MATHEMATICS MIDDLE SCHOOL

Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.x = 27/16
x = 13/8
x = 25/16
x = 7/4
Approximate the solution to the equation above using three iterations - 1

Answers

Answer 1
Answer:

Answer:

x=25/16

Step-by-step explanation:

Approximate Roots of Functions:

We are required to find the root of  

\displaystyle 5^(-x)+7=\ 2x+4

Let's construct a function

\displaystyle f(x)=\ 5^(-x)+7-2x-4

Reducing:

\displaystyle f(x)= 5^(-x)-2x+3

The equation will have a solution when f(x)=0. We'll start from the approximate crossing point given in the graph (x=1.5)

\displaystyle f(1.5)=5^(-1.5)-2(1.5)+3\ =0.089

We'll move up on x=1.52  

\displaystyle f(1.52)=5^(-1.52)-2(1.52)+3=\ 0.046

We are closer to the solution, let's try some more up

\displaystyle f(1.54)=5^(-1.54)-2(1.54)+3=\ 0.0038

This value x=1.54 is close enough to the solution of the original equation

From the options given, (25)/(16) is the closest to our solution

\boxed{Answer:\ x=25/16}
Answer 2
Answer:

Answer:

it's 27/16

Step-by-step explanation:

got it right on the test

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Is 31.010 greater or less or equal to 31.01

Answers


Well, lets look at it  this way ... tell me if this does anything for you:

-- Take the number  31.01 .

-- Stick a zero on the end and make it  31.010 .

-- Zeros at the end of a number after the decimal point don't change
the value of the number.  So you haven't changed the value of  31.01 .

-- But now it looks exactly like the other number !

-- They must be equal.


Does this float your boat at all ?
31.010 is = to 31.01

the reason being that the 0 on the end of 31.010 is just there for to hold an unwanted place value.

Ex. 0.70 is the same as 0.7 because the zero is just holding a place value. It's not wrong to put in the zero but its better if you don't.
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