If a circle has a circumference of 40.82cm what would the diameter be show working out

Answer:

c)  124.96

Step-by-step explanation:

Geometric series:  100 + 20 + ... + 0.16

First we need to find which term 0.16 is.

General form of a geometric sequence: \(a_n=ar^{n-1}\)

(where a is the first term and r is the common ratio)

To find the common ratio r, divide one term by the previous term:

\(\implies r=\dfrac{a_2}{a_1}=\dfrac{20}{100}=0.2\)

Therefore, \(a_n=100(0.2)^{n-1}\)

Substitute \(a_n=0.16\) into the equation and solve for n:

\(\implies 100(0.2)^{n-1}=0.16\)

\(\implies (0.2)^{n-1}=0.0016\)

\(\implies \ln(0.2)^{n-1}=\ln0.0016\)

\(\implies (n-1)\ln(0.2)=\ln0.0016\)

\(\implies n-1=\dfrac{\ln0.0016}{\ln(0.2)}\)

\(\implies n=\dfrac{\ln0.0016}{\ln(0.2)}+1\)

\(\implies n=5\)

Therefore, we need to find the sum of the first 5 terms.

Sum of the first n terms of a geometric series:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

Therefore, sum of the first 5 terms:

\(\implies S_5=\dfrac{100(1-0.2^5)}{1-0.2}\)

\(\implies S_5=124.96\)

The point on the curve y = 3x² - 2x where the slope of the tangent line is -267 is (-9,423).

To find the point on the curve where the slope of the tangent line is -267, we need to differentiate the equation y = 3x² - 2x with respect to x to find the derivative. Taking the derivative, we have dy/dx = 6x - 2.

Setting the derivative equal to -267, we can solve for x:

6x - 2 = -267

6x = -265

x = -265/6

x ≈ -44.17

Now that we have the x-coordinate, we can substitute it back into the original equation to find the corresponding y-coordinate:

y = 3(-44.17)² - 2(-44.17)

y ≈ 19527.19

Therefore, the point on the curve y = 3x² - 2x where the slope of the tangent line is -267 is approximately (-44.17, 19527.19).

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In a normal distribution, the mean represents the center of the distribution and the standard deviation represents the spread of the distribution.

The higher the standard deviation, the more spread out the data is. The probability of a specific outcome occurring is given by the area under the curve of the normal distribution that corresponds to that outcome.

For example, if we wanted to find the probability of x being between 45 and 55, we would find the area under the normal curve between those two values. This can be done using a table of standard normal probabilities or by using a calculator or statistical software.

In general, if we know the mean and standard deviation of a normally distributed random variable, we can use that information to find probabilities for specific outcomes or ranges of outcomes.

you'll need to provide a specific range or value of X. Once you have that, you can use the Z-score formula or a standard normal distribution table to determine the probability.

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From the figure shown we notice that the angles 127° and 2 are supplementary, that means that:

We also notice that

and

furthermore

And

so we have the system of equations:

Solving for the angle 1 in the fourth equation we have

plugging this value in the second equation we have

Plugging this value in the third equation we have

The inverse sine function \(sin^{(-1)}(z)\) is shown to be a multiple-valued function given by \(sin^{(-1)}(z) = -i log[iz + (1 - z^2)^{(1/2)}]\). The multiple values of \(sin^{(-1)}(z)\) can be obtained by choosing a branch of the square root and a suitable branch of the logarithm. The derivative of sin^(-1)(z) is also derived using the chain rule and is given by \(dz/d(sin^{(-1)}(z)) = (1 - z^2)^(1/2)\) / (z ≠ ±1).

To derive the expression for \(sin^{(-1)}(z)\), we start with the equation z = sin(w), which can be written as \(z = (1/2i)(e^{(iw)} - e^{(-iw)})\). Rearranging, we have \(e^{(2iw)} - 2ize^{(iw)} - 1 = 0\)

By applying the quadratic formula, we can solve for e^(iw) and obtain \(e^{(iw)} = iz + (1 - z^2)^{(1/2)}\), where the square root is two-valued.

Taking logarithms on both sides, we have \(iw = log[iz + (1 - z^2)^{(1/2)}]\). Multiplying by -i, we obtain \(w = -i log[iz + (1 - z^2)^{(1/2)}]\), which represents the multiple values of \(sin^{(-1)}(z)\).

To obtain a specific branch of \(sin^{(-1)}(z)\), we need to choose a branch of the square root and a suitable branch of the logarithm. This allows us to define different values of \(sin^{(-1)}(z)\) based on the chosen branches.

The derivative of \(sin^{(-1)}(z)\) can be found using the chain rule. It is given by\(dz/d(sin^{(-1)}(z)) = (1 - z^2)^(1/2) /\) (z ≠ ±1), where the choice of the square root on the right must match the branch of sin^(-1)(z) used.

In conclusion, \(sin^{(-1)}(z)\) is a multiple-valued function obtained by selecting appropriate branches of the square root and logarithm. The derivative of \(sin^{(-1)}(z)\) is derived, providing the rate of change of \(sin^{(-1)}(z)\) with respect to z.

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No, multiplying by 10x10x10 is not the same as multiplying by 10 factors of 3.

Multiplying by 10x10x10 is not equivalent to multiplying by 10 factors of 3. When you multiply a number by 10, you're essentially adding a zero to the end of it, shifting all the digits one place to the left. So, multiplying by 10 three times (10x10x10) adds three zeros to the original number. However, when you multiply by 10 factors of 3, you are essentially multiplying the number by 3 ten times consecutively. This results in a different outcome.

For instance, if you start with the number 5 and multiply by 10x10x10, you would get 5,000. On the other hand, multiplying by 10 factors of 3 would yield a much larger number, 59,049, because each multiplication by 3 amplifies the result. Therefore, the two operations are not equivalent.

Therefore, multiplying by 10x10x10 and multiplying by 10 factors of 3 yield different outcomes. The former adds three zeros to the original number, while the latter multiplies the number by 3 repeatedly, resulting in a much larger value. It's crucial to understand the distinction between these operations to avoid confusion and accurately calculate mathematical expressions.

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Answer: Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42. I don’t know the second

Step-by-step explanation:

Answer:

64°

Step-by-step explanation:

Both triangles represent a right angle by the small box in the angle.

Right angles = 90°

Since the triangles are congruent, then they would have the same measurements in their angles an sides. All triangles also have a sum of 180°. So, we can just subtract (26 + 90) from 180 to get the third angle.

180 - (26 + 90)

180 - 116

64

So, the m∠KLM is 64°.

Answer:-60

Step-by-step explanation:

El area del rectangulo es 11/3 m²

Longitud = 15/6 m

Ancho=22/15 m

Área = Largo × Ancho

= 15/6 × 22/15

= 22/6

= 11/3 m²

Un rectángulo es una forma plana bidimensional que tiene dos pares de lados paralelos que son paralelos y de la misma longitud, y consta de cuatro ángulos rectos o 90⁰. Esta forma plana también tiene líneas diagonales que tienen la misma longitud.

Para comprender mejor las características de los rectángulos y poder explicar las diferencias con otras formas, es importante que los estudiantes conozcan las propiedades de los rectángulos.

Las propiedades de un rectángulo:

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The y-intercept is 5.5 inches, which is the initial height of the plant before it started growing.

We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, to solve the problem.

Since the plant is growing at a constant rate of 1.4 inches per day, the slope of the line that represents its growth is 1.4.

Let y be the height of the plant after x days. We know that the plant was 5.5 inches tall on day 0, so we have the point (0, 5.5) on the line.

Using the point-slope form of a linear equation, we get:

y - 5.5 = 1.4x

Simplifying, we get:

y = 1.4x + 5.5

Comparing the equation to the slope-intercept form, we see that the y-intercept is 5.5.

Therefore, the y-intercept is 5.5 inches.

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The actual height of the tower is 160 feet.

Given that, a scale model of a tower is 24 inches.

The scale is 1.5 inches:10 feet.

We know that, 1 foot = 12 inches

So, the scale 1.5 inches : 120 inches.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

1.5/120 = 24/The actual height of the tower

1.5×The actual height of the tower = 24×120

The actual height of the tower=2880/1.5

= 1920 inches

In feet = 1920/12

= 160 feet

Therefore, the actual height of the tower is 160 feet.

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Answer:

u = 4

Step-by-step explanation:

32 = 5u + 3u = 8u ( divide both sides by 8 )

4 = u

Step-by-step explanation:

u=4 after you add or combine like terms , you then divide both sides by the same factor

Answer:

Step-by-step explanation:

The answer is B, if we were to plug all the values of x with its corresponding value of y into the equation, everything matches up

Hope that helps

Answer:

Step-by-step explanation:

\(y=-x^2+4x+5\quad \implies\quad a=-1\,,\ b=4\,,\ c=5\\\\h=\dfrac{-b}{2a}=\dfrac{-4}{2(-1)}=2\\\\k=c-\dfrac{b^2}{4a}=5-\dfrac{4^2}{4(-1)}=5-\dfrac{16}{-4}=5+4=9\)

Or by completing the square:

\(y=-x^2+4x+5\\\\y=-(x^2-4x)+5\\\\y=-(\underline{x^2-2\cdot x\cdot 2+2^2}-2^2)+5\\\\y=-\left((x-2)^2-4\right)+5\\\\y=-(x-2)^2+4+5\\\\y=-(x-2)^2+9\quad\implies\quad h=2\,,\ k=9\)

Answer:

slope = 4

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (1, 4 ) ← 2 points on the line

m = \(\frac{4-0}{1-0}\) = \(\frac{4}{1}\) = 4

Answer:

60

Step-by-step explanation:

Tangents to a circle from a common external point are congruent, thus

JA = JB = 6

AL = KC = 11

CK = KB = 13

Thus

perimeter = 2(6) + 2(11) + 2(13) = 12 + 22 + 26 = 60

The perimeter of a triangle JKL is 60 units. Therefore, option D is the correct answer.

A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet. The lengths of tangents drawn from an external point to a circle are equal.

Given that,

Given that, JK, KL and LJ are all tangent to O. JA=6, AL=11 and CK=13.

In the figure,

From the external point J, tangents JA=JB

JB=6

From the external point L, tangents AL=LC

LC=11

From the external point K, tangents KB=KC

BK=13

So, JL=JA+LA

JL=6+11=17

LK=LC+CK

= 11+13

= 24

JK=JB+KB

= 6+13

= 19

Now, the perimeter is JL+LK+JK

= 17+24+19

= 60 units

Therefore, option D is the correct answer.

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Answer:

19.0064

Step-by-step explanation:

Answer:

1=8

2=25

3=isosceles

4=no traingle can be formed

Answer:

3 1/2

3 whole trapezoids and half trapezoid

Answer:

Your answer is on

g o o g l e

Answer:

X=4

Step-by-step explanation:

3x-2y=8

x+y=6

multiply second equation by 2 so you can eliminate y

2(x+y)=2(6)

2x+2y=12

now add two equations together

first equation:                          3x-2y=8

modified second equation     2x+2y=12

added together eliminates y. 5x+0=20

                                                   X=4

Answer:

.

Step-by-step explanation:

Answer: 46.619 units.

Step-by-step explanation:

To find the length of the spiraling polar curve, we need to use the formula:

L = int_a^b sqrt[r^2 + (dr/d\theta)^2] d\theta

where r is the polar curve, dr/d\theta is its derivative with respect to theta, and a and b are the limits of integration.

In this case, we have:

r = 7 e^{4 \theta}

dr/d\theta = 28 e^{4 \theta}

And the limits of integration are a = 0 and b = 2\pi.

Substituting these into the formula, we get:

L = int_0^(2\pi) sqrt[(7e^{4\theta})^2 + (28e^{4\theta})^2] d\theta

Simplifying this expression using algebra, we get:

L = int_0^(2\pi) 7e^{4\theta} sqrt[1 + 16e^{8\theta}] d\theta

This integral cannot be solved analytically, so we need to use numerical methods to approximate its value. One way to do this is to use a numerical integration technique such as the trapezoidal rule or Simpson's rule.

Using Simpson's rule with a step size of h = \pi/1000, we get:

L \approx 46.619

Therefore, the length of the spiraling polar curve r = 7 e^{4 \theta} from 0 to 2 \pi is approximately 46.619 units.

Answer:

I think it would be Maxine's, since they did more tests.

Answer:o * + = 1

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

A trapezoid only has one pair and parallelogram need two pair.

Answer:

no

Step-by-step explanation:

no because a parallelogram must have at least two opposite parallel lines

A trapezoid only has one

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Answer:

9

Let's view the list of factors 36 and 45 have, starting with 36

4 × 9 = 36

5 × 9 = 45

That said, the greatest common factor of 36 and 45 is 9

Given: diameter of 8m , depth is 1.4m and water is pumped into pool at a rate of 19 meter cube.

Find: number of hours to fil the pool.

Explanation: the formula for the volume of a cylinder is

the problem gives d=8m , so r=4m

the pool holds

At a rate of 19 meter cube per hour :

Final answer: the required answer is 3.7018 hr

The number of cup of butter used to make 20 is 15.

What is simplification?

Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner. Making something simpler is making it less complex.

Given,

3 cups of butter = 4 batches

for 1 batch the cup of butter = 3/4

for 20 batch, the cup of butter = 3(20)/4

= 3*5

=15

Therefore, 15 cups of butter used.

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