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2 years ago

Which property is illustrated? 8(a + c) = 8a+ 8c

Mathematics

1 answer:

alekssr [168]2 years ago

4 0

Answer:

Distributive property

Step-by-step explanation:

Here, we want to evaluate the property illustrated

From what we can see, we have that each of the inner values are multiplied by the outside value

This is simply a display of distributivity

We can conclude that we have a right distributive property in place here

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How is this answer D?

kompoz [17]

It's a equilateral triangle with each side being equal to the radius.

So the area is $\dfrac{8^2\sqrt 3}{4}=\dfrac{64\sqrt3}{4}=16\sqrt3$

7 0

2 years ago

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

2 years ago

Richard work 20 hours this week he also got a Bonus of $25 if he made at least $185 how much does he get paid per hour

OlgaM077 [116]

Answer:

It’s the third choice : x ≥8

Step-by-step explanation:

the third choice means he made equal to or greater than $8 an hour.

185-25=160

160÷20=8

7 0

2 years ago

Please answer this correctly

katen-ka-za [31]

Answer:

Step-by-step explanation:

Okay so there is 32 cups in 8 quarts and he sold 6 cups Saturday and 18 cups Sunday.

Add 8+18

Subtract 24-32 to get 8

6 0

3 years ago

Read 2 more answers

Eighty-five more than the square of a number is the same as the square of the quantity that is 17 less than the number. What is

mario62 [17]

We can turn this word problem into the following equation:
x^2 + 85 = (x - 17)^2
x^2 + 85 = x^2 - 34x + 289
-85 -85
_______________________
x^2 = x^2 - 34x + 204
+34x +34x
_______________________
x^2 + 34x = x^2 + 204
-x^2 -x^2
____________________
34x = 204
Divide 34 on both sides
x = 6.
The number is 6.

5 0

2 years ago

Which property is illustrated? 8(a + c) = 8a+ 8c​

Which property is illustrated? 8(a + c) = 8a+ 8c