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3 years ago

What is the exact value of sin(-345°) in fraction form?

Mathematics

1 answer:

Damm [24]3 years ago

5 0

You draw the reference angle of 45° but clockwise. The exact value of sin(-345°) is 1/√2.

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A scale drawing has a scale of 0.25 in. : 12 ft. Find the length on the drawing for an actual length of 15 ft.

lesya [120]

If 0.25 in on a drawing is 12 ft in real life, than 1 in on the drawing is 48 ft in real life.

Just divide 15 by 48

15/48=0.3125

So the length of 15 in real life to a drawing is 0.3125 inches.

7 0

3 years ago

Captain Jessica has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Michael and his merciless band of th

konstantin123 [22]

Answer: 1/12

Step-by-step explanation:

1/2 x 1/6= 1/12

6 0

3 years ago

The-------- of a figure is a measurement of the space inside it.

Natalka [10]

Answer:

Area

Step-by-step explanation:

5 0

3 years ago

Solve each quadratic equation by completing the square. Give exact answers--no decimals.

denis-greek [22]

Answer:

$x_1 = \frac{3}{2} + \frac{1}{2}(\sqrt{47})i\\\\x_2 = \frac{3}{2} - \frac{1}{2}(\sqrt{47})i\\\\$

Step-by-step explanation:

In this problem we have the equation of the following quadratic equation and we want to solve it using the method of square completion:

$x ^ 2 -3x +14 = 0$

The steps are shown below:

For any equation of the form: $ax ^ 2 + bx + c = 0$

1. If the coefficient a is different from 1, then take a as a common factor.

In this case $a = 1$ .

Then we go directly to step 2

2. Take the coefficient b that accompanies the variable x. In this case the coefficient is -3. Then, divide by 2 and the result squared it.

We have:

$\frac{-3}{2} = -\frac{3}{2}\\\\(-\frac{3}{2}) ^ 2 = (\frac{9}{4})$

3. Add the term obtained in the previous step on both sides of equality:

$x ^ 2 -3x + (\frac{9}{4}) = -14 + (\frac{9}{4})$

4. Factor the resulting expression, and you will get:

$(x -\frac{3}{2}) ^ 2 = -(\frac{47}{4})$

Now solve the equation:

Note that the term $(x -\frac{3}{2}) ^ 2$ is always > 0 therefore it can not be equal to $-(\frac{47}{4})$

The equation has no solution in real numbers.

In the same way we can find the complex roots:

$(x -\frac{3}{2}) ^ 2 = -(\frac{47}{4})\\\\x -\frac{3}{2} = \±\sqrt{-(\frac{47}{4})}\\\\x = \frac{3}{2} \±\frac{1}{2}\sqrt{-47}\\\\x = \frac{3}{2} \±\frac{1}{2}(\sqrt{47})i\\\\x_1 = \frac{3}{2} + \frac{1}{2}(\sqrt{47})i\\\\x_2 = \frac{3}{2} - \frac{1}{2}(\sqrt{47})i\\\\$

7 0

3 years ago

Read 2 more answers

(gh)^0 I'm very confused can you show me how to solve this

lana [24]

The expression is:

$(9d^{10})^{-2}$

Simplify the expression:

1. Multiply the exponent outside the parenthesis with every exponent inside the parenthesis,

$\begin{gathered} (9d^{10})^{-2}=9^2d^{(-10)\times2} \\ (9d^{10})^{-2}=9^{-2}d^{-20} \end{gathered}$

Since, exponents in negative form are express as fraction with 1 as numerator.

$\begin{gathered} \mleft(9d^{\mleft\{10\mright\}}\mright)^{\mleft\{-2\mright\}}=9^{-2}d^{\mleft\{-20\mright\}} \\ \mleft(9d^{\mleft\{10\mright\}}\mright)^{\mleft\{-2\mright\}}=\frac{1}{9^2}\times d^{\mleft\{-20\mright\}} \\ \mleft(9d^{\mleft\{10\mright\}}\mright)^{\mleft\{-2\mright\}}=\frac{1}{81}^{}d^{\mleft\{-20\mright\}} \end{gathered}$

Answer: 1/81d^(-20)

3 0

1 year ago