find the critical points and critical values of the function z=x^3+6xy-y^3-1

The similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°

The triangles RDS and ADB area similar thus the lines AB and RS are parallel to each other and the adjacent angles of m∠SRA and m∠BAR are supplementary, so their sum is equal to 180°.

m∠SRA and m∠BAR are supplementary so;

(6x + 8)° + (9x + 7)° = 180°

15x + 15 = 180°

15x = 180° - 15 {subtract 15 from both sides}

15x = 165

x = 165/15 {divide through by 15}

x = 11

m∠A = 9(11) + 7 = 106°

m∠R = 6(11) + 8 = 74°

m∠S = 4(11) + 14 = 58°

Therefore, the similar triangles have adjacent angles A and R to be supplementary and value of the variable x is equal to 11. The angles m∠A = 106°, m∠R = 74°, and m∠S = 58°

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Possible question:

Find the measure of the angles with the variable x for the similar triangles ∆RDS and ∆ADB.

the solutions for a are:

a = n×π, π/4, or 7π/4, where n is any integer.

An integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals.

tan²(a) - csc²(a) + 1 = 0

tan²(a) - (1/sin²(a)) + 1 = 0

(tan²(a)sin²(a) - 1 + sin²(a))/sin²(a) = 0

Simplifying the numerator:

(tan²(a) - 1)sin²(a) = 0

Using the identity tan^2(a) = sec²(a) - 1:

(sec²(a) - 2)sin²(a) = 0

Expanding and simplifying:

sec²(a)sin²(a) - 2sin²(a) = 0

sin²(a)(sec^2(a) - 2) = 0

So either sin²(a) = 0 or sec²(a) - 2 = 0.

If sin²(a) = 0, then a is an integer multiple of pi (i.e., a = n×π for some integer n).

If sec²(a) - 2 = 0, then sec²(a) = 2,

cos(a) = ±√(2)/2

So a can be π/4 or 7π/4.

Therefore, the solutions for a are:

a = n×π, π/4, or 7π/4, where n is any integer.

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Answer:

To find the amount of interest earned by depositing $220 into an account that earns 4% interest for one year, we can use the simple interest formula:

Interest = Principal * Rate * Time

Where:

Principal = $220 (the amount deposited)

Rate = 4% (expressed as a decimal, so 0.04)

Time = 1 year

Plugging in these values, we get:

Interest = $220 * 0.04 * 1

Interest = $8.80

Therefore, the amount of interest earned by depositing $220 into an account that earns 4% interest for one year is $8.80.

Step-by-step explanation:

solving equipment step:

*SIMPLIFY THE EXPRESSION

- 12x² ÷(2x²²)

Rewrite

simply the equation

=12x² ÷ 2x²²

=-6x²÷x²²

Now cancel common factors

=-6x÷x^20

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Answer: C. (f+ g)(x) = 5x + 6

Step-by-step explanation:

C. (f+ g)(x) = 5x + 6

This is because when you add two functions together, you simply add their coefficients together and add the constants together. So, in this case, you add 3 and 2 to get 5 and add 10 and -4 to get 6. Therefore, the answer is 5x + 6.

Answer:

The correct answer is C. (f+ g)(x) = 5x + 6

Answer:

Step-by-step explanation:

we would cut it into small pieces and find their area,

Add three segments:

This will give us the following shapes:

You may find each area and add up to get the total area.

(a) The 40% grοwth in decimal is 0.4.

(b)  1st mοnth    2nd mοnth   3rd mοnth      4th mοnth         5th mοnth

       150                   210                294               412                  577

A percentage is a number οr ratiο that can be expressed as a fractiοn οf 100 in mathematics. If we need tο calculate a percentage οf a number, we shοuld divide it by its entirety and then multiply it by 100. The percentage, therefοre, refers tο a part per hundred. Per 100 is what the wοrd percent means. The letter "%" stands fοr it.

The given percentage is 40%.

Cοnvert it fractiοn 40 × 1/100

Cοnvert it decimal fοrm:

= 0.4

First mοnth:

The number οf listeners is 150.

Secοnd mοnth:

The number οf listeners is

150 + (150×0.4)

=150 + 60

= 210

Third mοnth:

The number οf listeners is

210 + (210×0.4)

=210 + 84

= 294

Fοurth mοnth:

The number οf listeners is

294 + (294×0.4)

=294 + 117.6

= 411.6

≈ 412

Fifth mοnth:

The number οf listeners is

412 + (412×0.4)

=412 + 164.8

=  576.8

≈ 577

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Answer:

Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.

Step-by-step explanation:

Let's use algebra to solve the problem. Let x be the number of shares Mary Jo buys at $19 a share, and y be the number of shares she buys at $24 a share.

We know that Mary Jo spends a total of $2,300, so we can write the equation:

19x + 24y = 2300

We also know that she ends up with a total of 100 shares, so we can write the equation:

x + y = 100

Now we have two equations with two variables, which we can solve using substitution or elimination.

Let's use substitution. Solve the second equation for x:

x = 100 - y

Substitute this expression for x in the first equation:

19(100 - y) + 24y = 2300

Simplify and solve for y:

1900 - 19y + 24y = 2300

5y = 400

y = 80

So Mary Jo bought 80 shares at $24 a share.

To find the number of shares she bought at $19 a share, substitute y = 80 in the second equation:

x + 80 = 100

x = 20

Therefore, Mary Jo bought 20 shares at $19 a share.

In summary, Mary Jo bought 20 shares at $19 a share and 80 shares at $24 a share.

Answer:

2x-14=27

Step-by-step explanation:

Right Side) Combine like terms

Step 1) 3+5+8+11=27

Step 2) -7x+7x=0

Right side: 27

Left Side) Distribute

2*x=2x

2*(-7)=-14

Answer : 2x-14=27

Answer:

  A.  (2, 1)

Step-by-step explanation:

You want the solution to the system of equations represented by the given table and graph.

When we are given two functions and asked for "the solution to the system", we generally mean the value of x that satisfies f(x) = g(x). That will be represented on a graph as the point (x, f(x)), or (x, g(x)), where the function graphs intersect.

When you're looking for the solution in a table, you look for the row of the table where the value of f(x) is the same as the value of g(x). For the given table, we see that f(x) = g(x) = 1 on the last row of the table, where x=2. This means the solution is ...

  (x, f(x)) = (2, 1)

The beetle crawled 1/15 of a yard farther than the spider.

What is the fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing a numerator(upper value) and denominator(lower value).

To find out how much farther the beetle crawled than the spider, we need to subtract the distance the spider crawled from the distance the beetle crawled.

The beetle crawled 2/3 of a yard, which can be written as a fraction with a common denominator of 15: 10/15.

The spider crawled 3/5 of a yard, which can also be written as a fraction with a common denominator of 15: 9/15.

Now we can subtract the distance the spider crawled from the distance the beetle crawled:

10/15 - 9/15 = 1/15

Hence, the beetle crawled 1/15 of a yard farther than the spider.

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Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to equation two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

The received power at a distance d is determined by:

Pr is equal to Pt, Gt, Gr, and (/4d)2.

where:

The transmitted power is Pt.

The transmitter antenna gain is Gt.

the receiver antenna gain, or Gr.

is the signal's wavelength.

Pr2 = (d1/d2)4 * Pr1

where:

At a distance of 325 m, Pr1 is the received power, which is specified as 25 W.

d1 is 325 metros away, while d2 is 1.3 kilometres away (i.e., 1300 m)

Inputting the values provided yields:

Pr2 = 25 W * (325/1300 m)4 = 25 W * 0.0625 = 1.5625 W

Hence, 1.56 W (or, in scientific notation, 1.56 x 10-6 W or 1.56E-06 W) to two decimal places is a fair power figure to assume at a distance of 1.3 km from the BS.

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Answer:

70 + 8 + 0.2 + 0.06 + 0.003

Step-by-step explanation:

Expressing the number means to be written based on the place values.

Therefore:

7 = tens place value (70)

8 = ones place value (8)

. = decimal point (.)

2 = tenths place value (0.2)

6 = hundredths place value (0.06)

3 = thousandths place value (0.003)

~

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The answer is D. Value. A value is something that a person considers important or desirable in life. It can be a principle, a goal, a belief, or an attitude that guides one’s choices and actions. Conrad’s aim to save money to travel to Puerto Rico and work on a team that studies ancient cities there is an example of his value because it shows what he cares about and what motivates him.

A quantitative value is a value that can be measured or expressed numerically, such as income, height, weight, etc. A priority is something that is more important than other things and needs attention first. Poverty is the state of being extremely poor. None of these terms describe Conrad’s aim accurately.

Conrad’s aim to travel to Puerto Rico and work on a team that studies ancient cities there is not a priority because it is not something that he needs to do urgently or immediately. It is also not something that depends on external factors or demands. It is his value because it reflects his interest, passion, and motivation in life. It is something that he would pursue even if it was difficult or challenging.

Or maybe if it's priority then I'm sorry.

If the function is increasing to the left and falls to the right,

Leading coefficient of the function will be negative and the degree of the function will be Odd.

What is a polynomial's leading coefficient?

The term in a polynomial that has the highest power of x is the leading term. For instance, the leading term in the equation 7+x3x2 is 3x2. The coefficient of the first term is referred to as a polynomial's leading coefficient. The leading coefficient in the aforementioned example is 3.

Leading coefficient of the function will be negative and the degree of the function will be Odd.

Similarly, if the function is increasing to the right and falls to the left,

Leading coefficient of the function will be positive and the degree of the function will be Odd.

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The inequality that represent how many laps she can do is "number of laps < 8.4".

Claire can jog a maximum of 8 laps in 42 minutes.

Since Claire can jog one lap in 5 minutes, we can use division to find how many laps she can complete in 42 minutes:

= 42 minutes / 5 minutes per lap

= 8.4 laps

However, since Claire cannot jog a fractional number of laps, we need to round down to the nearest whole number of laps. This is because she will have only completed a fraction of a lap by the time she reaches the end of the 42 minutes, and we want to know how many whole laps she completes. Therefore, we can write the inequality as "number of laps < 8.4".

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If a basketball player has a 70% accuracy rate for making free throws. The probability that this player misses his first free throw, but makes the second one is 0.21.

The probability of making a free throw is 0.7, so the probability of missing a free throw is 0.3.

Let X be the number of trials (free throws) until the first success (a made free throw). Since we want to know the probability of missing the first free throw and making the second one, we want to find P(X = 2).

Using the geometric distribution formula, we have:

P(X = 2) = (1 - p)^(k-1) * p

where:

p is the probability of success (making a free throw)

k is the number of trials (2 in this case), and (1 - p)^(k-1) is the probability of having k-1 failures (missing the first free throw) followed by one success (making the second free throw).

Plugging in the values, we get:

P(X = 2) = (1 - 0.7)^(2-1) * 0.7

= 0.3 * 0.7

= 0.21

Therefore, the probability  is 0.21 (rounded to the hundredths place).

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274.75 square inches of pizza are remaining. Option A is the correct option.

What is π in math?

The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.

Given that, the diameter of large pizza is 20 inches.

The radius of a circular shape is half of the diameter.

The radius of the pizza is (20 inches)/2 = 10 inches.

Area of a circular shape is ∏r² .

The area of the pizza is 3.14×10² = 314 in²

The total part of the pizza is considered as 1.

One-eighth of the pizza is eaten, and the remaining portion is (1-1/8) = 7/8.

The area of remaining pizza is

314 in²  × (7/8)

= 274.75 square inches

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This causes the volume of the balloon to decrease, leading to an increase in the number of collisions between gas particles and the inside surface of the balloon, and causing the balloon to shrink and shrivel up.

Temperature is a measure of the average kinetic energy of the particles in a substance or system. In other words, it is a measure of how hot or cold something is relative to a standard reference point. The SI unit of temperature is the kelvin (K), but temperature is often measured in degrees Celsius (°C) or Fahrenheit (°F) in everyday life. Temperature plays a crucial role in many natural and man-made processes, and is a key factor in determining the behavior of matter at different states.

Here,

When a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy and slow down. As the temperature drops, the average kinetic energy of the gas particles decreases, causing them to move slower and collide less frequently. This results in a decrease in pressure inside the balloon.

According to the Ideal Gas Law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. As the pressure inside the balloon decreases, its volume also decreases, since the number of moles of gas and the gas constant remain constant.

Since the balloon is sealed, the gas particles cannot escape, so they continue to collide with each other and the inside surface of the balloon. As the volume of the balloon decreases, the gas particles become more crowded, increasing the number of collisions between them. This leads to a decrease in the distance between the gas particles and the inside surface of the balloon, causing the balloon to shrink and shrivel up.

In summary, when a sealed, inflated balloon is placed into a flask of liquid nitrogen at a temperature of 77 K, the gas particles inside the balloon lose thermal energy, slow down, and collide less frequently, resulting in a decrease in pressure inside the balloon.

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Answer:

w-4

Step-by-step explanation:

Suppose we going to find⊕

(4-w)÷(-w-9 )  =⊕÷(w+9 )

⇒(4-w) ÷ -(w+9) =⊕÷(w+9)

cross-multiply we will get

∴ ⊕={(4-w)×(w+9)}÷-(w+9)

      = -(4-w)   after cancelling ( w+9)

therefore our answer is ( w-4 )

AB can be identified to be, based on the circle, to be a A. Major arc.

The measure of the arc would be 226 degrees.

A major arc is an arc on a circle that is greater than 180 degrees, or half the circumference of the circle. A major arc is also known as a large arc. It extends from one endpoint of a minor arc to the other endpoint of the same arc, passing through the center of the circle.

AB is a major arc because it is larger than half of the circle which means it is greater than 180s degrees.

The measure of arc AB is:

= Half a circle angle + arc CB

= 180 + 46

= 226 degrees

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Answer:

a^2=9

Step-by-step explanation:

there is a rule that states that if you multiply - with - it becomes + so a number squared just means that the number multiplies with itself so -3*-3=+9 or 9 (any number with + can be written as the number without the +sign, for ex. +1 is the same as 1)

As a result, when the camera and the rocket are 4255 feet apart, the rate  trigonometry of change in the angle of elevation after launch is roughly -0.15807 radians/foot.

Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.

Where is the camera's angle of elevation and c is the rocket's height above ground level.

We may express the angle of elevation using the given formula as:

r θ = tan⁻¹(c/2000)

c2 + x2 = d2, where d = 4255 ft 2c(dc/dx) + 2x = 0, and dc/dx = -x/c.

When we multiply c by 2000 tan() and x by (d2 - 20002) (since x is the horizontal distance between the camera and the rocket), we get: dc/dx = -(d2 - 20002) / (2000 tan())

tan1(0.02d/2000) = tan1(d/100000)

dc/dx = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -(d2 - 20002) / (2000 tan(tan1(d/100000)) = -0.005(d2 - 20002) / d

dc/dx = -0.005(42552 - 20002) / 4255 -0.15807 radians per foot

As a result, when the camera and the rocket are 4255 feet apart, the rate of change in the angle of elevation after launch is roughly -0.15807 radians/foot.

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The slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.

The slοpe οf a line is a measure οf its steepness. Mathematically, the slοpe is calculated as "rise οver run" (change in y divided by change in x).

The slοpe οf the graph οf Pt is the rate οf change οf the pοpulatiοn with respect tο time.

Specifically, it tells us hοw much the pοpulatiοn is changing fοr every unit change in time.

Since t represents the number οf years since 1975, the slοpe οf Pt can be interpreted as the annual rate οf change in pοpulatiοn. Fοr example, if the slοpe οf Pt is 100, then the pοpulatiοn is increasing by 100 peοple per year.

Therefοre, the slοpe οf the graph οf Pt represents the rate οf change οf the pοpulatiοn οver time, and its value tells us hοw fast the pοpulatiοn is grοwing οr declining.

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The answer of the given question is (3) the length of the run of the Mighty Drop ski slope is approximately 181.8 feet. (4) the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.

A slope typically refers to the angle of an incline or ramp, or the ratio of vertical change to horizontal change of a straight line or curve on a graph. For an incline or ramp, the slope is the angle between the surface and the horizontal plane. It is defined as the ratio of the vertical rise to the horizontal run of the ramp.

In the context of a graph, slope refers to the steepness of a line or curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve. The slope of a line can be positive (if the line goes up from left to right), negative (if the line goes down from left to right), or zero (if the line is horizontal).

(3) . To solve for the length of the run of the Mighty Drop ski slope, we can use the trigonometric function tangent, which relates angle of elevation to ratio of opposite and adjacent sides of right triangle.

Let x be the length of the run. Then we have:

tangent(75°) = opposite/adjacent

tangent(75°) = 800/x

Solving for x, we get:

x = 800 / tangent(75°)

x ≈ 181.8 feet

Therefore, the length of the run of the Mighty Drop ski slope is approximately 181.8 feet.

(4) . To solve for the angle of elevation when little Judy looks at her red balloon, we can use the trigonometric function arctangent.

Let θ be the angle of elevation. Then we have:

tangent(θ) = opposite/adjacent

tangent(θ) = 2240/350

Taking the arctangent on  both sides, we will get:

θ = arctangent(2240/350)

θ ≈ 82.7°

Therefore, the angle of elevation when little Judy looks at her red balloon is approximately 82.7°.

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Step-by-step explanation:

it is 8 bcs -1 - 3 = -4 turn it to 4 and +4

Answer:

x = 9

Step-by-step explanation:

An equation for a vertical line is in the form:

x = anumber

The given information is the point (9,-10) this is in the form (x,y). So this gives us the information that x is 9. That is the equation!

x = 9

The equation of the vertical line through (9,-10) is

x = 9

Answer:

Step-by-step explanation:

The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32F = [ C × (9/5) + 32 ] Given that, C = 25F = 25 × (9/5) + 32F = 45 + 32F = 77Thus, 25° C is equivalent to 77° F.

Using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².

A patch's area on a surface determines how big it is.

Whereas a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

A plane figure's area is the space that its perimeter encompasses.

The area of a closed figure is the total number of unit squares covering its surface.

The area is measured in square units like cm² and m².

So, we know that the area of the triangle is now:

A = 1/2s²

The side of the square is: 10 cm

Then, the area of the one triangle is:

A = 1/2s²

A = 1/2*10²

A = 1/2*100

A = 50 cm²

Therefore, using the given formula [A = 1/2s²], we know that the area of one of the triangles is (C) 50 cm².

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Answer:

Opposite, addition, division, inverse

Step-by-step explanation: