A) Find The Differential Dy. Y = Cos X Dy = ____________ B) Evaluate Dy For The Given Values Of X And Dx. (Round Your Answer To Three Decimal Places.) X = Pi/3 And Dx = .1 Dy = _____________
a) find the differential dy.
y = cos x
dy = ____________
b) evaluate dy for the given values of x and dx. (round your answer to three decimal places.)
x = pi/3 and dx = .1
dy = _____________

Answer:

Answer = 13.5

Step-by-step explanation:

A square has 4 sides

54 / 4 = 13.5

The side of the square will be 7.34 inches.

A square is a quadrilateral having all the sides equal to each other and the sum of the angles will be 360 degrees. The area is defined as the space occupied by the shape in a two-dimensional plane.

Given that a square has an area of 54 sq in . the length of each side is the same.

The side of the square will be calculated as below:-

Area of square = Side²

54 = Side²

Side = √54

Side = 7.34 inches.

Therefore, the side of the square will be 7.34 inches.

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Answer:9342

Step-by-step explanation:

I am smart UwU

Answer:

C

Step-by-step explanation:

Answer:

The answer is A :)

brainliest pls

½×½ which will be ¼

Step-by-step explanation:

because

Probability that the starting player wins:

\(P_{n} =\)  m /n + m + n(n-1) /(n + m)(n+m -1) × \(P_{n-2}\)

Let us say that the probability that the first player wins is \(P_{n}\). Then this can be happen in two ways:

If the first player wins in the first move which has a probability: m /n + m

If the first player wins after the second move which has a probability :

n(n-1) /(n + m)(n+m -1) × \(P_{n-2}\)

Therefore by the law of probability,

\(P_{n} =\)  m /n + m + n(n-1) /(n + m)(n+m -1) × \(P_{n-2}\)

This will allow us to find out the probability of first player winning the game recursively.

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the correct statement is e. It will cause bond prices to rise.

If the Reserve Bank of Australia decides to decrease the cash rate, several effects can be expected:

e. It will cause bond prices to rise:

A decrease in the cash rate typically leads to a decrease in interest rates across the economy. When interest rates decline, the demand for bonds increases because they offer relatively higher returns compared to other investments. This increased demand for bonds leads to an increase in bond prices.

b. It will have no impact on other interest rates:

A decrease in the cash rate by the Reserve Bank of Australia can influence other interest rates in the economy. When the central bank reduces the cash rate, commercial banks are encouraged to lower their lending rates, which can lead to reduced borrowing costs for businesses and individuals. As a result, other interest rates, such as mortgage rates or business loan rates, may decrease as well.

c. It will have no impact on share or bond prices:

This statement is not accurate. As mentioned earlier, a decrease in the cash rate can lead to an increase in bond prices due to the increased demand for bonds. However, the impact on share prices is not certain and can vary depending on various factors such as market conditions, investor sentiment, and company-specific factors. It is possible that lower interest rates can stimulate economic activity and corporate profits, which may lead to an increase in share prices. However, the relationship between interest rates and share prices is complex and can be influenced by numerous factors.

d. It will likely cause mortgage interest rates to rise:

This statement is incorrect. A decrease in the cash rate typically leads to lower borrowing costs for individuals and businesses, including mortgage rates. When the central bank lowers the cash rate, it aims to stimulate economic activity by making borrowing more affordable. As a result, mortgage interest rates are likely to decrease rather than rise.

a. It will cause share prices to fall:

This statement is not accurate. As mentioned earlier, the impact of a decrease in the cash rate on share prices is not straightforward and can be influenced by various factors. Lower interest rates can potentially stimulate economic activity and support corporate profits, which may have a positive impact on share prices. However, the relationship between interest rates and share prices is complex and can be affected by multiple factors beyond just the cash rate.

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Answer:

Step-by-step explanation:

Ratio = 4 :3

Other two sides = 4x , 3x

Pythagorean theorem

(4x)²  + (3x)² = 20²

16x² + 9x²  = 400

          25x² = 400

             x² = 400 ÷ 25

            x²  = 16

             x = √16

x = 4 cm

4x = 4*4 = 16

3x = 3*4 = 12

Sides = 16cm  , 12 cm

Null hypothesis (H0): The mean wait time for emergency room patients is equal to or less than 38 minutes (H0: μ ≤ 38).
Alternative hypothesis (Ha): The mean wait time for emergency room patients is more than 38 minutes (Ha: μ > 38).

The null hypothesis, denoted as H0, is a statement that assumes there is no significant difference or relationship between variables in a statistical analysis. In this case, the null hypothesis is that the mean wait time for emergency room patients is equal to or less than 38 minutes, represented as H0: μ ≤ 38.
On the other hand, the alternative hypothesis, denoted as Ha or H1, is a statement that contradicts or opposes the null hypothesis. It suggests that there is a significant difference or relationship between variables. In this scenario, the alternative hypothesis is that the mean wait time for emergency room patients is more than 38 minutes, represented as Ha: μ > 38.
To summarize:
- Null hypothesis (H0): The mean wait time for emergency room patients is equal to or less than 38 minutes (H0: μ ≤ 38).
- Alternative hypothesis (Ha): The mean wait time for emergency room patients is more than 38 minutes (Ha: μ > 38).
In hypothesis testing, we collect data to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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9514 1404 393

Answer:

  b = 2

  c = 4

  e = 3

  g = 6

Step-by-step explanation:

b) The number remaining under the radical is what's left after the perfect squares 25 and x² are removed. That is b = 2.

__

c) The number outside the radical is the root of the perfect square constant inside the radical: √16 = c = 4.

__

e) As with c, √9 = e = 3.

__

g) As with c, √36 = g = 6.

The "n" in the formula for calculating degrees of freedom for a correlation coefficient represents the sample size. The correct option is a.

Explanation: In statistics, the correlation coefficient measures the strength and direction of the linear relationship between two variables. When calculating the degrees of freedom for a correlation coefficient, the "n" represents the sample size. Degrees of freedom (df) refers to the number of independent observations in a statistical analysis. It represents the number of values that are free to vary after certain restrictions or conditions have been imposed.

In the context of correlation, the formula for degrees of freedom is given by (n - 2), where "n" is the sample size. The subtraction of 2 is because the calculation of the correlation coefficient involves estimating the parameters of the line that best fits the data, which requires two degrees of freedom. Subtracting 2 ensures that the degrees of freedom accurately reflect the number of independent observations available for analysis.

Therefore, the correct answer is (a) sample size. The larger the sample size, the greater the degrees of freedom, which generally improves the reliability and precision of the correlation coefficient estimate.

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Answer:

x ( 10 y + 10 )

Step-by-step explanation:

10 x ( y + 1 )

10 x y + 10 x

x ( 10 y + 10 )

hope i helped!

Answer:

2A=A+A

Step-by-step explanation:

2A=A*A, not A+A

The total electric force on the 7.00−μC charge is 0.872 N at an angle of 330°.

The force exerted on the 7.00−μC charge by the 2.00−μC charge is

F₁​ ​= \(k_{e}\)q₁q₂​​/r₂ r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(2.00×10^−6C) ×(cos60°i^+sin60°j^​)]/ (0.500m)²

F₁ ​= (0.252i^+0.436j^​)N

Similarly, the force on the 7.00μC charge by the −4.00−μC charge is

F₂​ ​= \(k_{e}\)q₁​q₃/​r² ​​r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(−4.00×10^−6C)​×(cos60°i^−sin60°j^​)]/(0.500m)²

F₂​ ​=(0.503i^−0.872j^​)N

Hence, the total force on the charge 7.00−μC  is

F = F₁​​+F₂​

​=(0.755i^−0.436j^​)N

We can also note the total force as:

F = (0.755N)i^−(0.436N)j^​ = 0.872N

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--This question is incomplete; the complete question is

"Three charged particles are located at the corners of an equilateral triangle, as shown in Figure. Calculate the total electric force on the 7.00−μC charge."--

The word problem 4 and one tenth times negative 4 times 5 over 12 have a product of negative 8 and one fifth

Multiplication is one of the basic mathematical operator which is used to solve the given problem. It is the inverse of division. the result of multiplication is called the product

Rewriting the word problem 4 and one tenth times negative 4 times 5 over 12 to figures

4 1/10 * -4 * 5/10

solving the equation

= 4 1/10 * -4 * 5/10

= 41/10 * -4 * 5/10

= -41/5

= -8 1/5

The product of the multiplication is negative 8 and one fifth

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Answer:

5 and then 2:5

Step-by-step explanation:

For every 2 triangles, there are 5 total shapes, therefore the simplified of triangles to total shapes is 2:5

Answer:

\(D. \\x>\frac{3}{2}\)

Step-by-step explanation:

12(1/2x - 1/3) > 8 - 2x

6x - 4 > 8 - 2x

6x + 2x - 4 > 8 - 2x + 2x

8x - 4 > 8

8x - 4 + 4 > 8 + 4

8x > 12

8x ÷ 8 > 12 ÷ 8

x  > 1.5

Answer:

80 pages

Step-by-step explanation:

x = number of pages of articles

x = 110 - (23 + 14/2)

x = 110 - (23 + 7)

x = 110 - 30

x = 80

Answer:

12 crossed by 3

Step-by-step explanation:

The graph of the given functions is (see in attachments).

From the question, we have

g(x) = 0.44√3.2x−4.1

Graph:

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

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The final image will fit in a similar portfolio with an area of 160 square inches.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

The dimensions for this problem are given as follows:

24 inches, 36 inches.

With the reduction with a scale factor of 1/3, the dimensions are given as follows:

8 inches,  12 inches.

With the enlargement by a factor of 1.25, the dimensions are given as follows:

10 inches and 15 inches.

Hence the area is given as follows:

15 x 10 = 150 square inches.

As the area of 150 square inches is less than 160 square inches, the final image will fit in a similar portfolio with an area of 160 square inches.

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Answer:

Height of the tree is 40.0 meters.

Step-by-step explanation:

From ΔABC,

m∠ABC = 90°

Since, m∠ABC = m∠CBD + m∠ABD

90° = 6° + m∠ABD

m∠ABD = 90°- 6° = 84°

By triangle sum theorem in ΔABD,

m∠ABD + m∠BDA + m∠DAB = 180°

84° + 29° + m∠BDA = 180°

m∠BDA = 180° - 113°

             = 67°

By sine rule in ΔABD,

\(\frac{\text{sin}(\angle BDA)}{d}= \frac{\text{sin}(\angle ABD)}{h}\)

\(\frac{\text{sin}(67)}{37}= \frac{\text{sin}(84)}{h}\)

h = \(\frac{\text{sin}(84)\times 37}{\text{sin}(67)}\)

h = 39.98

h ≈ 40.0 meters

Therefore, height of the tree is 40.0 meters.

The sine rule is the ratio of the side length to the sine of the opposite angles. Then the height of the tree is 40 meters.

Trigonometry deals with the relationship between the sides and angles of a triangle.

Because of prevailing winds, a tree grew so that it was leaning 6º from the vertical.

At a point d = 37 meters from the tree, the angle of elevation to the top of the trees is a = 29° (see figure).

∠ABC = 90

We have

In ΔABC

∠ABC = ∠CBD + ∠ABD

∠ABD = 90 - 6

∠ABD = 84

By triangle sum in ΔABD, we have

∠ABD + ∠BDA + ∠DAB = 180

                            ∠BDA = 180 - 84 - 29

                            ∠BDA = 67

Then by the sine rule, we have

\(\begin{aligned} \dfrac{\sin \angle BDA}{d} &= \dfrac{ \sin \angle ABD }{h}\\\\\dfrac{\sin 67}{37} &= \dfrac{\sin 84}{h}\\\\h &= \dfrac{\sin 84} \times 37{\sin 67}\\\\h &= 39.98 \approx 40 \end{aligned}\)

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The total value in cents of all coins in the any row would be 16 cents.

In the pattern you described, the coins are arranged in rows such that each subsequent row has one more coin than the previous row. Let's analyze the values of the coins to determine the total value in cents of all the coins in the th row.

Assuming the values of the coins are as follows:

Penny: 1 cent

Nickel: 5 cents

Dime: 10 cents

We can observe that the pattern repeats after every three coins. The first three coins in the pattern are penny, nickel, dime. These coins have a total value of 1 + 5 + 10 = 16 cents.

For the subsequent rows, the pattern repeats with an offset of 3. For example, in the fourth row, the coins are penny, nickel, dime, which have the same total value as the first row, i.e., 16 cents.

So, regardless of the value of "th" (the row number), the total value in cents of all the coins in that row will always be 16 cents.

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Answer:

1) See below for table.

2) Domain: \(\{1, 2, 3, 4\}\)

Range: \(\{160, 160, 205, 250\}\)

Yes, this is a function.

Step-by-step explanation:

We know that the electrician charges a base fee of $70 plus $45 for each hour of work.

We also know that the minimum the electrician charges is $160.

Let's write an equation. Let x denote the number of hours worked and y denote the total price. There's also a base fee of $70. So, we can write the following equation:

\(y=45x+75\)

Part 1)

Let's create our table for 1, 2, 3, and 4 hours. To do so, we simply need to substitute each value for x in our equation.

1 Hour:

We have:

\(y_1=45(1)+70\)

Multiply and add:

\(y_1=45+70=\$115\)

However, notice that the minimum the electrician charges is $160. Therefore, for one hour of work, the electrician will still charge $160. So:

\(y_1=\$160\)

2 Hours:

Substitute 2 for x:

\(y_2=45(2)+70=90+70=\$160\\\)

So:

\(y_2=\$160\)

3 Hours:

Substitute 3 for x:

\(y_3=45(3)+70=135+70=\$205\)

So:

\(y_3=\$205\)

4 Hours:

Substitute 4 for x:

\(y_4=45(4)+70=180+70=\$250\)

So:

\(y_4=\$ 250\)

Therefore, for 1, 2, 3, and 4 hours of work, the prices will be $160, $160, $205, and $250, respectively.

We can create the following table (please scroll down to see the table. Also, y is measured in dollars).

Part 2)

The domain of a relation are the input values.

In this context, our input values are the amount of hours worked, and we calculated for 1, 2, 3, and 4 hours of work.

Therefore, our domain in this context is:

\(\{1, 2, 3, 4\}\)

The range of a relation are the output values.

In this context, the output values are the price for x hours of work.

Therefore, our range in this context is:

\(\{160, 160, 205, 250\}\)

This relation does represent a function. Remember that a function cannot have repeating input values. In other words, no one input can be equal to two or more different outputs. However, one output can be mapped to two or more different inputs.

For our table, none of the inputs are repeating. So, our relation is a function.

And we're done!

Answer:

y = 2x - 5

Step-by-step explanation:

Using the slope intercept formula y2 - y1 / x2 -x1...

You get a slope of 2 so y = 2x +b

Then to find b the intercept, you plug in one of the coordinates like so...

1 = 2(3) + b

Then solve to get an intercept of -5.

So the slope-intercept form would be...

y = 2x - 5

credits to the owner:lisboa, another brainly expert

Using logarithmic differentiation to the derivative of y is dy/dx = ( X^2 +1)^3 (x – 1)^6 x^2 [3(2x)/(x^2 + 1) + 6/(x - 1) + 2/x]

Logarithmic differentiation is a technique used to find the derivative of a function by taking the natural logarithm of both sides. By applying this method to the given expression, we obtain the derivative dy/dx.

After expanding and simplifying the expression, the derivative is expressed as a product of the original function and a combination of terms involving x.

This approach allows us to differentiate complicated functions by taking advantage of the properties of logarithms. The final expression represents the derivative of the given function with respect to x.

Taking the natural logarithm of both sides, we get:

ln y = 3 ln (x^2 + 1) + 6 ln (x - 1) + 2 ln x

Now, differentiating both sides with respect to x:

1/y (dy/dx) = 3(2x)/(x^2 + 1) + 6/(x - 1) + 2/x

Multiplying both sides by y:

dy/dx = y [3(2x)/(x^2 + 1) + 6/(x - 1) + 2/x]

Substituting the expression for y:

dy/dx = ( X^2 +1)^3 (x – 1)^6 x^2 [3(2x)/(x^2 + 1) + 6/(x - 1) + 2/x]

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Answer:

9.) 5x - 18 = 4x + 7 10.) x = 25 11.) m∠MNQ = 107° 12.) m∠MNR = 73°

Step-by-step explanation:

9. & 10.)

∠MNQ and ∠RNP are vertical angles meaning they are equivalent to each other. Knowing that, we can set their values equal to each other and solve for x.

5x - 18 = 4x + 7 (Given)

x - 18 = 7 (Subtract 4x on both sides)

x = 25 (Add 18 on both sides)

Therefore, we know the equation is 5x - 18 = 4x + 7 and we know that x = 25.

Now we can solve for the angles.

11.)

5(25) - 18

125 - 18 = 107

Therefore, m∠MNQ = 107°.

12.)

∠MNR and ∠MNQ are supplementary angles meaning their angles will add up to 180°

∠MNR + 107 = 180

∠MNR = 73

Therefore, m∠MNR = 73°.

Answer:

1.

\((x+y)2\\ (-3+14)2\\ -6+28\\ 22\\ \\\)

2.

\(-2x+17\\ -2(8)+17\\ -16+17\\ 1\)

3.

\(10-3m\\ 10-3(5)\\ 10-15\\ -5\)

Answer:

\(13- 0.75 * (12) + 8 * (\frac{1}{2} ) = 13-9+4\\\\13-5=8\)

Step-by-step explanation:

Evaluate 13-0.75w+8x13−0.75w+8x13, minus, 0, point, 75, w, plus, 8, x when w=12w=12w, equals, 12 and x=\dfrac12x= 2 1 ​ x, equals, start fraction, 1, divided by, 2, end fraction.

For this case we have the following expression:

 \(13-0.75w + 8x\)

Evaluate for the following values:

 w = 12

 x = 1/2

 We Substituting the values we have:

\(13- 0.75 * (12) + 8 * (\frac{1}{2} ) = 13-9+4\\\\13-5=8\)