Can someone pls help me with 25 26 and 28

8090 [49]

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a 2 − b 2 = ( a + b ) ( a − b ) where a = 7 and b = a + x . − ( 7 + a + x ) ( a + x − 7 )

7 0

1 year ago

Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$

Substitute:

$\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}$

Combine fractions:

$\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}$

Simplify:

$6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}$

Q.E.D.

6 0

2 years ago

Consider a population of size N = 100 with the three individual mutants with relative growth rate rA = 2, rB = 1.01, and rC = 0.

Salsk061 [2.6K]

Answer 1 / 25

Step-by-step explanation:

The probability that the first

of the three mutants will take over the population = 2 / 100

The probability that the second

of the three mutants will take over the population = 1.01 / 100

The probability that the third

of the three mutants will take over the population = 0.99 / 100

Therefore, the probability that each of the three mutants will take over the population = probability of the first,second or third = 2 / 100 + 1.01 / 100 + 0.99 / 100 = (2+1.01+0.99)/100 = 4 / 100 = 2/25

7 0

2 years ago

Luke drove 325 miles in 5 hours. What was his average speed in miles per hour?

Stolb23 [73]

Answer:

65mph

Step-by-step explanation:

8 0

2 years ago

I need help on this problem. I got half of it right but I don’t know how I got the last answer wrong... Can anyone please help m

morpeh [17]

I got the same answer as you. Try to ask your teacher about it since it’s a math problem online or something.

8 0

2 years ago