. use implicit function theorem to verify whether the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation

The measure of the angle ∠DBC, m∠DBC, found by writing an equation based on the angle addition postulate is m∠DBC = 30°

An equation consists of two expressions that are specified as being equivalent, by joining them by an equals to '=' sign.

The specified information are;

m∠ABD = (3·x+ 15)° and m∠DBC = (2·x)°, m∠ABC = 90°

The angle addition postulate indicates that we get;

m∠ABC = m∠ABD + m∠DBC

m∠ABC = 90° = (3·x+ 15)°  + (2·x)° (substitution property)

90° = (3·x+ 15)°  + (2·x)°  = (5·x+ 15)°

(5·x + 15)° = 90°

5·x = 90° - 15° = 75°

5·x = 75°

x = 75°/5 = 15°

x = 15°

m∠DBC = 2·x

Therefore, m∠DBC = 2 × 15° = 30°

m∠DBC = 30°

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Answer:

2347

2347 * 2347 = 5508409

Step-by-step explanation:

Hope it helps! =D

A function which has the same horizontal asymptote as the function graphed above include the following: A. f(x) = 4^{x + 2} - 3.

In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 3, as shown in the image attached below.

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the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is illustrated in the figure below.

b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.

b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:

∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy

Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:

∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0

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Step-by-step explanation:

to solve an equation with a variable we want to transform the equation, so that in the end we have the variable alone on one side of the equation, and everything else on the other side.

so, when we look at

(n + 8)/2 - 4 = 16

what blocks us from reading the value of n ?

several things on the left side.

I would start with the "- 4".

to get rid of that from the side of the variable we need to add 4. and to keep the equality true, we need to add this on both sides :

(n + 8)/2 - 4 + 4 = 16 + 4

and we get

(n + 8)/2 = 20

what blocks us now ?

I would say the fraction, this division by 2.

how do we get rid of that ?

by multiplying everything by 2 :

2×(n + 8)/2 = 2×20

and we get

n + 8 = 40

still, something is blocking us from reading the value of n : the "+ 8".

how do we get rid of that ?

by subtracting 8 from both sides :

n + 8 - 8 = 40 - 8

and we get

n = 32

that's it. we are finished. goal achieved.

Answer:

m = 5/4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0, -3) (4,2)

We see the y increase by 5 and the x increase by 4, so the slope is

m = 5/4

The side ratio theorem states that the value of x is 9.6 when BD/DA = BE/EC when DA = 12 and BE = 8 and EC = 10.

Given it has triangles and three vertices, each triangle qualify as a polygon. It belongs to the primitive geometric. Triangle ABC is the term utilized to refer to a triangle with the points A, B, and C. Once the three components are not collinear, a unique rectangle and square in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the main parts of the triangle merge are called to as the triangle's corners. Three triangle ratios are multiplied to yield 180 degrees.

given

by Side ratio theorem

BD/DA = BE/EC

= x/12 = 8/10

x = 8*12/10

x = 9.6

The side ratio theorem states that the value of x is 9.6 when BD/DA = BE/EC when DA = 12 and BE = 8 and EC = 10.

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The quadratic equation x² - 9 has two real roots.

The quadratic equation x² + 3 · x - 10 has two real roots.

The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.

According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is  a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:

b² + 4 · a · c < 0

Now we proceed to check each quadratic equations:

Case 1: (a = 1, b = 0, c = - 9)

D = 0² - 4 · 1 · (- 9)

D = 36

The equation has no complex conjugate roots.

Case 2: (a = 1, b = 3, c = - 10)

D = 3² - 4 · 1 · (- 10)

D = 9 + 40

D = 49

The equation has no complex conjugate roots.

The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:

18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0

Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)

D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²

D = - 28

The equation has a real root and two complex conjugate roots.

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Answer:

Step-by-step explanation:

Answer: f = 14h (f is total fee, h is the hour luke worked)

Step-by-step explanation:

By merging information from several sources, a pooled estimate of the population is utilised to gain a better picture of the population mean as a whole.

When a person or organisation needs to combine data from several sources to better understand a population, they utilise a pooled estimate of the population. This can be accomplished in a number of ways, such as by integrating data from several surveys, data from various time periods, or data from various geographical regions .A more complete and accurate view of the population can be acquired by combining the data from several sources. Because it enables a more precise assessment of a population's needs and traits, this is particularly helpful for making judgements about policy or resource distribution. The comparison of several populations or the analysis of changes across time can both be done using pooled estimates. This is necessary to comprehend population change and determine the most effective resource allocation.

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An inequality that best represents this situation is: x - 1300 > 2500.

a) Let x be the amount of money Sara has in savings. We know that the amount she wants to spend on vacation is $1300, so we have x - 1300 > 2500.

b) To solve for x, we can add 1300 to both sides: x > 3800.

c) The value of x in this situation represents the amount of money Sara has in savings.

The inequality x > 3800 means that Sara must have more than $3800 in savings in order to spend $1300 on a vacation while following the financial planner's suggestion to spend less than $2500.

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Answer:

is 2

because it's below for and two is the closest answer to the function variable answer to this question that you have here

The equation of the tangent line to the curve 3x3,  3[tex]y^{2}[/tex] - 11 = 4xy - x at the point (1,−1) , then the slope = [tex]-\frac{3}{2}[/tex].

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

A slope graph looks like a line graph, but with an important difference: there are only two data points for each line.

Given that,

The equation of the tangent line to the curve 3x3 ,

3[tex]y^{2}[/tex] - 11 = 4xy - x

3[tex]y^{2}[/tex] - 4xy + x - 11 = 0

Differentiate both side with respect to 'x'

6y [tex]\frac{dy}{dx}[/tex] - 4 ( x  [tex]\frac{dy}{dx}[/tex] + y ) - 1 = 0

For slope at point ( 1 , -1 ) put x = 1 and y = -1

6(1)  [tex]\frac{dy}{dx}[/tex] - 4 ( 1  [tex]\frac{dy}{dx}[/tex] - 1 ) -1 = 0

6  [tex]\frac{dy}{dx}[/tex] - 4 [tex]\frac{dy}{dx}[/tex] + 4 -1 = 0

2  [tex]\frac{dy}{dx}[/tex] + 3 = 0

2  [tex]\frac{dy}{dx}[/tex] = 0 - 3

2  [tex]\frac{dy}{dx}[/tex] = - 3

[tex]\frac{dy}{dx}[/tex] = -3/2

slope = [tex]-\frac{3}{2}[/tex]

Therefore,

The equation of the tangent line to the curve 3x3,  3[tex]y^{2}[/tex] - 11 = 4xy - x at the point (1,−1) , then the slope = [tex]-\frac{3}{2}[/tex].

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Dont worry I gotchu

Answer: 33.7°

Answer: -7

Step-by-step explanation:

Here we will show you step-by-step with detailed explanation how to calculate 98 divided by 14 using long division.

Instead of saying 98 divided by 14 equals 7, you could just use the division symbol, which is a slash, as we did above.

Also note that all answers in our division calculations are rounded to three decimals if necessary.

Here are some other ways to display or communicate that 98 divided by 14 equals 7:

98 ÷ 14 = 7

98 over 14 = 7

98⁄14 = 7

The easiest way we found to answer the question "what 98 divided by 14 means", is to answer the question with a question: How many times does 14 go into 98?

Answer: c

Step-by-step explanation:

quite easy because y=mx+b (y=3x-1)

the -1 is the y-intercept. (Where the line meets the y line. c is the only one where the y-intercept is -1

The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.

The equation that can be used to determine the total cost of renting shoes at both locations is:

total cost = fixed cost + variable cost

Total cost of renting at Bowler World = $5 + $1.1x

Total cost of renting at Lucky Spares = $3 + $1.50x

Where

x = number of games played

In order to determine the number of games that would make the cost

equal in both locations, the following steps would be taken:

$5 + $1.1x = $3 + $1.50x

Combine similar terms

$5 - $3 = $1.50x - $1.1x

$2 = $0.40x

Divide both sides of the equation by $0.4

x = 2 / 0.4

x = 5 games

Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50

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The range between which the radius of the circle lies is -

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  .

Inequality in mathematics is a relation that is used to compare two or more expressions in mathematics. For example -

(ax + b) > (cx + d)    

kx < 6

Given is the inequality statement as -

"The area of a circle is more than 2 square units but less than 4 square units".

The area of a circle is -

{A} = πr²

Mathematically, we can write the inequality statement as -

2 < {A} < 4

2 < πr² < 4

(2/π) < r² < (4/π)

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  

Therefore, the range between which the radius of the circle lies is -

[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]  .

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The perimeter ratio of the figures is given as follows:

9:16.

Considering the side length ratio of a:b, the perimeter ratio has the proportion given as follows:

a:b.

This is because both the side lengths and the perimeter are measured in units, hence the perimeter ratio is the same as the side length ratio.

Considering that the area is measured in square units and the volume in cubic units, their ratios would be given as follows:

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The value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [tex][1,4][/tex] is -5.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.

The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

Given that ????(1) = 8, ????(4) = 7, ???? '(1) = 9, and ???? '(4) = -3, we can use the method of integrating by parts to evaluate the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4].

Let u = ????(x) and dv = x dx. Then du = ???? '(x) dx and v = x^2/2.

Using the method of integrating by parts, we have:

∫[tex]x????"(x)????(x) dx= x????(x)[/tex] ×[tex]\frac{x}{2} -[/tex]∫[tex](\frac{x^{2} }{2} )????'(x) dx[/tex]

We can use the same method of integrating by parts to evaluate the second integral on the right-hand side. Let [tex]u=\frac{x^{2} }{2}[/tex] and [tex]dv=????'(x) dx[/tex]. Then [tex]du=x dx[/tex] and [tex]v=????(x)[/tex].

So we have:

∫[tex]x????"(x)????(x) dx = x????(x)[/tex]× [tex]\frac{x}{2} - \frac{x}{2} ^{2}????(x) + c[/tex]

Where C is an arbitrary constant of integration.

We can use the given values of ????(1) and ????(4) to evaluate the definite integral:

∫[tex]x????"(x)????(x) dx[/tex] = 4????(4) * 4/2 - (4^2/2)????(4) + 4????(1) * 1/2 - (1^2/2)????(1)

= 28 - 14 * 7/2 + 4 * 8/2 = 28 - 49 + 16 = -5.

Therefore, the value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4] is -5.

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The number of unique committees is 240 / 4 = 60. So the answer is d. 60.

What is the combination?

The permutation is to select an object and then arrange it and it cares about the orders while Combination is about only selecting an object without caring about the orders.

To form a committee with 2 women and 2 men, we have 4 choices for the first woman, 3 choices for the second woman, 5 choices for the first man, and 4 choices for the second man.

Therefore, the number of ways to form a committee is 4 * 3 * 5 * 4 = 240. This is the total number of combinations, and to find the number of unique committees,

we need to divide by the number of ways to arrange the members within each committee.

As the members are distinguishable, the number of arrangements is simply 2! * 2! = 4.

Therefore, the number of unique committees is 240 / 4 = 60. So the answer is d. 60.

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The greatest common factor of 12 and 80 is 12, so we can use the distributive property to factor that out.

Identify the greatest common factor (GCF). In this case, it's 12.

Rewrite the expression so the GCF is outside of the parentheses. 12 + 80 = 12(1 + 80/12).

Simplify the expression inside the parentheses. 1 + 80/12 = 7.

Substitute the simplified expression back into the original equation. 12 + 80 = 12(7).

Simplify the expression. 12 + 80 = 84.

Therefore, 12 + 80 = 84 after applying the distributive property to factor out the greatest common factor of 12.

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Answer:

-10+4=-x

-x_=-6_

x=6

if you don't understand

negative x over negative x and negative x over 6 the negative will cancle the negative you will get x to be 6

The probability that the profit is greater than $400 is 0.0082.

The cumulative distribution function (CDF) of the normal distribution can be used to calculate the likelihood that the profit will be larger than $400.

We may determine the likelihood that a random variable will be less than or equal to a certain value using the CDF of the normal distribution. We can deduct the CDF from 1 to get the likelihood that the random variable is greater than a specific value.

The normal standard variable that correlates to x will be referred to as z. By taking the mean away and dividing it by the standard deviation, we may standardize x:

z = (x - $360) ÷ $50

The CDF of the standard normal distribution can be found using a standard normal table.

Calculating the value of z we get.

z = (400 - $360) ÷ $50 = 2.4

Therefore, the probability that x > $400 is given by:

p(x > $400) = 1 - p(x <= $400) = 1 - φ(2.4)

where φ is the standard normal CDF.

A standard normal table can be used to estimate the value of φ.

Using the standard normal table φ = 0.9918.
Substituting the values we get,

p(x > $400) = 1 - 0.9918 = 0.0082

This means that there is about a 0.82% chance that the store will make a profit greater than $400 on a randomly selected day.

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Answer:

An obtuse triangle is always an isosceles triangle.

Step-by-step explanation:

When 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.

Dividend/Divisor is the quotient.

Divide the dividend by the divisor to obtain the quotient.

Here, Dividend = 1/4

Divisor = 3

Divisor/Dividend =(1/4)/3 = 1/12

So, when 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.

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Answer:

s= 19/-9

s≈-2.111

Step-by-step explanation:

s is being multiplied by -9

so, to get s by itself we divide both sides by -9

s= [tex]\frac{19}{-9}[/tex]

if you need it in decimal form, s≈-2.111