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ankoles [38]
3 years ago
13

Find an equation of the plane that passes through the origin and its perpendicular to the vector [1,-2,5]

Mathematics
1 answer:
Volgvan3 years ago
8 0

Answer:

x - 2y + 5z = 0

Step-by-step explanation:

The standard equation is of the form, Ax + By + Cz = 0

The equation of the plane that passes through the origin(0, 0, 0)  and is perpendicular to [1, -2, 5] is

A = 1, B = -2, C = 5

x = y = z = 0 (at origin)

A(x-0) + B(y-0) + C(z-0) = 0

(x - 0) -2(y-0) + 5(z-0) = 0

x - 2y + 5z = 0

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Graph each circle given below right the center and the radius of each circle
Paraphin [41]

Answer:

Center: (-1,8)

Radius: 1

The graph is attached.

Step-by-step explanation:

The equation of the circle has the form:

(x -h)^{2}+(y-k)^{2}=r^{2}

Where (h,k) is the  point of the center of the circle and r is the radius of the circle.

The equation given in the problem is

(x +1)^{2}+(y-8)^{2}=1

 Therefore:

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k=8

 Then, the center is (-1,8) and radius is 1.

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A bowl of Halloween candy has 17 Kit-Kats, 23 Hershey bars, 11 Starbursts, and 14 Skittles packets.
gladu [14]

Answer:

a.) 8/13 = 0.6154.

b) 11/65 = 0.1692

c.) 0.0267

d.) 0.0222

Step-by-step explanation:

firstly, we determine total number of candies.

17 kit kat(K)+ 23 hershey(H) + 11 starburst(B) + 14 skittles(S) = 65 candies.

Since, Probability = favourable outcome / possible outcome.

With replacement,

a.) probability of chocolate candy (kitkat or hershey) = 17/65 or 23/65

= 17/65 + 23/65

=40/65 = 8/13

b.) probability of selecting a starburst = 11/65

When without replacement:,

c) 2 kit kats, 1 skittles as first three picks and one chocolate candy as the last pick, = [KKSK], [KSKK], [SKKK], [KKSH], [KSKH], [SKKH]

[(17/65 * 16/64 * 14/63 * 15/62) × 3] + [(17/65 * 16/64 * 14/63 * 23/62) ×3]

Note: first bracket and fourth brackets are multiplied by 3 because the value of the first bracket is same for the first three brackets and the second three brackets also have the same values.

Re:chocolate candy means either KitKat or Hershey.

=[(51720/16248960) × 3] + [(87584/16248960) ×3]

=0.0105 +0.0162

= 0.0267.

d.) 1 kitkat, 1 skittles and 1 hershey as first 3 picks and one Starburst as the last pick.

= [KSHB], [KHSB], [SKHB], [SHKB], [HKSB], [HSKB]

= [(17/65 * 14/64 * 23/63 * 11/62) × 6]

note: multiplied by 6 because we will have the same value for all 6 brackets

= 60214/16248960 * 6

= 0.0222.

5 0
3 years ago
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