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Rina8888 [55]
3 years ago
7

How do you do this question?

Mathematics
1 answer:
alina1380 [7]3 years ago
7 0

Answer:

(8√2) / 15

Step-by-step explanation:

A curve bounded by the y-axis is represented by in terms of dy;

\int \:x\:dt

When the curve crosses the y-axis, x will be 0. In this case x is the function of t, so we have to solve for x(t) = 0;

0 = t^2 + 2t --- (1)

Solution(s) => t = 0, t = 2

dy = (1/2 * 1/√t)dt --- (2)

Our solutions (0, 2) are our limits. The area of the curve is in the form A\:=\:\int _b^a\:f\left(t\right)g'\left(t\right)dt , so now let's introduce the limits of integration, x(t) and dy/dt. Remember, dy/dt = (1/2 * 1/√t) (second equation). 1/2 * 1/√t can be rewritten as 1/2 * t^(-1/2)....

A\:=\:\int _2^0\:\left(t^2-2t\right)\left(\frac{1}{2}t^{-\frac{1}{2}}\right)dt\\\\= \int _2^0\:\left(\frac{1}{2}t^{\frac{3}{2}}-t^{\frac{1}{2}}\right)dt\\\\= \left[\frac{t^{\frac{5}{2}}}{5}-\frac{2t^{\frac{3}{2}}}{3}\right]_2^0\\\\= 0\:-\:\left(\frac{4\sqrt{2}}{5}-\frac{4\sqrt{2}}{3}\right)\\\\= \frac{8\sqrt{2}}{15}

Your solution is 8√2 / 15

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Step-by-step explanation:

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3 years ago
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Graph y = 3(x + 2)3 - 3 and describe the end behavior.
-BARSIC- [3]
1) The function is 3(x + 2)³ - 3

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3) Since the polynomial is of odd degree you can predict that the ends head off in opposite direction. The limits confirm that.

4) The limit when x approaches negative infinity is negative infinity, then the left end of the function heads off downward (toward - ∞).

5) The limit when x approaches positive infinity is positivie infinity, then the right end of the function heads off upward (toward + ∞).

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- critical points: local maxima, local minima, and inflection points.


7) x-intercepts ⇒ y = 0

⇒ <span>3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>

<span>⇒ (x + 2)³ = -1 ⇒ x + 2 =  1 ⇒ x = - 1
</span>

8) y-intercepts ⇒ x = 0

y = <span>3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21
</span><span>
</span><span>
</span><span>9) Critical points ⇒ first derivative = 0
</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒ x = - 2
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</span><span>ii) second derivative: to determine where x = - 2  is a local maximum, a local  minimum, or an inflection point.
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</span><span>y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.
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</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an inflection point at x =  -2.
</span><span>
</span><span>
</span><span>Using all that information you can graph the function, and I attache the figure with the graph.
</span>


3 0
3 years ago
What the answer now hurry up
maxonik [38]

Answer:

Below

Step-by-step explanation:

The equation of a circle is written as:

(x-a)^2 + (y-b)^2 = r^2

● ( a,b) are the coordinates of the center . Here (0,-2)

● r is the radius (here 12)

So the equation is:

x^2 + (y+2)^2 = 12^2

6 0
3 years ago
Please explain your answer<br> WIll mark as brainliest.
navik [9.2K]

Answer:

sorry don't know

Step-by-step explanation:

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Solve this please!! Best answer will get brainliest &lt;3
Fudgin [204]

Answer:

1. (-3 , 3)    (-8 , 8)

2. (3 , -3)    (8 , -8)

3. (0 , 0)     (5 , 5)

Step-by-step explanation:

1. Multiply the X values by negative 1 to reflect across the X axis.

2 Multiply the Y values by negative 1 to reflect across the Y axis.

3. Subtract 3 from each value when everything is getting moved towards a lower number.

5 0
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