Use implicit differentiation to determine dy/dx given the equation xy+e^x=sin(y).
dy/dx= ?

The area of a shape is the amount of space it can occupy.

The value of r is 13

From the question (see attachment), we have:

\(\mathbf{A =176}\) --- area of the shaded region

\(\mathbf{w = 2}\) --- the width of the shaded region

The area of the complete circle would be:

\(\mathbf{A_1 =\pi (r + w)^2}\)

The area of the small circle is:

\(\mathbf{A_2 =\pi r^2}\)

So, the area of the shaded region is:

\(\mathbf{A = A_1 - A_2}\)

Substitute known values

\(\mathbf{176 =\pi (r + w)^2 - \pi r^2 }\)

Substitute 2 for w

\(\mathbf{176 =\pi (r + 2)^2 - \pi r^2 }\)

Expand

\(\mathbf{176 =\pi (r^2 + 4r + 4) - \pi r^2 }\)

Open brackets

\(\mathbf{176 =\pi r^2 + 4\pi r + 4\pi - \pi r^2 }\)

Cancel out line terms

\(\mathbf{176 =4\pi r + 4\pi }\)

Divide through by 4

\(\mathbf{44 =\pi r + \pi }\)

Factor out pi

\(\mathbf{44 =\pi(r+ 1) }\)

Divide through by pi

\(\mathbf{r + 1= \frac{44}{ \pi} }\)

Substitute 22/7 for pi

\(\mathbf{r + 1= \frac{44}{ 22/7} }\)

Using a calculator, we have

\(\mathbf{r + 1= 14}\)

Solve for r

\(\mathbf{r= 14 -1}\)

\(\mathbf{r= 13}\)

Hence, the value of r is 13

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Answer:

Step-by-step explanation:

6x15=90

90miles

Answer:

the graph represents a function.

Step-by-step explanation:

The vertical line test is a test to check if a graph represents a function.

To proceed, draw (imaginary) vertical lines through the entire domain of the graph.  If any of the line intersects the graph at any value of x, then the graph does not represent a function.

Here it is not possible to draw a vertical line to intersect the red curve at any point, therefore the graph represents a function.

Answer:

Yes, the graph represents a function.

Step-by-step explanation:

The vertical line test is a test you can do to determine if a graph is a function. Basically, you draw straight vertical lines, and if it intersects with the line more than once, the graph is not a function.

This is because in a function, each input can only have one output.

So, we can draw vertical lines through the graph, and you'll find that each line will only intersect with the line once.

Based on this, the given graph would represent a function.

Answer:

x= 11

y= 1

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Answer:

Step-by-step explanation:

scale factor bigger than one,  in math   greater than,  the figure is larger than the object being used    a figure smaller than 1 creates a figure smaller than the original  

Luckily you can just use your web browser to scale a screen up or down in it's scale.  try it.. top right  ellipse for go ogle chrome lets you scale over 100 per cent  or 1  and also under 100 per cent  or less than 1  remember   100 per cent = 1.00  

Answer:

Hello there! I would say the answer is C,

Step-by-step explanation:

I hope this helps!!!

The slope of all the given options  are equal and it is equal to slope of given equation .

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

Given

Equation of a given line is x+2 y=6

Lets find out slope m by writing the equation in \($y= \mathbf{m}+\mathbf{b}$\) form

\($$\begin{aligned}& x+2 y=6 \\& 2 y=-x+6 \\& y=\frac{-1}{2} x+6\end{aligned}$$\)

The slope of the line is \($\frac{-1}{2}$\)

Now we find slope of each option using formula \($m=\frac{y_2-y_1}{x_2-x_1}$\)

Lets pick two points from the graph to find out slope

Pick (0,3) and (6,0)

\($$\begin{aligned}& m=\frac{y_2-y_1}{x_2-x_1} \\& m=\frac{0-3}{6-0}=\frac{-1}{2}\end{aligned}$$\)

Now pick two points from option \($\mathbf{B}$\) to find slope

(-10,-3) and (0,-8)

\(m=\frac{-8+3}{0+10}=\frac{-1}{2}$$\)

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Answer:

5.625

Step-by-step explanation:

4.5/0.8 = 5.625

Answer:

Step-by-step explanation:

The answer would be 15.

It is 15 because you have to start from the left then mark the first one off then go to the right and continue that until you have one number left in the middle.

Next you will draw a little line under the first left number then go all the way to the middle number you got from marking off.

Then you will do the other side from the right to the left to the middle of the number you got from marking off.

Finally, you will go to the right side and you will do the same thing on the right side of the box you just created on the right and do the same mark off.

Answer:

36 ounces or if over 150 lbs drink more water than 36 ounces

Step-by-step explanation:

For every pound of sweat you lose you need to drink 16 ounces of water!

The probability that exactly 4 students will withdraw is approximately 0.2048.

The problem asks us to calculate the probabilities related to student withdrawals in an introductory statistics course. We are given that 20% of students withdraw from the course and that 20 students registered for the course.

a. To compute the probability that 2 or fewer students will withdraw, we need to calculate the cumulative probability of the binomial distribution. We can use the binomial probability formula:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Using the formula, the probability can be calculated as follows:

P(X = 0) = (20 choose 0) * (0.2^0) * (0.8^20) ≈ 0.0115

P(X = 1) = (20 choose 1) * (0.2^1) * (0.8^19) ≈ 0.0729

P(X = 2) = (20 choose 2) * (0.2^2) * (0.8^18) ≈ 0.1948

Therefore, P(X ≤ 2) ≈ 0.0115 + 0.0729 + 0.1948 ≈ 0.2792

b. To compute the probability that exactly 4 students will withdraw, we use the binomial probability formula:

P(X = 4) = (20 choose 4) * (0.2^4) * (0.8^16) ≈ 0.2048

Therefore, the probability that exactly 4 students will withdraw is approximately 0.2048.

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The possible algebraic equations, obtained based on the algebraic expressions in the question are;

1. \(\frac{x}{8} = y\)

2. 15 - n = m

3. 25 + x = y

An algebraic expression is a collection of numbers and variables that are combined together, but without indicating the value indicated by the collection.

What is an algebraic equation?

An algebraic equation is a mathematical statement that expresses the equivalence of two expressions.

The algebraic expressions can be presented as follows;

1. Some number divided by 8

Let x represent the number divided by 8, and let y represent the result when x is divided by 8. The variables x and y can be defined based on the details in the question

The equation with x as the number and y as the result can be presented as follows;

2. n less than 15

The expression n less than 15 is; 15 - n

Let m represent the value of the expression; 15 - n, an algebraic equation based on the details is therefore;

3. 25 more than a number

Let x represent the number, we get

25 more than a number = 25 + x

The y represent the result or value of the expression 25 + x, we get the following algebraic equation;

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Answer:

parallel lines

Step-by-step explanation:

im pretty sure this is it hope this helps

Answer:

E)  x^5

Step-by-step explanation:

example, \(\sqrt{3}\) = 3^1/2 where '1' is the coefficient of 3

\(\sqrt{3}\) is the same as \(\sqrt[2]{3}\) (it's assumed to be 2 unless another number is there)

so, √x^10 is the same as x^(10/2) which is x^5

To calculate the probability that none of the five randomly selected adults own a car, we need to use the concept of independent events.

Since the probability of an individual owning a car is 76%, the probability of an individual not owning a car is 100% - 76% = 24%. Now, we can calculate the probability of none of the five adults owning a car by multiplying the probabilities of each individual not owning a car, assuming independence.

P(none owning a car) = (0.24) ^ 5 = 0.00173 ≈ 0.17%.

Therefore, the correct answer is not one of the options provided. The closest option is 0.33%, but the correct probability is approximately 0.17%.

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Answer:

f(x)=20+4x = -5

Step-by-step ;

answer is -5 .

Answer:

Step-by-step explanation:

a = -4 , b = 16 and c = -17

\(x =\dfrac{-b}{2a}\\\\x = \dfrac{-16}{2*(-4)}\\\\\\ =\dfrac{-16}{-8}\\\\\\\\\)

x = 2

y = -4(2)² + 16*2 - 17

   = -4*4 + 32 - 17

   = -16 + 32 - 17

y = -1

Vertex (2, -1)

axis of symmetry: x = 2

Multiple regression offers a more comprehensive and nuanced analysis by considering the influence of multiple predictors, capturing complex relationships, controlling for confounding variables, and enhancing predictive capabilities.

A study using multiple regression has several advantages over a study using bivariate correlation:

Multivariate analysis: Multiple regression allows for the inclusion of multiple predictor variables, which enables the examination of their individual contributions while controlling for the effects of other variables. This helps to identify the unique influence of each predictor on the outcome variable, considering their interrelationships.

Complex relationships: Multiple regression can capture complex relationships between variables by accounting for their combined effects. Bivariate correlation can only assess the linear relationship between two variables, whereas multiple regression can handle non-linear relationships and interactions between predictors.

Control of confounding variables: Multiple regression enables the control of confounding variables by including them as predictors in the model. By controlling for potential confounders, the relationship between the predictor and outcome variables can be more accurately assessed, reducing the likelihood of spurious associations.

Increased predictive power: Multiple regression can improve the predictive power of the model by incorporating multiple predictors. By considering multiple factors simultaneously, it can provide a more comprehensive understanding of the factors influencing the outcome variable and better predict its values.

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Answer:

x = 11

Step-by-step explanation:

The angles in a square are right , that is 90°

The diagonals bisect the angles , then

6x - 21 = 45 ( add 21 to both sides )

6x = 66 ( divide both sides by 6 )

x = 11

The length of the third side of the triangle is approximately 12.00 units.

Given the sides and angle of a triangle, we need to find the length of a side of the triangle. The given sides of the triangle are

a=10,

b=10 .

and the angle between them is A=50. We can use the Law of Cosines to find the length of the third side, which is c. The Law of Cosines states that \(c\² = a\² + b\² - 2\ ab\ cos(C)\),

where C is the angle opposite to side c. Since we know two sides and an angle that are not opposite to side c, we need to find the angle C first.

Angle C is the angle opposite to side c. Since we know angle A and the sum of the angles in a triangle is 180°, we can find angle C as:

C = 180° - A - B,

where B is the angle opposite to side b.

Since the triangle has two equal sides, a=10 and

b=10,

angles A and B opposite to them are also equal.

Therefore, we can find angle B as:

B = (180° - A)/2

= (180° - 50°)/2

= 65°

Now that we know angle C, we can use the Law of Cosines to find the length of side c.c² = a² + b² - 2ab cos(C)c²

= 10² + 10² - 2(10)(10) cos(65°)c²

≈ 144.13c

≈ √144.13c

≈ 12.00

Therefore, the length of the third side of the triangle is approximately 12.00 units. Answer: 12.00.

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Answer:

Find the area of the shape

First the two triangles

3 x 4 = 12 so the area of both triangles is twelve

Now it is only 1 big rectangle left

The side lengths can be added 3 + 4 + 5 = 12

12 x 11 = 132

132+12=144

144 is the surface area/area

If you have any questions please ask

Step-by-step explanation:

Answer:

cos R is 44/55

sin S is 33 / 55

The equation of the plane containing the point (7, -2, -5) and perpendicular to the line passing through (-3, 0, 4) and (3, 2, 1) is 6x + 2y - 3z = D.

To find the equation of the plane containing the point (7, -2, -5) and perpendicular to the line passing through (-3, 0, 4) and (3, 2, 1), we can use the following approach:

First, we need to find the direction vector of the line passing through (-3, 0, 4) and (3, 2, 1). The direction vector is obtained by subtracting the coordinates of the initial point from the coordinates of the terminal point:

Direction vector = (3, 2, 1) - (-3, 0, 4) = (6, 2, -3)

Now, we have a point on the plane (7, -2, -5) and a normal vector perpendicular to the plane (6, 2, -3). We can use the point-normal form of the equation of a plane to find the equation:

The equation of the plane is given by:

Ax + By + Cz = D

To find the values of A, B, C, and D, we substitute the coordinates of the given point (7, -2, -5) into the equation and use the components of the normal vector (6, 2, -3): A(7) + B(-2) + C(-5) = D

Now, substituting the components of the normal vector into the equation, we have:

6x + 2y - 3z = D

Therefore, the equation of the plane containing the point (7, -2, -5) and perpendicular to the line passing through (-3, 0, 4) and (3, 2, 1) is:

6x + 2y - 3z = D

In summary, the equation of the plane is given by 6x + 2y - 3z = D, where D is determined by substituting the coordinates of the given point (7, -2, -5) into the equation.

This equation represents a plane that contains the specified point and is perpendicular to the line passing through the given points.

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R-11 was the preferred low pressure centrifugal refrigerant. R-123 is now the preferred low pressure centrifugal refrigerant for environmental reasons.

A refrigerant is a working fluid that is utilised in the refrigeration cycle of air conditioners and heat pumps. In this cycle, they typically go through numerous phase changes from a liquid to a gas and back again.

A chlorofluorocarbon is trichlorofluoromethane, commonly known as freon-11, CFC-11, or R-11. It is an odourless, colourless liquid that boils at a temperature close to body temperature. Class 1 ozone-depleting CFC-11 harms the ozone layer that protects the Earth's atmosphere.

In low pressure HVAC and refrigeration systems, 2,2-dichloro-1,1,1-trifluoroethane, also known as HCFC-123, is a replacement to CFC-11 but should not be utilised in foam blowing or solvent applications. It serves as the main ingredient in the fire-extinguishing combination used in the Halotron I.

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The confidence interval for the mean is (10.7485, 11.6515)

Given Data:

n = 225

×= 11.2

s = 4.1

Note that, Population standard deviation(\(\alpha\)) is unknown. So we use t distribution.

Our aim is to construct a 90% confidence interval.

c = 0.90

\(\alpha\) = 1- c = 1- 0.90 = 0.10

\(\alpha\)/2 = 0.10/2 = 0.05

Also, d.f = n - 1 = 225 - 1 = 224

t\(\alpha\)/2.d.f- = t\(\alpha\)/2.n-1 = t0.05,224 = 1.652

( use t table or t calculator to find this value..)

The margin of error is given by

E = t\(\alpha\)/2,d.f. * (s / \(\sqrt{n}\))

= 1.652 * (4.1/ √225)

= 0.4515

Now , confidence interval for mean(\mu) is given by:

(× - E ) <  μ< x + E)

(11.2 - 0.4515) < μ < (11.2 + 0.4515)

10.7485 < μ< 11.6515

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Answer:

Q = 108°

R = 72°

Step-by-step explanation:

Quadrilateral means this is a four-sided shape. Parallelogram means that both sets of opposite side are parallel, so all the angles are either equal or add up to 180° (supplementary)

The order of the letters matters bc PQRS means that you go along an edge from P to Q, but you have to go thru the middle of the shape to get from P to R. So P and Q add up to 180°.

P + Q = 180°

72° + Q = 180°

Q = 108°

Opposite from each other, across the middle of the shape, P and R are equal.

P = R = 72°