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agasfer [191]
3 years ago
12

Simplify: (2x^5y^3)^3

Mathematics
2 answers:
romanna [79]3 years ago
5 0

Answer:

8x^15y^9

Step-by-step explanation:

kiruha [24]3 years ago
3 0

Answer:

8x

​15

​​ y

​9

​​  

Step-by-step explanation:

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D: c^2 + (x+5)^2 = 841

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4 0
2 years ago
That's population of turtles in a lake is estimated at 1,000. The population projected to increase 12% per year.
worty [1.4K]

Answer:

(1,000 * (100 + 12))/100 = 1,120 - 1,000 = 120 turtles/ per year

Step-by-step explanation:

7 0
2 years ago
A movie is 7 1 8hours long. After 45 minutes, how much of the movie is left?
kkurt [141]

Answer: 382.5 minutes

Step-by-step explanation:

7 1/8 = 7.125

7.125*60=427.5

Thus, the movie is 427.5 minutes long

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5 0
3 years ago
I need help please?!!!
nexus9112 [7]

The y intercept is where the line passes throught the y axis, or when x=0 so therfor the line is parellel to the y axis,never crossing it.

3 0
2 years ago
The angles of depression of two ships from the top of the light house are 45° and 30° towards east. If the ships are 200 m apart
azamat

Answer:

273 meters

Step-by-step explanation:

See image attached for the diagram I used to represent this scenario.

The distance between the ships, at angles 30 and 45, is 200 meters. The distance between the left ship and the lighthouse is x meters.

We can use trigonometric ratios to solve this problem. We can use the tangent ratio \big{(} \frac{\text{opposite}}{\text{adjacent}} \big{)} to create an equation with the two angles.

  • \displaystyle \text{tan(45)} = \frac{h}{x}
  • \displaystyle \text{tan(30)} = \frac{h}{x+200} }

Let's take these two equations and solve for x in both of them.

<h2>\textbf{Equation I}</h2>
  • \displaystyle \text{tan(45)} = \frac{h}{x}  

tan(45) = 1, so we can rewrite this equation.

  • \displaystyle 1=\frac{h}{x}

Multiply x to both sides of the equation.

  • \displaystyle x = h
<h2>\textbf{Equation II}</h2>
  • \displaystyle \text{tan(30)} = \frac{h}{x+200} }

Multiply x + 200 to both sides and divide h by tan(30).

  • \displaystyle \text{x + 200} = \frac{h}{\text{tan (30)}}  

Subtract 200 from both sides of the equation.

  • \displaystyle \text{x} = \frac{h}{\text{tan (30)}} - 200

Simplify h/tan(30).

  • x=\sqrt{3}h - 200  
<h2>\textbf{Equation I = Equation II}</h2>

Take Equation I and Equation II and set them equal to each other.

  • h=\sqrt{3}h-200

Subtract √3 h from both sides of the equation.

  • h-\sqrt{3}h=-200

Factor h from the left side of the equation.

  • h(1-\sqrt{3}) =-200

Divide both sides of the equation by 1 - √3.

  • \displaystyle h=\frac{-200}{1-\sqrt{3} }

Rationalize the denominator by multiplying the numerator and denominator by the conjugate.

  • \displaystyle h=\frac{-200}{1-\sqrt{3} } \big{(} \frac{1+\sqrt{3} }{1+\sqrt{3}} \big{)}
  • \displaystyle h=\frac{-200+200\sqrt{3} }{1-3}
  • \displaystyle h =\frac{-200+200\sqrt{3} }{-2}

Simplify this equation.

  • \displaystyle h=100+100\sqrt{3}
  • h=273.20508075

The height of the lighthouse is about 273 meters.

5 0
2 years ago
Read 2 more answers
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