Answer:
13 units
Step-by-step explanation:
Using the right triangle formed by the 2 legs and the slant height s
The legs are 12 and 10 ÷ 2 = 5, with hypotenuse s
Using Pythagoras' identity in the right triangle, then
s² = 12² + 5² = 144 + 25 = 169 ( take the square root of both sides )
s = 
= 13
Your first differential equation is incomplete, so I'll just look at the second one.
<em>y'</em> + 2<em>xy</em> = 4<em>x</em>
Multiply both sides by exp(<em>x</em> ²):
exp(<em>x</em> ²) <em>y'</em> + 2<em>x</em> exp(<em>x</em> ²) <em>y</em> = 4<em>x</em> exp(<em>x</em> ²)
The left side is the derivative of a product:
(exp(<em>x</em> ²) <em>y</em> )<em>'</em> = 4<em>x</em> exp(<em>x</em> ²)
Integrate both sides:
exp(<em>x</em> ²) <em>y</em> = ∫ 4<em>x</em> exp(<em>x</em> ²) d<em>x</em>
For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em> :
exp(<em>x</em> ²) <em>y</em> = 2 ∫ exp(<em>u</em>) d<em>u</em>
Solve for <em>y</em> :
exp(<em>x</em> ²) <em>y</em> = 2 exp(<em>u</em>) + <em>C</em>
exp(<em>x</em> ²) <em>y</em> = 2 exp(<em>x</em> ²) + <em>C</em>
<em>y</em> = 2 + <em>C</em> exp(-<em>x</em> ²)
Answer:
0.4
Step-by-step explanation:
Multiply without the decimal points, then put the decimal point in the answer
2 has 0 decimal places
0.2 has decimal place
Therefore the answer has 1 decimal places
The triangle's height would have to be 2 times that of the rectangles. To know this, you canlook at the formulas for the Area of each shape.
Rectangle: bh
Triangle: bh/2
A triangle is just a rectangle cut in half. In order for the areas to be the same asleep as the bases, the only way it can be true is if the height were 2 times larger than the height of the rectangle.
