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3 years ago

Why does (x-2)^2+9=0 have no real solutions?

Mathematics

1 answer:

alex41 [277]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Given

(x - 2)² + 9 = 0 ( subtract 9 from both sides )

(x - 2)² = - 9 ( take the square root of both sides )

x - 2 = ± $\sqrt{-9}$

$\sqrt{-9}$ yields no real solutions

There is no real number when multiplied by itself gives - 9

In fact the solutions to $\sqrt{-9}$ are said to be imaginary, that is ± 3i

where i = $\sqrt{-1}$

If interested investigate further.

You might be interested in

The compound interest on Rs. 50000 at 4% per annum for 2 years compound annually is

statuscvo [17]

Answer:

$54080

Step-by-step explanation:

Step one:

given

principal= Rs. 50000

rate= 4%= 0.04

time= 2 years

Required

The final Amount A

Step two

Applying

A= P(1+r)^t

substitute

A= 50000(1+0.04)^t

A= 50000(1.04)^2

A= 50000*1.0816

A= 54080

$54080

6 0

3 years ago

what formulas could be used to determine the surface area of a cylinder sandwiched between one cone and half of a sphere?

skelet666 [1.2K]

Answer: Rectangle around the cylinder, Lateral surface of the cone, Half a sphere

To find this surface area, you have 3 different parts. First, you need the rectangular portion of the cylinder, because the circles will be on the inside of the composite shape. Then, you will need the lateral side of the cone, that's everything but the circular base. Again, the circle will be on the interior. Finally, you should find the surface area of half of the sphere.

4 0

4 years ago

A football is thrown from the top of the stands, 50 feet above the ground at an initial velocity of 62 ft/sec and at an angle of

Anvisha [2.4K]

a. i. The parametric equation for the horizontal movement is x = 43.84t

ii. The parametric equation for the vertical movement is y = 50 + 43.84t

b. the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

<h2>a. Parametric equations</h2>

A parametric equation is an equation that defines a set of quantities a functions of one or more independent variables called parameters.

<h3>i. Parametric equation for the horizontal movement</h3>

The parametric equation for the horizontal movement is x = 43.84t

Since

the angle of elevation is Ф = 45° and
the initial velocity, v = 62 ft/s,

the horizontal component of the velocity is v' = vcosФ.

So, the horizontal distance the football moves in time, t is x = vcosФt

= vtcosФ

= 62tcos45°

= 62t × 0.7071

= 43.84t

So, the parametric equation for the horizontal movement is x = 43.84t

<h3>ii Parametric equation for the vertical movement</h3>

The parametric equation for the vertical movement is y = 50 + 43.84t

Also, since

the angle of elevation is Ф = 45° and
the initial velocity, v = 62 ft/s,

the vertical component of the velocity is v" = vsinФ.

Since the football is initially at a height of h = 50 feet, the vertical distance the football moves in time, t relative to the ground is y = 50 + vsinФt

= 50 + vtcosФ

= 50 + 62tsin45°

= 50 + 62t × 0.7071

= 50 + 43.84t

<h3>b. Location of football at maximum height relative to starting point</h3>

The location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Since the football reaches maximum height at t = 1.37 s

The x coordinate of its location at maximum height is gotten by substituting t = 1.37 into x = 48.84t

So, x = 43.84t

x = 43.84 × 1.37

x = 60.0608

x ≅ 60.1 ft

The y coordinate of the football's location at maximum height relative to the ground is y = 50 + 48.84t

The y coordinate of the football's location at maximum height relative to the starting point is y - 50 = 48.84t

So, y - 50 = 48.84t

y - 50 = 43.84 × 1.37

y - 50 = 60.0608

y - 50 ≅ 60.1 ft

So, the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)

Learn ore about parametric equations here:

brainly.com/question/8674159

5 0

2 years ago

What is the side length of the largest square that can fit into a circle with a radius of 5 units?

Mariana [72]

So 1st consider that it's a square! That's very important. So for a square, all 4 sides are equal.

And now considering that the given information is the diameter. So any angle made at the circle extended from the 2 points of diameter gives an angle of 90°

Now consider one triangle. So we already know that 2 sides of the triangle are equal (because they are 2 sides of a square) , has a side of 10 (diameter) and and angle of 90°. So remaining 2 angles are 45°

Now solve it by applying

$\sin(45) \: \: \: \: = x \div 10 \\ (1 \div \sqrt{2} ) = (x \div 10) \\ 10 \div \sqrt{2} \: = x$

5 0

3 years ago

The price of one share of stock in BadInvestment.com plunged 14 points in 4 weeks. Find the average change in stock price per da

mariarad [96]

$averge\ change=\frac{number\ of\ points}{number\ of\ days}\\\\
4week=28days\\\\
average\ change=\frac{14}{28}=0,5\frac{stock}{day}\\\\Solution\ is\ 0,5\frac{stock}{day}.$

7 0

3 years ago