Answer:
Options A-C-F
Step-by-step explanation:
we know that
<em>The circumference of a circle is equal to</em>
or
where
D is the diameter and r is the radius
therefore
or
The number pi is the ratio circumference - diameter or is the ratio circumference - 2 times radius
<em>The area of the circle is equal to</em>
therefore
The number pi is the ratio Area - radius squared
The equation that represents the array (rectangles and area) multiplication model that sows two grey shaded columns of length one ninth each and three rows with dots of width one fourth each is option <em>a</em>
a) The equation with fractions two ninths times three fourths is equal to six thirty sixths
An array representation of a multiplication is a rectangular visual order of positioning of rows and columns that indicates the terms of a multiplication equation.
Please find attached the area model to multiply the fractions
The terms of the equation represented by the model are indicated by the two columns of length one ninth each shaded grey and the three rows of width one fourth each covered with dots, such that the equation can be presented as follows;
The equation that the model represents is therefore;
Learn more about multiplication models here:
#SPJ1
If we evaluate the function at infinity, we can immediately see that:
Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.
We can solve this limit in two ways.
<h3>Way 1:</h3>By comparison of infinities:
We first expand the binomial squared, so we get
Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.
<h3>Way 2</h3>Dividing numerator and denominator by the term of highest degree:
Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.