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maxonik [38]
3 years ago
8

What is the slope of the equation y - 3 = -4(x - 5)?

Mathematics
2 answers:
Reil [10]3 years ago
6 0

Answer:

Step-by-step explanation:

A

MissTica3 years ago
3 0

Answer:

A - 4

Step-by-step explanation:

Given equation of line is:

y - 3 = -4(x - 5) \\ equating \: it \: with \\ y-y_1 =m(x-x_1)  \\ \purple{ \bold{ slope \: (m) =  - 4}}

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a bottling machine can fill 300 bottles in 5 minutes at this rate how many bottles can be filled in 8 minutes
kirill [66]
480 bottles because 300 divided by 5 is 60 so then you multiply 60 by 8 and you get 480!
6 0
3 years ago
Read 2 more answers
Find the exact length of the curve. 36y2 = (x2 − 4)3, 5 ≤ x ≤ 9, y ≥ 0
IrinaK [193]
We are looking for the length of a curve, also known as the arc length. Before we get to the formula for arc length, it would help if we re-wrote the equation in y = form.

We are given: 36 y^{2} =( x^{2} -4)^3
We divide by 36 and take the root of both sides to obtain: y = \sqrt{ \frac{( x^{2} -4)^3}{36} }

Note that the square root can be written as an exponent of 1/2 and so we can further simplify the above to obtain: y =  \frac{( x^{2} -4)^{3/2}}{6} }=( \frac{1}{6} )(x^{2} -4)^{3/2}}

Let's leave that for the moment and look at the formula for arc length. The formula is L= \int\limits^c_d {ds} where ds is defined differently for equations in rectangular form (which is what we have), polar form or parametric form.

Rectangular form is an equation using x and y where one variable is defined in terms of the other. We have y in terms of x. For this, we define ds as follows: ds= \sqrt{1+( \frac{dy}{dx})^2 } dx

As a note for a function x in terms of y simply switch each dx in the above to dy and vice versa.

As you can see from the formula we need to find dy/dx and square it. Let's do that now.

We can use the chain rule: bring down the 3/2, keep the parenthesis, raise it to the 3/2 - 1 and then take the derivative of what's inside (here x^2-4). More formally, we can let u=x^{2} -4 and then consider the derivative of u^{3/2}du. Either way, we obtain,

\frac{dy}{dx}=( \frac{1}{6})( x^{2} -4)^{1/2}(2x)=( \frac{x}{2})( x^{2} -4)^{1/2}

Looking at the formula for ds you see that dy/dx is squared so let's square the dy/dx we just found.
( \frac{dy}{dx}^2)=( \frac{x^2}{4})( x^{2} -4)= \frac{x^4-4 x^{2} }{4}

This means that in our case:
ds= \sqrt{1+\frac{x^4-4 x^{2} }{4}} dx
ds= \sqrt{\frac{4}{4}+\frac{x^4-4 x^{2} }{4}} dx
ds= \sqrt{\frac{x^4-4 x^{2}+4 }{4}} dx
ds= \sqrt{\frac{( x^{2} -2)^2 }{4}} dx
ds=  \frac{x^2-2}{2}dx =( \frac{1}{2} x^{2} -1)dx

Recall, the formula for arc length: L= \int\limits^c_d {ds}
Here, the limits of integration are given by 5 and 9 from the initial problem (the values of x over which we are computing the length of the curve). Putting it all together we have:

L= \int\limits^9_5 { \frac{1}{2} x^{2} -1 } \, dx = (\frac{1}{2}) ( \frac{x^3}{3}) -x evaluated from 9 to 5 (I cannot seem to get the notation here but usually it is a straight line with the 9 up top and the 5 on the bottom -- just like the integral with the 9 and 5 but a straight line instead). This means we plug 9 into the expression and from that subtract what we get when we plug 5 into the expression.

That is, [(\frac{1}{2}) ( \frac{9^3}{3}) -9]-([(\frac{1}{2}) ( \frac{5^3}{3}) -5]=( \frac{9^3}{6}-9)-( \frac{5^3}{6}-5})=\frac{290}{3}


8 0
3 years ago
What single transformation was applied to quadrilateral A to get quadrilateral B?
Helen [10]
B : rotation.

Translation is if you are moving the shape from one place to the other. Reflection is if you are flipping the shape over a line ( which it is not ) and dilation is when the shape is becoming bigger or smaller.
6 0
2 years ago
The lowest point in Death Valley is Badwater at 282 feet below sea level. The highest point in
Finger [1]

Answer:

Step-by-step explanation:

Given

Badwater = -282ft

Telescope\ Peak = 11043ft

The position of badwater is negated because it is below sea level

The interpretation of the question, is to calculate the distance between the two given points.

This is calculated as:

Difference = Telescope\ Peak - Badwater

Difference = 11043ft - (-282ft)

Open bracket

Difference = 11043ft+282ft

Difference = 11325ft

<em>Hence, the distance between both is 11325ft</em>

8 0
3 years ago
If m(angle sign)1=34 then what is m(angle sign)4
sergejj [24]
The m (angle sign) for 4 is 38. I hope i helped. 
4 0
3 years ago
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