Answer:
Step-by-step explanation:
a+b+c=0, a+b=-c,a+c=-b, b+c=-a
(a+b+c)^3=(a+b+c)^2*(a+b+c)=(a^2+b^2+c^2+2ab+2ac+2bc)*(a+b+c)=
a^3+ab^2+ac^2+2a^2b+2a^2c+2abc+a^2b+b^3+bc^2+2ab^2+2abc+2b^2c+a^2c+b^2c+c^3+2abc+2ac^2+2bc^2=a^3+b^3+c^3+3a^2b+3a^2c+3ac^2+3ab^2+3bc^2+3b^2c+6abc=
a^3+b^3+c^3+3a^2*(b+c)+3c^2(a+b)+3b^2(a+c)+6abc=
a^3+b^3+c^3+3a^2*(-a)+3c^2*(-c)+3b^2*(-b)+6abc=
a^3+b^3+c^3-3a^3-3c^3-3b^3+6abc=
6abc-2a^3-2b^3-2c^3=2(3abc-a^3-b^3-c^3)=
2*[3abc-(a^3+b^3+c^3)]=0
so 3abc-(a^3+b^3+c^3)=0
so a^3+b^3+c^3=3abc
Answer:
(a) 120 square units (underestimate)
(b) 248 square units
Step-by-step explanation:
<u>(a) left sum</u>
See the attachment for a diagram of the areas being summed (in orange). This is the sum of the first 4 table values for f(x), each multiplied by 2 (the width of the rectangle). Quite clearly, the curve is above the rectangle for the entire interval, so the rectangle area underestimates the area under the curve.
left sum = 2(1 + 5 + 17 + 37) = 2(60) = 120 . . . . square units
<u>(b) right sum</u>
The right sum is the sum of the last 4 table values for f(x), each multiplied by 2 (the width of the rectangle). This sum is ...
right sum = 2(5 +17 + 37 +65) = 2(124) = 248 . . . . square units
Answer:
Yes MNO is similar to PQO
1 basket is between 9 and 10 minutes .
<u>Step-by-step explanation:</u>
Here we have , John kept track of how many baskets were made in a basketball game. After 4 minutes, 5 baskets were made. We need to find How many baskets were made between 9 and 10 minutes . Let's find out:
In order to calculate baskets between 9 min and 10 min we will find baskets at 10 min and at at 9 min , will subtract than !
Baskets at 10 min :
At 4 min we have 5 baskets so , in 10 min
⇒ 
⇒ 
⇒ 
Baskets at 9 min :
At 4 min we have 5 baskets so , in 9 min
⇒ 
⇒ 
⇒ 
So , Baskets between 10 & 9 min is
, which on rounding off gives 1 . Therefore , 1 basket is between 9 and 10 minutes .

First, square both sides (d.) leaving 3x + 1 = 16
Second, subtract 1 from both sides (a.) leaving 3x = 15
Third, divide by 3 from both sides (e.) leaving x = 5
Answer: First D, then A, then E