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3 years ago

Find the area shown below. 1 13 12 6

Mathematics

1 answer:

Sonja [21]3 years ago

7 0

Answer:

Step-by-step explanation:

sides of the three sided figure==13,12,6

the longest side is the hypotenuse

this is 13

area of a triangle is height x base x 1/2

if so ... aarea is 12 x 6 x 1/2

that is equivalent to 36

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I have calculus problems that I need help with.

aleksklad [387]

a. Note that $f(x)=x^ne^{-2x}$ is continuous for all $x$ . If $f(x)$ attains a maximum at $x=3$ , then $f'(3) = 0$ . Compute the derivative of $f$ .

$f'(x) = nx^{n-1} e^{-2x} - 2x^n e^{-2x}$

Evaluate this at $x=3$ and solve for $n$ .

$n\cdot3^{n-1} e^{-6} - 2\cdot3^n e^{-6} = 0$

$n\cdot3^{n-1} = 2\cdot3^n$

$\dfrac n2 = \dfrac{3^n}{3^{n-1}}$

$\dfrac n2 = 3 \implies \boxed{n=6}$

To ensure that a maximum is reached for this value of $n$ , we need to check the sign of the second derivative at this critical point.

$f(x) = x^6 e^{-2x} \\\\ \implies f'(x) = 6x^5 e^{-2x} - 2x^6 e^{-2x} \\\\ \implies f''(x) = 30x^4 e^{-2x} - 24x^5 e^{-2x} + 4x^6 e^{-2x} \\\\ \implies f''(3) = -\dfrac{486}{e^6} < 0$

The second derivative at $x=3$ is negative, which indicate the function is concave downward, which in turn means that $f(3)$ is indeed a (local) maximum.

b. When $n=4$ , we have derivatives

$f(x) = x^4 e^{-2x} \\\\ \implies f'(x) = 4x^3 e^{-2x} - 2x^4 e^{-2x} \\\\ \implies f''(x) = 12x^2 e^{-2x} - 16x^3e^{-2x} + 4x^4e^{-2x}$

Inflection points can occur where the second derivative vanishes.

$12x^2 e^{-2x} - 16x^3 e^{-2x} + 4x^4 e^{-2x} = 0$

$12x^2 - 16x^3 + 4x^4 = 0$

$4x^2 (3 - 4x + x^2) = 0$

$4x^2 (x - 3) (x - 1) = 0$

Then we have three possible inflection points when $x=0$ , $x=1$ , or $x=3$ .

To decide which are actually inflection points, check the sign of $f''$ in each of the intervals $(-\infty,0)$ , $(0, 1)$ , $(1, 3)$ , and $(3,\infty)$ . It's enough to check the sign of any test value of $x$ from each interval.

$x\in(-\infty,0) \implies x = -1 \implies f''(-1) = 32e^2 > 0$

$x\in(0,1) \implies x = \dfrac12 \implies f''\left(\dfrac12\right) = \dfrac5{43} > 0$

$x\in(1,3) \implies x = 2 \implies f''(2) = -\dfrac{16}{e^4} < 0$

$x\in(3,\infty) \implies x = 4 \implies f''(4) = \dfrac{192}{e^8} > 0$

The sign of $f''$ changes to either side of $x=1$ and $x=3$ , but not $x=0$ . This means only $\boxed{x=1}$ and $\boxed{x=3}$ are inflection points.

4 0

1 year ago

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Please help! I have no idea how to do this, it’s very confusing

Vsevolod [243]

I like that you left How you did it on there. When I was in school I did it the same way. I would assume you’re using is over of equals percent over 100. The problem however is that the above number is always the total which means it should be on the bottom.

X/72= 45/100. Similar to what you have written. Solve the proportion. 100x=72x45
100x= 3240
X = 32.4

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3 years ago

The height of Mountain Pis 1,086 feet. The height of Mountain Q is 4 times the

Afina-wow [57]

Answer:

4,344 feet

Step-by-step explanation:

Mt. P is 1,086 feet tall. It says that Mt. Q is 4 times that. 1,086 x 4 is 4,344.

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2 years ago

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viktor has $250 in his bano account. he withdraws $15 per week. let x represent the number of weeks that he makes withdrawals an

antiseptic1488 [7]

The answer is y=$250-$15x.

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4 years ago

Use mental math to solve for the missing number:

Vaselesa [24]

Answer:

Step-by-step explanation:

Let the number be x.

The quotient of x and 3 is 13.

x/3 = 13

Multiply both sides by 3.

x = 13 × 3

x = 39

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3 years ago

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