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3 years ago

U6 D2 Identify the Dependent Quantity

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

5 0

Answer:

B: How many boxes of candles Frank will buy.

Step-by-step explanation:

It would be b, since the amount of boxes Frank buys is affected by how old his grandmother is. This makes it the dependent quantity.

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Can someone please help me with this on ill mark you brainiest if correct

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We cannot find the 3rd Side unless & until the perimeter of triangle is not given!

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3 years ago

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Simplify the following expression. 33.414 - 33.36

jeyben [28]

Answer:

Step-by-step explanation:

33.414−33.36

=33.414−33.36

=33.414+−33.36

=0.054

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4 years ago

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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:

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

The integral of right-side is:

$\int\limits {4} \, dt = 4t + C$

We can join the constants, and this is the implicit general solution

$-\ln \left|5-B\right|+C=4t + C\\-\ln \left|5-B\right|=4t + D$

If we want to find the explicit general solution of the differential equation

We isolate B

$-\ln \left|5-B\right|=4t + D\\\ln \left|5-B\right|=-4t+D\\\left|5-B\right|=e^{-4t+D}$

Recall the definition of |x|

$|x|=\left \{ {{x, \:if \>x\geq \>0 } \atop {-x, \:if \>x0}} \right.$

$\left|5-B\right|=e^{-4t+D}\\5-B= \pm \:e^{-4t+D}\\B=5 \pm \:e^{-4t+D}\\B=5\pm \:e^{-4t}\cdot e^{D}\\B=5+Ae^{-4t}$

where $A=\pm e^{D}$

Now B(1) =30 implies

$B=5+Ae^{-4t}\\30=5+Ae^{-4}\\30-5=Ae^{-4}\\25e^{4}=A$

And the solution is

$B=5+(25e^{4})e^{-4t}\\B=5+25e^{-4t+4}$

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4 years ago

The gas tank of Tyrell's truck holds 19.8. Gallons. When the tank is empty, Tyrell fills it with gas that costs $3.65 per gallon

vovangra [49]

It would cost about $72.27 to fill the tank, but if it’s asking for estimate then you might have to round it to $70

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3 years ago

Amelia had $175,000 in a CD at Treasure Trove Bank, which just failed. If the FDIC insurance limit per depositor per bank is $25

uysha [10]

Answer:

The correct option is A. Amelia will get $175,000.

Step-by-step explanation:

It is given that Amelia had $175,000 in a CD at Treasure Trove Bank, which just failed and FDIC insurance limit per depositor per bank is $250,000.

It means the FDIC insurance company will settle the loss till $250,000.

If the deposited amount of depositors is less than $250,000, then they will get their total deposited amount and if the deposited amount of depositors is greater than or equal to $250,000, then they will get only $250,000.

Since the deposited amount of Amelia is $175,000, which is less than $250,000, therefore she will get her total deposited amount.

$175,000$

Therefore correct option is A. Amelia will get $175,000.

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3 years ago

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