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3 years ago

Find the lengths of the missing sides of the 30°-60°-90° triangle. a=? ft, b=? ft, c=12 ft

Mathematics

1 answer:

Agata [3.3K]3 years ago

7 0

You know the long leg (the side across from the 60-degree angle). Divide this side by the square root of 3 to find the short side. Double that figure to find the hypotenuse. Finding the other sides of a 30-60-90 triangle when you know the hypotenuse.

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3. Mr. Wonka hoped that:

professor190 [17]

Answer:

Step-by-step explanation:

6 0

3 years ago

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

Please help ASAP!

g100num [7]

So all you have to do to solve these problems is substitute the y coordinate and the x coordinate into the equation.

So question 1 would be true because when you substitute the numbers in it equals the y value.

Question 2 is (4, -7)

Question 3 is False

Question 4 is true

Question 5 is true

See if you can do the rest!

8 0

3 years ago

Caroline wants to give 8 friends equal size packets of flower seeds to her friends. She has 1/2 pound of flower seeds. How much

Katena32 [7]

You just have to divide the 1/2 a pound by 8, or equivalently multiply by (1/8):

(1/2)*(1/8) = 1/16 of a pound

4 0

3 years ago

What is the side length of a cube that has a volume of 0.008 m

Nataliya [291]

Let the side lenght of cube is a
voluem of cube= 0.008
a^3=0.008
a =0.2
side of lenght is 0.2

8 0

3 years ago