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3 years ago

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A stream is flowing down a slope into a larger river. The elevation of the head of the stream is 2,200 feet above sea level. The

elevation of the mouth of the stream is 1,000 feet. The horizontal distance along the stream between those two points is 63,360 feet. What is the gradient of the slope the stream is flowing over in ft/mi

1 answer:

Trava [24]3 years ago

7 0

Answer:

$100\ \text{ft/mi}$

Step-by-step explanation:

Elevation of the head of the stream is 2,200 feet above sea level

Elevation of the mouth of the stream is 1,000 feet

Rise = $2200-1000=1200\ \text{ft}$

Distance between the two points = $63360\ \text{ft}=\dfrac{63360}{5280}=12\ \text{mi}$ = Run

Gradient is given by

$\dfrac{\text{Rise}}{\text{Run}}=\dfrac{1200}{12}\\ =100\ \text{ft/mi}$

The gradient of the slope the stream is flowing over is $100\ \text{ft/mi}$ .

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devlian [24]

Answer:

The length is 40 units.

Step-by-step explanation:

You need to use a triangle for the base then use the hypotenuse of the base as the base of the diagonal shown in the prism.

$0.5*8*2=\\4*2=\\16$

The hypotenuse of the triangle of the base is 16.

$0.5*16*5=\\8*5=\\40$

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3 years ago

If the actual distribution of tusk lengths does not match the ones predicted with the H-W equation, it may indicate that natural

Anna [14]

Answer:

See explanation below

Step-by-step explanation:

It depends on what null hypothesis is under consideration.

One of the most common null hypothesis that are subject of study in a given statistical model is <em>the mean</em> predicted by the model.

In this case, the scientist probably observed that the mean of tusk lengths she obtained in a sample did not match the one predicted with the H-W equation.

So, she decided to perform a statistical study by collecting random samples and measuring the tusk lengths to determine a new possible mean and contrast it against the one predicted by the H-W equation.

<em>Let's call M the mean predicted by the H-W equation, and S the mean obtained by the scientist. </em>

If M different of S and the p-value is 0.021, that means that <em>there is at most 2.1% of probability that the difference between M and S could be due to a random sampling error. </em>

It should be kept in mind that the p-value does not represent the probability that the scientist is wrong.

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3 years ago

What is the value of g(2)?

n200080 [17]

Answer:

g(2)=1

Step-by-step explanation:

We need to use the second definition of the function since x=2

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3 years ago

Solving Systems of Linear Equations by graphing. 3y+4x=3 and x+3y=-6. Can someone help me with where the lines intersect and sho

Greeley [361]

The best way to do this question is to use elimination. Elimination is a way to find out the POINT OF INTERSECTION between two lines. Let me show you how.

3y+4x=3
x+3y=-6

Elimination is a way to remove any same variable with the same coefficient. In this case, there is 3y in both equations. In this case, we subtract to eliminate.

3y-3y+4x-x=3+6 It's plus 6 because two negatives become positive.
3x=9 Divide both sides by 3
x=3

Now you can find y.

x+3y=-6
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Therefore, the POI is (3,-3). I hope you understand this. Make sure to mark as brainliest.

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4 years ago

Find the exact values of the remaining five trigonometric functions of theta, suppose theta is an angle in the standard position

nexus9112 [7]

Answer:

$\sin(\theta)=60/61\text{ and } \csc(\theta)=61/60\\\cos(\theta)=11/61\text{ and } \sec(\theta)=61/11\\\tan(\theta)=60/11\text{ and } \cot(\theta)=11/60$

Step-by-step explanation:

So, we know that:

$\tan(\theta)=60/11\text{ and } 90\textdegree$

Since θ is in QI, this means that <em>all</em> of our trig ratios will be positive. Recall All Students Take Calculus. Since it's QI, we refer to A in All. The A tells us that all the ratios will be positive.

Now, let's figure out the remaining ratios knowing that all of them is positive. First, let's find the hypotenuse. Recall that tangent is the ratio of the <em>opposite side to the adjacent side</em>. So, we can use the Pythagorean Theorem to find the hypotenuse. So:

$a^2+b^2=c^2$

Substitute 60 for a and 11 for b:

$60^2+11^2=c^2$

Solve for c. Square both numbers:

$3600+121=c^2$

Add:

$c^2=3721$

Take the square root of both sides:

$c=61$

Therefore, the hypotenuse is 61.

So, our side lengths are: Opposite=60; Adjacent=11; and Hypotenuse=61.

Now that we know the lengths, we can find the other trig ratios:

Sine and Cosecant:

$\sin(\theta)=opp/hyp$

Substitute 60 for Opp and 61 for Hyp:

$\sin(\theta)=60/61$

Cosecant is the reciprocal of sine. So:

$\csc(\theta)=61/60$

Cosine and Secant:

$\cos(\theta)=adj/hyp$

Substitute 11 for Adj and 61 for Hyp:

$\cos(\theta)=11/61$

Secant is the reciprocal of cosine. So:

$\sec(\theta)=61/11$

Tangent and Cotangent:

We are already given that tangent is:

$\tan(\theta)=60/11$

Cotangent is the reciprocal of tangent. So:

$\cot(\theta)=11/60$

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4 years ago