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evablogger [386]
2 years ago
13

Find the equation of a line that passes through A(3, 5) and with slope m=4

Mathematics
2 answers:
chubhunter [2.5K]2 years ago
4 0

Answer:

I believe the answer is

y = 4x - 7

Step-by-step explanation:

hope thai HELPS!

if you want an explanation ask me in the comments.

Setler [38]2 years ago
3 0
Yes go on yt and it’ll give you the answer immediately
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Help plz!!!!!!!!!<br><br><br> *tysm*
Dennis_Churaev [7]

-7.5x = -5.61 - 0.39

x = -6 /-7.5

x = 0.8

5 0
3 years ago
How do you solve this step by step? “ I’m thinking of a number. If you multiply it by 6 and then add 7, you will get 55. What is
lozanna [386]

Answer:

8

Step-by-step explanation:

55 -7 = 48

48/6= 8

Check answer:

8x6= 48

48+7= 55

5 0
3 years ago
Read 2 more answers
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
Find the area of the square rug if its side is (6x + 1) feet.<br> The area of the square rug is ( )
Assoli18 [71]

Area of a square:

A= side^2

= (6x + 1) ^2

=<u> 36x^2 + 12x + 1  feet^2</u>

8 0
2 years ago
batteries which normally sell for $1.89 a pack are on sale for $3.40 for two packs. approximately what percentage markdown does
aev [14]
Normally, two packs of batteries cost $1.89*2=$3.78.  The discounted price of $3.40 divided by the standard price of $3.78 for two packs is approximately .9, or 90 percent.  Therefore, we have an approximately ten percent discount with the sale.
6 0
2 years ago
Read 2 more answers
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