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12345 [234]
3 years ago
13

A team of scientists is traveling by boat to study a pod, or group, of dolphins. The equation y = 0.2x can be used to find the d

istance, y, in miles the boat travels in x minutes. The dolphins are currently 8.4 mi from the boat. If the dolphins stay to where they are, how long will it take the boat to reach them? Show your work.
Mathematics
1 answer:
Alenkinab [10]3 years ago
6 0

Answer:

42 minutes.

Step-by-step explanation:

We know that:

y = 0.2*x

is the equation that that defines the distance, in miles, that the boat travels in x minutes.

We know that the dolphins are at 8.4 miles from the boat.

Then when we have y = 8.4, this will mean that the boat reached the dolphins.

Then we need to solve the equation:

y = 8.4 = 0.2*x

for x

To do that, we just need to isolate x in one side of the equation, so we can just divide both sides by 0.2 to get:

8.4/0.2 = (0.2*x)/0.2

42 = x

And x is time in minutes, thus, the boat needs to travel for 42 minutes to reach the dolphins.

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(1/1+sintheta)=sec^2theta-secthetatantheta pls help me verify this
Xelga [282]

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta

Simplify. The denominator uses the difference of two squares pattern:

\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta

Split into two separate fractions:

\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta

Rewrite the two fractions:

\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=}  \sec^2\theta - \sec\theta\tan\theta

Hence verified.

8 0
2 years ago
Which represents the domain of the relation {(–1, 4), (2, –3), (0, –2), (1, –3)}?
Fantom [35]
Domain means the “input” which is like when u input a number in a vending machine and then the output is you getting the chips or whatever u got from imputing the number. So the answer would be C because is is asking for the front numbers in the relation or plots of points.
7 0
3 years ago
What is the surface area of the rectangular prism below?
seropon [69]

Answer:

A

Step-by-step explanation:

multiply 9 by 12 to get the surface area of the end of the rectangle.

you should get 108.

multiply 12 by 9 to get the surface area of the side.

you should get 135.

multiply 12 by 15 to get the surface area of the bottom.

you should get 180.

then add all your answers and multiply by 2  this will give you the total surface area and you will find that the answer is A.

3 0
3 years ago
What is the dimensions of a box 8 cubic feet
Nesterboy [21]

You can't tell.  The volume doesn't tell you the dimensions.  It only tells you
what the product of the three dimensions is, but not what anyone of them is.
There are an infinite number of different possibilities.

Example:  Volume = 8 cubic feet

The dimensions of the box could be

Length = 2-ft,  Width = 2-ft,  Height = 2-ft
or
1 x 1 x 8
or
1 x 2 x 4
or
1 x 3 x 2-2/3
or
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or
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or
2 x 6 x 2/3
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2 x 7 x 4/7
or
2 x 8 x 1/2
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etc.


8 0
3 years ago
What is the mode?<br> What is the median?<br> What is the range?
Marina CMI [18]

<h2>ANSWER : </h2>

<h2><<< In this case, the mode is 9 seconds. The median is the middle number in a list of numbers ordered from smallest to largest. so 10 is the median of this set of results. The range is the difference between the lowest value and the highest value, so the range here is 15 - 9 = 6. </h2>

8 0
2 years ago
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