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vichka [17]
2 years ago
11

What is the area of a triangle that has a base of 15 1/4 in and a height of 18 in?

Mathematics
1 answer:
Aleonysh [2.5K]2 years ago
4 0
The area of a triangle = 1/2 base * height (basically half of a rectangle)

so 1/2 * 18 * 15.25 = 9*15.25 = 137.25

don't forget units so the answer is 137.25 inches squared
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Step-by-step explanation:

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The exterior angle is = to the 2 interior angles.
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So They want the angles
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I need some help with solving inequalitys 9x-9 greater thab or equal to 2(8x-15)
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3 years ago
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. width units height units
dmitriy555 [2]

This question is incomplete, the remaining part of the question is upload as an image alongside this answer.

Answer:

Width = 2x = 2( r/√2 ) =  √2 r units

Height = 2y = 2( r/√2 ) =  √2 r units

Step-by-step explanation:

From the Figure on the image; lets consider the circle of radius r, centered at the origin.  

let ABCD be the largest rectangle that can be inscribed inside the circle.  

Let the half width of the rectangle be x, then in right triangle ONB using Pythagorean theorem,  

half height of rectangle y = √(r² - x²)

Thus the width of the inscribed rectangle = 2x and height of the inscribed rectangle = 2√(r² - x²)

thus the area of the inscribed rectangle = length × width

⇒ A(x) = 2x(2√(r² - x²))

⇒ A(x) = 4x√(r² - x²)  

now in order to maximize the area, we find critical points.

so we find the derivative and set that zero, that is Ai(x) = 0.

so using product rule, we get

A'(x) = 4x × ( -2x / 2√(r² - x²) ) + ( 4 × √(r² - x²)  )

A'(x) = ( -4x² / √(r² - x²) ) + ( 4√(r² - x²)  )

Now for critical points, set A'(x) = 0

so

( -4x² / √(r² - x²) ) + ( 4√(r² - x²)  ) = 0

( 4x² / √(r² - x²) ) =  ( 4√(r² - x²)  )

x² = r² - x²

2x² = r²

x² = r²/2

x = ±√(r²/2)

Now since x represent the with, it cannot be negative, Thus

x = r/√2

hence

y = √(r² - x²) = √(r² -  r²/2) = √(r²/2) =  r/√2

Therefore, the dimensions of the rectangle of largest area will be;

Width = 2x = 2( r/√2 ) =  √2 r units

Height = 2y = 2( r/√2 ) =  √2 r units

6 0
2 years ago
Simultaneous equation<br><br> 3x+y=16<br><br> What's the answer?
Elanso [62]
Easy
3x + y = 16
Substract -y both sides
3x = -y + 16
Now divide both sides by 3
Answer is x= -1/3 + 16/3
8 0
3 years ago
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