What is the approximate area of a circle with radius 6 cm?

The arc length of the polar curve r = e^4θ where 0 ≤ θ ≤ 2π is approximately 32.59 units.

To find the arc length of a polar curve, we use the formula:

L = ∫[a,b] √[r² + (dr/dθ)²] dθ

In this case, we have:

r = e^4θ

dr/dθ = 4e^4θ

0 ≤ θ ≤ 2π

So, the arc length is:

L = ∫[0,2π] √[e^8θ + 16e^8θ] dθ

L = ∫[0,2π] e^4θ √(17) dθ

Using integration by substitution with u = e^4θ, we get:

L = (1/4√(17)) [u√(u² + 1)]|[u=e^4θ]^[u=1]

L = (1/4√(17)) [(e^4θ)√(e^8θ + 1) - √2]

L = (1/4√(17)) [(e^(4π)√(e^(8π) + 1) - √2) - (√(e^8 + 1) - √2)]

L ≈ 32.59

So the arc length of the polar curve r = e^4θ where 0 ≤ θ ≤ 2π is approximately 32.59 units.

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we are given the function f(x) = -0.1x - 0.15x^3 - 0.5x^2 - 0.25x + 1.2 and asked to perform various derivative calculations using finite difference approximations.

Firstly, we find the first derivative at x = 0.5 using forward,, and central finite differences with a step size of h = 0.1.

Next, we determine the first derivative over the interval x = 0 to 1 using forward and backward finite differences with a step size of h = 0.25.

Then, we calculate the first derivative with a second-order error using a step size of h = 0.1 at x = 0.7.

Moving on, we find the second derivative at x = 0.5 using central finite differences with a step size of h = 0.25.

Lastly, we determine the second derivative at x = 1 using central finite differences with a step size of h = 0.1.

The calculations involve evaluating the function at specific points and applying the finite difference formulas to approximate the derivatives. These approximations allow us to estimate the rate of change and curvature of the function at the given points.

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Answer: Ahmad earns 120 dollars if he tutors for 3 hours.

Step-by-step explanation: In the question, it states that, “For each hour that he tutors, he earns 40 dollars. Our question tells us to multiply by 3. 40 x 3 = 120 dollars.

Answer:

27.2

Step-by-step explanation:

x is the hypotenuse.

For the 54-deg angle, 22 is the opposite leg.

The trig ratio that relates the opposite leg to the hypotenuse is the sine.

In general:

sin A = opp/hyp

We have:

sin 54 = 22/x

x sin 54 = 22

x = 22/sin 54

x = 27.193

Answer: 27.2

A system of linear equations for line h and j are y = -3x/4 - 5 and y = -5x/4 + 1 respectively.

An equation for the exponential function graphed is \(f(x)=\frac{1}{3}^{x}\)

First of all, we would determine the slope of line h as follows;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 7)/(-8 + 16)

Slope (m) = -6/8

Slope (m) of line h = -3/4.

At data point (-8, 1) and a slope of -3/4, a linear equation in slope-intercept form for line h can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -3/4(x + 8)

y - 1 = -3x/4 - 6

y = -3x/4 - 5

At data point (-4, 6) and a slope of -5/4, a linear equation in slope-intercept form for line j can be calculated by using the point-slope form as follows:

y - 6 = -5/4(x + 4)

y - 6 = -5x/4 - 5

y = -5x/4 + 1

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

\(f(x) = a(b)^x\)

Since this exponential function passes through the points (0, 1) and (-1, 3), we have:

1 = ab⁰

1 = a

3 = a(b)⁻¹

3 = 1 × (b)⁻¹

3 = 1/b

b = 1/3

Therefore, the graphed exponential function is given by;

\(f(x) = a(b)^x\\\\f(x) = 3^{-x}\\\\f(x)=\frac{1}{3}^{x}\)

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Answer:

1:1 and 1:87

Step-by-step explanation:

Answer:

(-150, 45)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

My best guess from the graph is

(-150, 45)

The first five terms of the Maclaurin series are given as ϕ(x) = 1 + 3x + 6x² + 10x³ + 15x⁴+....

a) Maclaurin series is a special case of Taylor series expansion where we choose

x0 = 0.ϕ(x) = 1 - x1.

To find the first five terms of the Maclaurin series for ϕ(x), we need to expand the function as follows:

ϕ(x) = 1 - x

ϕ'(x) = -1

ϕ''(x) = 0

ϕ'''(x) = 0

ϕ''''(x) = 0

Therefore,

ϕ(x) = ∑(n=0)^∞ (ϕ^(n)(0)/n!) xⁿ

ϕ(0) = 1

ϕ'(0) = -1

ϕ''(0) = 0

ϕ'''(0) = 0

ϕ''''(0) = 0

So,

ϕ(x) = 1 - x + 0 + 0 + 0 + ...

Hence, the first five terms of the Maclaurin series for (b) are given as ϕ(x) = 1 + 3x + 6x² + 10x³ + 15x⁴ +

Therefore, we can find the Maclaurin series of a given function by finding its derivatives at x = 0 and substituting them in the general formula ∑(n=0)^∞ (ϕ^(n)(0)/n!) xⁿ.

The Maclaurin series provides a useful way to approximate a function using a polynomial of finite degrees.

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Answer:

c

Step-by-step explanation:  3 is not bigger than 9 so it can't bump it up so it stays like that.

Answer:

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example

You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).

Step-by-step explanation:

Answer:shrinking

Step-by-step explanation:

Answer:

bringing iron in

Step-by-step explanation:

hoped this helped let me know if it did

Answer: \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

Step-by-step explanation:

The given expression: \(\sqrt{\dfrac{16n}{m^3}}\)

'

since \(16=4^2\)

\(m^3=m^{2+1}= m^2\times m\)   [\(a^{n+m}=a^n\times a^m\)]

Now, the given expression becomes,

\(\sqrt{\dfrac{4^2n}{m^2\timesn}}=\dfrac{4\sqrt{n}}{m\sqrt{m}}\)

Since there is root in denominator , so we need to rationalize

\(\dfrac{4\sqrt{n}}{m\sqrt{m}}\times\dfrac{\sqrt{m}}{\sqrt{m}}=\dfrac{4\sqrt{mn}}{m\times\sqrt{m}\times\sqrt{m} }\\\\=\dfrac{4\sqrt{mn}}{m\times m}\\\\=\dfrac{4\sqrt{mn}}{m^2}\)

Hence, the correct option is \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

Answer:

What should be the indication on the magnetic compass as you roll into a standard rate turn to the left turn from an east heading into the northern hemisphere?

Step-by-step explanation:

Option 4 (x - y)(x + 1) is the invalid boolean expression among the options provided.

A boolean expression is an expression that can either be true or false. These expressions have variables, constants, and logical operators that determine their truth value based on the values assigned to the variables. Boolean expressions are commonly used in programming and logical operations.

Let's verify each option:

x': It is a valid boolean expression because it represents the negation of variable x.

x + y: It is a valid boolean expression because it represents the logical OR operation on variables x and y.

(x + y)(x + 1): It is a valid boolean expression because it represents the logical AND operation on (x + y) and (x + 1).

(x - y)(x + 1): It is an invalid boolean expression because it includes the subtraction operator, which is not a valid logical operator. Therefore, (x - y) is an invalid boolean expression, and the entire expression is invalid.

Option 4 (x - y)(x + 1) is the invalid boolean expression among the options provided.

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The double fact of the equation is 7+ 7 = 14.

What is a double fact equation?

A doubles fact is a number sentence that repeats the same addend, such as 3 + 3 = 6 or 8 + 8 = 16.

Here we have to find the double facts of the equation:

Equation:

7 + 7 = 14

When a number is added to itself the result is twice that number

Example:

2 + 2 = 2× 2 = 4

3 + 3 = 2× 3 = 6

5 + 5 = 2× 5 = 10

Similarly, we have to solve for 7+ 7 = 14

So,

7 + 7 = 14

In the same manner, we can also do that:

7 × 2 =  14

Hence, the double facts of the equation is 7+ 7 = 14.

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Answer:

The rate of change of a linear function is always the same.

The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.

The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.

Step-by-step explanation:

Vote brainiest

The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

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Answer:

8.03

Step-by-step explanation:

43 min = 3.75 miles

90 min = X

99 min×3.75÷42=8.03

The test statistic for the sample mean is given byz = (x - μ) / (σ / √n)Where,x = 49, μ = 50, σ = 15, n = 55z = (49 - 50) / (15 / √55)≈ -1.24 From the z-tables, we find that the area to the left of z = -1.24 is 0.1089. This implies that the p-value = 0.1089 > α = 0.01.

Given information Random sample of 55 second-gradersSample mean score is x=49The standard deviation of test scores is σ = 15The nationwide average score on this test is 50.The school superintendent wants to know whether the second-graders in her school district have weaker math skills than the nationwide average.Level of significance (α) = 0.01Null hypothesis (H0):

The average math score of second-graders in the school district is greater than or equal to the nationwide average math score.Alternative hypothesis (Ha): The average math score of second-graders in the school district is less than the nationwide average math score.The test statistic for the sample mean is given byz = (x - μ) / (σ / √n)Where,x = 49, μ = 50, σ = 15, n = 55z = (49 - 50) / (15 / √55)≈ -1.24 From the z-tables, we find that the area to the left of z = -1.24 is 0.1089. This implies that the p-value = 0.1089 > α = 0.01.Since the p-value is greater than the level of significance, we fail to reject the null hypothesis.

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Answer:

False

Step-by-step explanation:

When triangles are similar, their sides are proportional, not congruent.

I hope this helps :))

Answer:

h=5

Step-by-step explanation:

Let's solve your equation step-by-step.

5h−13=12

Step 1: Add 13 to both sides.

5h−13+13=12+13

5h=25

Step 2: Divide both sides by 5.

5h /5 = 25 /5

h=5

I this helps may I get brianliest?

Answer: h = 5

Step-by-step explanation: 5h + 13 = 12  -13 + 5h = 12  ( h ) 0 + 5h = 12+13 5h = 25 ~ 5

Answer:

Yeah I think you're correct I got the same

Step-by-step explanation:

750 mL is equivalent to 25.36 oz.

When measuring liquids, the metric system and the US customary system are commonly used. In the metric system, the standard unit of measurement for liquids is milliliters (mL) and in the US customary system, it's ounces (oz).

To convert between these units, you can use a conversion factor.

One way to convert mL to oz is to use the conversion factor of 1 oz = 29.5735 mL. To find the number of ounces in 750 mL, you can use this conversion factor to set up an equation:

750 mL = x oz

Where x is the number of ounces you want to find. To solve for x, you can divide both sides of the equation by the conversion factor:

x = 750 mL / 29.5735 mL/oz

x = 25.36 oz

It's important to note that this is an approximation and for more accurate measurements, you should use an online calculator or consult a chart.

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Answer:

x = -0.24 or 3.73

Step-by-step explanation:

\(\frac{-b + \sqrt{b^{2} -4ac } }{2a}\) (There's supposed to be a ± between '-b' and the square root)

\(x^{2}\) + 4x + 1 ( \(ax^{2} + bx + c\) )

a = -1 ( there's no number before \(x^{2}\) so its 1 )

b = 4

c = 1

Substitute into the quadratic equation.

\(\frac{-4 + \sqrt{4^{2} -4x1x-1 } }{2x-1}\) ( the \(x\) is just the multiplication sign )

=  \(\frac{-4 + \sqrt{{16} +4 } }{-2}\)

\(\frac{-4 + \sqrt{{20} } }{-2}\) = -0.24    [OR]     \(\frac{-4 - \sqrt{{20} } }{-2}\) = 3.73

( The answers are to 2 decimal places )

Answer:

Option (C)

Step-by-step explanation:

This question is incomplete; here is the complete question.

Morris is showing his work in simplifying,

(-6.7 + 4.3) - 1.2

Step 1: (4.3 - 6.7) - 1.2

Step 2: 4.3 - (6.7 + 1.2)

Step 3: 4.3 - 7.9

Step 4: -3.6

Which statement is true ?

A). Step 1, Morris used the commutative property.

B). Step 2, Morris used the distributive property.

C). Step 3, Morris used the associative property.

D). Step 4, Morris's answer is incorrect.

In associative property,

a + (b + c) = (a + b) + c

By this property,

(-6.7 + 4.3) - 1.2

Step 1, (-6.7 + 4.3) - 1.2 = (4.3 - 6.7) - 1.2

Step 2, (4.3 - 6.7) - 1.2 = 4.3 - (6.7 + 1.2) [Use of associative property]

Step 3, 4.3 - 7.9

Step 4, -3.6

Answer:

dont really know buy im thinking its A.

Step-by-step explanation:

hope this helps somewhat

Answer:

The answer would be 64%

Step-by-step explanation:

The concept used here is the fundamental concept is that someone will nearly surely occur. Meaning (favorable event/ total event)

Step 1: There are 25 total marbles because.

2+4+10+9=25

Step 2: Subtract the favorable event from the whole.

25/25-9/25= 16/25

Step 3: Rewrite as a percentage

1.00-0.36=

0.64

Step 4: Answer

64%