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mihalych1998 [28]

2 years ago

10

If you wanted to mix pure methane with water and end up with 70 gallons of 20% methane, how many gallons of each should you use?

You should use gallons of water and gallons of methane > Next Question

1 answer:

PtichkaEL [24]2 years ago

3 0

Answer:

You want 40% of 140 gallons to be methane,

so 60% of 140 gallons is water

methane: 0.4(140) = 56 gallons

water: 0.6(140) = 84 gallons

Step-by-step explanation:

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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

Find the y intercept of a line with a slope of -4 and point (2,1)

Oxana [17]

Is this a rise over run question

6 0

3 years ago

How do you factor this expression by dividing by the GCF first. 15c-25

chubhunter [2.5K]

15c-25
15c=25
your answer is c=13.5

4 0

3 years ago

If the current in a circuit is 2 +j2 amps and the resistance is 3-j2 ohms, what is the voltage

victus00 [196]

Answer:

The voltage is 10 + 2j volts.

Step-by-step explanation:

Ohm's first law:

By Ohm's first law, the voltage is the multiplication of the current by the resistance, that is:

$V = R*i$

The voltage is measured in Volts, the current in amps and the resistance in ohms.

In this question:

Both the current and the resistance have complex parts. We have to know that:

$j^{2} = -1$

We have that:

$R = 3 - 2j, i = 2 + 2j$

Then

$V = R*i$

$V = (3 - 2j)*(2 + 2j)$

$V = 6 + 6j - 4j - 4j^{2}$

$V = 6 + 2j - 4(-1)$

$V = 10 + 2j$

The voltage is 10 + 2j volts.

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3 years ago

Jack plans on using network Atms about 4 times per month. What would be jacks total estimated annual fees for a checking account

Inga [223]

Answer: $104

Step-by-step explanation:

https://quizlet.com/_25qqj5

this link may help with more questions

7 0

2 years ago