Algebra

A square mile is an area measurement, not a specific shape. They could be just about anything, as long as they multiply together to make one square mile.

1 mile by 1 mile is a square mile. Two miles by half a mile is a square mile. 1 foot by 5280 miles is a square mile. This means that 8 square miles can be 2 miles by 4 miles or 1 mile by 8 miles.

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To find the equation of a line in slope-intercept form (y = mx + b) that is parallel to the line ( y = 2x + 6 ), we need to use the same slope, which is 2. Using the point (4, -4) to find the y-intercept ( b ), we substitute into the equation:

(-4 = 2(4) + b )

This simplifies to (-4 = 8 + b), so ( b = -12 ). Therefore, the equation of the parallel line is ( y = 2x - 12 ).

Horizontal change refers to the difference in the horizontal position of a point or object, often measured along the x-axis in a coordinate system. It can be calculated by subtracting the initial x-coordinate from the final x-coordinate. This concept is commonly used in mathematics, physics, and engineering to analyze motion, graph functions, or assess distances in a two-dimensional space.

The independent variable is the temperature. In experiments or studies examining the relationship between temperature and pressure, temperature is typically manipulated to observe how it affects pressure, which is the dependent variable. This allows researchers to understand how changes in temperature influence pressure in a given system.

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The goal in solving equations is to find the value(s) of the variable(s) that make the equation true. This involves manipulating the equation through various algebraic techniques to isolate the variable on one side. Ultimately, solving the equation allows us to understand relationships between quantities and to make predictions based on those relationships.

a2 + 62 = 122

a2 + 62 - 62 = 122 - 62

a2 = 144 - 36

a2 = 108

taking the square root of each side, we get a equal plus or minus the square root of 108, or plus or minus 6 times the square root of 3.

f(x) = (1 - x^(2) ^(1/2)

Let y= (1 - x^(2)) ^(1/2)

Use Chain Rule

dy/dx = dy/du X du/dx

Let u = 1 - x^(2)

Hence y = u^(1/2)

dy/du = (1/2)u^(-1/2)

du/dx = -2x

Hence

dy/dx = dy/du X du/dx = (1/2)u^(-1/2) X ( -2x)

dy/dx = (1/2)u( 1 -x^(2)^(-1/2) X ( -2x)

Tidying up

dy/dx = (-2x/(2(1 - x^(2))^(1/2))

dy/dx = -x/ [(1 - x^(2)]^(1/2)

f(x) = 3x4 - 2x2 + 7

The function

f'(x) = 12x^(3) - 4x

!st Derivative

f''(x) = 36x - 4

2nd derivative. The answer!!!!!

The expression ( y = ax - h + k ) represents a linear equation in slope-intercept form, where ( a ) is the slope, ( -h ) is a horizontal shift, and ( k ) is a vertical shift. The term ( h ) adjusts the x-coordinate of the graph, moving it left or right, while ( k ) adjusts the y-coordinate, moving it up or down. Overall, this equation describes how a line can be transformed from its standard position based on shifts and slope.

The equation ( y = x - 11 ) is in slope-intercept form ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Here, the slope ( m ) is 1, and the y-intercept ( b ) is -11. This means the line rises one unit for every unit it moves to the right, and it crosses the y-axis at the point (0, -11).

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A fractional exponent means the 'root'.

e.g. Square Root (4) = 4^(1/2) = 2

Cube root (8) = 8^(1/3) = 2

Fourth Root (16) = 16^(1/4) = 2

When you have something like

4^(3/2) split it up into (4^(1/2))^(3) =

[2]^(3) =>

8 The answer!!!!!

The rule being [a^(n)]^(m) = a^(nm)

2 ^(1/3) = 125992105.....

(1/216)^(1/3) = 1/6

216^(1/3) = 6

Remember Sin( angle) = opposite / hypotenuse.

Hence

Sin(A) = 30/90

Cancel down by '30'0

Sin(A) = 1/3 = 0.333333.....

A = Sin^(-1) 0.33333.....

A = 19.47122063..... degrees.

NB Careful with your triangle labelling.

Angles are always shown with a CAPITAL letter. 'A'.

The side opposite to the given angle is small/lower case of the same letter 'a'.

Similarly , ;B; & 'b; and 'C' & 'c'.

Sin(Angle) = 0.6329

Tale the ArcSin

Angle - Sin^(-1) 0.6329

Angle = 39.2644.... degrees.

A = pi r^(2)

and 2r = d

Substituting

8pi = pi r^(2)

Cancel down by 'pi'

8 = r^(2) r = 2sqrt(2)

So 2r = d = 2(2sqrt(2) = 4sqrt(2). The answer !!!!

Numerically 4sqrt(2) = 5.656.... units of length .

A(cic) = pi r^(2)

Where 'r' is the radius.

NB The diameter is two radii long .

So with a diameter of 30 meters , the radius is 15 m.

pi = 3.141592....

Substituting

A = pi 15m^(2)

Hence

A = 3.141592... 225 m^(2)

A = 706.858... m^(2) .

At point X on the planet, a full rotation on its axis would result in a complete cycle of day and night. As the planet turns, point X would experience sunlight when it is facing the star or sun and darkness during the side that faces away. This rotation typically takes about 24 hours, leading to changes in temperature and environmental conditions as it transitions from day to night. Depending on the planet's axial tilt, there may also be variations in the intensity and duration of sunlight received at point X throughout the year.

The metacorpus, a part of the human brain, is primarily involved in the integration and processing of sensory information, particularly in relation to motor control and coordination. It plays a crucial role in fine-tuning motor functions and supporting complex movements. Additionally, the metacorpus contributes to cognitive functions, such as decision-making and problem-solving, by facilitating communication between different brain regions.

It seems there might be a typo in the equation you've provided for the circle. A standard equation for a circle is usually in the form ((x - h)^2 + (y - k)^2 = r^2). If you clarify the correct equation of the circle, I can help determine which point lies outside of it. Please provide the full equation or more context.