The answer is: [D]: 0.211 .
____________________________________________________________
Explanation:
________________________
Given: 2(7)^(3x+1) = 48<span>; Solve for "x" (using "ln");
______________________________________________
First, divide EACH side of the equation by: "2" ;
____________________________________________
</span>→ [<span>2(7)^(3x+1)] / 2 = 48 / 2 ;
_____________________________________
to get: </span> → 7^(3x+1) = 24 ;
____________________________
→ Now, take the "ln" of EACH side of the equation:
____________________________________________
→ ln [7^(3x+1)] = ln 24 ;
→ (3x+1) ln 7 = ln 24 ;
→ Divide EACH side of the equation by "ln 7" ;
→ [(3x+1) (ln 7)] / ln 7 = (ln 24 / ln 7) ;
→ 3x + 1 = (ln 24 /ln 7)
_____________________________
(Using calculator, "(ln 24 / ln 7)" equals: "1.63319659538");
___________________________________________
→ 3x + 1 = 1.63319659538 ;
→ Subtract "1" from EACH side of the equation;
→ 3x + 1 − 1 = 1.63319659538 − 1 ;
→ 3x = 0.63319659538 ;
→ Now, divide EACH side of the equation by "3"; to isolate "x" on one side of the equation; and to solve for "x" ;
_______________________________________________
→ 3x / 3 = 0.63319659538 / 3 ; (using calculator);
____________________________
to get:
____________________________________________
→ x = 0.2110655317933333 ; which is:
Answer choice: [D]: 0.211 (rounded).
The volume of the remaining paint is:
V1 = (1/4) * (pi) * (r ^ 2) * (h)
Where,
r: radio
h: height
Substituting values we have:
V1 = (1/4) * (3.14) * (8 ^ 2) * (20)
V1 = 1004.8 cm ^ 3
The smallest can volume is:
V2 = pi * r ^ 2 * h
Substituting values:
V2 = (3.14) * 5 ^ 2 * h
Matching the volumes:
V2 = V1
(3.14) * 5 ^ 2 * h = 1004.8
Clearing h:
h = (1004.8) / ((3.14) * 5 ^ 2)
h = 12.8 cm
Answer:
The height of the smallest part of the paint is:
h = 12.8 cm
taller, a 90% error??? I 'm not sure, but the first one I am sure.
If K=C+273.15
and in a. C=200° then K=200+273.15
The diameter of the table is 42 inches. The radius of the table is half of the diameter of the table, so the radius of the table is 42/2 = 21 inches.
Add on 8 inches to the table radius to get: 21+8 = 29
So the radius of the table cloth is r = 29
Plug this into the area of a circle formula
A = pi*r^2
A = pi*29^2
A = pi*841
A = 841pi
A = 841*3.14
A = 2640.74
The approximate area of the table cloth is 2640.74 square inches.
