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3 years ago

Solve for 2. Round to the nearest tenth, if necessary.

Mathematics

1 answer:

inysia [295]3 years ago

6 0

Answer:

Step-by-step explanation:

The reference angle is given as 63 degrees. The sides in question, x and 1, are adjacent to and opposite of this angle, respectively. The trig ratio that utilizes the sides adjacent to and opposite of angles is the tangent ratio; namely:

$tan(63)=\frac{1}{x}$ and rearrange algebraically to get

$x=\frac{1}{tan(63)}$ to get

x = .5

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Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance o

g100num [7]

Answer:

The value is $k =109.6 \ miles$

Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

The distance from city A to B is AB = 467.3 miles

The bearing from B to C is $\theta_{BC} = N 28.7E$

The bearing from B to A is $\theta_{BA} = N 60.7E$

The bearing from A to B is $\theta_{AB} = S60.7W$

The bearing from A to C is $\theta_{AC} = S79.1W$

Generally from the diagram

$\theta_A = 180 - 60.7 -79.1$

=> $\theta_A = 40.2 ^o$

Also

$\theta_B = 32^o$

and

$\theta_C = 180 - (\theta_A +\theta_B )$

=> $\theta_C = 180 - (40.2 + 32 )$

=> $\theta_C = 107.8 ^o$

Generally according to Sine Rule

$\frac{BC}{sin (\theta_A)} = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}$

=> $\frac{BC}{sin (40.2)} = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}$

$\frac{BC}{sin (40.2)} = \frac{467.3 }{sin (107.8)}$

=> $BC = 316.8 \ miles$

Also

$\frac{CA}{sin (32)} = \frac{467.3 }{sin (107.8)}$

$CA = 260 .1 \ miles$

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct flight is mathematically represented as

$k = [CA +BC] - AB$

=> $k = [260 .1 +316.8]- 467.3$

=> $k =109.6 \ miles$

4 0

3 years ago

1.) What are the zeros of the polynomial? f(x)=x^4-x^3-16x^2+4x+48.

Lerok [7]

Answer:

3.) $\displaystyle [x - 2][x^2 + 2][x + 4]$

2.) $\displaystyle 2\:complex\:solutions → x^2 + 3x + 6 >> -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2}$

1.) $\displaystyle 4, -3, 2, and\:-2$

Step-by-step explanation:

3.) By the Rational Root Theorem, we would take the Least Common Divisor [LCD] between the leading coefficient of 1, and the initial value of −16, which is 1, but we will take 2 since it is the fourth root of 16; so this automatically makes our first factor of $\displaystyle x - 2.$ Next, since the factor\divisor is in the form of $\displaystyle x - c$ , use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

2| 1 2 −6 4 −16

↓ 2 8 4 16

__________________

1 4 2 8 0 → $\displaystyle x^3 + 4x^2 + 2x + 8$

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x⁴ + 2x³ - 6x² + 4x - 16]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x³, the 4x² follows right behind it, bringing 2x right up against it, and bringing up the rear, 8, giving you the quotient of $\displaystyle x^3 + 4x^2 + 2x + 8.$

However, we are not finished yet. This is our first quotient. The next step, while still using the Rational Root Theorem with our first quotient, is to take the Least Common Divisor [LCD] of the leading coefficient of 1, and the initial value of 8, which is −4, so this makes our next factor of $\displaystyle x + 4.$ Then again, we use Synthetic Division because $\displaystyle x + 4$ is in the form of $\displaystyle x - c$ :

−4| 1 4 2 8

↓ −4 0 −8

_____________

1 0 2 0 → $\displaystyle x^2 + 2$

So altogether, we have our four factors of $\displaystyle [x^2 + 2][x + 4][x - 2].$

__________________________________________________________

2.) By the Rational Root Theorem again, this time, we will take −1, since the leading coefficient & variable\degree and the initial value do not share any common divisors other than the special number of 1, and it does not matter which integer of 1 you take first. This gives a factor of $\displaystyle x + 1.$ Then start up Synthetic Division again:

−1| 1 3 5 −3 −6

↓ −1 −2 −3 6

__________________

1 2 3 −6 0 → $\displaystyle x^3 + 2x^2 + 3x - 6$

Now we take the other integer of 1 to get the other factor of $\displaystyle x - 1,$ then repeat the process of Synthetic Division:

1| 1 2 3 −6

↓ 1 3 6

_____________

1 3 6 0 → $\displaystyle x^2 + 3x + 6$

So altogether, we have our three factors of $\displaystyle [x - 1][x^2 + 3x + 6][x + 1].$

Hold it now! Notice that $\displaystyle x^2 + 3x + 6$ is unfactorable. Therefore, we have to apply the Quadratic Formula to get our two complex solutions, $\displaystyle a + bi$ [or zeros in this matter]:

$\displaystyle -b ± \frac{\sqrt{b^2 - 4ac}}{2a} = x \\ \\ -3 ± \frac{\sqrt{3^2 - 4[1][6]}}{2[1]} = x \\ \\ -3 ± \frac{\sqrt{9 - 24}}{2} = x \\ \\ -3 ± \frac{\sqrt{-15}}{2} = x \\ \\ -3 ± i\frac{\sqrt{15}}{2} = x \\ \\ -\frac{3 - i\sqrt{15}}{2}, -\frac{3 + i\sqrt{15}}{2} = x$

__________________________________________________________

1.) By the Rational Root Theorem one more time, this time, we will take 4 since the initial value is 48 and that 4 is the root of the polynomial. This gives our automatic factor of $\displaystyle x - 4.$ Then start up Synthetic Division again:

4| 1 −1 −16 4 48

↓ 4 12 −16 −48

___________________

1 3 −4 −12 0 → $\displaystyle x^3 + 3x^2 - 4x - 12$

We can then take −3 since it is a root of this polynomial, giving us the factor of $\displaystyle x + 3:$

−3| 1 3 −4 −12

↓ −3 0 12

_______________

1 0 −4 0 → $\displaystyle x^2 - 4 >> [x - 2][x + 2]$

So altogether, we have our four factors of $\displaystyle [x - 2][x + 3][x + 2][x - 4],$ and when set to equal zero, you will get $\displaystyle 4, -3, 2, and\:-2.$

I am delighted to assist you anytime.

3 0

3 years ago

There are 8 students on the minibus.Five of the students are boys. What fraction of the students are boys

Nimfa-mama [501]

Since 5 of the 8 students are boys, the fraction would be 5/8. The fraction would roughly be around 63%

5 0

3 years ago

Read 2 more answers

Riley started selling bracelets. During the first month she sold 400 bracelets at $10 each. She tried raising the price, but for

love history [14]

I would just divide 400 and 10 and then try to come up with the salary

8 0

3 years ago

Please help me answer this

Ronch [10]

Answer:

10.77

Step-by-step explanation:

by using Pythagoras theorem we can find the distance between the points,

so...

distance between the points, which is the hypotenuse will be xy

difference between the y coordinates will be dy

difference between the x coordinates will be dx

according to pythagoras theorem,

$xy^{2} = dx^{2} + dy^{2} \\xy^{2} = (-6-(-2))^{2} + (-5-5)^{2}\\xy^{2} =(-4)^{2} +(-10)^{2} \\xy^{2} =16+100\\xy^{2} =116\\xy =\sqrt{116} \\xy=10.77$

8 0

2 years ago