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seropon [69]
2 years ago
8

M(t)M, left parenthesis, t, right parenthesis models the distance (in millions of \text{km}kmstart text, k, m, end text) from Ma

rs to the Sun ttt days after it's at its furthest point. Here, ttt is entered in radians.
M(t) = 21\cos\left(\dfrac{2\pi}{687}t\right) + 228M(t)=21cos(
687
2π
​
t)+228M, left parenthesis, t, right parenthesis, equals, 21, cosine, left parenthesis, start fraction, 2, pi, divided by, 687, end fraction, t, right parenthesis, plus, 228
How many days later does Mars first reach 220220220 million \text{km}kmstart text, k, m, end text from the Sun?
Round your final answer to the nearest whole day.
Mathematics
1 answer:
lana [24]2 years ago
5 0

Answer:

214

Step-by-step explanation:

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The answer is letter A.
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You and a friend are playing a game by tossing two coins. If both coins land
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Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
   -3x² - x⁴ = -4
   x⁴ + 3x² - 4 = 0
   (x² + 4)(x² - 1) = 0
   (x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
   y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
   = -3 + i(±1)²(-4)
   = -3 - 4i

   x² + y + 4i
   = (±1)² - 4 + 4i
   = 1 - 4 + 4i
   = -3 + 4i

They result in conjugates
4 0
2 years ago
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Sandy evaluated the expression below. (negative 2) cubed (6 minus 3) minus 5 (2 + 3) = (negative 2) cubed (3) minus 5 (5) = 8 (3
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Answer:

should be - 8

Step-by-step explanation:

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An insurance company collected data from a class of high school sophomores on whether or not they have a cell phone and whether
NeX [460]

Answer:

C. Those who have a car tend to have a cell phone.

Step-by-step explanation:

The relative frequency for a data set n is calculated by dividing each frequency x_i by n.

We have a table that relates the use of cars and cell phones.

First, we take from the table the population that has a car.

n = 18

Then, of the students who have a car, 12 have a cell phone and 6 do not have a cell phone.

Then we calculate the relative frequencies f_{x_i} for those who have a cell phone and those who do not.

______________________________________________

Relative frequency   Students with car  n = 18.

-------------------------------------------------- --------------------------------------

C<em>ell phone     No cell phone      Total n</em>

 12/18                    6/18                     18

_______________________________________________

_______________________________________________

Relative frequency   Students with car  n = 18.

-------------------------------------------------- --------------------------------------

C<em>ell phone     No cell phone      Total n</em>

  0.666              0.333                   18

________________________________________________

Most students who have a car also have a cell phone.

Now we calculate the relative frequency for students who do not have a car.

_______________________________________________

Relative frequency  Students without a car  n = 7

-------------------------------------------------- --------------------------------------

<em>Cell phone       No cell phone             Total  n</em>

 2/7                     5/7                          7

_______________________________________________  

_______________________________________________

Relative frequency  Students without a car  n = 7

-------------------------------------------------- --------------------------------------

<em>Cell phone</em>      <em>  No</em> <em>cell phone           Total  n</em>

 0.286                 0.714                              7

_______________________________________________

Most students who do not have a car do not have a cell phone either.

<em>Then these data suggest that. Those who have a car tend to have a cell phone.</em>

Option C

6 0
2 years ago
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