A. Translate each of the following into algebraic expressions: (1 point each)
1.x plus y squared ---> x + y^2
2.8 times a number, x, decreased by y ---> 8x - y
3.the sum of x and y, squared ---> (x + y)^2
4.3 times the difference of x and y ---> 3( x - y)
5.6 less than x cubed --- > x^3 - 6
B. Translate the following phrases into algebraic expressions. Explain,
in complete sentences, the difference between the two. (3 points)
´twice the sum of x and y ---> 2(x + y)
´the sum of twice x and y ---> 2x + y
The first one adds first x and y, and then doubles the result, while the second one first doubles de value of x and the adds y.
C. Create your own example of a mathematical phrase you might hear in
the real world and provide the translation for it. Be sure to identify
what part of the phrase i
The sales of this year exceeded the sales of last year in tweny millions.
y = x + 20,000,000, where x represents the sales of last year and y represents the sales of this year,
Answer:
-x¹⁴ / 5040
-½ < x < ½
Step-by-step explanation:
f(x) = e^(-x²)
The Taylor series for eˣ centered at 0 is:
eˣ = ∑ (1/n!) xⁿ
Substitute -x²:
e^(-x²) = ∑ (1/n!) (-x²)ⁿ
e^(-x²) = ∑ (1/n!) (-1)ⁿ x²ⁿ
The 14th degree term occurs at n=7.
(1/7!) (-1)⁷ x¹⁴
-x¹⁴ / 5040
ln(1 + x) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ xⁿ / n
If we substitute 4x²:
ln(1 + 4x²) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ (4x²)ⁿ / n
Using ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺² (4x²)ⁿ⁺¹ / (n+1)] / [(-1)ⁿ⁺¹ (4x²)ⁿ / n]│< 1
lim(n→∞)│-1 (4x²) n / (n+1)│< 1
4x² < 1
x² < ¼
-½ < x < ½
Answer:
7.) 18.86m
8.) 15 inches
9.) 32 and 34
10.) 21 and 29
11.) change all the decimals in the equation into fractions.
Step-by-step explanation:
<h3>Given:</h3>
<h3>Note that:</h3>
<h3>To find:</h3>
The volume of the given cone.
<h3>Solution:</h3>


Let's solve!
Substitute the values according to the formula.


<u>Therefore</u><u>,</u><u> </u><u>the</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>cone</u><u> </u><u>is</u><u> </u><u>2863.6</u><u>8</u><u> </u><u>cubic</u><u> </u><u>feets</u><u>.</u>