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3 years ago

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What is the answer to 10n=40

1 answer:

elixir [45]3 years ago

4 0

Solving for variables is easy as all we must do is isolate the variable and simplify. In this case, to isolate the variable, we simply need to divide "n" by 10 (because the "n" is being multiplied by 10).

10n=40
/10 /10
n=4

Using the math above, we can see that n=4.

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Let f(x) = tan(x) - 2/x. Let g(x) = x^2 + 8. What is f(x)*g(y)?

Tema [17]

Answer:

$f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}$

Step-by-step explanation:

We are given that

$f(x)=tan(x)-\frac{2}{x}$

$g(x)=x^2+8$

We have to find $f(x)\times g(y)$

To find the value of $f(x)\times g(y)$ we will multiply f(x) by g(y)

$g(y)=y^2+8$

Now,

$f(x)\times g(y)=(tanx-\frac{2}{x})(y^2+8)$

$f(x)\times g(y)=tan(x)(y^2+8)-\frac{2}{x}(y^2+8)$

$f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}$

Hence,

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3 years ago

Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

Brums [2.3K]

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

$AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775$

Substitute these in the above equation

$20:x/2 = 20 + x + 14: 1775$

$20:x/2 = x + 34: 1775$

Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

$\frac{40}{x} = \frac{x + 34}{1775}$

Cross multiply

$x *(x + 34) = 1775 * 40$

Open bracket

$x^2 + 34x = 71000$

Rewrite as:

$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

$x - 250 = 0 \ or\ x + 284= 0$

Solve for x

$x = 250 \ or\ x =- 284$

x can't be negative;

So:

$x = 250$

6 0

3 years ago