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Nuetrik [128]
3 years ago
11

Rewrite in simplest radical form 1/x^-3/6.

Mathematics
1 answer:
Aneli [31]3 years ago
6 0
\cfrac{1}{x^{- \frac{3}{6} }} = \cfrac{1}{x^{- \frac{1}{2} }} =x^{ \frac{1}{2} }= \sqrt{x}
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a regular rectangular pyramid has a base and lateral faces that are congruent equilateral triangles. it has a lateral surface ar
Margarita [4]
A pyramid is regular if its base is a regular polygon, that is a polygon with equal sides and angle measures.
(and the lateral edges of the pyramid are also equal to each other)

Thus a regular rectangular pyramid is a regular pyramid with a square base, of side length say x.

The lateral faces are equilateral triangles of side length x.

The lateral surface area is 72 cm^2, thus the area of one face is 72/4=36/2=18  cm^2.

now we need to find x. Consider the picture attached, showing one lateral face of the pyramid.

by the Pythagorean theorem: 

h= \sqrt{ x^{2} - (x/2)^{2}}= \sqrt{ x^{2}- x^{2}/4}= \sqrt{3x^2/4}= \frac{ \sqrt{3} }{2}x

thus, 

Area_{triangle}= \frac{1}{2}\cdot base \cdot height\\\\18= \frac{1}{2}\cdot x \cdot \frac{ \sqrt{3} }{2}x\\\\ \frac{18 \cdot 4}{ \sqrt{3}}=x^2

thus:

x^2 =\frac{18 \cdot 4}{ \sqrt{3}}= \frac{18 \cdot 4 \cdot\  \sqrt{3} }{3}=24 \sqrt{3}       (cm^2)

but x^{2} is exactly the base area, since the base is a square of sidelength = x cm.


So, the total surface area = base area + lateral area =  24 \sqrt{3}+72   cm^2


Answer: 24 \sqrt{3}+72   cm^2

4 0
3 years ago
Jenifer is 1 year older than twice Zack's age. Write an expression that repersents Jenifer's age in relation to zack.
Sedbober [7]

Answer:

j = 2z + 1

jennifer is one year older or jennifer is plus one.

twice zacks age or two times zacks age.

jennifer's age is two times zacks age plus one or

j = 2z + 1

3 0
3 years ago
Find the equation for the plane through the points Upper P 0 (4 comma 5 comma negative 3 )P0(4,5,−3)​, Upper Q 0 (1 comma 4 comm
alexira [117]

Answer:

  4x -4y +z = -7

Step-by-step explanation:

The direction vector will be perpendicular to any/all vectors between the given points. It can be found, for example, using the cross product:

  d = (P0Q0) × (P0R0) = (-3, -1, 8) × (-4, -3, 4)

The cross product can be computed by hand or by any of a number of calculators or web tools. Here it will be ...

  d = (20, -20, 5)

These can be the coefficients of x, y, and z in the plane equation. However, the equation is better written using coefficients that are mutually prime, so we choose the direction vector to be ...

  d = (4, -4, 1)

The constant C in the plane equation

  d·(x, y, z) = C

will be the dot product of this direction vector (d) any any of the given points. Using R0, we find the constant to be ...

 C = (4, -4, 1)·(0, 2, 1) = 4·0 +(-4)·2 +1·1 = -8+1 = -7

so, the plane equation is ...

  4x -4y +z = -7

6 0
3 years ago
To calculate the total amount of satin you need you add 4.5 and 3.25 and find that you need 7.75 yards of satin. Is this correct
Nostrana [21]
4.5 and 3.25 gets you to 7.75, you are correct
7 0
3 years ago
A sequence is shown.
marin [14]

Answer:

Step-by-step explanation:

The given sequence of numbers is increasing in geometric progression. The consecutive terms differ by a common ratio, r

Common ratio = 6/3 = 12/6 = 2

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 3

r = 2

The function, f(n), representing the nth term of the sequence is

f(n) = 3 × 2^(n - 1)

6 0
3 years ago
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