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2 years ago

Solve inequality -3m > 75

Mathematics

2 answers:

Dahasolnce [82]2 years ago

8 0

Step-by-step explanation:

-3m > 75

3m < -75

m < -25

that's it.

Ivahew [28]2 years ago

7 0

Answer:

m< - 25

Step-by-step explanation:

-3m > 75

(-3m)/(-3) <75/(-3) (divide both members by (-3) (which is a negative number so ">" becames "<")

m<-25

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Martha drew the following shape on her

zalisa [80]

Answer:

right angles and obtuse angles

Step-by-step explanation:

We assume that anything that looks like a right angle is a right angle.

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3 years ago

Find the area of the circle [?] square units

xxMikexx [17]

Answer:

169π or 530.93

Step-by-step explanation:

The formula for the area of a circle is πr²

Here, the radius is given to be 13.

So, let's just plug it into the formula as r

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4 years ago

Find the solution to the differential equation dB/dt+4B=20 with B(1)=30

natita [175]

Answer:

The solution of the differential equation is $B=5+25e^{-4t+4}$

Step-by-step explanation:

The differential equation $\frac{dB}{dt}+4B=20$ is a first order separable ordinary differential equation (ODE). We know this because a separable first-order ODE has the form:

$y'(t)=g(t)\cdot h(y)$

where g(t) and h(y) are given functions.

We can rewrite our differential equation in the form of a first-order separable ODE in this way:

$\frac{dB}{dt}+4B=20\\\frac{dB}{dt}=20-4B\\\frac{dB}{dt}=4(5-B)\\\frac{1}{5-B}\frac{dB}{dt}=4$

Integrating both sides

$\frac{1}{5-B}\frac{dB}{dt}=4\\\frac{1}{5-B}\cdot dB=4\cdot dt\\\\\int\limits {\frac{1}{5-B}} \, dB=\int\limits {4} \, dt$

The integral of left-side is:

$\int\limits {\frac{1}{5-B}} \, dB\\\mathrm{Apply\:u-substitution:}\:u=5-B\\\int\limits {\frac{1}{5-B}} \, dB=\int\limits {\frac{1}{u}} \, dB\\\mathrm{du=-dB}\\-\int\limits {\frac{1}{u}} \,du\\\mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)\\-\int\limits {\frac{1}{u}} \,du =-\ln \left|u\right|\\\mathrm{Substitute\:back}\:u=5-B\\-\ln \left|5-B\right|\\\mathrm{Add\:a\:constant\:to\:the\:solution}\\-\ln \left|5-B\right|+C$