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3 years ago

Can someone help me answer these?

Mathematics

1 answer:

Romashka [77]3 years ago

4 0

Answer:

The Answer is as below:

Step-by-step explanation:

x y = 3x + x y = 2x - 3 + x

3 12 6

2 8 3

1 4 0

0 0 -3

-1 -4 -6

-2 -8 -9

-3 -12 -12

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An approximate solution to an equation is found using this iterative process.

mihalych1998 [28]

Answer:

a) i) -0.5

ii) -0.28125

b) -0.254102 (6 d.p.)

Step-by-step explanation:

Given iteration formula:

$x_{n+1}=\dfrac{\left(x_n\right)^3-1}{4} \quad \textsf{and} \quad x_1=-1$

Part (a)(i)

Substitute the value of x₁ into the formula and solve for x₂ :

$\begin{aligned}\implies x_2 & =\dfrac{\left(x_1\right)^3-1}{4}\\\\& =\dfrac{\left(-1\right)^3-1}{4}\\\\ & = \dfrac{-1-1}{4}\\\\ & = \dfrac{-2}{4}\\\\ & = -0.5\end{aligned}$

Part (a)(ii)

Substitute the value of x₂ into the formula and solve for x₃ :

$\begin{aligned}\implies x_3 & =\dfrac{\left(x_2\right)^3-1}{4}\\\\& =\dfrac{\left(-0.5\right)^3-1}{4}\\\\ & = \dfrac{-0.125-1}{4}\\\\ & = \dfrac{-1.125}{4}\\\\ & = -0.28125\end{aligned}$

Part (b)

To find the solution to 6 decimal places, keep substituting each new value into the iteration formula until the answers are the same when rounded to the required level of accuracy.

$\implies x_4=-0.2555618286...$

$\implies x_5=-0.2541728038...$

$\implies x_6=-0.2541051331...$

$\implies x_7=-0.2541018552...=-0.254102\:\: \sf (6 \:d.p.)$

$\implies x_8=-0.2541016964...=-0.254102\:\: \sf (6 \:d.p.)$

$\implies x_9=-0.2541016888...=-0.254102\:\: \sf (6 \:d.p.)$

Therefore, the solution is -0.254102 (6 d.p.).

7 0

2 years ago

Enter the amplitude of the function f(x) . f(x) = 5 sin x

mariarad [96]

Answer:

Step-by-step explanation:

The amplitude is the distance from the highest to lowest points divided that by 2.

Or the simpliest way when given the function

f(x) = A sin(x)

Where A is the amplitude

6 0

4 years ago

[TON OF POINTS] [3 QUESTIONS - Easy money :)]

kherson [118]

The correct answers are:

1/6πd³;
3; and
9 cm.

Explanation:

For the first question:

The formula for the volume of a sphere is:

$V=\frac{4}{3}\pi r^3$

We have the diameter, not the radius. The diameter is twice as much as the radius; this means to find the radius using the diameter, we divide by 2. This gives us:

$V=\frac{4}{3}\pi (\frac{d}{2})^3$

When we raise a fraction to a power, we raise both the numerator and the denominator to that power. This gives us:

$V=\frac{4}{3}\pi(\frac{d^3}{2^3})
\\
\\=\frac{4}{3}\pi(\frac{d^3}{8})$

We start multiplying this:
$V=\frac{4\pi}{3}(\frac{d^3}{8})
\\
\\=\frac{4\pi d^3}{3\times 8}
\\
\\=\frac{4\pi d^3}{24}
\\
\\=\frac{4}{24}\pi d^3
\\
\\=\frac{1}{6}\pi d^3$

For the second question:

The planes of symmetry are the planes through which we can fold the figure in half. These are in the middle horizontally through the figure; in the middle vertically (through the width) through the figure; and in the middle vertically (through the length) through the figure. This makes 3.

For the third question:

The formula for the volume of a triangular prism is:

$V=\frac{1}{3}(\frac{1}{2}bh)H$ ,

where b is the base of the triangular base of the pyramid, h is the height of the triangular base of the pyramid, and H is the height of the pyramid.

We know the volume is 90; the base of the triangle is 12 and the height is 5:

$90 = \frac{1}{3}(\frac{1}{2}\times 12\times 5)H
\\
\\90 = \frac{1}{3}(\frac{1}{2}\times 60)H
\\
\\90 = \frac{1}{3}(30)H
\\
\\90 = 10H$

We divide both sides by 10:

90/10 = 10H/10
9 = H

4 0

4 years ago

What is the smallest number to be subtracted from 1860 to get a perfect square.

faltersainse [42]

Answer:

So 11 must be subtracted to get a perfect square. The square root of 3 is starts with 1.7, so the square root of 300 will start with 17. So indeed 289=300–11 is the largest square number smaller than 300, so 11 is the smallest number we can subtract from 300 to make it a square.

Step-by-step explanation:

3 0

3 years ago

5x - 4y = 19 x + 2y = 8

klemol [59]

Answer:

(5x-4y)=19

5×19-4×19

95-76

Step-by-step explanation:

x+2y=8

x=8-2

x=6

7 0

3 years ago