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3 years ago

Express the radical using the imaginary unit, i.

Mathematics

1 answer:

Trava [24]3 years ago

5 0

The foundation of imaginary numbers is that $i = \sqrt{-1}$ .

When simplifying radicals involving square roots of negative numbers, your first step is to separate the negative from the number and turn it into $i$ .

$\begin{aligned}\sqrt{-14} &= \sqrt{-1 \cdot 14}\\[0.5em] &= \sqrt{-1 }\cdot \sqrt{14}\\[0.5em] &= i\cdot \sqrt{14}\end{aligned}$

At this point, you can turn to the $\sqrt{14}$ and decide if this can be simplified or not. (Ask youself if there are any perfect squares that divide into 14.)

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A surveyor determines that the angle of elevation to the top of a building from a point on the ground is 31∘. he then moves back

atroni [7]

<h2>Hello!</h2>

The answer is:

The height of the building is 94.29 feet.

To solve the problem, we need to consider that two triangles are formed depending on the distance where the surveyor is standing.

We have a first triangle which its base will be called "x" and its height will be called "h" with an angle of elevation from a point on the ground, equal to 31°.

Also, we have a second triangle which base is equal to "x" + 57.1 feet, and a height "h", with an angle of elevation from a point on the ground, equal to 23.8°

We need to use a trigonometric identity that establishes a relationship between the height and the base. So, using the tangent trigonometric identity, we have:

$Tan(\alpha)=\frac{Opposite}{Adjacent}$

For the first triangle:

$Tan(31\°)=\frac{h}{x}$

$0.60=\frac{h}{x}$

$h=0.60*x=0.60x$

For the second triangle:

$Tan(23.8\°)=\frac{h}{x+57.1feet}$

$0.44=\frac{h}{x+57.1feet}$

$(0.44)*(x+57.1feet)=h$

$h=0.44x+25.14feet$

Then, making both equation equals, in order to find "x", we have:

$0.60x=0.44x+25.14feet$

$0.60x-0.44x=25.14feet$

$0.16x=25.14feet$

$x=\frac{25.14feet}{0.16}=157.13feet$

Then, we substituting "x" into any of the equations, we have:

Substituting into the first equation:

$h=0.60*x\\\\h=0.60*(157.13feet)=94.29feet$

Hence, the height of the building is 94.29 feet.

Have a nice day!

6 0

3 years ago

Read 2 more answers

What is 2a+a+2a+a ????

koban [17]

Just combine like terms

7 0

3 years ago

Read 2 more answers

Which expression is equivalent to the following?

4vir4ik [10]

Answer:

1.32 * 10^2

Step-by-step explanation:

Given the expression;

(5×10−3)+(6×10−3)2.2×10^4

First we need to do the multiplication first;

= (5×10−3)+(13.2×10−3+4)

= (5×10−3)+(13.2×10^1)

= 0.005 + 132

= 132.005

= 1.32 * 10^2

Hence the equivalent expression is 1.32.0 * 10^2

3 0

3 years ago

The expression log 3 (x-4) is undefined for all values such that

suter [353]

Translate it

remember that $log_a(b)=c$ translates to $a^c=b$
so we can say it equals y
so
$log_3(x-4)=y$ translates to $3^y=x-4$

we want to find the values of x that make it undefined
well, we know that $3^y$ must be greater than 0
so we do
it is defined for
x-4>0
add 4
x>4

it is defined for all values such that x>4

7 0

3 years ago

If the pictured triangles are congruent what reason can be given

igor_vitrenko [27]

Answer:

SAS Postulate.

Step-by-step explanation:

Two triangles are congruent if anyone of the following postulates is true:

SAS - Two corresponding sides and the included angles are congruent to each other.

SSS - All the three corresponding sides are congruent.

ASA - Two corresponding angles and the included sides are congruent to each other.

AAS - Two corresponding consecutive angles and sides adjacent to either of the angles are congruent.

HL - If the corresponding hypotenuses and one corresponding legs are congruent to each other.

Here, in the figure, two corresponding sides and the included angle between them are congruent to each other.

So, the two triangles are congruent by SAS postulate.

8 0

3 years ago