Area of the parabolic region = Integral of [a^2 - x^2 ]dx | from - a to a =

(a^2)x - (x^3)/3 | from - a to a = (a^2)(a) - (a^3)/3 - (a^2)(-a) + (-a^3)/3 =

= 2a^3 - 2(a^3)/3 = [4/3](a^3)

Area of the triangle = [1/2]base*height = [1/2](2a)(a)^2 = a^3

ratio area of the triangle / area of the parabolic region = a^3 / {[4/3](a^3)} =

Limit of a^3 / {[4/3](a^3)} as a -> 0 = 1 /(4/3) = 4/3

3 0

3 years ago

How do i write a two column proof for this?? Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST

Nikolay [14]

Answer:

PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom)

Step-by-step explanation:

Given: PG ≅ SG and PT ≅ ST

To Prove: ∠GPT ≅ ∠GST

Proof: PG ≅ SG (Given)

PT ≅ ST (Given)

GT = GT (Common)

∴ ∠GPT ≅ ∠GST (SSS Congruency Axiom).

SSS Congruency Axiom: If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

Congruence: Two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

7 0

4 years ago

harriet is cultivating a strain of bacteria has doubled by the end of every second hour. how many bacteria will harriet have in

Black_prince [1.1K]

Answer:

n2^3 bacteria, n being the initial population.

Step-by-step explanation:

compound growth equation: P=n2^t

P is total population

n is initial population

t is time

since it doubles every second hour, and there are 6 hours

6hours/2hours= doubles 3 times, thats why t=3.

7 0

3 years ago