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2 years ago

What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.

Mathematics

2 answers:

myrzilka [38]2 years ago

4 0

I hope this helps you

babymother [125]2 years ago

3 0

We can use t=x^2 to solve this
Once we do that we will have simple square equation which we know how to solve.

t^2 + 3t + 2 = 0

t1 = -1
t2 = -2

x1 = √-1 = i
x2 = -i

x3 = √-2 = i√2
x4 = -i√2

Make sure you know that i^2 = -1 and (-i)^2 = -1 which gives us solutions we got...

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Cube-shaped blocks are packed into a cube-shaped storage container. The edge length of the storage container is 212 feet. The

igor_vitrenko [27]

Answer:

The volume of cube-shaped block is 0.125 cubic feet.

Step-by-step explanation:

We are given the following in the question:

Edge length of storage container =

$2\dfrac{1}{2}\text{ feet}$

Edge length of block =

$\dfrac{1}{5}\times \text{Edge length of container}$

Putting value we get,

Edge length of block =

$\dfrac{1}{5}\times 2\dfrac{1}{2}\\\\=\dfrac{1}{5}\times \dfrac{5}{2}\\\\=\dfrac{1}{2}\text{ feet}$

Volume of cube-shaped block = Volume of cube

$V = \text{(Edge)}^3\\\\V =(\dfrac{1}{2})^3\\\\V = \dfrac{1}{8}\text{ cubic feet}\\\\V = 0.125\text{ cubic feet}$

Thus, the volume of cube-shaped block is 0.125 cubic feet.

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2 years ago

Danica is in the observation area of the sears tower in chicago overlooking lake michigan. She sights two sailboats going due ea

inessss [21]

Answer:

The boats are far apart by 4506.1 feet

Step-by-step explanation:

from the graph attached

i) BC = 1353 $\times tan(71\textdegree)$ = 2761.82 feet

ii) BD = 1353 $\times tan(58\textdegree)$ = 1744.28 feet

iii) the boats are far apart by = CD = CB + BD = 2761.82 + 1744.28 = 4506.1 feet

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2 years ago

The distance traveled by a small car varies directly to the amount of fuel it consumes. The small car traveled 120 miles on 3 ga

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1 year ago

Find the perimeter of $\triangle CDE$ . Round your answer to the nearest hundredth. A trapezoid A B C D is plotted on a coordina

guapka [62]

Answer:

The answer is below

Step-by-step explanation:

We are asked to find the perimeter of triangle CDE. The perimeter of a shape is simply the sum of all its sides, hence:

Perimeter of tiangle CDE = |CD| + |DE| + |CE|

Given that C(4, -1), D(4, -5), E(2, -3).

The distance between two points $X(x_1,y_1)\ and\ Y(x_2,y_2)$ is given as:

$|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Therefore the lengths of the triangle are:

$|CD|=\sqrt{(4-4)^2+(-5-(-1))^2} =4\ units\\\\|DE|=\sqrt{(2-4)^2+(-3-(-5))^2} =2.83\ units\\\\|CE|=\sqrt{(2-4)^2+(-3-(-1))^2} =2.83\ units$

Perimeter of CDE = 4 + 2.83 + 2.83 = 9.66 units

8 0

2 years ago

To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expressi

myrzilka [38]

Revenue = 7.5x - 100
Operation Costs = 5.8x + 79.86

To break even, operation cost = Revenue
⇒ 7.5x - 100 = 5.8x + 79.86
7.5x = 5.8x + 179.86 (Add 100 to both sides)

7.5x - 5.8x = 179.86
1.7x = 179.86
x = 105.8

This implies that the company will need to sell at least 106 items to make a profit.

The inequality that will determine the number of items at need to be sold to make a profit is x ≥ 106

The solution to the inequality is as follows

Revenue = 7.5x - 100
if x =106
Revenue = 7.5(106) - 100
Revenue = 695

Operational Cost = 5.8x + 79.86
if x = 106
Operational Cost = 5.8(106) + 79.86
Operational Cost = 694.66

Profit ≥ (695 - 694.66)
Profit ≥ 0.34

The company must sell at least 106 items to make a profit.

7 0

2 years ago

Read 2 more answers