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3 years ago

What is the diameter of circle T?

Mathematics

1 answer:

Ratling [72]3 years ago

5 0

Answer:

$Diameter = 16$

Step-by-step explanation:

Given

$\theta = 72$

$Sector = \frac{64}{5}\pi$

Required

Calculate the diameter

The area of a sector is:

$Area = \frac{\theta}{360} * \pi r^2$

Substitute values for Area and $\theta$

$\frac{64}{5}\pi = \frac{72}{360} * \pi r^2$

Divide both sides by $\pi$

$\frac{64}{5} = \frac{72}{360} * r^2$

Make $r^2$ the subject

$\frac{64*360}{5*72} = r^2$

$\frac{64*360}{360} = r^2$

$64 = r^2$

Take positive square roots of both sides

$\sqrt{64} = r$

$8 = r$

$r = 8$

The diameter is then calculated as:

$Diameter = 2r$

$Diameter = 2*8$

$Diameter = 16$

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GREYUIT [131]

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3 years ago

Find the remainder when x^5 - 3x^3 + x - 5 is divided by x - 2

Viktor [21]

Given info:- Find the remainder when x^5 - 3x^3 + x - 5 is divided by x - 2

Solution:-

Given,

p(x) = x^5 - 3x^3 + x - 5 , g(x) = x - 2

Let g(x) = x-2 will be the factor of p(x) if p(2) = 0.

Now, p(x) = x^5 - 3x^3 + x - 5

p(2) = (2)^5 - 3(2)^3 + 2 - 5

= (2*2*2*2*2) - 3(2*2*2) + 3 - 5

= 32 - 3(8) + 3 - 5

= 32 - 24 + 3 - 5

= 31 - 24 - 2

= 31 - 26

= 5 Remainder.

Hence, when x^5 - 3x^3 + x - 5 is divided by x - 2 , we get the remainder as 5.

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3 years ago

if a sacretary types 55 words in one minute how long will it take the secretary to type a 2000 word report

Delvig [45]

Answer:

37 minutes

Step-by-step explanation:

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3 years ago

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NNADVOKAT [17]

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Step-by-step explanation:

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3 years ago

Read 2 more answers

MAT 171

steposvetlana [31]

Using the Factor Theorem, the polynomials are given as follows:

1. $P(x) = x^5 + 2x^4 - 7x^3 + x^2$

2. $P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)$

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

Item a:

The parameters are:

$a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4$

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

$P(x) = x^5 + 2x^4 - 7x^3 + x^2$

Item b:

The roots are:

$x_1 = x_2 = 4, x_3 = 0, x_4 = -4$

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

$P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)$

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

$P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)$

Item 3:

The roots are:

$x_1 = x_2 = 3, x_3 = -2$

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

More can be learned about the Factor Theorem at brainly.com/question/24380382

#SPJ1

5 0

2 years ago