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2 years ago

A man ran 20 miles in 2 hours. Calculate the average time that it took the man to run each mile in minutes.

Mathematics

1 answer:

konstantin123 [22]2 years ago

3 0

Answer:

he ran 3 miles in 8 mins

Step-by-step explanation:

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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by

WARRIOR [948]

Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

$z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1$

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

$z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\$

$z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]$

3 0

3 years ago

Find the value of x in each case: (Will give brainliest)

Novay_Z [31]

Answer:

x= 22.5°

Step-by-step explanation:

∠DEA= ∠BAE (alt. ∠s, DE// AB)

Substitute ∠DEA= 2x:

∠BAE= 2x

∠AEB +∠BEF= 180° (adj. ∠s on a str. line)

Substitute ∠BEF= 4x:

∠AEB +4x= 180°

∠AEB= 180° -4x

∠ABE +∠CBE= 180° (adj. ∠s on a str. line)

Substitute ∠CBE= 6x:

∠ABE +6x= 180°

∠ABE= 180° -6x

∠BAE +∠AEB +∠ABE= 180° (∠ sum of triangle)

2x +180° -4x +180° -6x= 180°

-8x +360°= 180°

8x= 360° -180°

8x= 180°

x= 180° ÷8

x= 22.5°

6 0

2 years ago

What is the value of x to the power of 6 + y to the power of 2 when x=1 and y=11

siniylev [52]

Answer: 122

Step-by-step explanation: Substitute the values of x and y into the expression.

$x^6+y^2 \\ \text{ is like } \\ ( )^6 + ( )^2$

"Fill in the blanks" with the numbers given for x and y.

$(1)^6+(11)^2 = 1+121=122$

4 0

3 years ago

I need help with C, thank you.

guapka [62]

Simple....

$\frac{3}{4} x\ \textless \ \frac{9}{2}$

x<6

This means that on your graph at 6 it's a circle (not colored in) and it goes to the left indefinitely...

Thus, your answer.

6 0

2 years ago

A customer pays $3.27 for oranges and $4.76 for pears. How many pounds of fruit does the customer buy?

ruslelena [56]

Take 3.27 and divide that by 1.09 (for the oranges)
3.27/1.09=3lbs. of oranges
then take 4.76 and divide that by 1.19 (for the pears)
4.76/1.19=4lbs. of pears
add 4+3 to get how many lbs. in all
4+3=7

3 0

2 years ago