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3 years ago

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:

Step-by-step explanation:

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An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters,

Marina86 [1]

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

Step-by-step explanation:

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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

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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

427.5-45 = 382.5

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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.

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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