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Anton [14]
2 years ago
9

A sedan will drive ten miles north, 15 miles east, 13 miles south, 15 miles west, and 22 miles north. The sedan gets 20 miles pe

r gallon, and there are five gallons of gas left in the tank. Compute the relative distance and the total distance. Then decide if there is enough fuel for the trip.
Mathematics
1 answer:
larisa [96]2 years ago
3 0
You would have enough gas to go another 25 miles
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Use a graph in a (-2π, 2π, π/2) by (-3, 3, 1) viewing rectangle to complete the identity.
yaroslaw [1]

First, notice that:

2\tan (\frac{x}{2})=2\cdot(\pm\sqrt[]{\frac{1-cosx}{1+\cos x})}

And in the denominator we have:

1+\tan ^2(\frac{x}{2})=1+\frac{1-\cos x}{1+\cos x}=\frac{1+cosx+1-\cos x}{1+cosx}=\frac{2}{1+\cos x}

then, we have on the original expression:

\begin{gathered} \frac{2\tan(\frac{x}{2})}{1+\tan^2(\frac{x}{2})}=\frac{2\cdot\pm\sqrt[]{\frac{1-\cos x}{1+cosx}}}{\frac{2}{1+\cos x}}=\frac{2\cdot(\pm\sqrt[]{1-cosx})\cdot(1+\cos x)}{2\cdot(\sqrt[]{1+cosx})} \\ =(\sqrt[]{1-\cos x})\cdot(\sqrt[]{1+\cos x})=\sqrt[]{(1-\cos x)(1+\cos x)} \\ =\sqrt[]{1-\cos^2x}=\sqrt[]{\sin^2x}=\sin x \end{gathered}

therefore, the identity equals to sinx

8 0
1 year ago
Plz help me with this
Agata [3.3K]

Answer:

It's the first option.

Step-by-step explanation:

y = cos x transformed  to cos (x - π/2) moves  the graph  π/2 units to the right.

Multiplying by 3 to give 3 cos(x -  π/2)  stretches the graph 3 units parallel to the y-axis and adding 3 to this moves the graph up 3 units.

So the required equation is y = 3(cos x -  π/2) + 3.

3 0
2 years ago
The step work of the question along with the answer​
Travka [436]

Answer: RM 31631

Step-by-step explanation:

We are given the following formula, used to calculate the value of an used car according to the years after the car was originally bought:

RM 57000(\frac{8}{9})^{n}

Where RM 57000 is the price of the car when it was bought new, and n=5 is the number of years the car was used.

Solving the formula with the given data:

RM 57000(\frac{8}{9})^{5}=RM 31630.95 This is the value of the car according to the formula.

However, this value can be approximated to:

RM 31631

6 0
3 years ago
The answer to the question to my test
wel

Answer:

Option C, 262 cm^3

Step-by-step explanation:

<u>Step 1:  Substitute 5 for radius and 10 for height</u>

V = 1/3 * pi * r^2 * h

V = 1/3 * pi * (5)^2 * (10)

V = 1/3 * pi * 25 * 10

V = 250pi/3

V = 261.79

Answer:  Option C, 262 cm^3

7 0
3 years ago
The owner of a football team claims that the average attendance at games is over 523, and he is therefore justified in moving th
USPshnik [31]

Answer:

C) There is not sufficient evidence to support the claim that the mean attendance is greater than 523.

Step-by-step explanation:

Let μ be the the average attendance at games of the football team

The claim: the average attendance at games is over 523

Null and alternative hypotheses are:

  • H_{0}: μ=523
  • H_{a}: μ>523

The conclusion is failure to reject the null hypothesis.

This means that <em>test statistic</em> is lower than <em>critical value</em>.  Therefore it is not significant, there is no significant evidence to accept the <em>alternative</em> hypothesis.

That is no significant evidence that the average attendance at games of the football team is greater than 523.

7 0
2 years ago
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