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melisa1 [442]
2 years ago
12

What is the value of log(x exponent 2 y exponent 3 divided by z) when given the following:

Mathematics
1 answer:
Gekata [30.6K]2 years ago
7 0

Answer:

B. 13

Explanation:

\sf\:Given\:expression: log(\dfrac{x^2 y^3}{z} )

Logarithm rules:

\sf (i)  \ \sf log(ab) = log(a) + log(b)\\ \\ (ii) \  log(a/b) = log(a) - log(b)\\\\ (iii) \ log(a^n) = n log(a)

Breakdown of the expression:

\rightarrow \sf log\left(\dfrac{x^2y^3}{z}\right)

\rightarrow \sf log\left(x^2\right) + log\left(y^3\right) - log(z)

\rightarrow \sf 2\log\left(x\right)+3\log \left(y\right)-\log \left(z\right)

insert given values

\rightarrow \sf 2(3)+3(2)-(-1)

\rightarrow \sf 13

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Answer:

x/2 inches

Step-by-step explanation:

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Dima020 [189]

Answer:

Step-by-step explanation:

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8 0
2 years ago
Write the expression as a square of a binomial:<br><br> a^2x^2–2abx +b^2
Nataly [62]

Answer:

{(ax - b)}^{2}

Step-by-step explanation:

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4 0
3 years ago
70 POINTSS!!!! URGETT PLS HELP!! Vectors t = −5i + 2j, u = −3i + 7j, and v = 8i + 20j are given.
LUCKY_DIMON [66]

The angle between the vectors t and u is 45°. And the vector t and vector w are orthogonal to each other.

<h3>What is a vector?</h3>

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

The vectors are given below.

t = −5i + 2j, u = −3i + 7j, and v = 8i + 20j

Part A: Then the angle between vectors t and u will be

\cos \theta = \dfrac{\overrightarrow{a} \cdot \overrightarrow{b}}{|\overrightarrow{a}| + |\overrightarrow{b}|}

Then we have

cos θ = [(−5i + 2j)(−3i + 7j)] / [√{(-5²) + 2²} + √{(-3)² + 7²}]

cos θ = 1 / √2

      θ = 45°

Part B: c is a scalar

If \rm \overrightarrow{\rm v} = (a, b), then \rm c\overrightarrow{\rm v} = c(ca, cb)

Let c = 2, then we have

\overrightarrow{\rm w} = c\overrightarrow{v}\\\\\overrightarrow{\rm w} = (2*8, 2*20)\\\\\overrightarrow{\rm w} = (16, 40)

Part C: Use the dot product to determine if t and w are parallel or orthogonal.

\overrightarrow{\rm t} \cdot  \overrightarrow{\rm w} = (-5, 2)(16, 40)\\\\ \overrightarrow{\rm t} \cdot  \overrightarrow{\rm w} = -5*16+ 2*40\\\\ \overrightarrow{\rm t} \cdot  \overrightarrow{\rm w} = -80+ 80\\\\ \overrightarrow{\rm t} \cdot  \overrightarrow{\rm w} = 0

More about the vector link is given below.

brainly.com/question/13188123

#SPJ1

6 0
1 year ago
if a wheel with a diameter of 30 inches spins at a rate of 40 revolutions per minute, find the approximate linear velocity in mi
Anton [14]
A) Linear velocity, v = ωr           ω = Angular velocity, r = radius.

ω = 40 revolutions per minute.  1 minute = (1/60) hour.

= 40*2π radians / (1/60) hour = 4800π radians per hour          π = 3.14

= 4800*3.14 = 15072 radians / hour

but radius, r = 30 inches,  63360 inches = 1 mile,  30 inches = (30/63360) mile  

Linear velocity, v = ωr

                       v = 15072 radians / hour *  (30/63360) mile  
                       v ≈  7.136 miles / hour

b) Linear velocity, v = ωr
                           v = 8.9 radians/second * 20 cm
                           v = 178 cm/s
4 0
2 years ago
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