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3 years ago

15

What is the measure of the angle in standard position?

1 answer:

mars1129 [50]3 years ago

3 0

Answer:

Step-by-step explanation:

What's inside the set of parenthesis is a description of the angle in terms of cos and sin. This says that the angle has a cos of square root of 3 over 2, and a sin of negative 1 over 2.

The cos of this angle is the line directly horizontal ON the x axis, since cos is the same as x.

The sin of this angle is the line that would be there if you dropped an altitude from the arrow on the x line to the arrow on the other line.

The tangent ratio, being side opposite over side adjacent will give us the angle we need. Use the inverse tangent and enter in those values and you'll get that the angle is -30.

OR

even easier than that, look at your unit circle to see where there is a cos, sin combination of those values. It will be located at -30 degrees, which is also 330 degrees.

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F(x)=x^2+10x-12

weqwewe [10]

Answer:

Therefore the two values required are 2.08 and -11.08.

Step-by-step explanation:

i) f(x) = $x^{2}$ + 10x - 12 is a quadratic equation and a quadratic equation will have two roots whose values when substituted in to the given quadratic equation will give the value.

ii) The question is therefore essentially asking us to find the roots of the given quadratic equation.

This can be done by equating the given quadratic equation to zero and then solving the equation for its roots.

∴ $x^{2}$ + 10x -12 = 0 ⇒ x = (-10 ± $\sqrt{10^{2} +(48)}$ ) ÷ 2

= (-10 ± 12.166)÷2 = 2.08, -11.08

Therefore the two values required are 2.08 and -11.08

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The path of a skateboarder can be modeled by the equation (x – 3)2 = –8(y – 8), where distance is in feet and air resistance is

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The maximum height and horizontal distance is required.

Maximum height 8 feet; horizontal distance 16 feet

The given path is $(x-3)^2=-8(y-8)$

If the skateboarder jumps at x = 0 she will land at y = 0. However there will be at horizontal displacement.

$(x-3)^2=-8(0-8)\\\Rightarrow (x-3)^2=8^2\\\Rightarrow x-3=\pm 8\\\Rightarrow x-3=8\\\Rightarrow x=11$

or

$x-3=-8\\\Rightarrow x=-5$

The distance between -5 and 11 is $11-(-5)=16$

Middle point would be $\dfrac{16}{2}=8$ from $-5$ .

$-5+8=3$

So, $x=3$

The maximum height will be

$(3-3)^2=-8(y-8)\\\Rightarrow y-8=0\\\Rightarrow y=8$

The maximum height is 8 feet and the horizontal distance is 16 feet.

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Step-by-step explanation: Since 11 is ruled out, answer is 12 people

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In 1970 the male incarceration rate in the U.S. was approximately 190 inmates per 100,000 population. In 2008 the rate was 960 i

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Answer:

40.53%

Step-by-step explanation:

$Percentage Increase = \frac{New Value - Old Value}{Old Value}\times100$

Here, New Value = 960÷100,000

Old Value = 190÷ 100,000

∴ $Percentage Increase = \dfrac{\frac{960}{100,000} - \frac{190}{100 ,000} }{\frac{190}{100,000}}\times100$

⇒ Percentage Increase = 40.53%

Thus, percent increase in the male incarceration rate during given period is 40.53%.

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the answer is D. All points to the left of zero are negative.

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