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mafiozo [28]
3 years ago
9

Solve (1/8)^-3a=512^3a

Mathematics
2 answers:
lukranit [14]3 years ago
5 0
Solve (1/8)^-3a = 512^3a
A=0

I took the assignment it’s right.
melamori03 [73]3 years ago
5 0

Answer:

Using exponent rule:

\frac{1}{a^n}=a^{-n}

(a^n)^m = a^{nm}

Solve:

(\frac{1}{8})^{-3a} =(512)^{3a}

We can write 512 as:

512 = 8 \cdot 8 \cdot 8 = 8^3

then;

(\frac{1}{8})^{-3a} =(8^3)^{3a}

⇒(\frac{1}{8})^{-3a} =(8)^{9a}

Using exponent rule we have;

⇒(8^{-1})^{-3a} =(8)^{9a}

⇒(8)^{3a} =(8)^{9a}

On comparing both sides we have;

3a = 9a

⇒9a-3a = 0

⇒6a = 0

⇒a = 0

Therefore, the value of a = 0

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A cone and a cylinder have the same base and height, as shown below. A cone is inside of a cylinder with same base and height. T
lord [1]

Answer:

The volume of the cone = 28 inch³

Step-by-step explanation:

First let's consider the formula for the volume of the shapes

For cylinder

Volume= πr²h

For cone

Volume= 1/3 πr²h

So we'd notice that no much difference except that the volume if a cylinder is divided by two to get that off a cone.

So if the volume of the cylinder is

84π inch

The volume of the cone is 84/3 = 28

The volume of the cone = 28 inch³

3 0
3 years ago
in the circuit diagram, what does the symbol made of two long lines and two short lines with a positive and the negative sign at
GrogVix [38]
The symbol is the electric current that is inputted into the circuit.
3 0
3 years ago
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What is the measurement of ∠BAC and ∠ABC? Explain your process of solving.
Paraphin [41]

Answer:

<BAC = 78

<ABC = 68

Step-by-step explanation:

The remote angles theorem states that when one extends a side of a triangle, the angle formed between the extension and one of the sides of the triangle is equal to the sum of the two non-adjacent angles inside the triangle. One can apply this theorem here and state the following,

<BAC + <ABC = <ACD

Substitute,

(5y + 3) + (4y + 8) = (146)

Simplify,

9y + 11 = 146

Inverse operations,

9y + 11 = 146

     -11     -11

9y = 135

/9      /9

y = 15

Now substitute this value back into the expressions to find the numerical measurement of (<BAC) and (<ABC),

<BAC = 5y + 3

5(15) + 3

78

<ABC = 4y + 8

4(15) + 8

68

5 0
3 years ago
Consider the vectors x=(1,2,3,4) and y=(4,2,4,5) in R4 . Find the angle between them.
Law Incorporation [45]

Answer:

Angle between the two vectors is 20.7718°.

Step-by-step explanation:

The given two vectors are x = (1,2,3,4) and y = (4,2,4,5)

Now the dot product between two vector is defined as

x.y = ║x║║y║cosθ

Now, x.y( dot product of x and y) = 1×4 + 2×2 + 3×4 + 4×5 = 40

║x║= \sqrt{1+4+9+16} = \sqrt{30}

║y║= \SQRT{16+4+16+25} = \sqrt{61} '

Thus, we get

40 = \sqrt{30}×\sqrt{61}×Cos θ

Thus, Cos θ = \frac{40}{\sqrt{30}\sqrt{61}}

Cos θ = 0.935

θ = Cos^{-1} (0.935)

θ = 20.7718°

4 0
3 years ago
Julie had 2730 cards and Kim had 3570 cards at first.
Anna71 [15]

Answer:

1155

Step-by-step explanation:

Total number of cards is 2730+3570=6300

Since Kim now has 3 times the card of Julie so Julie must have 6300/4=1575.

So, Julie gave 2730-1575=1155

4 0
3 years ago
Read 2 more answers
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