Find dy/dx if y= (1+x)e^x^2

Answers

Answer 1

Answer: $y=(1+x)e^(x^2)\ny'=(1+x)'\cdot e^(x^2)+(1+x)\cdot(e^(x^2))'\ny'=1\cdot e^(x^2)+(1+x)\cdot e^(x^2)\cdot (x^2)'\ny'=e^(x^2)+(1+x)e^(x^2)\cdot2x\ny'=e^(x^2)(1+(1+x)\cdot2x)\ny'=e^(x^2)(1+2x+2x^2)\ny'=e^(x^2)(2x^2+2x+1)\n$

Answer 2

Answer: You first need to know that:

$If\quad y=u\cdot v\n \n \frac { dy }{ dx } =u\frac { dv }{ dx } +v\frac { du }{ dx } \n \n$

Knowing that u is a function of x and that v is a function of x.

So:

$y=\left( 1+x \right) { e }^{ { x }^( 2 ) }=u\cdot v\n \n u=1+x,\n \n \therefore \quad \frac { du }{ dx } =1$

$\n \n v={ e }^{ { x }^( 2 ) }={ e }^( p )\n \n \therefore \quad \frac { dv }{ dp } ={ e }^( p )={ e }^{ { x }^( 2 ) }\n \n p={ x }^( 2 )\n \n \n \therefore \quad \frac { dp }{ dx } =2x$

$\n \n \therefore \quad \frac { dv }{ dp } \cdot \frac { dp }{ dx } =2x{ e }^{ { x }^( 2 ) }=\frac { dv }{ dx }$

And this means that:

$\frac { dy }{ dx } =\left( 1+x \right) \cdot 2x{ e }^{ { x }^( 2 ) }+{ e }^{ { x }^( 2 ) }\cdot 1\n \n =2x{ e }^{ { x }^( 2 ) }\left( 1+x \right) +{ e }^{ { x }^( 2 ) }$

$\n \n ={ e }^{ { x }^( 2 ) }\left( 2x\left( 1+x \right) +1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2x+2{ x }^( 2 )+1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2{ x }^( 2 )+2x+1 \right)$

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Pls help its urgentttt

Answers

Answer:

-21 is the answer is this true or false

A zoo has 9 lions. 6 are males. Find the ratio of female lions to male lions.

Answers

the ratio of female lions to male lions is 3:6

The ratio is 3:6! Hope this helps!

Mateo is doing an experiment for Physics class. He drops a bouncy ball off abalcony from a height of 12 meters. The ball's next bounce is always 75% of
the height of the previous bounce. Let n = bounce number. Before the ball is
dropped, n = 0, because the ball has not yet bounced. Which explicit formula
represents the height of the ball after n bounces?

Answers

Final answer:

The height of the ball after n bounces is given by the formula a_n = 12 * 0.75^(n - 1). This formula represents a geometric sequence where each height is 75% of the previous height.

Explanation:

The height the bouncy ball reaches after each bounce is a geometric sequence, where each subsequent height is found by multiplying the previous height by the common ratio, 75%, or 0.75. The initial term is the original height from which the ball is dropped, which is 12 meters.

The explicit formula for a geometric sequence is a_n = a_1 * r^(n - 1). Replacing a_1 with 12 (the initial height), r with 0.75 (the common ratio), and n with the bounce number, the explicit formula to find the height of the ball after n bounces is a_n = 12 * 0.75^(n - 1).

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Answer:

Max. height following bounce # n is 12(¾)n because each prior height is multiplied by three fourths.

Step-by-step explanation: it jus is

What are the approximate solutions of 2x2 − 7x = 3, rounded to the nearest hundredth?A: No real solutions
B: x ≈ −0.77 and x ≈ 7.77
C: x ≈ −0.39 and x ≈ 3.89
D: x ≈ −3.89 and x ≈ 0.39

Answers

Answer:

Option C is the correct option.

Step-by-step explanation:

The given equation is 2x² - 7x - 3 = 0

In this quadratic equation we will use quadratic formula to get the roots of x.

$x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}$

By putting values of a = 2, b = -7 and c = -3 in the quadratic formula

$x=\frac{7\pm \sqrt{(-7)^(2)-4* 2* (-3)}}{2* 2}$

$=(7\pm √(49+24))/(4)$

$=(7\pm √(73))/(4)$

Now we get two values for x

$x=(7+√(73))/(4)$

$=(7+8.54)/(4)=3.89$

and $x=(7-√(73))/(4)$

$=(7-8.54)/(4)$

$=-(1.54)/(4)=-0.39$

Therefore option C. is the answer.

The approximate solutions of equation 2x² - 7x = 3 are,

C: x ≈ −0.39 and x ≈ 3.89

We have to given that,

An expression is,

⇒ 2x² - 7x = 3

Now, We can find the approximate solutions of equation as,

⇒ 2x² - 7x = 3

⇒ 2x² - 7x - 3 = 0

By using quadratic formula, we get;

⇒ x = - (- 7) ± √(- 7)² - 4×2×- 3 / (2×2)

⇒ x = (7 ± √49 + 24) / 4

⇒ x = (7 ± √73) / 4

⇒ x = (7 ± 8.5) / 4

This give two solutions,

⇒ x = (7 - 8.5) / 4

⇒ x = - 1.5 / 4

⇒ x = - 0.39

⇒ x = (7 + 8.5) / 4

⇒ x = 15.5 / 4

⇒ x = 3.89

Therefore, The approximate solutions of equation 2x² - 7x = 3 are,

C: x ≈ −0.39 and x ≈ 3.89

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Solve for L: d=LM/R2+R1

Answers

d=LM/(R2+R1)
d(R2+R1)=LM
[d(R2+R1)]/M=L

Answer:

Given the equation: $d = (LM)/(R_2+R_1)$ .....[1]

Cross multiply states that an equation of fractions when each of the side consists of a fraction with a single denominator by multiplying the numerator of each side by the denominator of the other side and equating these two products obtained.

Apply the cross multiply in [1], we get;

$d(R_2 +R_1) = LM$

Divide both sides by M we get;

$L = (d(R_2+R_1))/(M)$

$L = (dR_2+dR_1)/(M)$

In accordance with 14 CFR Part 107, at what maximum altitude can you operate an sUAS when inspecting a tower with a top at 1,000 ft AGL at close proximity (within 100 feet)?

Answers

Answer:

The max altitude you can operate an sUAS on these given conditions is 1400ft AGL.

Step-by-step explanation:

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