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3 years ago

Solve for all solutions of the equation: x^3 - 8 = 0

Mathematics

1 answer:

djyliett [7]3 years ago

8 0

Answer:

x=2

Step-by-step explanation:

x^3=8

x=2 (take the cubed root of both sides)

This can be solved by adding 8 to both sides, then taking the cubed root of both sides

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A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses

mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for $x$ days.

So, for $x$ days the total expense = $360

Thus the daily expense in dollars can be given by = $\frac{360}{x}$

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

Tour duration now = $(x+4)$ days

On extension, his daily expense is cut by $3

New daily expense in dollars = $(\frac{360}{x}-3)$

Total expense in dollars can now be given as: $(x+4)(\frac{360}{x}-3)$

Simplifying by using distribution (FOIL).

$(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))$

$360-3x+\frac{1440}{x}-12$

$348-3x+\frac{1440}{x}$

We know total expense remains the same which is = $360.

So, we have the equation as:

$348-3x+\frac{1440}{x}=360$

Multiplying each term with $x$ to remove fractions.

$348x-3x^2+1440=360x$

Subtracting $348x$ both sides

$348x-348x-3x^2+1440=360x-348x$

$-3x^2+1440=12x$

Dividing each term with -3.

$\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}$

$x^2-480=-4x$

Adding $4x$ both sides.

$x^2+4x-480=-4x+4x$

$x^2+4x-480=0$

Solving using quadratic formula.

For a quadratic equation: $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values from the equation we got.

$x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}$

$x=\frac{-4\pm\sqrt{16+1920}}{2}$

$x=\frac{-4\pm\sqrt{1936}}{2}$

$x=\frac{-4\pm44}{2}$

So, we have

$x=\frac{-4+44}{2}$ and $x=\frac{-4-44}{2}$

$x=\frac{40}{2}$ and $x=\frac{-48}{2}$

∴ $x=20$ and $x=-24$

Since number of days cannot be negative, so we take $x=20$ as the solution for the equation.

Thus, the original duration of the tour = 20 days

6 0

3 years ago

What is 6% of 1 trillion dollars written in expanded form?

Otrada [13]

Im think the answer is: 60000000000

6 0

3 years ago

Which of the following correlation coefficients would generate the most benefit in terms of risk reduction for a 2-asset portfol

mart [117]

Answer:

Asset B generate most benefit.

Step-by-step explanation:

Correlation shows the strength of relation between two variables.

Greater the correlation coefficient greater the strength between two variables.

Since here It is given that Correlation Coefficient between risk reduction and Asset B is higher (i.e. 60%) than the Correlation Coefficient between risk reduction and Asset A (i.e. 40%).

Thus, Asset B generate most benefit.

8 0

3 years ago

The average cost of a compact car at a certain dealership over the last ten years has ranged from $14,000 to $18,500. Suppose yo

mezya [45]

Answer:

Part (A): The scale of y: 1 interval being equal to 500 units and from 14,000 to 18,500.

Part (B): The good interval to use for the y-axis should be 1 to 10.

Step-by-step explanation:

Consider the provided information.

As we know the X axis represents the independent variable, since years are the independent variable. So, X axis represents the years.

Y axis represents the dependent variable, since average cost is dependent variable. So, Y axis represents the average cost.

Part (A) what is a good scale to use for the y-axis?

It is given that range is from $14,000 to $18,500.

So, 1 interval being equal to 500 units, so that it will suitable for 18,500.

The scale of y should be 14,000 to 18,500 as 14,000 is the starting average cost and 18,500 is the last average cost.

Part (b) what is a good interval to use for the y-axis?

The scale for x should be 1 year. As It should start from 1 to 10.

The good interval to use for the y-axis should be 1 to 10.

The required scale is shown in figure,

8 0

3 years ago

Find general solution of 3sinx=2tanx

AveGali [126]

Step-by-step explanation:

remember, tan = sin/cos.

of course, one solution is x = 0. sin(0) = 0, tan(0)=0).

for the general solution we look at x <> 0.

3×sin(x) = 2×tan(x) = 2×sin(x)/cos(x)

3 = 2/cos(x)

3×cos(x) = 2

cos(x) = 2/3

x = 48.1896851...°

6 0

2 years ago