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

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Gelatin Methacryloyl Hydrogels in the Absence of a Crosslinker as 3D Glioblastoma Multiforme (GBM)-Mimetic Microenvironment

scoray [572]

For the eradication of malignancies like the aggressive type of human brain tumour known as glioblastoma multiforme (GBM), 3D platforms are crucial for tracking tumour growth and assessing treatment candidates.

<h3>What is Glioblastoma Multiforme (GBM)?</h3>

Glioblastoma (GBM), commonly known as a grade IV astrocytoma, is an aggressive brain tumour that grows quickly. The local brain tissue gets invaded, but it typically does not spread to distant organs. GBMs can develop from lower-grade astrocytomas or develop from new brain tumours.

Some characteristics of GBM are-

We explore cellular behavior, expression profiles of malignancy, and apoptosis-related genes within this novel network using suspension and spheroid-based models of GBM.
In-depth research is also done on the sensitivity to the anticancer medication Digitoxigenin.
According to the research, GelMA hydrogels contain high levels of prosurvival Bcl-2 gene expression and sparse or spheroid U373 cells, which have much lower expressions of apoptosis-activating genes like Bad, Puma, and Caspase-3.
The up regulation of matrix-metalloproteinase genes within GelMA suggests that gels have a beneficial effect on the extracellular remodelling of cancer cells.
Through the investigation of 3D malignant cancer cell behavior, this special photo curable gelatin shows significant promise for the practical translation of cancer research and, consequently, for more effective treatment techniques for GBM.

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2 years ago

Select the correct answer. Evaluate the following expression when x = -4 and y = 4. A. B. C. D.

andriy [413]

The value of given expression when x=-4 and y=4 is 1250.

The expression is missing in the question which is $\dfrac{x^6-x}{4y}$ .