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1 year ago

Complete the following:

1 answer:

5 0

1) A mathematical ratio is known as the golden ratio. It is frequently found in nature, and when employed in a design, it encourages compositions that look organic and natural and are visually appealing.

2) The algebraic form of golden ratio is root of x2-x-1 = 0

3) The golden ratio number is approximately equal to 1.618

4) When a line is split into two equal sections, the sum of the two parts, (a) + (b), divided by (a), equals 1.618, and this is known as the Golden Ratio

5) When designing forms, logos, layouts, and other things, this formula might be useful. By dividing each number in the Fibonacci series by its direct predecessor, the golden ratio is obtained. Mathematically speaking, the quotient F(n)/F(n-1) will become closer to the limit 1.618 for rising values of n if F(n) describes the nth Fibonacci number. The golden ratio is a more popular name for this restriction.

Learn more about golden ratio here: brainly.com/question/2263789

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Billy's plant grows at least 2 inches a month.

emmainna [20.7K]

We can assume that this growth rate can be expressed as y = mx + b as long as the slope is constant, because a quadratic or exponential formula wouldn't make much sense in this situation. If it is growing at least 2 inches a month, the slope (m) will be 2. As x (month) increases by 1 month, y (plant's height) increases by 2 inches. You could make it more, but as long as you plot the points in such a way that the slope for these points are 2 or higher, you will get the answer correct. If you have any other questions or need to clarify more about what you wanted let me know and I'll help.

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3 years ago

Read 2 more answers

Find dy/dx by implicit differentiation for ysin(y) = xcos(x)

tatyana61 [14]

Answer:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

Step-by-step explanation:

So we have:

$y\sin(y)=x\cos(x)$

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

$\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]$

Let's do each side individually.

Left Side:

We have:

$\frac{d}{dx}[y\sin(y)]$

We can use the product rule:

$(uv)'=u'v+uv'$

So, our derivative is:

$=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]$

We must implicitly differentiate for y. This gives us:

$=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]$

For the sin(y), we need to use the chain rule:

$u(v(x))'=u'(v(x))\cdot v'(x)$

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

$=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})$

Simplify:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}$

And we are done for the right.

Right Side:

We have:

$\frac{d}{dx}[x\cos(x)]$

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

$=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]$

Differentiate:

$=\cos(x)-x\sin(x)$

So, our entire equation is:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)$

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

$\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)$

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

And we're done!

5 0

3 years ago

What are the coordinates of the point on the directed line segment from (-6, -6)(−6,−6) to (9, -1)(9,−1) that partitions the seg

GrogVix [38]

Answer:

(0, -4)

Step-by-step explanation:

The coordinates of the points from which the directed line segment extends = (-6, -6) to (9, -1)

The ratio the required point partitions the line = 2 to 3

The formula for finding the coordinate of a point that partitions a line AB into a ratio 'a' to 'b', where the coordinates of, A = (x₁, y₁) and B = (x₂, y₂) is given as follows;

$\left(\dfrac{a}{a + b} \times (x_1 - x_2)+ x_1, \ \dfrac{a}{a + b} \times (y_1 - y_2)+ y_1 \right)$