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sveta [45]
3 years ago
14

The fuel tank of a certain airplane can hold up to 400 gallons of fuel. Let W be the total weight of the airplane (in pounds). L

et F be the total amount of fuel in its tank (in gallons). Suppose that =W+7F5000 gives W as a function of F . Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
Mathematics
1 answer:
Lady bird [3.3K]3 years ago
7 0
A reasonable function is W = 7F + 5000


Where W is the weight of the plane and F is the number of gallons of fuel.


The domain is the set of possible values for F. That is from 0 (empty tank) to 400 (full tank).


So the domain is F = [0,400], or what is equivalente 0 ≤ F ≤ 400.


The range is the set of values of W.


The minimum value of W is when F = 0 => W = 7(0) + 5000 = 5,000.


The maximum value of W is when F = 400 => W = 7(400) + 5000 = 7,800 


So the range is W = [5,000 ; 7,800], pr 5000 ≤ W ≤ 7,800. 
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Use special right triangles to find the exact value (no decimals).
fgiga [73]

Let’s find some exact values using some well-known triangles. Then we’ll use these exact values to answer the above challenges.

sin 45<span>°: </span>You may recall that an isosceles right triangle with sides of 1 and with hypotenuse of square root of 2 will give you the sine of 45 degrees as half the square root of 2.

sin 30° and sin 60<span>°: </span>An equilateral triangle has all angles measuring  60 degrees and all three sides are equal.  For convenience, we choose each side to be length 2.  When you bisect an angle, you get 30 degrees and the side opposite is 1/2 of 2, which gives you 1.  Using that right triangle, you get exact answers for sine of 30°, and sin 60° which are 1/2 and the square root of 3 over 2 respectively.

Now using the formula for the sine of the sum of 2 angles,

sin(A + B) = sin A cos<span> B</span> + cos A sin B,

we can find the sine of (45° + 30°) to give sine of 75 degrees.

We now find the sine of 36°, by first finding the cos of 36°.

<span>The cosine of 36 degrees can be calculated by using a pentagon.</span>

<span>that is as much as i know about that.</span>

5 0
4 years ago
last night, julie's pet hamster zoe kept julie awake for at least an hour running on her exercise wheel and scratching at the co
borishaifa [10]

Answer: x+y\geq 1, x>\frac{1}{4} ,  x\geq 2y and y\geq 0

Step-by-step explanation:

Here,  x represents the number of hours Zoe spent running on her wheel and y represents the number of hours spent scratching her cage.

Julie was awoke for at least an hour running on her exercise wheel and scratching the of her cage.

⇒ x+y\geq 1

She ran on her wheel at least twice as long as she scratched at the corners of her cage.

⇒ x\geq 2y

Also, She spent more than 1/4 hour running on her wheel.

⇒ x>\frac{1}{4}

And, we know that number of hours can not be negative.

⇒  y\geq 0

Therefore, the complete system of inequality which shows the given situation is,

x+y\geq 1, x>\frac{1}{4} and x\geq 2y, y\geq 0

Note: the feasible region ( covered by the given system) is shown in the below graph.


6 0
3 years ago
Please send me answer. tomorrow is my exam.​
masha68 [24]

Answer:

The table is attached below and ogive also.

Step-by-step explanation:

Given

The following distribution is given below

First we find the cumulative frequency.

And then we convert it into a less than type ogive.

find the cumulative frequency shown below clearly

And convert it into less than type of cumulative frequency distribution is also done in next table, the daily income is less than daily income upper limit.

In this graph x-axis is daily income and y-axis is number of workers

6 0
3 years ago
Height: 15 ft <br> area: 285 square feet <br><br> find the missing dimension for the triangle
seraphim [82]
A=1/2 B×h
285=1/2×B×15
B=38 feet, so the base of the triangle is 38 feet. Hope it help!
4 0
3 years ago
Just do these two problems for me and I’ll be so happy
Nady [450]

Answer:

See below

Step-by-step explanation:

5) y = x + 7

6) y = -x + 1

7 0
2 years ago
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