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3 years ago

(3x/2)^4 any answers

Mathematics

2 answers:

avanturin [10]3 years ago

8 0

Simplify the expression by distributing the exponent of 4 to both 3, x and 2:

3 raised to the 4th power is 81, x raised to the fourth power is x^4 and 2 raised to the 4th power is 16.

So your answer is 81x^4/16.

:)))

Anika [276]3 years ago

6 0

$\bf \left( \cfrac{3x}{2} \right)^4\implies \left( \cfrac{(3x)^4}{2^4} \right)\implies \left( \cfrac{3^4x^4}{2^4} \right)\implies \cfrac{81x^4}{16}$

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10x+8=3(x-2) 10x+8=3x-6

d1i1m1o1n [39]

Answer:

x = -2

Step-by-step explanation:

10x+8=3x-6

subtract 10x-3x

7x+8= -6

subtract -6-8

7x=-14

divide 7 into -14

x = -2

Hope this helps!

4 0

2 years ago

which of the following is a non depository financial institution? a.Retail Bank b.commercial bank c.life insurance d.credit unio

Artyom0805 [142]

Answer: it was online bank

Step-by-step explanation:

5 0

2 years ago

Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

2 years ago

SOMEONE HELP ME PLEASE!!

Drupady [299]

Answer:

ok first

follow me. ...........................

3 0

2 years ago

Read 2 more answers

A prism, bases of which are equilateral triangles, circumscribes a sphere of radius 6. What is the volume of the prism?

koban [17]

Answer:

1296√3 cubic units

Step-by-step explanation:

The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.

The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...

B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units

The volume of the prism is then ...

V = Bh = (108√3)(12) = 1296√3 . . . cubic units

_____

<em>Comment on the geometry</em>

The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.

6 0

3 years ago