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2 years ago

The slope of the line below is -1/7.

Mathematics

1 answer:

KatRina [158]2 years ago

3 0

Answer:

y = (-1/7)x + (24/7)

Step-by-step explanation:

The general structure of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

You have been given the value of the slope (m = -1/7). You have also been given values for "x" and "y" from the point (3,3). Therefore, you can substitute these values in for their variables and simplify to find the value of the y-intercept.

y = mx + b <----- Slope-intercept form

y = (-1/7)x + b <----- Plug -1/7 into "m"

3 = (-1/7)(3) + b <----- Plug in "x" and "y" values from point (3,3)

3 = -3/7 + b <----- Multiply -1/7 and 3

24/7 = b <----- Add 3/7 to both sides

Now that you know that m = -1/7 and b = 24/7, you can determine the formula satisfying the given information.

y = (-1/7)x + (24/7)

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a pyramid whose altitude is 5ft weighs 800lbs. at what distance from its vertex must it be cut by a plane parallel to its base s

slavikrds [6]

A structure which has a square base and four triangular sides meeting at a point is called pyramid.

At distance of 3.97 feet from its vertex , pyramid is cut by plane so that the two solids of equal weight will be formed.

<u>It is assumed that weight of pyramid is proportional to its volume.</u>

So, $w = k V$ , where V is volume of original pyramid and v is volume of small pyramid and k is constant.

Let us consider that at h distance, pyramid is cut from its vertex. So a small pyramid is also formed.

Assume that base area of original pyramid is A and base of small pyramid is a.

Volume of original pyramid is, $V= \frac{1}{3} *A* 5$

So, weight of original pyramid, $W = k *(\frac{1}{3} *A* 5) = 800$

Volume of small pyramid is, $v = \frac{1}{3}* a* h$

So, weight of small pyramid, $w = k*(\frac{1}{3}* a* h)=400$

<u>Since, base and height of small pyramid and original pyramid are in proportion.</u>

So, $\frac{a}{A} = (\frac{h}{5}) ^{2}$

$a = (\frac{h}{5} )^{2}A$

Substituting value of a in equation $k*(\frac{1}{3}* a* h)=400$

So, $k*(\frac{1}{3}* \frac{h^{2} }{25}A * h)=400$

$(k*\frac{1}{3}* A*5)*\frac{1}{5} *\frac{h^{2} }{25} * h)=400$

Since, $(k *\frac{1}{3} *A* 5) = 800$ , substitute in above equation.

So, $800*\frac{h^{3} }{125}=400\\\\h^{3}=\frac{125}{2}\\\\h=\sqrt[\frac{1}{3} ]{62.5}\\\\h=3.97 feet$

Learn more:

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Answer:

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Step-by-step explanation:

Find the diagram attached

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