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2 years ago

Help please I don’t understand this at all & been stuck here for a hour

Mathematics

1 answer:

ELEN [110]2 years ago

4 0

Answer:

Step-by-step explanation:

4b + 8 = 20

Subtract 8 from both sides

4b + 8 - 8 = 20 - 8

4b = 12

Now divide both sides by 4

4b/4 = 12/4

b = 3

Check:

LHS = 4b + 8

= 4*3 + 8

= 12 + 8

= 20 = RHS

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Which bacteria sample (A or B) had a smaller initial population? What was that value?

zubka84 [21]

Answer:

B has a smaller initial population of 500

Step-by-step explanation:

Given

See attachment for complete question

Required

The bacteria with the smaller initial population

The initial population is at x = 0

For bacteria A;

$A(x) = 600$ when $x = 0$

For bacteria B, we have:

$B(x) = 500(2)^x$

Substitute 0 for x

$B(x) = 500(2)^0$

$B(x) = 500*1$

$B(x) = 500$

So; when x = 0

$A(x) = 600$ and $B(x) = 500$

Because; 500 < 600

We can conclude that B has a smaller initial population of 500

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2 years ago

Solve the equation. StartFraction dx Over dt EndFraction equals StartFraction 1 Over x e Superscript t plus 7 x EndFraction An i

MAVERICK [17]

Answer:

$\frac{1}{49}(7x-1)e^{7x}+e^{-t}=C$

Step-by-step explanation:

We are given that

$\frac{dx}{dt}=\frac{1}{xe^{t+7x}}$

We have to find the implicit function

Using separation variable method

$\frac{dx}{dt}=\frac{1}{xe^t\cdot e^{7x}}$

By using property $x^a\cdot x^y=x^{a+y}$

$xe^{7x}dx=e^{-t}dt$

By using property $\frac{1}{x^a}=x^{-a}$

Taking integration on both sides

$\int xe^{7x}dx=\int e^{-t}dt$

Parts integration method

$\int u\cdot v dx=u\int vdx-\int (\frac{du}{dx}\int vdx)dx$

By parts integration method

$x\int e^{7x}dx-\int (\frac{dx}{dx}\int e^{7x}dx)dx=-e^{-t}+C$

Using formula $\int e^{ax} dx=\frac{e^{ax}}{a}+C$

$\frac{xe^{7x}}{7}-\frac{1}{7}\int e^{7x}dx=-e^{-t}+C$

$\frac{xe^{7x}}{7}-\frac{1}{49}e^{7x}+e^{-t}=C$

$\frac{1}{49}(7x-1)e^{7x}+e^{-t}=C$

We are given that

$F(x,t)=C$

$F(x,t)=\frac{1}{49}(7x-1)e^{7x}+e^{-t}=C$

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earnstyle [38]

Answer:

Step-by-step explanation:

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