Answer: Surface area = 29.32 inches²
Step-by-step explanation:
The surface area is the sum of areas of the faces. There are two triangular faces and three rectangular faces.
The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
Base = 2 inches
Height = 2 inches
Area = 1/2 × 2 × 2 = 2 inches²
Area of the 2 triangular faces
= 2 × 2 = 4 inches²
The area of the two equal rectangles is
Area = 2 × 2 × 4 = 16 inches²
To determine the width, w of the rectangular base, we would apply Pythagoras theorem.
Hypotenuse ² = opposite side² + adjacent side²
w² = 2² + 2²
w² = 4 + 4 = 8
w = √8 = 2.83
Area of the rectangular base is
2.83 × 4 = 11.32 inches²
Surface area = 4 + 16 + 11.32 = 31.32 inches²
L=Lim tan(x)^2/x x->0
Since both numerator and denominator evaluate to zero, we could apply l'Hôpital rule by taking derivatives.
d(tan^2(x))/dx=2tan(x).d(tan(x))/dx = 2tan(x)sec^2(x)
d(x)/dx = 1
=>
L=2tan(x)sec^2(x)/1 x->0
= (2(0)/1^2)/1
=0/1
=0
Another way using series,
We know that tan(x) = x+x^3/3+2x^5/15+.....
then tan^2(x), using binomial expansion gives
x^2+2*x^4/3+.... (we only need two terms)
and again apply l'Hôpital's rule, we have
L=d(x^2+2x^4/3+...)/d(x) = (2x+8x^3/3+...)/1
=0 as x->0
F(x)=2x
G(x)=x+5
Now
F(g(x))=2(x+5)
=2x+10
G(f(x))=2x+5
hello :<span>
<span>an equation of the circle Center at the
A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =4 and b = -1 (Center at the origin)
r = AP.... P(0.1)
r² = (AP)²
r² = (4-0)² +(-1-1)² = 16+4=20
an equation of the circle that satisfies the stated conditions.
Center at A(4,-1), passing through P(0, 1) is : </span></span>(x-4)² +(y+1)² = 20
