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3 years ago

Determine the equation of the inverse of y=1/4x^3-2

Mathematics

1 answer:

dedylja [7]3 years ago

7 0

Answer

y⁻¹ = ∛(4x+8)

Explanation

y=(1/4)x³ - 2.

To find the inverse of this equation, you first make x the subject of the formular.

y=(1/4)x³ - 2

Multiply both sides by 4;

4y = x³ - 8

Add 8 on both sides of the equation;

4y + 8 = x³

x³ = 4y + 8

Apply the cube root on both sides to get the value of x;

x = ∛(4y+8)

The inverse of y=(1/4)x³ - 2 is;

y⁻¹ = ∛(4x+8)

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At the base of a pyramid, a surveyor determines that the angle of elevation to the top is °. At a point meters from the base, th

riadik2000 [5.3K]

Answer:

$\frac{(\sin 18^\circ)}{75} = \frac{(\sin 35^\circ)}{x}$

Step-by-step explanation:

Incomplete question:

$\angle CBD = 53^\circ$

$\angle CAB = 35^\circ$

$AB = 75$

See attachment for complete question

Required

Determine the equation to find x

First, is to complete the angles of the triangle (ABC and ACB)

$\angle ABC + \angle CBD = 180$ --- angle on a straight line

$\angle ABC + 53= 180$

Collect like terms

$\angle ABC =- 53+ 180$

$\angle ABC =127^\circ$

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Collect like terms

$\angle ACB =- 127 - 35 + 180$

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Apply sine rule

$\frac{\sin A}{a} = \frac{\sin B}{b}$

In this case:

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Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance

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Answer:

i. When the temperature is above $616.712^{o}$ F, it changes to gas.

ii. When the temperature is below $-33.052^{o}$ F, it changes to solid.

Step-by-step explanation:

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Temperature scale of a given substance can be either in Celsius, Fahrenheit or Kelvin. And conversion from one scale to another can be achieved. Example, Celsius scale can be converted to Fahrenheit by:

F = $\frac{9}{5}$ θ + 32

where: F is the equivalent temperature in Fahrenheit, θ is the value of temperature in degree Celsius.

Given that: melting point of the substance = $-36.14^{o}$ C

⇒ F = $\frac{9}{5}$ x $-36.14^{o}$ + 32

= $-33.052^{o}$ F

The boiling point = $324.84^{o}$ C

F = $\frac{9}{5}$ x $324.84^{o}$ + 32

= $616.712^{o}$ F

The melting point of the substance is $-33.052^{o}$ F, and boiling point is $616.712^{o}$ F.

Therefore, the range of temperatures for which the substance is not in a liquid state are:

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ii. When the temperature is below $-33.052^{o}$ F, it changes to solid.

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dolphi86 [110]

Answer:

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