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3 years ago

What is the distance between the walls?

Mathematics

1 answer:

icang [17]3 years ago

5 0

If you flip the 30-60-90 triangles so they look similar, and find the difference between the length of 60, and the length of 40.

40÷60 =.6666 etc

You can prove this by plugging in
60 •.66666 = 39.9999 or about 40.

The triangle I started with had a length of 60, so just used the tangent of 60° to find the adjacent.
Since we know the relationship of the triangles,
Multiply your answer, 103.923 •.666666
Which equals 69.2819
69.2819 is the length of the 40 triangle.

Add them together, and you get 173.2049.

Or 173.20 m

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Find x? In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

7 0

3 years ago

The tail of a kite is 1.5 feet plus twice the length of the kite. Together, the kite and tail are 15.5 ft long. Find the length

Ivan

Answer:

We know that the kite with the tail is 15 feet and 6 inches. While 6 inches is 0,50 foot, it's 15,5 feet. If the lenght of the kite is x, then:

15,5 = x + 1,5 + 2x

15,5 = 3x + 1,5 / - 1,5 (both sides)

14 = 3x / : 3 (both sides)

x ≈ 4,66

The kite is approx .4,66 feet long. It means that the tail is about 15,5 - 4,66 = 10,84 feet long.

5 0

3 years ago

Read 2 more answers

Please help me with both! would really appreciate it

Tamiku [17]

Jus look and the answer above

7 0

3 years ago

Estimate each product 5/7×1/9=

Cerrena [4.2K]

Multiply it out to get 5/7*1/9=5/63. This is an exact value of the product.

8 0

3 years ago

What is the solution of log3x −725 = 2? x = −2 x = 2 x = 3 x = 4

SpyIntel [72]

The best and most correct answer provided from your question about the solution of a logarithmic equation is the fourth option which is x = 4. The solution to the equation is as follows:

We can transform the expression to:

(3x-7)^2 = 25

Solving for x using your algebra:

x = 4

I hope it has come to your help.

4 0

3 years ago