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1 year ago

(y^3/2 x^-1/2)^4 Use the properties of exponents

Mathematics

1 answer:

Zolol [24]1 year ago

6 0

Using the properties of exponents, the simplified form of the expression is (y^6 x^-2) OR (y⁶ x⁻²)

<h3>Evaluating an expression </h3>

From the question, we are to evaluate the given expression

The given expression is

(y^3/2 x^-1/2)^4

Using the properties of exponents, we can simplify the expression as shown below

(y^3/2 x^-1/2)^4

[y^(3/2×4) x^(-1/2×4)]

[y^(12/2) x^(-4/2)]

(y^6 x^-2)

(y⁶ x⁻²)

Hence, the simplified form of the expression is (y^6 x^-2) OR (y⁶ x⁻²)

Learn more on Evaluating an expression here: brainly.com/question/1403904

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3 years ago

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Find the 37th term of the arithmetic sequence: -38,-8,22,52

Leya [2.2K]

Answer:

1042

Step-by-step explanation:

-38,-8,22,52

The common difference is 52 - 22 = 30

a_1 = -38

a_2 = -38 + 30

a_3 = -38 + 2 * 30

a_4 = -38 + 3 * 30 (notice that the common difference is multiplied by 1 less than the term number)

a_n = -38 + (n - 1)30 (since the term number is n, we multiply the common difference by n - 1)

a_n = -38 + 30(n - 1)

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2 years ago

X^2-x-20 how do I write that in factored form

Rufina [12.5K]

Answer:

(x+4)(x-5)

Step-by-step explanation:

You need to find two numbers that multiply to be -20 but add up to be -1.

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3 years ago

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Make the eqaution equal 4,416 for alot of points

irga5000 [103]

Answer:

2 *( 3+7-9) =(1+5) - ( 8 -4 )

Step-by-step explanation:

2 _( 3_7_9) = (1_ 5) _ ( 8 _4 )

I just started playing with things

2 *( 3+7-9) = (1_5 ) _ ( 8 _4 )

2 * (10-9)

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So the left side is 2

Now to make the right side 2

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2 years ago

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The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If

attashe74 [19]

Answer:

$t=7.85 years$

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

$\frac{dP}{dt}=aP$

Where a is proportional constant, P the population variable, and t the time.

$\frac{dP}{P}=adt$

Integrating each side of the equation.

$\int \frac{dP}{P}=\int adt$

$ln(P)=at+c$

$P=e^{at+c}$

$P=e^{c}e^{at}=Ce^{at}$

To find C we need to use the initial condiction, it means evaluae P at t=0.

$P_{0}=Ce^{0}=C$

$P=P_{0}e^{at}$

Now, we use the sentence the population has doubled in 5 years.

$2P_{0}=P_{0}e^{a5}$

We can find "a" in this condition.

$2=e^{a5}$

$ln(2)=a5$

$a=\frac{ln(2)}{5}$

$a=0.14$

Finally, let's find how long will it take to triple.

$3P_{0}=P_{0}e^{0.14t}$

$3=e^{0.14t}$

$t=\frac{ln(3)}{0.14}$

$t=7.85 years$

I hope it helps you!

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2 years ago