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2 years ago

The workers in a senate office said that they received about 700 phone calls from

Mathematics

1 answer:

prohojiy [21]2 years ago

7 0

Answer:

672

Step-by-step explanation:

anything lower then 5 or in this case 50 would round down so 649 rounds to 600 anything higher would round up 672 to 709 763 to 800 and 751 to 800

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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).

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2 years ago

The length of a rectangle is 3 less than twice the width. The perimeter of the rectangle is 66. Find the length and width of the

posledela

Answer:

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Step-by-step explanation:

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2 years ago

a munfuctor of medical supplies produces 1 liter of bags of saline solution. the cost to produce x thousand bags of saline is gi

o-na [289]

A manufacturer of medical supplies produces 1 liter bags of saline solution. thecost to produce x thousand bags of saline is given by the cost func. ... thousand bags of saline isgiven by the cost function C(x)=1.7x^2-5.3x+3.2, ...

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2 years ago

Help me find the volume of the composite figure

Butoxors [25]

Answer:

$V = 97.911in^3$