30 POINTS FOR THIS QUESTION

Answer:

sorry I don't know please forgive because I can't copy the question

Assuming you mean [tex]f(x,y) = xy^2[/tex] over the domain

[tex]D = \left\{(x,y) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } x^2 + y^2 \le 3\right\}[/tex]

we first observe that [tex]f(x,y) = 0[/tex] for all [tex](x,y)[/tex] on the coordinate axes.

There are no critical points elsewhere in the interior of [tex]D[/tex], since

[tex]\dfrac{\partial f}{\partial x} = y^2 = 0 \implies y=0[/tex]

[tex]\dfrac{\partial f}{\partial y} = 2xy = 0 \implies x = 0 \text{ or } y = 0[/tex]

Parameterize the circular arc boundary by [tex]x=\sqrt3\cos(t)[/tex] and [tex]y=\sqrt3\sin(t)[/tex], where [tex]0\le t\le\frac\pi2[/tex]. Then

[tex]f(x(t), y(t)) = g(t) = 3\sqrt3 \cos(t) \sin^2(t) = 3\sqrt 3 (\cos(t) - \cos^3(t))[/tex]

Find the critical points of [tex]g[/tex].

[tex]g'(t) = -3\sqrt3 \sin(t) + 9\sqrt3 \cos^2(t) \sin(t) = 0[/tex]

[tex]-3 \sin(t) (1 - 3 \cos^2(t)) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } 1 - 3 \cos^2(t) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } \cos^2(t) = \dfrac13[/tex]

[tex]\sin(t) = 0 \text{ or } \cos(t) = \pm\dfrac1{\sqrt3}[/tex]

In the first case, we get

[tex]t = \sin^{-1}(0) + 2n\pi \text{ or } t = \pi - \sin^{-1}(0) + 2n\pi[/tex]

where [tex]n[/tex] is an integer; the only solution on the boundary of [tex]D[/tex] is [tex]t=0[/tex] corresponding to the point [tex](\sqrt3,0)[/tex].

In the second case, we get

[tex]t = \cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

with only one relevant solution at [tex]t=\cos^{-1}\left(\frac1{\sqrt3}\right)[/tex]  corresponding to [tex](1,\sqrt2)[/tex].

In the third case, we get

[tex]t = \cos^{-1}\left(-\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

but there is no [tex]t[/tex] in this family of solutions such that [tex]0\le t\le\frac\pi2[/tex].

So, we find

[tex]\min\left\{xy^2 \mid (x,y) \in D\right\} = 0 \text{ at } (0,0)[/tex]

(but really any point on either axis works)

[tex]\max \left\{xy^2 \mid (x,y) \in D\right\} = 2 \text{ at } (1,\sqrt2)[/tex]

The sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

Given that average rate of deposition is  per 1000 years of 1 centimeter.

We are required to find the type of sediment deposit that has an average rate of deposition (per 1000 years) of 1 centimeter.

Biogenic ooze, which is also called biogenic sediment, is any pelagic segment that contains more than 30 percent skeletal material. These sediments can be made up of either carbonate ooze or siliceous ooze.

In plagic sediments feldspar is obtained from local volcanic sources, whereas quartz may be introduced from the continents by wind,upsetting simple patterns.A large number of accessory minerals occur in shales.

Hence if the sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

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Using proportions, Nelly's total pay for last week was of £220.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From Monday to Friday, she worked 17 hours, hence:

On Saturday, she worked 5 hours, and was paid £16 per hour.

Hence her total payment is found as follows:

15 x 8 + 2 x 10 + 5 x 16 = £220.

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When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return false since the element is not found in the array.

About Binary Search Algorithm

The binary search algorithm, applied on arrays are of recursive type. The broad strategy is to look at the middle item on the list. The procedure of the binary search algorithm is either terminated (key found), the left half of the list is searched recursively, or the right half of the list is searched recursively, depending on the value of the middle element.

The function carrying out the binary search algorithm in a code returns true if the desired element is found in the array, else returns false. Since the element 10 is not present in the given array: [2, 3, 5, 6, 9, 13, 16, 19], the binary search algorithm will return false.

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In the hypothesis, based on the 90% confidence interval, (0.02, 0.12), there is convincing evidence that the new formula of laundry detergent is better because the interval is entirely above 0

Let's define the null hypothesis and alternative hypothesis first.

H0:p1-p2=0

Ha:p1-p2>0

Also, 90% CI is (0.02,0.12), we know that if the 0 of the null hypothesis is not in the confidence interval then we reject the null hypothesis.

In the given scenario 0 is not within the given interval, hence we reject the null hypothesis and accept the claim that new detergent A cleans better.

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Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

The body temperature is simply a measure of how well a human body can produce and get rid of heat. the normal body temperature is or 37 degrees Celsius or 98.6 degrees Fahrenheit.

Given the data in the question;

To get Aakash body temperature in the evening, we simply add the initial body temperature and the the temperature increase.

Temperature in the evening = 99.2° Fahrenheit + 3.4° Fahrenheit

Temperature in the evening = 102.6° Fahrenheit

Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

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The surface integral of the given surface [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex] in the intervals 0 ≤ x ≤ 4, 0 ≤ y ≤ 1 is 7.36615.

To evaluate the surface integral, the formula applied is

[tex]S=\int\limits^b_a\int\limits^d_c {f(x,y)} \ dy\ dx[/tex]

⇒ S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]

Where the differentiation is partial differentiation and f(x, y) = z.

The given function is

f(x, y) = [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex]

Then, applying the partial differentiation w.r.t x and y respectively,

dz/dx = [tex]\frac{2}{3}(\frac{3}{2})x^{1/2}[/tex] = [tex]x^{1/2}[/tex]

dz/dy = [tex]\frac{2}{3}(\frac{3}{2})y^{1/2}[/tex] = [tex]y^{1/2}[/tex]

Then,

we have surface integral  formula as

S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]

On substituting,

⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+(x^{1/2})^2+(y^{1/2})^2} \, dy } \, dx[/tex]

⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+x+y} \, dy } \, dx[/tex]

On integrating w.r.t y

⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}(1+x+y)^{3/2}} \,|_0^1 dx[/tex]

Applying limits,

⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}[(1+x+1)^{3/2}-(1+x+0)^{3/2} } \, dx[/tex]

⇒ S = [tex]\frac{2}{3} \int\limits^4_0 {[(x+2)^{3/2}-(x+1)^{3/2}}] \, dx[/tex]

Again applying the integration w.r.t x

⇒ S = [tex]\frac{2}{3}[\frac{2}{5}(x+2)^{5/2}-\frac{2}{5}(x+1)^{5/2}]|_0^4[/tex]

Applying the limits and simplifying,

⇒ S = [tex]\frac{4}{15}[(4+2)^{5/2}-(4+1)^{5/2}-(0+2)^{5/2}+(0+1)^{5/2}][/tex]

⇒ S = [tex]\frac{4}{15}[1+36\sqrt{6}-25\sqrt{5}-4\sqrt{2}][/tex]

∴ S = 7.36615

Therefore, the surface integral of the given function is 7.36615.

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The given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

An expression can be defined as a type of mathematical equation which is used to show the relationship that is existing between two or more variables and numerical quantities (integers).

In this exercise, you're required to fully simplify the given expression in the lowest terms. Thus, we would simplify the given expression completely by collecting like terms and performing the necessary arithmetic operations (addition and subtraction) as follows:

Collecting like terms, we have:

8h - 5h + 3w + 2w

Subtracting and adding the like terms respectively, we have:

3h + 5w.

In conclusion, we can logically deduce that the given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

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Complete Question:

Fully simplify 8h + 2w - 5h + 3w.

The frequency of the periodic function is given by: 0.0796.

From the graph, we have that the period is of 4pi hours, hence the frequency is:

f = 1/4pi = 0.0796.

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The true statements are:

The independent variable is the variable that determines the value of the dependent variable. There is a positive relationship between the number of people at the picnic and the total cost. This is because it can be seen as the number of people at the picnic increases, the total cost changes.

Rate of change = total cost / number of people

$52 / 6 = $8.67

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Answer:

A, B, D

Step-by-step explanation:

right on edge

The Probability that the total showing is either even or less than five = 5/6

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

The example space for rolling two dice is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

36 events total.

Events that have a sum that is even or less than Five .

Total instances when the aggregate is even or less than Five equals 30.

P(sum is even or less than 5)

= (Total no of favorable event)/(Total no of event)

= 30/36

=5/6

probability that the total showing is either even or less than five = 5/6

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GH 13000 is the amount of his sales for that month.

how to find sales of the month?

total income = salary + commission

total income = GH530 (given)

salary = GH200 (given)

Commission is 3% on the sales above Gh2000 (given)

Let sales be x

total income = salary + commission

530 = 200+3%(x-2000)

530-200=0.03(x-2000)

330/.03=x-2000

11000=x-2000

x= 13000

total sales = GH13000

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Answer:

7+21+15+19+.....+79

Here 21 be replaced by 11.

Now., common diffrence btw terms , d = 11-7 = 4

first term , a = 7

Last term , l = 79

number of terms = ( a + l ) ÷ d

=( 7 + 79 ) ÷ 4 = 86 ÷ 4 = 21.5 { It cannot be in decimal }

There's some mistake in the terms you provided please check your question again...

Answer:

17, 5

Step-by-step explanation:

Let the width be x

width = x

length = x + 12

length x width = x(x + 12)

length x width = x² + 12x

x² + 12x = 85

x² + 12x - 85 = 0

Now it is just a quadratic:

The 2 numbers we need are 17 and -5

(x + 17)(x - 5) = 0

x = -17 or x = 5.

Since width and length cannot be negative, x must equal 5.

Width = 5

length = 17

The answer is 17, 5.

We are given two things :

We can represent the length and width as x + 12 and x respectively.

Now, the formula for the area of a rectangle is :

Area = Length x width

Now, let's substitute the values for length and width in the formula along with the area.

We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.

Answer:

The value of x will be 2.5cm.

Step-by-step explanation:

Volume = Length*Width*Height

where,

[tex]v = l \times w \times h \: ...substitute \: values \\ 120cm {}^{3} = 12cm \times w \times 4cm \\ 120cm {}^{3} = 48cm {}^{2} \times w \: ...divide \: both \: \\ sides \:by \: 48cm {}^{2} \\ \frac{120cm {}^{3} }{48cm {}^{2} } = w \\ w = 2.5cm[/tex]

Answer:

I hope that you are doing well, during this weird time; and that this message finds you in a good place.

To get you started on this problem, you will want to think about how to go about graphing this linear function. You want to keep in mind that you want to plot your dependent variable on the y-axis, as it changes with respect to your independent variable (plotted on the x-axis). In this problem, the cost of the water bill depends on the amount of water used, in HCF. So the graph should be plotted with cost on the y-axis, and HCF on the x-axis.

It follows that you are given the coordinates of (16, $48.37) and (22, y2); where y2 represents the cost when using 22 HCF. You are also given the slope of your line (m, in y = mx + b format). You may recall that you can set-up a slope as the change in y over the change in x, or the "rise over the run" [m = (y2-y1) / (x2-x1)]. We can set this problem up, using this equation to solve for y2 (the cost at 22 HCF) algebraically.

So we would set up the problem as 1.65 = (y2-48.37)/(22-16). We then solve by combining like-terms and using inverse operations as follows:  

  1.65 = (y2 - 48.37) / 6

  1.65(6) = y2 - 48.37

  9.9 = y2 - 48.37

  y2 = $58.27

Step-by-step explanation:

Answer:

1/36

Step-by-step explanation:

Assuming the dice has 6 sides in total, we can set up a probability for each scenario.

The chances of the dice landing on 1 will be 1/6, since there are 6 total faces. Same goes for the second die and landing on 4.

Now that we have our 2 probabilities, we multiply them to get the final probability. 1/6 x 1/6 = 1/36.

Answer:

the triangle is a right angle triangle. I can't see the correct explanation here so I will explain

Step-by-step explanation:

to work out whether triangles are right angle you do :

square root of (5² + 12²) so it would be 25 + 144 =169 and the square root of 169 is 13 . we do this because the square root of both of the side lengths squares should make ths longer side in this case it makes 13 so it is a right angled triangled

i hope this helps . if you need any more help pls ask :)

Answer:

pi or 1 pi

Step-by-step explanation:

Area = 1/4 * pi * r^2 (because it is 1/4 of a full circle)

1/4 * pi * 2^2 (the radius is 2 because it is given in the picture)

1/4 * pi * 4 = 1 pi

area = pi

hope this helps! <3

The distance from Humood's house to the school is 500m

The given parameters are:

Humood's house is (-5,7)

The school is (3,1)

The distance between both points is calculated using

[tex]d = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2[/tex]

Substitute the known values in the above equation

[tex]d = \sqrt{(-5 - 3)^2 + (7 - 1)^2[/tex]

Evaluate

d = 10

Each unit in the graph is 50m.

So, we have

Distance =10 * 50m

Evaluate the product

Distance = 500m

Hence, the distance from Humood's house to the school is 500m

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Answer:

B. the second graph.

Step-by-step explanation:

Literally the photo is on the question.

Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.

The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.

Therefore, the correct option is option B.

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Answer:

Step-by-step explanation:

You can only multiply matrices if the number of columns in the matrix on the left is the same exact number as the number of rows in the matrix to the right of that other matrix.

The matrix on the left, |5 -2  4| has the dimensions

                                      1 x 3 (1 row, 3 columns)

The matrix to its right, |2  7  -3| has the dimensions

                                      1 x 3 (1 row, 3 columns).

Putting those dimensions next to each other in that order:

                  1 x 3     1 x 3

The bold print 3 and 1 have to be the same number (both 3's or both 1's) in order for the multiplication to work. This doesn't work; it's impossible.

Answer: -16

Step-by-step explanation:

i was on a unit exam typing in random numbers since i didn't know it and -16 is the right answer.

Answer:

  (-∞, ∞)

Step-by-step explanation:

Unless there are restrictions on the domain, the range of any odd-degree polynomial function is "all real numbers."

The given function is a linear function, degree 1. This is an odd degree, so the range of the function is "all real numbers."

  -∞ < f(x) < ∞

  (-∞, ∞) . . . . . in interval notation

Values of c and d make the equation true are c=6, d=2

Equations

                                [tex]\sqrt[3]{162x^{c}y^{5} } = 3x^{2} y^{3} \sqrt[3]{6y^{d} }[/tex]

                               [tex](\sqrt[3]{162x^{c}y^{5} })^{3} = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]

                                 [tex]{162x^{c}y^{5} } = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]

                                  [tex]{162x^{c}y^{5} } = 27x^{6} y^{3} ({6y^{d})[/tex]

                                     [tex]{x^{c}y^{5} } = x^{6} y^{3} ({y^{d})[/tex]

                                     [tex]{x^{c}y^{5} } = x^{6} y^{3+d}[/tex]

                                   c = 6

                                   d = 2

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Answer:

a) 18

b) 48

c) 192

a) 30

b) 150

Step-by-step explanation:

Answer:

1

a ) 18

b ) 48

c ) 144

2

a ) 30

b ) 150..

[tex]...[/tex]

Answer:

C

Step-by-step explanation:

Let's review some sets of numbers.

Natural numbers: 1, 2, 3, 4, ...

The natural numbers are the counting numbers. You normally start counting with 1, not 0, and you only count whole numbers.

Whole numbers: 0, 1, 2, 3, 4, 5, ...

The whole numbers are the counting numbers with the addition of zero. There are no negative numbers in the whole numbers.

Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...

The integers are the natural numbers, plus zero, plus the negatives of the natural numbers. All numbers are whole with no decimal part.

Rational numbers

The rational numbers are all numbers that can be written as a fraction of integers. For example, 1 can be written as 3/3, so 1 is a rational number. All natural numbers, whole numbers, and integers are rational numbers. Other rational numbers are numbers that are not whole, such as 2.5, 7/8, 1/4, etc. These numbers can be written as fractions of integers. Rational numbers written as decimal numbers will either be an integer, a terminating decimal, or a non-terminating, repeating decimal.

Up to here, each new set includes the previous set.

Now things change. If a number is rational, it is not irrational.

If a number is irrational, it is not rational.

Irrational numbers

Irrational numbers are always non-terminating, non-repeating decimals. They cannot be written as fractions of integers. Examples: √2, π

Now let's look at this problem.

We have a negative decimal number. The bar above the 12 means the digits 12 are repeating. This number can also be written as -0.121212...

Since our number is a non-terminating, repeating decimal, it is a rational number.

Answer: C

Answer:

4.25 × 10^-4

Step-by-step explanation:

0.00045-2.5x10^-5

= (4.5 × 10^-4) - (0.25 × 10¹ × 10^-5)

= (4.5 × 10^-4) - (0.25 × 10^{1-5} )

= (4.5 × 10^-4) - (0.25 × 10^-4)

= (4.5 - 0.25) × 10^-4

= 4.25 × 10^-4

Answer:

382 cm²

Step-by-step explanation:

Front face + Back face:

A = 2(a + b)h/2

A = 2(14 cm + 8 cm)(7 cm)/2

A = 154 cm²

Left face:

A = 7 cm × 6 cm = 42 cm²

Right face:

A = 9 cm × 6 cm = 54 cm²

Bottom face:

A = 14 cm × 6 cm = 84 cm²

Top face:

A = 6 cm × 8 cm = 48 cm²

Total surface area =

= (154 + 42 + 54 + 84 + 40) cm²

= 382 cm²