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Natalka [10]
4 years ago
15

If sin(theta°) = 0.5, and we know that cos (theta°) < 0, then what is the smallest possible positive value of theta?

Mathematics
1 answer:
9966 [12]4 years ago
4 0

Answer:

150°

Step-by-step explanation:

It is given that CosФ < 0 i.e CosФ is negative.

Therefore, the minimum the value of Ф for which CosФ <0 will be in the second quadrant i.e 90° < Ф < 180°.

Now it is also given that, Sin Ф =0.5 {the value of SinФ is positive because Sin value is positive in second quadrant.}

⇒ Ф =180° - Sin⁻¹ (0.5) = 180°-30° =150° (Answer)

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Identify the zeros of the function f(x) = 2x^2 − 4x + 5 using the Quadratic Formula
Nostrana [21]

For this case we have that by definition, the roots, or also called zeros, of the quadratic function are those values of x for which the expression is 0.

Then, we must find the roots of:

2x ^ 2-4x + 5 = 0

Where:

a = 2\\b = -4\\c = 5

We have to:x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}

Substituting we have:

x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (5)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-40}} {4}\\x = \frac {4 \pm \sqrt {-24}} {4}

By definition we have to:

i ^ 2 = -1

So:

x = \frac {4 \pm \sqrt {24i ^ 2}} {4}\\x = \frac {4 \pm i \sqrt {24}} {4}\\x = \frac {4 \pm i \sqrt {2 ^ 2 * 6}} {4}\\x = \frac {4 \pm 2i \sqrt {6}} {4}\\x = \frac {2 \pm i \sqrt {6}} {2}

Thus, we have two roots:

x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}

Answer:

x_ {1} = \frac {2 + i \sqrt {6}} {2}\\x_ {2} = \frac {2-i \sqrt {6}} {2}

3 0
4 years ago
Help please if anyone knows
larisa86 [58]
<u>Part A
</u>
<u />To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case, \frac{3}{5} and \frac{2}{3} equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about 3 gallons.

<u>Part B
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<u /><u />To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.

1 \frac{3}{5} \\ \\  (5*1)+3 =8 \\  \\  \frac{8}{5}  \\  \\  \\ \\  1 \frac{2}{3} \\  \\ (3*1)+2=5 \\  \\  \frac{5}{3}  &#10;

Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.

Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.

\frac{8}{5} *3 =   \frac{24}{15} \\  \\  \frac{5}{3} *5 =  \frac{25}{15}

Now, we can simply add our numerators.

25+24=49

We know that he needs \frac{49}{15} gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.

\frac{49}{15} \\  \\ 49 / 15 = 3(Remainder: 4) \\  \\  3\frac{4}{15}

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4 0
3 years ago
Convert 42 km/h to m/s
Marta_Voda [28]

42 km/h is equal to 0.00724933 m/s

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What would be the answer to x + 22 - 13x greater than or equal to 118
Fynjy0 [20]

Answer:.

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x+22-13x≥118

Collect like terms

x-13x≥118-22

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Divide both sides by -12

-12x/12≥96/-12

x≥96/-12

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The answer is x greater than or equal to -8

4 0
3 years ago
Read 2 more answers
Will award brainliest.
Nezavi [6.7K]
Your're lucky am going to help. Kidding. :D
All real  numbers but 3 and -3 

4 0
3 years ago
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