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uysha [10]
2 years ago
8

WILL MARK BRAINLEST IF YOU ANSWER CORRECTLY

Mathematics
1 answer:
muminat2 years ago
4 0

Answer:

7 units

Step-by-step explanation:

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What is the slope of a line that passes through the points (-4,0) and (0,4)?
Schach [20]

Answer:

1

Step-by-step explanation:

7 0
3 years ago
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Emma has saved £1.35 in 5p coins. How many 5p coins does Emma have?
valentinak56 [21]
To make calculation easier, we first multiply
1.35 × 100 = 135

then we need to find how many groups of 5 are there in 135.
to do so, we simply take 
135 ÷ 5 = 27

therefore, the answer is <u>27.</u>
8 0
3 years ago
URGENT Given the following functions f(x) and g(x), solve f over g (−5) and select the correct answer below:
svet-max [94.6K]

correct answer is 5, because f(-5) / g(-5) = -30/-6 = 5

5 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!
LekaFEV [45]

Answer:

500

Step-by-step explanation:

It's a box with a square base, so let's say the width and length are x and the height is y.

The surface area of the box without the top is:

A = x² + 4xy

300 = x² + 4xy

The volume of the box is:

V = x²y

Solve for y in the first equation and substitute into the second:

y = (300 − x²) / 4x

V = x² (300 − x²) / 4x

V = x (300 − x²) / 4

V = 75x − ¼ x³

To optimize V, find dV/dx and set to 0:

dV/dx = 75 − ¾ x²

0 = 75 − ¾ x²

x = 10

So the volume of the box is:

V = 75x − ¼ x³

V = 500

The maximum volume is 500 cm³.

4 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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