Find the value of each expression.10. |-41|12. -|1.5|

Mathematics

2 answers:

Bingel [31]3 years ago

5 0

Answer:

A.) 41

B.) -1.5

Step-by-step explanation:

Absolute value means to make whatever that is inside positive

10.) The absolute value of negative 41 would simply be positive 41

11.) Since the negative sign is on the outside of the absolute value, you do the absolute value of everything inside then apply a negative sign. Absolute value of 1.5 is just 1.5 because it's already positive. Then apply the negative sign, which would make it -1.5

Valentin [98]3 years ago

3 0

Step-by-step explanation:

10. |-41|= 41

12. -|1.5|= -1.5

You might be interested in

A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$