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12345 [234]
3 years ago
12

How can I solve it??ans= 1/2 -1/2x^2​

Mathematics
1 answer:
max2010maxim [7]3 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

Differentiate using the power rule

\frac{d}{dx}(ax^{n}) = nax^{n-1}

Simplify the expression by dividing both terms on the numerator by 2x²

\frac{x^3+x}{2x^2}

= \frac{x^3}{2x^2} + \frac{x}{2x^2}

= \frac{1}{2} x + \frac{1}{2} x^{-1}

Hence differentiating gives

\frac{1}{2} - \frac{1}{2}x^{-2}

= \frac{1}{2} - \frac{1}{2x^2}

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PLEASE HELP ME WITH THIS QUESTION PLEASE
Ugo [173]

Answer:

a. 2.2 m

b. 8 m

Step-by-step explanation:

4) a. Sin 32 = x/4

= (sin 32)(4) = x

b. Cos 65 = 4.5/x

x = 4.5/Cos 65

6 0
3 years ago
3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k
Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt

Evaluate the integral to solve for y :

\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt

\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x

\displaystyle y = x^3+2x^2+kx - 2

Use the other known value, f(2) = 18, to solve for k :

18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}

Then the curve C has equation

\boxed{y = x^3 + 2x^2 + 2x - 2}

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2

The slope of the given tangent line y=x-2 is 1. Solve for a :

3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1

So, the point of contact between the tangent line and C is (-1, -3).

7 0
3 years ago
Answer this questionnnnnnnnnnnn
-BARSIC- [3]
There would approximately be 36 ordered triples
4 0
3 years ago
A woodworker makes wooden checkerboards. her profit is a function of the price she charges. this graph shows her total profits,
pantera1 [17]

Answer:

Option B.

Step-by-step explanation:

Remember that the profit is defined as the difference between the revenue and the cost.

So, having a profit y = 0 means that the woodworker did not win nor lose anything.

Then the zeros of the function, the values of x such that the graph intersects the x-axis, are the prices such that she does not win nor loss anything.

In the graph we can see that the zeros are at:

x = 15 (the first one)

x = 70 (the second one)

so the zeros are at x = 15 and x = 70, and these are the prices such that the profit is zero, so at these prices she does not make nor lose money.

The correct option is B.

8 0
3 years ago
5x- 3ydnd-ht5bydvhtdtuufr57iihytyu-mhg
fomenos

Is this even a real question

7 0
3 years ago
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