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3 years ago

Write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation.

Mathematics

2 answers:

faust18 [17]3 years ago

6 0

The answer would be B: F(x) = 6x - 12

This line passes through both given points.

mylen [45]3 years ago

6 0

First, we must find the slope using the equation

$\frac{y_{2}-y_{1} } {x_{2}-x_{1}}$

We can substitute in our points and will get

$\frac{18-6}{5-3} =\frac{12}{2} = 6$

This means that our slope is m=6.

We can now use the point slope form to find the equation of the line. The equation for this is $y-y_{1} =m(x-x_{1})$

Now we can substitute in one of our point, (3,6) in this case.

$y-6 = 6(x-3)$

this simplifies to

$y= 6x-12$

now we can swap y for f(x) to put it in function notation

this means that the answer is $f(x) = 6x-12$ ; which means that the answer is b

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Factor 3x2 - x - 10.

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3 years ago

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4(x+2) help please.

inna [77]

Answer:

4x + 8

Step-by-step explanation:

4(x+2)

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

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3 years ago

How do you factor out the coefficient of 2.2x+4.4

NISA [10]

2.2x and 4.4 have a GCF of 2.2. So, you can factor that out like so:
2.2x+4.4 = 2.2*x+2.2*2 = 2.2(x+2)

Hope this helps!

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3 years ago

The L.L. Bean men’s cotton chambray shirt comes in the following colors: blue, stone, rust, green, plum, and indigo. In addition

bulgar [2K]

Answer:

60 types of cotton chambray shirts can be produced

Step-by-step explanation:

The shirt comes in the following colors: blue, stone, rust, green, plum, and indigo

Number of colors the shirt comes in = 6

The shirt comes in the following sizes: small (S), medium (M), large (L), extra large (XL), and extra extra large (XXL)

Number of sizes the shirt comes in = 5

The shirt comes in the following styles: short sleeves or long sleeves

Number of styles the shirt comes in = 2

Total number of cotton chambray shirts that can be produced are:

No. of colors * No. of sizes * No. of styles

6 * 5 * 2

60 shirts

So, 60 types of cotton chambray shirts can be produced from the given options of colors, sizes and styles.

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3 years ago