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attashe74 [19]
3 years ago
15

Find the volume of a regular tetrahedron whose altitude measures 10cm.

Mathematics
1 answer:
Marina CMI [18]3 years ago
5 0
H = 10 cm,  a - edge;
V = 1/3  a²√3  / 4   * h
h² = ( 2/3 * a√3 / 2 )² + a²
100 = a²/3  + a²
100 = 4 a² / 3
a² = 75
a = √75
a = 5 √3  cm
V = 1/2 * 75√3 / 4 * 10 = 250√3 / 4 = 62.5√3 cm³ ≈ 108.25 cm³
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7/9 - 4/3w = -5/6 <br> what is w
borishaifa [10]

Answer:

w=1 5/24

Step-by-step explanation:

7/9-4/3w=-5/6

-4/3w=-5/6-7/9

-4/3w=-15/18-14/18

-4/3w=-29/18

w=-29/18:(-4/3)

w=29/18*(3/4)

w=29*3/18*4

w=29/6*4

w=29/24

w=1 5/24

4 0
3 years ago
Solve for x:a(a²+b²)x²+b²x-a​
m_a_m_a [10]

Answer:

x = a/(a² + b²) or x = -1/a  

Step-by-step explanation:

a(a²+ b²)x² + b²x - a =0

Use the quadratic equation formula:

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1. Evaluate the discriminant D

D = b² - 4ac = b⁴ - 4a(a² + b²)(-a) = b⁴ + 4a⁴ + 4a²b²  = (b² + 2a²)²

2. Solve for x

\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-b^{2}\pm\sqrt{(b^{2}+2a^{2})^{2}}}{2a(a^{2} + b^{2})}\\\\ & = & \dfrac{-b^{2}\pm(b^{2}+ 2a^{2})}{2a(a^{2} + b^{2})}\\\\x = \dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}\\\\x =\dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\\end{array}

\begin{array}{rcl}x = \large \boxed{\mathbf{\dfrac{a}{a^{2} + b^{2}}}}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2b^{2}- 2a^{2}}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2(a^{2}+ b^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\large \boxed{\mathbf{-\dfrac{1}{a}}}\\\\\end{array}

5 0
4 years ago
S
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Answer:

x = 4

Step-by-step explanation:

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In trapezoid ABCD, BC and AD are the diagonals.

Hence BC = AD (property of isosceles trapezoid)

9x + 1 = 12x - 11

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8 0
3 years ago
Someone please help me answer this!!
Liula [17]

Answer:

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Step-by-step explanation:

a = 60 in

b = 80 in

c = ?

According to the Pythagorean theorem,

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c = 100 in

∴ the distance between the opposite corners of the bed is 100 in

7 0
3 years ago
Help ill give u lots of points dude
VLD [36.1K]

Answer:

?

Step-by-step explanation:

3 0
3 years ago
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