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2 years ago

Consider f(x)=cos^2x+2cosx over one complete period beginning with x=0

1 answer:

3 0

Period is from 0 to 2pi

take the deritivive then take it again
we get f''(x)=-4cos²(x)-2cos(x)+2

it is negative between 0 and pi/3 and also between 5pi/3 and 2pi

concave down in the interval
$[0, \frac{ \pi }{3}]$ U $[\frac{ 5\pi }{3},2\pi]$

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Suppose the integral from 2 to 8 of g of x, dx equals 12, and the integral from 6 to 8 of g of x, dx equals negative 3, find the

Artyom0805 [142]

$\displaystyle\int_2^8g(x)\,\mathrm dx=12$

$\displaystyle\int_6^8g(x)\,\mathrm dx=-3$

Use the fact that integrals are additive on their intervals. Mathematically, if $c\in[a,b]$ , then

$\displaystyle\int_a^bg(x)\,\mathrm dx=\int_a^cg(x)\,\mathrm dx+\int_c^bg(x)\,\mathrm dx$

So we have

$\displaystyle2\int_2^6g(x)\,\mathrm dx=2\left(\int_2^8g(x)\,\mathrm dx-\int_6^8g(x)\,\mathrm dx\right)=2(12-(-3))=30$

8 0

3 years ago

Five times the sum of a number and 3 is the same as 3 multiplied by 1 less than twice the number

Aneli [31]

Answer:-2

Step-by-step explanation:

(n + 3) 5 = 3 x 1 - n

distribute so 5n + 15= 3 - n

subtract three from both sides

5n - 12 = -n

subtract 5n from both sides

12 = −6n

Divide both sides by -6

n=-2

7 0

3 years ago

Is the quotient 2.7 divided by 3 greater or less than one

lozanna [386]

2.7/3=0.9
it is less than one

7 0

2 years ago

Read 2 more answers

Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Vikki [24]

Answer:

Height: 3/2 inches

Length: 12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

The new length of the cardboard = 15 -2x (because we cut from 4 corners)
The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = $4x^3 -44x^2 +105x$

To maximum volume, we use the first derivative of the volume

$\dfrac{dV}{dx} = 0$

<=> $12x^2-88x+105=0$

<=> $\left(2x-3\right)\left(6x-35\right) = 0$

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

$\dfrac{d^2V}{dx^2}$ = 24x -88

If x = 3/2, we have:

$\dfrac{d^2V}{dx^2}$ = 24(3/2) -88 = -52

If x = 35/6, we have:

$\dfrac{d^2V}{dx^2}$ = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0

2 years ago

seven less than the product of twice a number is greater than 5 more the same number which integer satisfies this inequality

JulsSmile [24]

To answer this question, we would have to use algebra.

Let the unknown number be A.

Now, as per the question, we have the equation ->
2A - 7 > 5 + A
==> 2A - A > 5+7
==> A > 12

So, the final answer is --> A > 12

4 0

2 years ago

Read 2 more answers