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3 years ago

What is the average rate of change for this exponential function for the interval from x = 2 to x = 4?

Mathematics

1 answer:

Hunter-Best [27]3 years ago

8 0

Answer:

The average rate of change over the interval is 120

Step-by-step explanation:

For a function f(x) the average rate of change over an interval [a,b] is given as;

f(b)-f(a)/b-a

in this case, a is 2 and b is 4

f(b) is 256 and f(a) is 16

Substituting these values in the equation for rate of change, we have;

(256-16)/(4-2) = 240/2 = 120

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What is the quotient of the following division problem? x 1 startlongdivisionsymbol x squared 3 x 2 endlongdivisionsymbol. minus

Monica [59]

The quotient of the provided division in which binomial is divided by a quadratic equation is x+2.

<h3>What is the quotient?</h3>

Quotient is the resultant number which is obtained by dividing a number with another. Let a number <em>a</em> is divided by number b. Then the quotient of these two number will be,

$q=\dfrac{a}{b}$

Here, (a, b) are the real numbers.

The given division expression is,

$\dfrac{x^2+3x+2}{x+1}$

Let the quotient of this division problem is f(x). Thus,

$f(x)=\dfrac{x^2+3x+2}{x+1}$

Factor the numerator expression as,

$f(x)=\dfrac{x^2+2x+x+2}{x+1}\\f(x)=\dfrac{x(x+2)+1(x+2)}{x+1}\\f(x)=\dfrac{(x+2)(x+1)}{x+1}\\f(x)={x+2}$

Thus, the quotient of the provided division in which binomial is divided by a quadratic equation is x+2.

Learn more about the quotient here;

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4. Stella says the equation x^2−8x+y^2+2y=5 has a center of (4,−1) and a radius of 5. Is she correct? Why or why not?

Ostrovityanka [42]

<h2>Stella is correct about center and wrong about radius </h2>

Step-by-step explanation:

Equation of circle with (h,k) as center and radius r is given by,

(x-h)²+(y-k)² = r²

Here equation is

x²−8x+y²+2y=5

Changing in to (x-h)²+(y-k)² = r² form

x²−8x + 16 - 16 +y²+2y+1 - 1=5

(x-4)² - 16 + (y+1)² -1 = 5

(x-4)² + (y+1)² = 22

(x-4)² + (y+1)² = 4.69²

Center is (4,-1) and radius is 4.69

Stella is correct about center and wrong about radius

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2 years ago