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Vladimir79 [104]

2 years ago

12

Tori sold 450 soft pretzels. If she sold them in groups of 15 soft pretzels, how many groups did she sell?. (Whole number only).

2 answers:

mafiozo [28]2 years ago

6 0

Answer:

30 Groups

Step-by-step explanation:

She would sell 30 groups of pretzels because 450 divided by 15 equals 30.

geniusboy [140]2 years ago

4 0

Answer:

30

Step-by-step explanation:

450/15

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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

Count by tens and ones to find the sum of 45+26

galben [10]

45+10= 55
55+10= 65
65+1= 66
66+1= 67
67+1= 68
68+1= 69
69+1= 70
70+1= 71

Because 10+10+1+1+1+1+1+1= 26,
71 is your answer :)

4 0

2 years ago

Find the volume of a right circular cone that has a height of 11.1 cm and a base with a diameter of 17.2 cm. Round your answer t

vovangra [49]

Answer:

$2577.8\text{ cm}^3$

Step-by-step explanation:

GIVEN: A right circular cone that has a height of $11.1$ cm and a base with a diameter of $17.2$ cm.

TO FIND: Volume of cone.

SOLUTION:

radius of cone $=\frac{\text{diameter}}{2}=\frac{17.2}{2}=8.6\text{ cm}$

height of cone $=11.1\text{ cm}$

Volume of cone $=\frac{1}{3}\pi r^2h$

putting values we get

Volume of cone $=\frac{1}{3}\times3.14\times8.6\times8.6\times11.1$

$=2577.8\text{ cm}^3$

Hence the volume of cone is $2577.8\text{ cm}^3$

3 0

3 years ago

Please help! Brainliest

Mama L [17]

1.301

Explanation:

Given:

$\log_a5 \approx 0.699$ and $\log_a2 \approx 0.301$

Note that from the properties of logarithms,

$\log_a20 = \log_a(5×4)$

$\:\:\:\:\:\:\:\:\:\:= \log_a(5×2^2)$

$\:\:\:\:\:\:\:\:\:\:=\log_a5 + \log_a(2)^2$

$\:\:\:\:\:\:\:\:\:\:=\log_a5 + 2\log_a2$

$\:\:\:\:\:\:\:\:\:\:\approx 0.699 + 2(0.301)$

$\:\:\:\:\:\:\:\:\:\:= 1.301$

6 0

2 years ago

Tara has a plastic string that is 3 feet long. She will cut the string to make bracelets that are each foot long.

Lady_Fox [76]

Answer:

Mark 3 and subtract 1 from each division

Step-by-step explanation:

Tara will mark the number line at point 3.

Then she will subtract 1 from 3 and mark at point 2.

Again subtracting 1 from 2 the next mark is at 1.

And the last mark is at 0.

The first mark at point 3 shows that the string is 3 feet long.

Now we need 1 foot divisions. So we subtract from 1 division from point 3 to get 1 foot long string. So we continue to get 3 equal parts each of 1 foot long by dividing the 3 feet long string into 3 equal divisions.

so the first piece is from 0-1 gives 1 foot long string

The 2nd piece is from 1-2 gives 1 foot long string

The 3rd piece is from 2-3 gives 1 foot long string

8 0

2 years ago