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ad-work [718]
2 years ago
12

What is the radius of the circle?in unitsplease help​

Mathematics
2 answers:
Allushta [10]2 years ago
7 0

Answer:4 units

Step-by-step explanation: A radius is half of the diameter

Sergio [31]2 years ago
4 0

Answer:

4 units

Step-by-step explanation:

i hope its right

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Solve 3(6b-1)-7(2b+3)=0​
babymother [125]

Answer:

24/13 or 1.8

Step-by-step explanation:

27b -3 - 14b -21 = 0

13b - 24 = 0

13b = 24

b = 24/13 or 1.8

5 0
2 years ago
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on january 1,1999,the price of gasoline was$1.39 per gallon .if the price of gasoline increased by 0.5%per month ,what was the w
arlik [135]
P(t)=1.39.(1.005)^t \ \ \ \ where t \ is \ time \ in \ months\\
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P(1)=1.39*1.005\\
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P(1)=\$ \ 1.40
4 0
3 years ago
What is the exact volume of a sphere with a diameter of 18 cm?<br><br><br> <img src="https://tex.z-dn.net/?f=%20%5Cpi%20" id="Te
Vesna [10]
Sphere Volume =  <span>( <span>π <span>•diameter^3) / 6
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Sphere Volume =  3.14159 * 18^3 / 6

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6 0
3 years ago
If a card is picked at random from a standard 52-card deck, what is the probability of getting a spade or a 8
g100num [7]

Answer:

1/4, 25%, or 0.25

Step-by-step explanation:

Therefore, as each suit contains 13 cards, and the deck is split up into 4 suits, that leaves us with a 13/52 chance to pick a spade.

That fraction is equivalent to 1/4, so that leaves us with a probability of picking a spade at:

1/4, 25%, or 0.25

8 0
3 years ago
The plane x+y+2z=8 intersects the paraboloid z=x2+y2 in an ellipse. Find the points on this ellipse that are nearest to and fart
DiKsa [7]

Answer:

The minimum distance of   √((195-19√33)/8)  occurs at  ((-1+√33)/4; (-1+√33)/4; (17-√33)/4)  and the maximum distance of  √((195+19√33)/8)  occurs at (-(1+√33)/4; - (1+√33)/4; (17+√33)/4)

Step-by-step explanation:

Here, the two constraints are

g (x, y, z) = x + y + 2z − 8  

and  

h (x, y, z) = x ² + y² − z.

Any critical  point that we find during the Lagrange multiplier process will satisfy both of these constraints, so we  actually don’t need to find an explicit equation for the ellipse that is their intersection.

Suppose that (x, y, z) is any point that satisfies both of the constraints (and hence is on the ellipse.)

Then the distance from (x, y, z) to the origin is given by

√((x − 0)² + (y − 0)² + (z − 0)² ).

This expression (and its partial derivatives) would be cumbersome to work with, so we will find the the extrema  of the square of the distance. Thus, our objective function is

f(x, y, z) = x ² + y ² + z ²

and

∇f = (2x, 2y, 2z )

λ∇g = (λ, λ, 2λ)

µ∇h = (2µx, 2µy, −µ)

Thus the system we need to solve for (x, y, z) is

                           2x = λ + 2µx                         (1)

                           2y = λ + 2µy                       (2)

                           2z = 2λ − µ                          (3)

                           x + y + 2z = 8                      (4)

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

Subtracting (2) from (1) and factoring gives

                     2 (x − y) = 2µ (x − y)

so µ = 1  whenever x ≠ y. Substituting µ = 1 into (1) gives us λ = 0 and substituting µ = 1 and λ = 0  into (3) gives us  2z = −1  and thus z = − 1 /2 . Subtituting z = − 1 /2  into (4) and (5) gives us

                            x + y − 9 = 0

                         x ² + y ² +  1 /2  = 0

however, x ² + y ² +  1 /2  = 0  has no solution. Thus we must have x = y.

Since we now know x = y, (4) and (5) become

2x + 2z = 8

2x  ² − z = 0

so

z = 4 − x

z = 2x²

Combining these together gives us  2x²  = 4 − x , so

2x²  + x − 4 = 0 which has solutions

x =  (-1+√33)/4

and

x = -(1+√33)/4.

Further substitution yeilds the critical points  

((-1+√33)/4; (-1+√33)/4; (17-√33)/4)   and

(-(1+√33)/4; - (1+√33)/4; (17+√33)/4).

Substituting these into our  objective function gives us

f((-1+√33)/4; (-1+√33)/4; (17-√33)/4) = (195-19√33)/8

f(-(1+√33)/4; - (1+√33)/4; (17+√33)/4) = (195+19√33)/8

Thus minimum distance of   √((195-19√33)/8)  occurs at  ((-1+√33)/4; (-1+√33)/4; (17-√33)/4)  and the maximum distance of  √((195+19√33)/8)  occurs at (-(1+√33)/4; - (1+√33)/4; (17+√33)/4)

4 0
3 years ago
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