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3 years ago

If f(x)= 3-2 and g(x)=1/x+5 what is the vue of (f/g) (8)

Mathematics

1 answer:

Lena [83]3 years ago

6 0

Answer:

The value of (f/g) (8) = -169

Step-by-step explanation:

<u>Step 1: explaining the question</u>

The quotient (f/g) is not defined at values of x ⇒ both the functions must be defined at a point for the combination to be defined.

⇒(f/g)(x) =(f(x)) / (g(x))

If f(x)= 3-2 and g(x)=1/x+5

⇒then according to the preceding formula: (f/g)(x) =(f(x)) / (g(x))

⇒(f/g)(8) = f(8) / g(8)

to solve this we have to find the value of both f(8) and g(8)

<u>Step 2: find value of f(8) and g(8)</u>

⇒ we know that f(x) = 3-2x and we know dat f(x) = f(8)

⇒ f(8) = 3-2(8)

f(8) = 3-16 = -13

⇒we know that g(x) = 1/x+5 and g(x) = g(8)

⇒ g(8) = 1/8+5

g(8) =1/13

These 2 equations we will insert in the following : ⇒(f/g)(8) = f(8) / g(8)

⇒ f/g (8) = -13 / (1/13) = -13 * 13/1 = -169

The value of (f/g) (8) = -169

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Harman [31]

solve: $\frac{10}{x}$ = 2

Answer:

a. x= 5

Step-by-step explanation:

To solve the question given, we will follow the steps below;

$\frac{10}{x}$ = 2

multiply x to both-side of the equation

$\frac{10}{x}$ × x= 2× x

at the left-hand side of the equation, x will cancel-out x, leaving us with 10

10 = 2x

divide both-side of the equation by 2

10/2 = 2x/2

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4 years ago

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) a

devlian [24]

Answer:

The area under the function $\int\limits^3_1 {9-x^2} \, dx \approx 7.25.$ .

Step-by-step explanation:

We want to find the Riemann Sum for $\int\limits^3_1 {9-x^2} \, dx$ with 4 sub-intervals, using right endpoints.

A Riemann Sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral.

The Right Riemann Sum is given by:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)$

where $\Delta{x}=\frac{b-a}{n}$

From the information given we know that a = 1, b = 3, n = 4.

Therefore, $\Delta{x}=\frac{3-1}{4}=\frac{1}{2}$

We need to divide the interval [1, 3] into 4 sub-intervals of length $\Delta{x}=\frac{1}{2}$ :

$\left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right], \left[2, \frac{5}{2}\right], \left[\frac{5}{2}, 3\right]$

Now, we just evaluate the function at the right endpoints:

$f\left(x_{1}\right)=f\left(\frac{3}{2}\right)=\frac{27}{4}=6.75$

$f\left(x_{2}\right)=f\left(2\right)=5=5$

$f\left(x_{3}\right)=f\left(\frac{5}{2}\right)=\frac{11}{4}=2.75$

$f\left(x_{4}\right)=f(b)=f\left(3\right)=0=0$

Next, we use the Right Riemann Sum formula

$\int\limits^3_1 {9-x^2} \, dx \approx \frac{1}{2}(6.75+5+2.75+0)=7.25$

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