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3 years ago

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −6y2 − 9y = −1

1 answer:

8 0

$-6y^2 - 9y = -1$

$y= \dfrac{-9+ \sqrt{9^2-4*-6} }{2*6}, \dfrac{-9-\sqrt{9^2-4*-6}}{2*6}$

$y= \dfrac{-9+ \sqrt{105} }{12}, \dfrac{-9- \sqrt{105} }{12}$

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Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

4 0

2 years ago

Can somebody please help me, i really didnt understand my teacher at all

Kamila [148]

Answer:

Step-by-step explanation:

It is a solution because if you plug in 84 for b you get 84/12 = 7

4 0

3 years ago

Felix bought x pounds of grapes that cost $1.25 per pound and y boxes of cereal that cost $2.50 per box. He spent less than $10.

erica [24]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Question 11

Anarel [89]

Answer:

the trainee calculated the incorrect amount

It should be 0.5 mL

Step-by-step explanation:

The physician orders penicillin 500,000 units for a patient while the concentration of the drug you have is 1,000,000 units/ 1mL. It's clear that 1mL drug is too much for the patient since 1,000,000 units are higher than 500,000 units.

The amount of penicillin in 1.5 mL will be definitely higher than 1,000,000 units, so it must be a lot higher than the physician's orders. We can roughly guess that the trainee draws an incorrect amount.

To calculate the exact volume you need, you have to divide the amount of the drug you need with the concentration of the drug. The calculation will be:

the volume needed = amount of the drug you need/ concentration of the drug

volume needed = 500,000 units / (1,000,000 units/ 1mL)= 1/2 mL = 0.5 mL

8 0

3 years ago

A researcher computes r = 0.45 using a sample of 18 participants. Is this Pearson correlation coefficient significant for a two-

Eduardwww [97]

Answer with explanation:

Given : The computed r -value = 0.45

Sample size : n=18

Degree of freedom : $df=n-2=18-2=16$

Now, the critical value for Pearson correlation coefficient for a two-tailed test at a .05 level of significance will be :

$r_c=0.468$ ( by critical correlation coefficient table)

Since , $r>r_c$ i.e. 0.45>0.468 , then we say that his Pearson correlation coefficient is not significant for a two-tailed test at a .05 level of significance.

3 0

2 years ago