All categories

2 years ago

Simplify: [3(2a)3/2]^2

Mathematics

1 answer:

stich3 [128]2 years ago

5 0

Answer:

24a³

Step-by-step explanation:

Simplify, then, 2.1 2³ divided by 2¹= 2 (³_¹)= 2²

( 3 . 4³ .2. =24a³.

You might be interested in

Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o

Brrunno [24]

Answer:

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

$Sin\ C = \frac{h}{a}$

Make h the subject:

$h = aSin\ C$

Also, in BOC (Using Pythagoras)

$a^2 = h^2 + x^2$

Make $x^2$ the subject

$x^2 = a^2 - h^2$

Substitute $aSin\ C$ for h

$x^2 = a^2 - h^2$ becomes

$x^2 = a^2 - (aSin\ C)^2$

$x^2 = a^2 - a^2Sin^2\ C$

Factorize

$x^2 = a^2 (1 - Sin^2\ C)$

In trigonometry:

$Cos^2C = 1-Sin^2C$

So, we have that:

$x^2 = a^2 Cos^2\ C$

Take square roots of both sides

$x= aCos\ C$

In triangle BOA, applying Pythagoras theorem, we have that:

$AB^2 = h^2 + (b-x)^2$

Open bracket

$AB^2 = h^2 + b^2-2bx+x^2$

Substitute $x= aCos\ C$ and $h = aSin\ C$ in $AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2$

Open Bracket

$AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C$

Reorder

$AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C$

Factorize:

$AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C$

In trigonometry:

$Sin^2C + Cos^2 = 1$

So, we have that:

$AB^2 = a^2 * 1 + b^2-2abCos\ C$

$AB^2 = a^2 + b^2-2abCos\ C$

Take square roots of both sides

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

6 0

3 years ago

What is 3.9 divided by 100.000

Amanda [17]

Answer: 0.039

Step-by-step explanation: you move the "3.9" 2 decimal places to the right. If you did the inverse (multiplying by 100) you would get 390.00

3 0

1 year ago

At the shelter,4% of the dogs are puppies.there are 1,675 dogs at the shelter.how many are puppies

VikaD [51]

The answer is 67 because you cross multiply 4/100 with x/1675 (:

5 0

3 years ago

The sum of two numbers x and y is 18 and their difference is 14. how is that written as an equation

MrRa [10]

Answer:

16 and 2

Step-by-step explanation:

16+2=18

16-2=14

5 0

2 years ago

PLEASE HELP!! ITS A TEST!!

irakobra [83]

Answer:

40°

Step-by-step explanation:

A parallelogram is a quadrilateral (a four-sided object) with parallel sides

Some of the characteristics of a parallelogram includes:

1. Opposite sides and angles are congruent.

2. Opposite angels are congruent

3. Consecutive angles are supplementary

4. The diagonals bisect each other

Angle DBC = ABD = 35 (alternate angles are equal)

Angle ADB = 180 - 35 - 105 = 40

I subtracted from 180 because sum of angles in a triangle is equal to 180

3 0

2 years ago