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2 years ago

Suppose you had d dollars in your bank account. You spent $22 but have at least $42 left. How much money did you have initially?

1 answer:

german2 years ago

4 0

1) What left

$\boxed {d-22 \geq 42}$

*Obs: remember that left at least 42 dollars. In other words, the left over is equal or more than 42 dollars.

2) At the beginning

$d-22 \geq 42 \\ \\ \boxed {d \geq 64}$

Letter C

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In the derivation of Newton’s method, to determine the formula for xi+1, the function f(x) is approximated using a first-order T

dimaraw [331]

Answer:

Part A.

Let f(x) = 0;

suppose x= a+h

such that f(x) =f(a+h) = 0

By second order Taylor approximation, we get

f(a) + hf'±(a) + $\frac{h^{2} }{2!}$ f''(a) = 0

$h = \frac{-f'(a) }{f''(a)}$ ± $\frac{\sqrt[]{(f'(a))^{2}-2f(a)f''(a) } }{f''(a)}$

So, we get the succeeding equation for Newton's method as

$x_{i+1} = x_{i} + \frac{1}{f''x_{i}} [-f'(x_{i})$ ± $\sqrt{f(x_{i})^{2}-2fx_{i}f''x_{i} } ]$

Part B.

It is evident that Newton's method fails in two cases, as:

1. if f''(x) = 0

2. if f'(x)² is less than 2f(x)f''(x)

Part C.

In case $x_{i+1}$ is close to $x_{i}$ , the choice that shouldbe made instead of ± in part A is:

f'(x) = $\sqrt{f'(x)^{2} - 2f(x)f''(x)}$ ⇔ $x_{i+1} = x_{i}$

Part D.

As given $x_{i+1}$ = $x_{i}$ = h

or h = $x_{i+1}$ - $x_{i}$

We get,

f(a) + hf'(a) +(h²/2)f''(a) = 0

or h² = -hf(a)/f'(a)

Also, ( $x_{i+1}$ - $x_{i}$ )² = -( $x_{i+1}$ - $x_{i}$ )(f( $x_{i}$ )/f'( $x_{i}$ ))

So, f(a) + hf'(a) - (f''(a)/2)(hf(a)/f'(a)) = 0

It becomes h = -f(a)/f'(a) + (h/2)[f''(a)f(a)/(f(a))²]

Also, $x_{i+1}$ = $x_{i}$ -f( $x_{i}$ )/f'( $x_{i}$ ) + [( $x_{i+1}$ - $x_{i}$ )f''( $x_{i}$ )f( $x_{i}$ )]/[2(f'( $x_{i}$ ))²]

6 0

3 years ago

Explain why 4xy and 5x²y are not like terms.

Gelneren [198K]

They aren’t like terms became 5x^2y has an exponent

We could have the numbers
5x^2 and 5x and they wouldn’t be like terms because one has an exponent

3 0

2 years ago

Find c in the pic below

Fiesta28 [93]

Answer:

Step-by-step explanation:

To find the angle inside the triangle (to the right side of 90 degree angle), we first have to find the adjacent angle (below it).

Angle 122 and that adjacent angle is same (parallel lines cut by transversal -- they are corresponding angles).

So that angle is 122.

The inside triangle angle (what we want) is adjacent to 122, so we can write:

Angle + 122 = 180 [straight angle/straight line is 180 degrees]

Solving for that angle, we have:

Angle = 180 - 122 = 58

Now, looking at the triangle, Side C is "opposite" of 58° and side "20" is the side that is "hypotenuse" [side opposite of 90 degree angle is hypotenuse).

Which trig ratio relates "opposite" and "hypotenuse"??

Yes, it is SIN. Thus we can write:

$Sin(58)=\frac{Opposite}{Hypotenuse}=\frac{C}{20}$

We can now solve for C:

$Sin(58)=\frac{C}{20}\\C=20*Sin(58)\\C=16.96$

Correct answer is A

7 0

3 years ago

Can someone help me on this math problem?

Verizon [17]

SOLUTION:

When looking at this diagram, you can see that CM is equivalent to AM as displayed below:

CM = AM

If:

CM = 7

Then that means that:

AM = 7

Therefore, your answer is:

AM = 7

5 0

2 years ago

During the calendar year of 1971 a total of 171 deaths were caused by influenza in a city of 450,000 persons. The temporal distr

masha68 [24]

Answer and Step-by-step explanation:

The computation of annual and quarterly mortality rates per 100,000 population is shown below:-

Quarterly mortality rates are

$= \frac{Deaths}{Population\ in\ the\ city}\times Population$