Answer:
26
Step-by-step explanation:
=15(2) - 2(2)
=30 - 4
=26
36m+25. ehhwienebtbtbrbve
Hello,
P(x)=x^4-6x²+2=(x-a)(x-b)(x-c)(x-d)
=x^4-(a+b+c+d)x^3+(ab+ac+ad+bc+bd+cd)x^2-(abc+abd+acd+bcd)x+abcd
==>
ab+ac+ad+bc+bd+cd=-6
abc+abd+acd+bcd=0
abcd=2
a+b+c+d=0 ==>(a+b+c+d)²=0=a²+b²+c²+d²+2(ab+ac+ac+bc+bd+cd)
==>a²+b²+c²+d²=0-2*(-6)=12
if a is a root P(a)=0==>a^4-6a²+2=0
if b is a root P(b)=0==>b^4-6b²+2=0
if c is a root P(a)=0==>c^4-6c²+2=0
if d is a root P(a)=0==>d^4-6d²+2=0
==>a^4+b^4+c^4+d^4-6(a²+b²+c²+d²)+4*2=0
==>a^4+b^4+c^4+d^4=-8+6*12=64
Answer:
The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.
Step-by-step explanation:
Geometrically speaking, the volume of the right circular cone (
), in cubic inches, is defined by the following formula:
(1)
Where:
- Radius, in inches.
- Height, in inches.
Then, we derive an expression for the rate of change of the volume (
), in cubic inches per second, by derivatives:
(2)
Where:
- Rate of change of the radius, in inches per second.
- Rate of change of the height, in inches per second.
If we know that 
, 
, 
and 
, then the rate of change of the volume is:
The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.
