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3 years ago

Зу = 2х +9 in slope intercept

Mathematics

2 answers:

romanna [79]3 years ago

8 0

Y=2/3x+3

Anything else

charle [14.2K]3 years ago

7 0

Y=2/3x+3 BAM there it is

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A group of students is arranging squares into layers to create a project. The first layer has 6 squares. The second layer has 12

posledela

Answer:

Explicit formula: $s_{n}=6(2)^{n-1}$

Step-by-step explanation:

Let the number of squares in $n^{th}$ layer be $s_{n}$

Given:

Number of squares in first layer, $s_{1}=6$

Number of squares in second layer, $s_{2}=12$

Therefore, the number of squares increases by a factor of 2.

So, it follows a geometric sequence with the first term as 6 and common ratio of 2.

For a geometric sequence, the $n^{th}$ term with common ratio $r$ is given as:

$s_{n}=s_{1}\times r^{n-1}$

Here, $r=2,s_{1}=6$

∴ Explicit formula: $s_{n}=6(2)^{n-1}$

7 0

3 years ago

Which of the following coordinate points have an x-value of 4? Select all that apply.

Alinara [238K]

B, C, and D all have an x-value of 4.

7 0

3 years ago

Read 2 more answers

Bailey went out to dinner. It cost $ 45.00. He wanted to leave a 20% tip for his waitress. Find the tip.

Ksivusya [100]

Answer:

The tip should be $9.00

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

**Spam answers will not be tolerated**

Morgarella [4.7K]

Answer:

$f'(x)=-\frac{2}{x^\frac{3}{2}}$

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

3 years ago

There are five wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be atta

docker41 [41]

Answer:

Number of Possible Sequence = 5 x 4 x 3 x 2 x 1 = 120 ways

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3 0

2 years ago