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1 year ago

Answer please??????????????????????????????/

Mathematics

1 answer:

kirill [66]1 year ago

7 0

The expression that represents the surface area of the square based pyramid is 36 + 15 + 15 + 15 + 15

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<h3>How to find the surface area of a square based pyramid?</h3>

The surface area of the pyramid is the sum of the area of the whole faces of the pyramid.

Therefore, the pyramid has 4 triangular faces and 1 square faces.

Therefore,

surface area of the pyramid = area of the square + 4(area of the triangle)

area of the square = 6² = 36

area of each triangular faces = 1 / 2 bh

where

b = base area
h = height

Therefore,

area of each triangular faces = 1 / 2 × 6 × 5 = 30 / 2 = 15

Hence, the expression is as follows:

surface area of the pyramid = 36 + 15 + 15 + 15 + 15

learn more on pyramid here: brainly.com/question/17615619

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2 years ago

Simplify: [5×(25)^n+1 - 25 × (5)^2n]/[5×(5)^2n+3 - (25)^n+1]

Alekssandra [29.7K]

$\green{\large\underline{\sf{Solution-}}}$

<u>Given expression is </u>

$\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} }$

can be rewritten as

$\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} }$

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\$

And

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\$

So, using this identity, we

$\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} }$

can be further rewritten as

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)}$

$\rm \: = \: \dfrac{4}{25 - 1}$

$\rm \: = \: \dfrac{4}{24}$

$\rm \: = \: \dfrac{1}{6}$

<u>Hence, </u>

$\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}$

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2 years ago

What is three quarters of £42 and a quarter of £42

maksim [4K]

$three \ quarters \to \frac{3}{4} \\\\ \frac{3}{4} \ of \ 42\£ = \\\\ =\frac{3}{4}*42\£= \\\\ =\frac{3}{2}*21\£= \\\\ =\frac{63\£}{2} = \\\\= \boxed{31.5\£} \\\\\\\ a \ quarter \to \frac{1}{4} \\\\ \frac{1}{4} \ of \ 42\£= \\\\ =\frac{1}{4}*42\£= \\\\ =\frac{21\£}{2}= \\\\ =\boxed{10.5\£}$