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antoniya [11.8K]
3 years ago
14

A commercial airplane travels 5,000 feet east and then ascends 3,000 feet from its starting point in the sky. Upon noticing a se

vere storm system on the horizon, the pilot decides to return to the starting point. A) how much distance does the plane have to travel to turn back? B) at what angle would the plane need to travel to return to its starting point. (1,000 feet = 1 unit)
Mathematics
1 answer:
svp [43]3 years ago
8 0

Answer:

A) 5830.95 B)59.04

Step-by-step explanation:

Solve for the hypotenuse of 5,000 and 3,000

Use tangent to find the angle

tanx = 5,000/3,000

x=59.04

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Can someone help me with my math homework?
zhenek [66]

See explanations

Step-by-step explanation:

6. The fraction can be written as;

\frac{x^2}{2y} /\frac{y^2}{4} \\\\\frac{x^2}{2y} *\frac{4}{y^2} \\\\

Divide 4 by 2

=\frac{2x^2}{y^3}

7.

The fraction can be written as;

\frac{b^2}{6} /\frac{b}{a}

introduce product sign as

\frac{b^2}{6} *\frac{a}{b} \\\\=b*a/6\\=\frac{ab}{6}

8.

The fraction can be written as;

\frac{x}{y} /\frac{yx}{2}

Introduce product sign

\frac{x}{y} *\frac{2}{yx} \\\\=\frac{2}{y^2}

9.

The fraction can be written as;

\frac{x}{y^2} /\frac{x}{y} \\\\\\=\frac{x}{y^2} *\frac{y}{x} \\\\\\=\frac{1}{y}

10.

The fraction is simplified to;

\frac{x}{3y} /\frac{9}{x} \\\\\\\frac{x}{3y} *\frac{x}{9} =\frac{x^2}{27y}

Learn More

Simplifying complex fractions:brainly.com/question/12214941

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6 0
3 years ago
Please solve, answer choices included.
qaws [65]
4. To solve this problem, we divide the two expressions step by step:

\frac{x+2}{x-1}* \frac{x^{2}+4x-5 }{x+4}
Here we have inverted the second term since division is just multiplying the inverse of the term.

\frac{x+2}{x-1}* \frac{(x+5)(x-1)}{x+4}
In this step we factor out the quadratic equation.


\frac{x+2}{1}* \frac{(x+5)}{x+4}
Then, we cancel out the like term which is x-1.

We then solve for the final combined expression:
\frac{(x+2)(x+5)}{(x+4)}

For the restrictions, we just need to prevent the denominators of the two original terms to reach zero since this would make the expression undefined:

x-1\neq0
x+5\neq0
x+4\neq0

Therefore, x should not be equal to 1, -5, or -4.

Comparing these to the choices, we can tell the correct answer.

ANSWER: \frac{(x+2)(x+5)}{(x+4)}; x\neq1,-4,-5

5. To get the ratio of the volume of the candle to its surface area, we simply divide the two terms with the volume on the numerator and the surface area on the denominator:

\frac{ \frac{1}{3} \pi  r^{2}h }{ \pi  r^{2}+ \pi r \sqrt{ r^{2}  +h^{2} }  }

We can simplify this expression by factoring out the denominator and cancelling like terms.

\frac{ \frac{1}{3} \pi r^{2}h }{ \pi r(r+ \sqrt{ r^{2} +h^{2} } )}
\frac{ rh }{ 3(r+ \sqrt{ r^{2} +h^{2} } )}
\frac{ rh }{ 3r+ 3\sqrt{ r^{2} +h^{2} } }

We then rationalize the denominator:

\frac{rh}{3r+3 \sqrt{ r^{2} + h^{2} }}  * \frac{3r-3 \sqrt{ r^{2} + h^{2} }}{3r-3 \sqrt{ r^{2} + h^{2} }}
\frac{rh(3r-3 \sqrt{ r^{2} + h^{2} })}{(3r)^{2}-(3 \sqrt{ r^{2} + h^{2} })^{2}}}=\frac{3 r^{2}h -3rh \sqrt{ r^{2} + h^{2} }}{9r^{2} -9 (r^{2} + h^{2} )}=\frac{3rh(r -\sqrt{ r^{2} + h^{2} })}{9[r^{2} -(r^{2} + h^{2} )]}=\frac{rh(r -\sqrt{ r^{2} + h^{2} })}{3[r^{2} -(r^{2} + h^{2} )]}

Since the height is equal to the length of the radius, we can replace h with r and further simplify the expression:

\frac{r*r(r -\sqrt{ r^{2} + r^{2} })}{3[r^{2} -(r^{2} + r^{2} )]}=\frac{ r^{2} (r -\sqrt{2 r^{2} })}{3[r^{2} -(2r^{2} )]}=\frac{ r^{2} (r -r\sqrt{2 })}{-3r^{2} }=\frac{r -r\sqrt{2 }}{-3 }=\frac{r(1 -\sqrt{2 })}{-3 }

By examining the choices, we can see one option similar to the answer.

ANSWER: \frac{r(1 -\sqrt{2 })}{-3 }
8 0
4 years ago
R2+2r-33=0 solve by completing the square
-BARSIC- [3]
R^2+2r-33=0  move constant to other side by adding 33 to both sides

r^2+2r=33   halve the linear coefficient, square it and add to both sides, in this case it is just one

r^2+2r+1=34  now the left side is a perfect square...

(r+1)^2=34  take the square root of both sides...

r+1=34^(1/2)  subtract 1 from both sides

r=-1+34^(1/2) and -1-34^(1/2)
8 0
3 years ago
On a school bus, the female teacher sitting in front of me asked if I passed gas, why did she ask me that out of nowhere and whi
Mice21 [21]

Answer:

to surprise you

Step-by-step explanation:

8 0
3 years ago
In the figure, m∠B = m∠C and ∠D is a right angle. cos B =
Rasek [7]

Answer: The correct option is (a), i.e., cos B= sin A.

Explanation:

It is given that the ∠B = ∠C and ∠D is a right angle.

Since two corresponding angles of both triangles are same, so by angel sum property three angles are also equal. Therefore by AAA rule both triangles are similar.

It is given that,

\angle B=\angle C

\cos B=\cos C

Using angle sum property angle C is written as,

\cos B=\cos (180-\angle D-\angle A)

\cos B=\cos (180-90-\angle A)

\cos B=\cos (90-\angle A)

By using quadrant concepts.

\cos B=\sin A

Therefore option A is correct.

5 0
3 years ago
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