Step-by-step explanation:
An important property of equations is one that states that you can add the same quantity to both sides of an equation and still maintain an equivalent equation. ... If you think of an equation as being like a balance scale, the quantities on each side of the equation are equal, or balanced.
Answer:
a) the radius of the balloon increases at a rate of 5.42 in/s
b) the surface area of the balloon increases at a rate of 3 in²/s
Step-by-step explanation:
a) since the volume of a sphere V is
V= 4/3*π*R³
where R= radius , then the rate of change of the volume is
V' = dV/dR= 4*π*R²
using the chain rule
dV/dt = dV/dR*dR/dt
thus
k = 4*π*R² * dR/dt
dR/dt = k/(4*π*R²)
replacing values
dR/dt = k/(4*π*R²) = (33 in³/s) /(4*π*(22 in)²] = 5.42 in/s
then the radius of the balloon increases at a rate of 5.42 in/s
b) since the surface area is
S=4*π*R²
then
S' = dS/dR= 8*π*R
and
dS/dt = dS/dR*dR/dt = 8*π*R * k/(4*π*R²) = 2*k/R
replacing values
dS/dt = 2*k/R = 2*(33 in³/s)/( 22 in) = 3 in²/s
then the surface area of the balloon increases at a rate of 3 in²/s
Add the 7 and 4, which =11.
multiply times the 5, =55
and 20-55= -35
Answer:
The slope is zero. Since both coordinates have the y-value of -1, they are on the same line on the graph and form a horizontal line with a slope of zero. (a straight horizontal line)
Step-by-step explanation:
use the formula
(y2-y1)/(x2-x1)
to calculate the slope using 2 points
so where (x1,y1) (x2,y2) can be subsituted
so putting it in the formula ...
(-1-(-1))/(7-10)=
0/-3=0
Oh bro big rip I need help on math too it’s not a fun class