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irga5000 [103]
3 years ago
6

What does the constant of the polynomial expression 14x squared plus 37x plus 5 represent?

Mathematics
1 answer:
snow_lady [41]3 years ago
5 0
<span>14x squared plus 37x plus 5 => 14x^2 + 37x + 5

Think of the most basic parabola:  y=x^2.  This curve opens up and has its vertex at (0,0).  Adding 5 to y=x^2 shifts the entire graph upward by 5 units; we call this "vertical translation."  Going back to y = </span>14x^2 + 37x + 5, we can easily conclude that 5 also results in vertical translation of the graph of y=14x^2 + 37x.  Whether or not the function y = 14x^2 + 37x + k has real roots or not depends upon the value of the constant k and can most easily be determined by calculating the discriminant b^2-4ac.

Here a=14, b=37 and c=5.

The discriminant is 37^2-4(14)(5) = 1089.  Because this is positive, the function has 2 real, unequal roots.  If we were to use some constant other than 5, then the discriminant would be 37^2-4(14)(k).  Set this equal to 0 and solve for k:  37^2/(4*14) = k, so that k = 24.45.  At this value of k, the function would have 2 real, equal roots.  If we pick a value for k such that the discriminant is negative, then the function would have 2 complex roots.
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1 ln(1) + 2 ln(2) + 3 ln(3) + ⋯ + 10 ln(10)
Lapatulllka [165]

Answer:

\ln(1\cdot2^{2} \cdot3^{3}\cdot4^{4}   ...\cdot10^{10}   )

Step-by-step explanation:

By logarithm rules

\ln1+2\ln2+3\ln3+....+10\ln10\\\ln1+\ln2^2+\ln3^3+....\ln10^{10}\\\ln(1\cdot2^{2} \cdot3^{3}\cdot4^{4}   ...\cdot10^{10}   )

6 0
3 years ago
On each round, Ann and Bob each simultaneously toss a fair coin. Let Xn be the number of heads tossed in the 2n flips which occu
CaHeK987 [17]

Answer:

P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}

Step-by-step explanation:

In a coin toss the  probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

R=\frac{2n!}{m!*(2n-m)!}

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of P_{case}=0.5^{2n} so:

P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}

<u>For example, to toss 4 heads in 5 rounds: </u>

  • n=5
  • 2n=10
  • m=4

P=\frac{10!}{4!*(10-4)!}*0.5^{10}

P=\frac{10*9*8*7*6!}{4!*6!}*0.5^{10}

P=\frac{10*9*8*7}{4!}*0.5^{10}

P=\frac{10*9*8*7}{4!}*0.5^{10}=0.205

8 0
3 years ago
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romanna [79]

Answer:

more detail

Step-by-step explanation:

8 0
3 years ago
Simplify.
Kazeer [188]
(1/2)^2 = 1/4
2-2/3 = 6/3 - 2/3 = 4/3

OK so:
(1/2)^2 - 6(2-2/3) = 1/4 - 6(4/3)
= 1/4 - 8
= 1/4 - 32/4
= -31/4
3 0
2 years ago
Please help quick ASAP
musickatia [10]
Answer is: 9.42cm^3
7 0
3 years ago
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