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3 years ago

Please help. if a line falls on the points (6,8) and (1,5) what is it’s slope?

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

4 0

Answer:

m= 3/5.

Step-by-step explanation:

The general equation of the line is:

(y - y0) = m ( x - x0), where "m" represents the slope is: (y1 - y0) / (x1 - x0).

From the statement we know that (x1, y1) = (6, 8) and (x0, y0) = (1,5)

Then the slope is:

m= (y1 - y0) / (x1 - x0) = (8 - 5)/(6 - 1) = 3/5.

The slope is 3/5

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This diagram of a rectangular city park was drawn using a scale of 1 centimeter to 20 meters

I am Lyosha [343]

Answer:

Scale factor for the drawing from actual park = $\frac{1}{20}$

Area of the actual park = 1200 cm²

Step-by-step explanation:

Length of the rectangular city park = 5 cm

Width of the rectangular park = 6 cm

Using scale factor 1 cm = 20 meters

Scale factor = $\frac{\text{length of the park in drawing}}{\text{Actual length of park}}=\frac{1}{20}$

$\frac{5}{\text{Actual length of park}}=\frac{1}{20}$

Actual length = 5 × 20 = 100 meters

Actual width = 6 × 20 = 120 meters

Area of the rectangular park = length × width

= 100 × 120

= 1200 square meters

Therefore, Scale factor from actual length to the length in drawing = 1 : 20

Area of the rectangular park = 1200 square feet

7 0

3 years ago

Integrate G(x,y,z)equalsz over the parabolic cylinder yequalszsquared, 0less than or equalsxless than or equals2, 0less than

yKpoI14uk [10]

I gather you're supposed to compute the integral of $G(x,y,z)=z$ over a surface $S$ that is the part of the parabolic cylinder $y=z^2$ with $0\le x\le2$ and $0\le z\le\frac{\sqrt{15}}2$ .

We can parameterize $S$ by

$\vec s(x,z)=x\,\vec\imath+z^2\,\vec\jmath+z\,\vec k$

with the given constraints on $x$ and $z$ . Take the normal vector to $S$ to be

$\vec s_x\times\vec s_z=-\vec\jmath+2z\,\vec k$

so that the surface element is

$\mathrm dS=\|\vec s_x\times\vec s_z\|\,\mathrm dx\,\mathrm dz=\sqrt{1+4z^2}\,\mathrm dx\,\mathrm dz$

Then in the integral, we have

$\displaystyle\iint_Sz\,\mathrm dS=\int_0^2\int_0^{\sqrt{15}/2}z\sqrt{1+4z^2}\,\mathrm dz\,\mathrm dx=\boxed{\frac{21}2}$

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3 years ago

I don’t really understand how you figure out the points of a figure on rotation, please explain!

Basile [38]

To rotate a figure
90 degrees(-y,x)
180 degrees(-x,-y)
270 degrees(y,-x)
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3 years ago

Which ones are the alternative exterior angles

lakkis [162]

Answer:

Step-by-step explanation:

Angle pair 1 and 8

and

Angle pair 2 and 7

7 0

3 years ago

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