In y = mx+b, m is the term that refers to slope
hope this helps
The equation is separable, so solving it is trivial:
![\dfrac{\mathrm dy}{\mathrm dt}=ky\implies\dfrac{\mathrm dy}y=k\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dt%7D%3Dky%5Cimplies%5Cdfrac%7B%5Cmathrm%20dy%7Dy%3Dk%5C%2C%5Cmathrm%20dt)
Integrating both sides gives
![\ln|y|=kt+C\implies y=e^{kt+C}=Ce^{kt}](https://tex.z-dn.net/?f=%5Cln%7Cy%7C%3Dkt%2BC%5Cimplies%20y%3De%5E%7Bkt%2BC%7D%3DCe%5E%7Bkt%7D)
Given
and
, we find
![24=C](https://tex.z-dn.net/?f=24%3DC)
![18=Ce^k=24e^k\implies e^k=\dfrac34\implies k=ln\dfrac34](https://tex.z-dn.net/?f=18%3DCe%5Ek%3D24e%5Ek%5Cimplies%20e%5Ek%3D%5Cdfrac34%5Cimplies%20k%3Dln%5Cdfrac34)
so the answer is E.
∛a² → C
From the ' law of exponents '
= ![\sqrt[n]{a^{m} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5E%7Bm%7D%20%7D)
Answer:
This is a complete lesson with instruction & exercises for 5th grade about multiplying decimals by decimals. The interpretation for multiplying a decimal by a decimal is to think of it as taking a fractional part of a decimal number (the symbol × translates to "of"). The lesson compares multiplication by a decimal to scaling & shrinking a stick. Lastly, it shows the common shortcut to decimal multiplication (multiply as if there were no decimal points; the answer has as many decimals as the factors have in total.)
In the video below, I explain the rule for multiplying decimals (put as many decimal digits in the answer as there are in the factors.) I explain where this rule comes from, using fraction multiplication. The lesson continues below the video.
Answer:
The profit of the company will be $224.85
Step-by-step explanation:
Let the equation of profit be termed as E(x)
we are given
amount of purchasing the policy (let a)= $1000
probability that women will live for at least 1 year (let b) = 0.9581
amount lost by insurance company if the women dies (let c) = 18,500-1000 = 17,500
the probability woman dies within one year (let d) = 1-0.9581=0.0419
the equation will be
E(x) of profit= a*b - c*d = 1000*0.9581 - 17500*0.0419
= 958.1 - 733.25
= 224.85