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2 years ago

Simplify the radical, the square root of x^13

2 answers:

8 0

Rewrite it as a perfect square.

√x¹²x

Write it as a product of two radicals.

√x¹²√x

Simplify √x¹² (divide for 2)

√x¹² * 1/2

x⁶√x

myrzilka [38]2 years ago

5 0

√(x^13) is equal to:

(x^13)^(1/2) which is equal to:

(x^12*x^1)^(1/2) which is equal to

(x^12)^(1/2)*(x^1)^(1/2)

and the applicable rule: (a^b)^c=a^(b*c) so

x^(12*1/2)*x^(1*1/2)

x^6*x^(1/2)

x^6√x

You might be interested in

To solve 16x18, I double and halve?

Goshia [24]

To solve 16x18, you may split it up into a smaller increment you understand. Like 16x2, which equals 32. (18/2 is 9) multiply 32 by 9. you get your answer 288.

8 0

2 years ago

What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFractio

aalyn [17]

Answer:

StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction

Step-by-step explanation:

Apparently you want to simplify ...

$\sqrt{\dfrac{72x^{16}}{50x^{36}}}$

The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

1/a^b = a^-b

(a^b)^c = a^(bc)

So the expression simplifies as ...

$\sqrt{\dfrac{72x^{16}}{50x^{36}}}=\sqrt{\dfrac{36}{25x^{36-16}}}=\sqrt{\dfrac{36}{25x^{20}}}\\\\\sqrt{\left(\dfrac{6}{5x^{10}}\right)^2}=\boxed{\dfrac{6}{5x^{10}}}$

9 0

2 years ago

answer A radio station located 120 miles due east of Collinsville has a listening radius of 100 miles. A straight road joins Col

melamori03 [73]

Answer:

168.7602 miles

Step-by-step explanation:

One way to solve this problem is by using an equation that describes the listening radius of the station, and another for the road, then the points where this two-equation intersect each other will represent when the driver starts and stops listening to the station, and the distance between the points is the miles that the driver will receive the signal.

The equation for the listening radius (the radio station is at (0,0)):

$x^2+y^2=100^2$

The equation for the road that past through the points (-120,0) and (80,100) (Collinsville and Harmony respectively):

$m=\frac{y_2-y_1}{x_2-x_1} =\frac{100-0}{80-(-120)}=\frac{100}{200}=\frac{1}{2}$

$y-y_1=m(x-x_1)\\y-0=\frac{1}{2}(x-(-120))\\ y=\frac{1}{2}x+60$

Substitutes the value of y in the equation of the circle:

$x^2+(\frac{1}{2}x+60)^2=100^2\\x^2+\frac{1}{4} x^2+60x+3600=10000\\\frac{5}{4} x^2+60x+3600=10000\\\frac{5}{4} x^2+60x+3600-10000=0\\\frac{5}{4} x^2+60x-6400=0\\5 x^2+240x-25600=0\\x^2+48x-5120=0\\$

The formula to solve second-degree equations:

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a} \\x_{1,2}=\frac{-48\pm\sqrt{48^2-4(1)(-5120)} }{2(1)}\\x_{1,2}=\frac{-48\pm\sqrt{2304+20480} }{2}\\x_{1,2}=\frac{-48\pm\sqrt{22784} }{2}\\x_{1,2}=\frac{-48\pm16\sqrt{89} }{2}\\x_{1,2}=-24\pm8\sqrt{89} \\x_1=-24+8\sqrt{89}\approx51.4718\\x_2=-24-8\sqrt{89}\approx-99.4718\\$

Using the values in x to find the values in y:

$y_1=\frac{1}{2}x_1+60\\y_1=\frac{1}{2}(-24+8\sqrt{89} )+60\\y_1=-12+4\sqrt{89}+60\\ y_1=48+4\sqrt{89}\approx85.7359$

$y_2=\frac{1}{2}x_2+60\\y_2=\frac{1}{2}(-24-8\sqrt{89} )+60\\y_1=-12-4\sqrt{89}+60\\ y_1=48-4\sqrt{89}\approx10.2641$

The distance between the points (51.4718,85.7359) and (-99.4718,10.2641) :

$d=\sqrt{(x_1 -x_2 )^2+(y_1 -y_2)^2} \\d=\sqrt{(-24+8\sqrt{89} -(-24-8\sqrt{89}) )^2+(48+4\sqrt{89} -(48-4\sqrt{89}) )^2}\\d=\sqrt{(-24+8\sqrt{89} +24+8\sqrt{89} )^2+(48+4\sqrt{89} -48+4\sqrt{89} )^2}\\d=\sqrt{(16\sqrt{89} )^2+(8\sqrt{89} )^2}\\d=\sqrt{22784+5696}\\d=\sqrt{28480}\\d=8\sqrt{445}\approx168.7602miles$

4 0

2 years ago

George saves 18% of his total gross weekly earnings from his 2 part-time jobs. He earns $6.25 per hour from one part-time job an

Readme [11.4K]

What do u mean man i don't get it ether sorry brah <span />

7 0

2 years ago

Suppose that Kevin can choose to get home from work by car or bus. When he chooses to get home by car, he arrives home after 7 p

astraxan [27]

Answer:

The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm = 0.838

Step-by-step explanation:

Let the probability that Kevin arrives home after 7 pm be P(L)

Probability that Kevin uses the bus = P(B)

Probability that Kevin uses the car = P(C)

Probability of arriving home after 7 pm if the car was taken = P(L|C) = 4% = 0.04

Probability of arriving home after 7 pm if the bus was taken = P(L|B) = 15% = 0.15

The bus is cheaper, So, he uses the bus 58% of the time.

P(B) = 58% = 0.58

P(C) = P(B') = 1 - P(B) = 1 - 0.58 = 0.42

The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm = P(B|L)

The conditional probability P(A|B) is given mathematically as

P(A|B) = P(A n B) ÷ P(B)

Hence, the required probability, P(B|L) is given as

P(B|L) = P(B n L) ÷ P(L)

But we do not have any of P(B n L) and P(L)

Although, we can obtain these probabilities from the already given probabilities

P(L|C) = 0.04

P(L|B) = 0.15

P(B) = 0.58

P(C) = 0.42

P(L|C) = P(L n C) ÷ P(C)

P(L n C) = P(L|C) × P(C) = 0.04 × 0.42 = 0.0168

P(L|B) = P(L n B) ÷ P(B)

P(L n B) = P(L|B) × P(B) = 0.15 × 0.58 = 0.087

P(L) = P(L n C) + P(L n B) = 0.0168 + 0.087 = 0.1038 (Since the bus and the car are the two only options)

The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm

= P(B|L) = P(B n L) ÷ P(L)

P(B n L) = P(L n B) = 0.087

P(L) = 0.1038

P(B|L) = (0.087/0.1038) = 0.838150289 = 0.838

Hope this Helps!!!

8 0

2 years ago