Step-by-step explanation:
Area of trapezium
=1/2 h(a+b)
=1/2 2(6+4)
=1/2 2.10
=1/2 20
=10cm. cm
Answer:
Hi ,
Cube of a number :
_______________
For a given number x we define cube
of x = x × x × x , denoted by x^3.
A given Natural number is a perfect
Cube if it can be expressed as the
product of triplets of equal factors.
Now ,
Write given number as product of
prime .
8788 = 2 × 4394
= 2 × 2 × 2197
= 2 × 2 × 13 × 169
= 2 × 2 × 13 × 13 × 13
= 2 × 2 × ( 13 × 13 × 13 )
Here we have only triplet of equal
factors i.e 13
To make 8788 into perfect Cube we
have multiply with 2.
Now ,
2 × 8788 = ( 2 × 2 × 2 ) × ( 13 × 13 × 13 )
17576 = ( 2 × 13 )^3 = ( 26 )^3 perfect
Cube
I hope this will useful to you.
Sid wrapped 8 gifts.
Look at the equation Sid wrote to caclulate the cost to wrap each gift. (6.80 + 7.35) / 8. 6.80 represents the total paid for wrapping paper. 7.35 represents the total amount paid for ribbon. Knowing that information, using the equation, and knowing who Sid wrapped gifts for, we can infer Sid wrapped gifts for 8 cousins.
You are given a rectangle that is placed around a semicircle. You are also given the width of the rectangle that is 8cm. You are asked to find the area of the shaded region. Let us assume that the semicircle is inscribed in the rectangle or inside the rectangle so that the diameter of the semicircle is the same as the side of the rectangle. Let us also assume that the shaded region are the ones not inside the semicircle.
Area of a circle = πD²/4
Area of a circle = π(8cm)²/4
Area of a circle = 16π cm²
Area of the rectangle = LW
Area of the rectangle = (8cm) ( 4cm)
Area of the rectangle = 32 cm²
Area of the shaded region = 16π cm² - 32 cm²Area of the shaded region = 18.265cm²
Given
<em>e</em> ˣʸ = sec(<em>x</em> ²)
take the derivative of both sides:
d/d<em>x</em> [<em>e</em> ˣʸ] = d/d<em>x</em> [sec(<em>x</em> ²)]
Use the chain rule:
<em>e</em> ˣʸ d/d<em>x</em> [<em>xy</em>] = sec(<em>x</em> ²) tan(<em>x</em> ²) d/d<em>x</em> [<em>x</em> ²]
Use the product rule on the left, and the power rule on the right:
<em>e</em> ˣʸ (<em>x</em> d<em>y</em>/d<em>x</em> + <em>y</em>) = sec(<em>x</em> ²) tan(<em>x</em> ²) (2<em>x</em>)
Solve for d<em>y</em>/d<em>x</em> :
<em>e</em> ˣʸ (<em>x</em> d<em>y</em>/d<em>x</em> + <em>y</em>) = 2<em>x</em> sec(<em>x</em> ²) tan(<em>x</em> ²)
<em>x</em> d<em>y</em>/d<em>x</em> + <em>y</em> = 2<em>x</em> <em>e</em> ⁻ˣʸ sec(<em>x</em> ²) tan(<em>x</em> ²)
<em>x</em> d<em>y</em>/d<em>x</em> = 2<em>x</em> <em>e</em> ⁻ˣʸ sec(<em>x</em> ²) tan(<em>x</em> ²) - <em>y</em>
d<em>y</em>/d<em>x</em> = 2<em>e</em> ⁻ˣʸ sec(<em>x</em> ²) tan(<em>x</em> ²) - <em>y</em>/<em>x</em>
Since <em>e</em> ˣʸ = sec(<em>x</em> ²), we simplify further to get
d<em>y</em>/d<em>x</em> = 2 tan(<em>x</em> ²) - <em>y</em>/<em>x</em>