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2 years ago

14

3. For what value of x is

1 answer:

liraira [26]2 years ago

7 0

Answer:

3. x=7

4. f(4)= -24

Step-by-step explanation:

2. Since the bases are equal, equate the powers;

2x+3=17

2x=14

x= 14/2

x=7

3. Putting x as 4 in the function

=3(4²) - 4[3(4) + 6]

=3(16) - 4(12+6)

=3(16) - 4(18)

=48 - 72

f(4) = -24

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Read 2 more answers

Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

5 0

2 years ago

Yeah thanks m8 for this

nikitadnepr [17]

Step-by-step explanation:

the process is shown in the picture.

4 0

2 years ago

See attached picture

yanalaym [24]

Answer:

$\frac{f(x+h)-f(x)}{h}$ $=2x + h$

Step-by-step explanation:

Given

$f(x)= x^2 + 2$

Required

Determine: $\frac{f(x+h)-f(x)}{h}$

First, we calculate f(x + h)

$f(x)= x^2 + 2$

$f(x+h) = (x+h)^2+2$

$f(x+h) = x^2+2xh+h^2+2$

So, we have:

$\frac{f(x+h)-f(x)}{h}$ $= \frac{x^2 + 2xh + h^2 + 2 - x^2 - 2}{h}$

$\frac{f(x+h)-f(x)}{h}$ $= \frac{x^2 - x^2+ 2xh + h^2 + 2 - 2}{h}$

$\frac{f(x+h)-f(x)}{h}$ $= \frac{2xh + h^2}{h}$

$\frac{f(x+h)-f(x)}{h}$ $=2x + h$

8 0

2 years ago