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3 years ago

7

I'm stuck on graphing this quadratic equation:

%2B%204x%20%2B%203" id="TexFormula1" title="y \leqslant {x}^{2} + 4x + 3" alt="y \leqslant {x}^{2} + 4x + 3" align="absmiddle" class="latex-formula">

1 answer:

rewona [7]3 years ago

7 0

Your welcome I hope it is right

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<span>point-slope form of the equation
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y - 2 = -2/3(x + 8)

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The slope f '(x) at each point (x, y) on a curve. y = f (x) is given along with a particular point (a, b) on the curve. Use this

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Step-by-step explanation:

Integrating each term with respect to x, we get:

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Find an equation of the tangent line to the hyperbola y = 3/x at the point (3, 1).

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Let's find the derivative of that hyperbola in order to find a slope formula to help us with this equation. We already have an x and y value. The derivative is found this way: $y'= \frac{x(0)-3(1)}{x^2}$ so $y'=- \frac{3}{x^2}$ . The derivative supplies us with the slope formula we need to write the equation. Sub in the x value of 3 to find what the slope is: $y'=- \frac{3}{3^2}=- \frac{3}{9}=- \frac{1}{3}$ . So in our slope-intercept equation, x = 3, y = 1, and m = -1/3. Use these values to solve for b. $1=- \frac{1}{3}(3)+b$ so b = 2. The equation, then, for the line tangent to that hyperbola at that given point is $y=- \frac{1}{3}x+2$

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3 years ago

A grain silo has the shape of a right circular cylinder surmounted by a hemisphere. If the silo is to have a volume of 505π ft3,

Romashka-Z-Leto [24]

Answer:

radius x = 3 ft

height h = 23,8 ft

Step-by-step explanation:

From problem statement

V(t) = V(cylinder) + V(hemisphere)

let x be radius of base of cylinder (at the same time radius of the hemisphere)

and h the height of the cylinder, then:

V(c) = π*x²*h area of cylinder = area of base + lateral area

A(c) = π*x² + 2*π*x*h

V(h) = (2/3)*π*x³ area of hemisphere A(h) = (2/3)*π*x²

A(t) = π*x² + 2*π*x*h + (2/3)*π*x²

Now A as fuction of x

total volume 505 = π*x²*h + (2/3)*π*x³

h = [505 - (2/3)* π*x³ ] /2* π*x

Now we have the expression for A as function of x

A(x) = 3π*x² + 2π*x*h A(x) = 3π*x² + 505 - (2/3)π*x³

Taking derivatives both sides

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x₁ = 0 we dismiss

6 - 2x = 0

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h = (505 - 18.84) / 6.28*3

h = 23,8 ft

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3 years ago