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Bezzdna [24]
2 years ago
6

3) x + y=4 how do I solve for y ​

Mathematics
1 answer:
harina [27]2 years ago
3 0

Answer:

y = 4 - x

because y is equal to four subtract x

when x goes to 4 , positive x is changed into negative x

You might be interested in
a line is perpendicular to y = 3/7x - 2 and intersects the point (3,3). What is the equation of this perpendicular line?
snow_lady [41]

Answer:

y = -7/3x + 10

Step-by-step explanation:

Step 1: Find the slope of the perpendicular line

Do this by taking the negative inverse of the first line

m = -7/3

Step 2: Find <em>b</em>

y = mx + b

y = -7/3x + b

3 = -7/3(3) + b

3 = -7 + b

b = 10

You should get y = -7/3x + 10 as your final answer.

6 0
2 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
2% of 0.00003 equals?
kakasveta [241]

Answer:

6e-7? i used a percentage calculator and this is what it gave me  so im not entirely sure

Step-by-step explanation:

3 0
2 years ago
A survey of 200 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take
Lina20 [59]

Answer:

The 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population proportion <em>P</em> is:

CI=p\pm z_{\alpha/2}\sqrt{\frac{p(1- p)}{n}}

The information provided is:

<em>x</em> = number of students who responded as"yes" = 70

<em>n</em> = sample size = 200

Confidence level = 95%

The formula to compute the sample proportion is:

p=\frac{x}{n}

The R codes for the construction of the 95% confidence interval is:

> x=70

> n=200

> p=x/n

> p

[1] 0.35

> s=sqrt((p*(1-p))/n)

> s

[1] 0.03372684

> E=qnorm(0.975)*s

> lower=p-E

> upper=p+E

> lower

[1] 0.2838966

> upper

[1] 0.4161034

Thus, the 95% confidence interval for the true proportion of university students who use laptop in class to take notes is (0.2839, 0.4161).

7 0
3 years ago
Read 2 more answers
If mikes salary is $62,500 this year and next year he will get 5.5% increase in salary. How much is his new salary.
rusak2 [61]

Answer:

65,937.5

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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