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3 years ago

12s+ 3p =b There’s the question and I need help understanding it

Mathematics

1 answer:

yaroslaw [1]3 years ago

8 0

Answer:

Step-by-step explanation:

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Find the circumference need help

marta [7]

Answer:

56.52

Step-by-step explanation:

c=2 $pi$ r

C=2*3.14*9

C=56.52

5 0

3 years ago

Choose the pair(s) of integers that can be substituted into the equation ax2 - 6x + c = 0 so that it has two real solutions.

Maksim231197 [3]

The options are not provided, but method is stated below

Answer:

Quadratic equation ax2 - 6x + c = 0

options would be given for a and c

substitute a and c
check for Discriminant
$b^2 - 4ac \geq 0$
36 -4ac $\geq 0$

These conditions will fetch us the result required among the options.

Note : the $\geq$ sign will give us the result for Two real unequal solutions and two real equal solutions. If we only need Real unequal solutions we only use > sign instead of $\geq$

4 0

3 years ago

Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?

OlgaM077 [116]

Answer:

$a_n = 16(\frac{1}{4})^{n - 1}$

Step-by-step explanation:

Given:

Fifth term of a geometric sequence = $\frac{1}{16}$

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence = $ar^{n - 1}$ , where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

$\frac{1}{16} = a*\frac{1}{4}^{5 - 1}$

$\frac{1}{16} = a*\frac{1}{4}^{4}$

$\frac{1}{16} = a*\frac{1}{256}$

$\frac{1}{16} = \frac{a}{256}$

Cross multiply

$1*256 = a*16$

Divide both sides by 16

$\frac{256}{16} = \frac{16a}{16}$

$16 = a$

$a = 16$

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term = $ar^{n - 1}$

nth term = $16*\frac{1}{4}^{n - 1}$

$a_n = 16(\frac{1}{4})^{n - 1}$

3 0

3 years ago

Find the circumference of a circle with the diameter of 10 inches. Leave your answers in form of pi

MrRa [10]

Answer:

Circumference = 10π

Step-by-step explanation:

First identify the circumference formula as such:

2πr (where r ⇒ radius, π ⇒ pi)

Knowing 2 times the radius (2r) in the formula can be rewritten as the diameter, the formula itself can be rewritten as:

πd (where d ⇒ diameter, π ⇒ pi)

If we know the diameter = 10 inches, substitute in the circumference formula πd to get:

π * 10 inches = 10 * π inches = 10π inches

4 0

3 years ago

A) Use the limit definition of derivatives to find f’(x)

Ann [662]

$\text{Given that,}\\\\f(x) = \dfrac{ 1}{3x-2}\\\\\text{First principle of derivatives,}\\\\f'(x) = \lim \limits_{h \to 0} \dfrac{f(x+h) - f(x) }{ h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{1}{3(x+h) - 2} - \tfrac 1{3x-2}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{1}{3x+3h -2} - \tfrac{1}{3x-2}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{3x-2-3x-3h+2}{(3x+3h-2)(3x-2)}}{h}\\\\\\$

$~~~~~~~= \lim \limits_{h \to 0} \dfrac{\tfrac{-3h}{(3x+3h-2)(3x-2)}}{h}\\\\\\~~~~~~~~= \lim \limits_{h \to 0} \dfrac{-3h}{h(3x+3h-2)(3x-2)}\\\\\\~~~~~~~~=-3 \lim \limits_{h \to 0} \dfrac{1}{(3x+3h-2)(3x-2)}\\\\\\~~~~~~~~=-3 \cdot \dfrac{1}{(3x+0-2)(3x-2)}\\\\\\~~~~~~~~=-\dfrac{3}{(3x-2)(3x-2)}\\\\\\~~~~~~~=-\dfrac{3}{(3x-2)^2}$

$\text{Given that,}~\\\\f(x) = \dfrac{1}{3x-2}\\\\\textbf{Power rule:}\\\\\dfrac{d}{dx}(x^n) = nx^{n-1}\\\\\textbf{Chain rule:}\\\\\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}\\\\\text{Now,}\\\\f'(x) = \dfrac{d}{dx} f(x)\\\\\\~~~~~~~~=\dfrac{d}{dx} \left( \dfrac 1{3x-2} \right)\\\\\\~~~~~~~~=\dfrac{d}{dx} (3x-2)^{-1}\\\\\\~~~~~~~~=-(3x-2)^{-1-1} \cdot \dfrac{d}{dx}(3x-2)\\\\\\~~~~~~~~=-(3x-2)^{-2} \cdot 3\\\\\\~~~~~~~~=-\dfrac{3}{(3x-2)^2}$

8 0

2 years ago