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2 years ago

Write the expression in exponential form. log . N = x

Mathematics

1 answer:

OleMash [197]2 years ago

4 0

Answer:

N = x2

Step-by-step explanation:

Follpwing the format

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Sin^2(x/2)=sin^2x <br> Find the value of x

Veronika [31]

$\sin^2\dfrac x2=\sin^2x$
$\dfrac{1-\cos x}2=1-\cos^2x$
$1-\cos x=2-2\cos^2x$
$2\cos^2x-\cos x-1=0$
$(2\cos x+1)(\cos x-1)=0$
$\implies\begin{cases}2\cos x+1=0\\\cos x-1=0\end{cases}$ $\implies\begin{cases}\cos x=-\frac12\\\cos x=1\end{cases}$

The first case occurs in $0\le x$ for $x=\dfrac{2\pi}3$ and $x=\dfrac{4\pi}3$ . Extending the domain to account for all real $x$ , we have this happening for $x=\dfrac{2\pi}3+2n\pi$ and $\dfrac{4\pi}3+2n\pi$ , where $n\in\mathbb Z$ .

The second case occurs in $0\le x$ when $x=0$ , and extending to all reals we have $x=2n\pi$ for $n\in\mathbb Z$ , i.e. any even multiple of $\pi$ .

6 0

2 years ago

Which equation represents the following diagram?

lys-0071 [83]

Answer:

wheres the diagram..?

Step-by-step explanation:

..i think you forgot the diagram lol

7 0

2 years ago

Read 2 more answers

Plz i need help walk me through it, thanks

SVETLANKA909090 [29]

Answer:

$p=36^{\circ}$

Step-by-step explanation:

We can prove that a tangent will always be perpendicular to the radius touching it. So, the other angle in the diagram is $90^{\circ}$ .

Because all the angles of a triangle sum to $180^{\circ}$ , we have that $p+54+90=180$ .

We combine like terms on the left side to get $p+144=180$ .

We subtract $144$ on both sides to get $p=36$ .

So, $\boxed{p=36^{\circ}}$ and we're done!

6 0

2 years ago

Need help with this

snow_tiger [21]

Answer:

x y

15 -1

12 0

9 1

6 2

3 3

0 4

Step-by-step explanation:

This is a function table. For a linear function, find the average rate of change between the listed points called slope. Then use the slope to fill in other inputs and outputs for the function.

$m = \frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-12} =\frac{4}{-12} =- \frac{1}{3}$

This means for every 3 units made in the input, the function moves down 1 output.

x y

15 -1

12 0

9 1

6 2

3 3

0 4

6 0

2 years ago

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle

dem82 [27]

Answer:

229.23 feet.

Step-by-step explanation:

The pictorial representation of the problem is attached herewith.

Our goal is to determine the height, h of the tree in the right triangle given.

In Triangle BOH

$Tan 60^0=\dfrac{h}{x}\\h=xTan 60^0$

Similarly, In Triangle BOL

$Tan 50^0=\dfrac{h}{x+60}\\h=(x+60)Tan 50^0$

Equating the Value of h

$xTan 60^0=(x+60)Tan 50^0\\xTan 60^0=xTan 50^0+60Tan 50^0\\xTan 60^0-xTan 50^0=60Tan 50^0\\x(Tan 60^0-Tan 50^0)=60Tan 50^0\\x=\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0} ft$

Since we have found the value of x, we can now determine the height, h of the tree.

$h=\left(\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0}\right)\cdotTan 60^0\\h=229.23 feet$

The height of the tree is 229.23 feet.

5 0

2 years ago