Mathematics, 27.01.2020 03:31 alliemeade1

Solve the following equation for x using a table of values (to the nearest fourth of a unit), graphing technology, and successive approximation (three iterations). the solution to the equation lies between x = 1 and x = 2.

-x + 4 = 3^x -3

drag the solution and the level of accuracy to the correct location in the table for the three techniques for solving an equation.

Solve the following equation for x using a table of values (to the nearest fourth of a unit), graphi

Answers: 1

Show answers

Answers

Answer from: davidoj13

Table of values
For the table of values let's just estimate the equation by using the values 1, 1.25, 1.5, 1.75, and 2 (we have selected these values based on the given range of the solution).

x Equation
1 3=0 (WRONG)
1.25 2.75=0.948 (WRONG)
1.5 2.5=2.20 (NEAR)
1.75 2.25=3.83 (WRONG)
2 2=6 (WRONG)

As we can see, only 1.5 had the nearest answer thus, according to the table of values, 1.50 is the answer.

Graphing technology
For this method I will utilize Desmos to determine the answer. I have inputted the equation in Desmos and I have attached here the graph it produced. The red line is the value of x that satisfies the equation according to Desmos. As we can see, the red line is between 1.5440 and 1.5445 therefore we can say that the answer to the equation according to the graphing technology is 1.544.

When plugged into the equation, this will yield the simplified equation 2.456 = 2.453 which is as close as it can get.

Successive approximation
To be able to approximate, let us note the equation as a function.

$f(x)=-x+4- 3^{x} +3=0$
$f(x)=-x-3^{x}+7=0$

For the first two iterations, let us plug 1.5 and 1.75 as the values of x.

$f(1.5)=-1- 3^{1}+7=0.304$
$f(1.75)=-2- 3^{2}+7=-1.588$

For our third iteration, we need to treat (1.5,0.304) and (1.75,-1.588) as two points in a straight line. We determine the point where y is equal to zero from the line that the two points formed.

$y=mx+b= \frac{-1.588-0.304}{1.75-1.5}x+b= \frac{-1.892}{0.25} x+b$

Let's get the y-intercept (b) for the equation first before we know the x-intercept.

0.304=-7.568(1.5)+b=-11.352+b

We then set y to zero and get the value of x

0=-7.568x+11.656

Therefore, the last iteration would be x = 1.540

Simplifying the original equation, we will get 2.46=2.43.

While this value of x (1.540) is not among the choices, this is only one of the methods of successive approximation and there may be other ways to get to the nearest answer. You can try starting with other values and see if following the same process will yield you one of the answers among the choices (the method of approximation may depend on your instructor).

IN SUMMARY:
Solutions Accuracy
Table of Values 1.5 Lowest
Graphing Tech 1.544 Highest
Approximations 1.540 Intermediate

Keep in mind that if you get a more accurate/less accurate result for the approximation, the level of accuracy may change.
Solve the following equation for x using a table of values (to the nearest fourth of a unit), graphi

Solve the following equation for x using a table of values (to the nearest fourth of a unit), graphi

Answer from: Quest

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to $\frac{1}{60} hr\\$

then mult. both sides by 75 we get the ratio

75 mi. to $\frac{75}{60} hr\\$

simplifying we get

75 mi. to $\frac{5}{4} hr$

or 1.25 hr.

Answer from: Quest

Y’all got the baby baby money in

Another question on Mathematics

Mathematics, 21.06.2019 18:10

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Write the rational number in lowest terms 99/-15

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

Which two transformations are applied to pentagon abcde to create a'b'c'd'e'? (4 points) translated according to the rule (x, y) ? (x + 8, y + 2) and reflected across the x-axis translated according to the rule (x, y) ? (x + 2, y + 8) and reflected across the y-axis translated according to the rule (x, y) ? (x + 8, y + 2) and reflected across the y-axis translated according to the rule (x, y) ? (x + 2, y + 8) and reflected across the x-axis

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Find the equation of the ellipse with the following properties. the ellipse with foci at (0, 6) and (0, -6); y-intercepts (0, 8) and (0, -8).edit: the answer is x^2 over 28 + y^2 over 64 = 1

Answers: 2

Answer

You know the right answer?

Solve the following equation for x using a table of values (to the nearest fourth of a unit), graphi...

Questions