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3 years ago

Evaluate without using a calculator 899^2 - 2 * 899 * 898 + 898^2

Mathematics

1 answer:

Yanka [14]3 years ago

3 0

Answer:

The answer is 1

Step-by-step explanation:

You can use the formula, a²-2ab+b² = (a-b) to evaluate the following question:

899² - 2(899)(898) + 898² = (899-898)²

= 1

(Hooe this can help)

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Chris can make 8 shoes per hour on a good day. If a customer needs 24 shoes, how long will it take him to make the shoes?

Lunna [17]

Answer:

3 or more days depending on how his day is going

Step-by-step explanation:

8 0

3 years ago

1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

3 years ago

What is the domain of the function

Valentin [98]

Answer:

Step-by-step explanation:

Hopefully this helps!

8 0

4 years ago

Little Melinda has nickels and quarters in her bank. She has nine fewer nickels than quarters. She has $4.65 in the bank. How ma

erastovalidia [21]

Answer:

Step-by-step explanation:

n=q-9

5n+25q=465, using n from above this becomes

5(q-9)+25q=465

5q-45+25q=465

30q-45=465

30q=510

q=17, and since n=q-9

n=17-9

n=8

So Melinda has 8 nickels and 17 quarters.

8 0

3 years ago

2=(1+r/100n)^nt

klasskru [66]

Answer:

a) Log ( 2 ) = 4t Log ( 83/80 )

b) 4.7 years

Step-by-step explanation:

Attached below is the detailed solution

<u>a) exponential statement in log form for an investment at 15% quarterly </u>

Log ( 2 ) = 4t Log ( 83/80 )

n = 4 , r = 15

<u>b) using change to base to find double time in yr </u>

Double time in yr

t = Log ( 2 ) / 4log ( 83/80 )

= 4.7 years

5 0

3 years ago