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steposvetlana [31]
3 years ago
14

Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math.

To help her concentrate better on math, she spends 20 minutes more dancing than doing math.
How much time does Pam spend on practicing math every day?
Mathematics
2 answers:
Kisachek [45]3 years ago
8 0
80/2= 20 then take away the extra 20 from the math for dance and you have the answer... 20 get it?
Varvara68 [4.7K]3 years ago
4 0

Answer: 20

Step-by-step explanation:

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Which expression is a fourth root of -1+isqrt3?
aleksklad [387]

Answer:

Step-by-step explanation:

\sf n^{th} roots of a complex number is given by DeMoivre's formula.

   \sf \boxed{\bf r^{\frac{1}{n}}\left[Cos \dfrac{\theta + 2\pi k}{n}+i \ Sin \ \dfrac{\theta+2\pi k}{n}\right]}

Here, k lies between 0 and (n -1) ; n is the exponent.

\sf -1 + i\sqrt{3}

a = -1 and b = √3

\sf \boxed{r=\sqrt{a^2+b^2}} \ and \ \boxed{\theta = Tan^{-1} \ \dfrac{b}{a}}

\sf r = \sqrt{(-1)^2 + 3^2}\\\\ = \sqrt{1+9}\\\\=\sqrt{10}

                   \sf \theta = tan^{-1} \ \dfrac{\sqrt{3}}{-1}\\\\ = tan^{-1} \ (-\sqrt{3})

                   \sf = \dfrac{-\pi }{3}

n = 4

For k = 0,

          \sf z = \sqrt[4]{10}\left[Cos \ \dfrac{\dfrac{-\pi}{3} +0}{4}+iSin  \ \dfrac{\dfrac{-\pi}{3}+0}{4}\right] \\\\\\z= \sqrt[4]{10} \left[Cos \ \dfrac{ -\pi  }{12}+iSin  \ \dfrac{-\pi}{12}\right]\\\\\\z = \sqrt[4]{10}\left[-Cos \ \dfrac{\pi}{12}-i \ Sin \ \dfrac{\pi}{12}\right]

For k =1,

         \sf z = \sqrt[4]{10}\left[Cos \ \dfrac{5\pi}{12}+i \ Sin \ \dfrac{5\pi}{12}\right]

For k =2,

       z = \sqrt[4]{10}\left[Cos \ \dfrac{11\pi}{12}+i \ Sin \ \dfrac{11\pi}{12}\right]

For k = 3,

      \sf z = \sqrt[4]{10}\left[Cos \ \dfrac{17\pi}{12}+i \ Sin \ \dfrac{17\pi}{12}\right]

For k = 4,

      \sf z =\sqrt[4]{10}\left[Cos \ \dfrac{23\pi}{12}+i \ Sin \ \dfrac{23\pi}{12}\right]

4 0
1 year ago
Consider an arbitrary ellipse x 2 a 2 + y 2 b 2 = 1. (Assume a, b > 0.) (a) Find a parametrization of the ellipse using the d
uysha [10]

Answer:

α(t) = (-a*Sin(t), b*Cos (t))    where t ∈ [0, 2π]

Step-by-step explanation:

Given an arbitrary ellipse (x²/a²) + (y²/b²) = 1       (a, b > 0)

The parametrization can be as follows

x = -a*Sin(t)

y = b*Cos (t)

then

α(t) = (-a*Sin(t), b*Cos (t))    where t ∈ [0, 2π]

If  t = 0

α(0) = (-a*Sin(0), b*Cos (0)) = (0, b)

If  t = π/2

α(π/2) = (-a*Sin(π/2), b*Cos (π/2)) = (-a, 0)

If  t = π

α(π) = (-a*Sin(π), b*Cos (π)) = (0, -b)

If  t = 3π/2

α(3π/2) = (-a*Sin(3π/2), b*Cos (3π/2)) = (a, 0)

If  t = 2π

α(2π) = (-a*Sin(2π), b*Cos (2π)) = (0, b)

We can see the sketch in the pic.

7 0
3 years ago
Read 2 more answers
Suppose that the probability that your mail is delivered before 2pm is .90. What is the probability that your mail will be deliv
Elden [556K]
1. The probability that your mail is delivered before 2 pm is 0.9, so the probability that the mail is delivered at 2 pm or after 2 pm (so not before 2 pm) is 1-0.9=0.1.

Remark: 0.9=9/10=90/100=90%, and 0.1 is 10%

2. Probability of the mail being delivered before 2 pm for 2 consecutive days is 
\frac{90}{100}*  \frac{90}{100}= \frac{9}{10}*  \frac{9}{10}= \frac{81}{100}=0.81

3. take a look at the picture attached, the tree diagram is another method we could use. 

4 0
3 years ago
.......................................................
valkas [14]
Hope this helps lol :)

7 0
1 year ago
-2 ×^2 - 4y +6. x=-3. y=-2 <br> evaluate ​
gladu [14]

Answer:

<u><em>Answer is below</em></u>

Step-by-step explanation:

<em><u>-2 ×^2 - 4y +6</u></em>

<em><u>Evaluate simply means to form an idea of something</u></em>

<em><u>So Evaluate for x=−3,y=−2</u></em>

<em><u>−2(−3)2−(4)(−2)+6</u></em>

<em><u>−2(−3)2−(4)(−2)+6</u></em>

<em><u>Answer =−4</u></em>

8 0
3 years ago
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