = 2w + 9

53 - 9 = 2w

44 = 2w

44/2 = w

w = 22

Check:

From Eq. 2

150 = 2(a+w)

150 = 2(53+22)

150 = 2*75

Step 1: Calculate the total amount of flour used.

200 g of sugar is used, so the amount of flour used is 300 g (because it follows the ratio 2:3).

Step 2: Calculate the amount of butter used.

Since flour and butter are mixed in the ratio 3:1, for every 3 units of flour, 1 unit of butter is used. So for 300 g of flour, 100 g of butter should be used.

Therefore, the mass of butter used to make the sweet is 100 g.

Answer:

To factor 30b³-54b², we can factor out the greatest common factor of 6b² to get:

30b³-54b² = 6b²(5b-9)

To factor 35-48y³, we can notice that it is a difference of cubes:

35-48y³ = (5)³ - (4y)³ = (5-4y)(25+20y+16y²)

To factor x³+8, we can use the sum of cubes formula:

x³+8 = (x+2)(x²-2x+4)

To factor 3-64, we can use the difference of squares formula:

3-64 = (1)² - (8)² = (1+8)(1-8) = -7(-9) = 63

To factor 8c³+343, we can use the sum of cubes formula:

8c³+343 = (2c)^3 + 7³ = (2c+7)(4c²-14c+49)

To add or subtract complex polynomials, we simply combine like terms. For example:

(3x²+2x-5) + (4x²-3x+7) = 7x²-x+2

To multiply complex polynomials, we can use the distributive property and FOIL method. For example:

(2x+1)(3x-4) = 6x²-5x-4

To factor complex polynomials, we can use various methods such as factoring out the greatest common factor, using the difference of squares formula, using the sum or difference of cubes formula, or factoring by grouping.

The formulas provided are for factoring the sum or difference of cubes:

These formulas can be useful for factoring complex polynomials that have a cube term or a constant term in addition to the quadratic and linear terms.

With a [tex]12[/tex]% price rise, the smart mug now costs AED [tex]1003.52[/tex].

The sale price is the price an user pays to purchase a thing or a commodity. It is a cost that is higher than the market cost and also includes a portion of the profit. The cost price refers to the price paid by the seller for the item or service.

Price is the process of figuring out how much a something or service is worth. Price establishes a customer's cost, although it can or cannot be linked to the price a firm pays to manufacture a good or service.

We need to multiply the initial price by [tex]1.12[/tex] which represents a [tex]12[/tex]% increase in decimal form,

New price [tex]=[/tex] Initial price [tex]*[/tex] (1 [tex]+[/tex] Percent increase in decimal form)

New price[tex]= 896 * (1 + 0.12)[/tex]

New price [tex]= 896 * 1.12[/tex]

New price [tex]= 1003.52[/tex]

Therefore, the new price of the smart mug is AED [tex]1003.52[/tex] after a [tex]12[/tex]% increase.

To know more about price visit:

https://brainly.com/question/19091385

#SPJ1

How does cellular respiration help maintain homeostasis in animals?

Answer: Cellular respiration helps animals maintain homeostasis by breaking down glucose to produce ATP, which is the energy currency of the cell. ATP is necessary for many cellular processes that help maintain homeostasis such as active transport and protein synthesis.

Explain why cells separate and expel waste.

Answer: Cells separate and expel waste to prevent the accumulation of toxic substances that can disrupt cellular function and lead to disease. The waste products are transported out of the cell and into the bloodstream where they are filtered and excreted by organs such as the kidneys.

Why do cells in organisms such as animals reproduce?

Answer: Cells in organisms such as animals reproduce to replace damaged or dying cells, and to enable growth and development. Reproduction ensures that the organism maintains the proper balance of cells and that there is enough tissue to perform necessary functions.

Explain how plant cells use photosynthesis to maintain homeostasis?

Answer: Plant cells use photosynthesis to maintain homeostasis by converting light energy into chemical energy in the form of glucose. This glucose is then used to produce ATP, which is necessary for cellular processes such as active transport and protein synthesis. Additionally, plants use photosynthesis to produce oxygen, which is necessary for respiration.

I hope this helps :)

The literary device used in the sentence is a metaphor.

The metaphor in this statement is a literary tactic. It is an example of a figure of speech that contrasts one object with another of a specific type in order to emphasise or make a description more understandable. The figurative statement the pendulum could swing back alludes to prospect of a scenario reversing or shifting.

The analogy makes a comparison between a scenario that can go either way and a pendulum, which swings back and forth. In this instance, the author is warning the parents that the current circumstance, whatever it may be, could alter and go the other way. The metaphor places a strong emphasis on the notion of change and the potential for unpredictability in the future.

Read more about metaphors on:

https://brainly.com/question/27250460

#SPJ4

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The greatest time that the fourth runner can run for the team to reach its goal is 63.23 seconds.

To find the greatest time that the fourth runner can run for the team to reach its goal, we need to subtract the total time of the first three runners from the goal time of 4 minutes (240 seconds).

Total time of the first three runners = 57.38 seconds + 60.92 seconds + 58.47 seconds = 176.77 seconds

Greatest time the fourth runner can run = Goal time - Total time of the first three runners = 240 - 176.77 = 63.23 seconds

https://brainly.com/question/34215040

#SPJ3

If thrice a number increased by 11 and the result is 35, then the number is 8

Let's call the number we're trying to find "x".

According to the problem, "thrice a number increased by 11" is equal to 35. So we can write this as an equation:

3x + 11 = 35

To solve for x, we need to isolate it on one side of the equation. We can start by subtracting 11 from both sides:

3x + 11 - 11 = 35 - 11

Simplifying the left side and evaluating the right side, we get:

3x = 24

Now we can solve for x by dividing both sides by 3:

3x/3 = 24/3

x = 8

Learn more about equation here

brainly.com/question/16882938

#SPJ4

In response to the stated question, we may state that area of shaded square region = 30 - 9.8125 = 20.1875 in sq.

According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is often referred to as a rectangle with two nearby sides of equal length.

A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles.

Also, the diagonals of the square are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles.

Here is the area of square = 5*6 = 30 in sq.

Area of semi-circle[tex]= 1/2*3.14*2.5*2.5 = 9.8125[/tex] in sq.

Area of shaded region  [tex]= 30 - 9.8125 = 20.1875[/tex] in sq.

Therefore, A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

Learn more about square here:

https://brainly.com/question/28776767

#SPJ1

Beth receives £103.45 when she changes €120 back into pounds.

An exchange rate is the value of one currency expressed in terms of another currency. In other words, it is the rate at which one currency can be exchanged for another currency.

Pound is a unit of currency that is used in several countries, including the United Kingdom, Egypt, Lebanon, and Sudan, among others. The pound symbol is "£".

In the given question,

If the exchange rate is £1 = €1.16, this means that for every euro, Beth will get £1/€1.16.

Therefore, the number of pounds Beth receives when she changes €120 back into pounds is:

120 euros * £1/€1.16 = £103.45 (rounded to two decimal places)

So Beth receives £103.45 when she changes €120 back into pounds.

To know more about exchange rates, visit:

https://brainly.com/question/30540100

#SPJ1

Answer:

21 male students

Step-by-step explanation:

For every teacher on the trip, 3 male students and 5 female students are there

If there are 35 female students, we have to divide that by 5 to find the number of teachers

35 divided by 5 is 7

There are seven teachers, so we multiply by 3 to find the number of male students

7 x 3 = 21

There are 21 male students on the school field trip

Answer:

(x-7)(x+6)

factor and see what works

The population of the town in 5 years will be approximately 28,982.

A data pattern known as exponential growth exhibits faster expansion over time. Compounding generates exponential profits in finance. Exponential growth is possible in savings accounts with a compounding interest rate. Compound returns in finance lead to exponential development. One of the most potent forces in finance is the power of compounding. With the help of this idea, investors may generate sizable sums with little start-up money. Compound interest savings accounts are typical instances of exponential development.

Given that, population of a town increases by 3% each year.

The population after 5 years is calculated by:

Population in 5 years = Initial population x (1 + rate) raised to time.

That is,

Population in 5 years = 25,000 x (1 + 0.03)⁵

Population in 5 years = 25,000 x 1.159274

Population in 5 years = 28,981.85

Hence, the population of the town in 5 years will be approximately 28,982.

Learn more about exponential growth here:

https://brainly.com/question/11487261

#SPJ1

Answer:

4.54714 × 103

Step-by-step explanation:

There were 8-1 = 7 more students who slept for 4-7 hours than for 12-15 hours.

In a survey conducted by Mr. Hamilton, he asked his class about the total number of hours they slept the previous night. The histogram provided in the question shows the distribution of their responses. To find out how many more students slept for 4-7 hours than 12-15 hours, we need to count the number of bars in the 4-7 hours range and subtract it from the number of bars in the 12-15 hours range. By counting the bars in the histogram, we can see that there are 9 bars in the 4-7 hours range and 4 bars in the 12-15 hours range. Therefore, there were 5 more students who slept for 4-7 hours than 12-15 hours.

Learn more about histogram here: brainly.com/question/30354484

#SPJ4

Complete question:

Mr. Hamilton surveyed his class to find the total number of hours each of his students slept the previous night. The histogram shows the results of the survey. How many more students slept 4 – 7 hours than 12 – 15 hours? Amount of Sleep Mr: Hamilton surveyed his class to find the total number of hours each of his students slept the previous night The histogram shows the results of the survey: How many more students slept 4 ~ 7 hours than 12 15 hours? L 0 -3 8 _ [1 12 - 15 submit Time (hours)'

Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b) .

A graph that displays the distribution of a collection of continuous data is called a histogram. It is composed of a number of bars, each of which represents a set of values, and whose height denotes the frequency or number of data points that lie within a given range. Histograms are used to depict a distribution's shape, centre, and spread graphically. They are frequently used to find patterns and trends in data in areas like statistics, data analysis, and scientific study.

given

(A) We must first identify the data's range before dividing it into 5 intervals of equal width in order to construct a frequency table with 5 classes. The values are in the range of 0 to 18.

(b) We plot the class intervals on the x-axis and the frequency on the y-axis to generate a histogram from the frequency chart. The counts are used to illustrate how frequently each class interval occurs.

Part (a) of this sentence displays the frequency chart, and part (c) displays the histogram (b).

To know more about histogram visit :-

https://brainly.com/question/16819077

#SPJ1

Jo has read 14% of the book if she has read 35 pages of a 250 pages book.

If Jo has read 35 pages out of a 250-page book, we can calculate what percentage of the book she has read by dividing the number of pages she has read by the total number of pages and multiplying by 100:

Percentage of book read = (35 / 250) x 100%

Percentage of book read = 0.14 x 100%

Percentage of book read = 14%

Therefore, Jo has read 14% of the book. Percentage is a way of expressing a number as a fraction of 100. It is often used to describe the relationship between a part and a whole, where the part represents a portion of the whole. Percentages are commonly used in various fields, including mathematics, finance, and statistics, to measure changes or represent data in a more accessible format.

To learn more about percentage click here

brainly.com/question/16797504

#SPJ4

Step-by-step explanation:

6x - 2 = 4x + 36

2x - 2 = 36

2x = 38

x = 19

4*19 + 36= 76 + 36= 112

180-112= 68

m<N= 68 degrees

Step-by-step explanation:

let's first transform these terms into real fractions :

2/5 = 2/5

4 1/8 = (4×8 + 1)/8 = 33/8

2 1/4 = (2×4 + 1)/4 = 9/4

first we need to handle the division (remember the priorities of arithmetic operations) :

-33/8 / -9/4 = (-33×4) / (-9×8) = 33 / (9×2) = 33/18

then we have to calculate

2/5 + 33/18

to do that we have to bring both fractions to the same denominator (must be divisible by 18 and by 5, so in this case it is 5×18 = 90) :

2/5 = 2/5 × 18/18 = 36/90

33/18 = 33/18 × 5/5 = 165/90

so,

36/90 + 165/90 = 201/90 = 67/30 = 2 7/30

a) To find a linear function that expresses temperature in Celsius in terms of degrees Fahrenheit, we need to use the formula for converting Fahrenheit to Celsius:

C = (F - 32) * 5/9

This formula shows that to convert Fahrenheit to Celsius, we first subtract 32 from the Fahrenheit temperature, then multiply by 5/9.

If we rearrange this formula, we can solve for C in terms of F:

C = (F - 32) * 5/9

C = 5/9 * F - 5/9 * 32

C = 5/9 * F - 160/9

So the linear function C that expresses temperature in Celsius in terms of degrees Fahrenheit is:

C = 5/9 * F - 160/9

b) To use this function to convert 110ºF to Celsius, we simply substitute F = 110 into the equation:

C = 5/9 * F - 160/9

C = 5/9 * 110 - 160/9

C = 61.11ºC

Therefore, 110ºF is equivalent to 61.11ºC.

Answer:

a) To find a linear function that expresses temperature in Celsius in terms of degrees Fahrenheit, we can use the formula:

C = (F - 32) * 5/9

where C is the temperature in Celsius and F is the temperature in Fahrenheit.

b) To convert 110ºF to Celsius, we can plug in F = 110 into the formula above and simplify:

C = (110 - 32) * 5/9

C = 78 * 5/9

C = 43.33ºC

Therefore, 110ºF is equivalent to 43.33ºC in Celsius.

(please mark my answer as brainliest)

c. The mean of the random variable X is calculated as:

mean(X) = (-5)(1/4) + (0)(1/2) + (5)(1/4) = 0

The variance of X is calculated as:

var(X) = (-5 - 0)^2(1/4) + (0 - 0)^2(1/2) + (5 - 0)^2(1/4) = 25/2

d. The mean of the random variable X is calculated as:

mean(X) = (-5)(.01) + (0)(.98) + (5)(.01) = 0

The variance of X is calculated as:

var(X) = (-5 - 0)^2(.01) + (0 - 0)^2(.98) + (5 - 0)^2(.01) = 50.25

e. The mean of the random variable X is calculated as:

mean(X) = (-50)(.0001) + (0)(.9998) + (50)(.0001) = 0

The variance of X is calculated as:

var(X) = (-50 - 0)^2(.0001) + (0 - 0)^2(.9998) + (50 - 0)^2(.0001) = 500

g. The mean of the random variable X is calculated as:

mean(X) = (0)(1/2) + (2)(1/2) = 1

The variance of X is calculated as:

var(X) = (0 - 1)^2(1/2) + (2 - 1)^2(1/2) = 1

h. The mean of the random variable X is calculated as:

mean(X) = (.01)(.01) + (1.01)(.99) = 1

The variance of X is calculated as:

var(X) = (.01 - 1)^2(.01) + (1.01 - 1)^2(.99) = .098

For more questions like Variable click the link below:

https://brainly.com/question/17344045

#SPJ11