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3 years ago

How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Mathematics

1 answer:

Nina [5.8K]3 years ago

7 0

<h3>Explanation:</h3>

For a system of 2 equations in 2 unknowns, there are 3 cases:

slopes are different — one solution
slopes are the same and y-intercepts are different — no solutions
slopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at one point, the solution.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence no solutions. If the lines are the same line, they intersect at all points, so there are infinitely many solutions.

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A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can cost

Advocard [28]

Answer:

Radius = 1.12 inches and Height = 4.06 inches

Step-by-step explanation:

A soup can is in the shape of a right circular cylinder.

Let the radius of the can is 'r' and height of the can is 'h'.

It has been given that the can is made up of two materials.

Material used for side of the can costs $0.015 and material used for the lids costs $0.027.

Surface area of the can is represented by

S = 2πr² + 2πrh ( surface area of the lids + surface are of the curved surface)

Now the function that represents the cost to construct the can will be

C = 2πr²(0.027) + 2πrh(0.015)

C = 0.054πr² + 0.03πrh ---------(1)

Volume of the can = Volume of a cylinder = πr²h

16 = πr²h

$h=\frac{16}{\pi r^{2}}$ -------(2)

Now we place the value of h in the equation (1) from equation (2)

$C=0.054\pi r^{2}+0.03\pi r(\frac{16}{\pi r^{2}})$

$C=0.054\pi r^{2}+0.03(\frac{16}{r})$

$C=0.054\pi r^{2}+(\frac{0.48}{r})$

Now we will take the derivative of the cost C with respect to r to get the value of r to get the value to construct the can.

$C'=0.108\pi r-(\frac{0.48}{r^{2} })$

Now for C' = 0

$0.108\pi r-(\frac{0.48}{r^{2} })=0$

$0.108\pi r=(\frac{0.48}{r^{2} })$

$r^{3}=\frac{0.48}{0.108\pi }$

r³ = 1.415

r = 1.12 inch

and h = $\frac{16}{\pi (1.12)^{2}}$

h = 4.06 inches

Let's check the whether the cost is minimum or maximum.

We take the second derivative of the function.

$C"=0.108+\frac{0.48}{r^{3}}$ which is positive which represents that for r = 1.12 inch cost to construct the can will be minimum.

Therefore, to minimize the cost of the can dimensions of the can should be

Radius = 1.12 inches and Height = 4.06 inches

5 0

3 years ago

X-20 = y+20 2Y - 44 = X + 22

nordsb [41]

X-20 = Y+20........ X-Y = 20+20........

X-Y = 40

AND

2Y-44=X+22............. Y-X= 44+22

Y-X=66

NOW, LET'S FIND X AND Y FROM THESE TWO EQUATIONS....

X-Y =40

Y-X= 66

IF WE COLLECT ....... 2Y = 106 AND Y = 53

THEN, USE Y IN ANY EQUATIONS FOR FINDING X

X-53 = 40 ..... X= 53+40 .......... X= 93

X= 93

Y=53

8 0

3 years ago

What is the common factor for 90 and 96?

Ierofanga [76]

Answer:

Step-by-step explanation:

Greatest common factor of 90 and 96 is 6.

6 0

3 years ago

Read 2 more answers

Greenville County, South Carolina, has 461,299 adult residents, of which 59,969 are 65 years or older. A survey wants to contact

Salsk061 [2.6K]

The proportion would be the number of the sample (x) over the population size (n)

Here we have x = 59,969 and n= 461,299

P = x/n = 59969/461299

P = 0.13

5 0

3 years ago

Plz help with this math. Can't find the area of the triangular faces.

Zina [86]

First of all, you have to find the area of both triangles:
$\frac{bh}{2}$
$\frac{4*4}{2}$
Or just 16 because there are 2 of the same triangles.

Now you have to find the area of the 3 rectangles.

The two that are in the front are 4*3 (l*h) or 12*2 (because there are 2 congruent rectangles. The area of those rectangles is 24 square mm.

Now you find the area of the back rectangle:
5.7*3 = 17.1

Finally, you add all the found numbers to figure out the surface area.
17.1 + 16 + 24 = 57.1 square millimeters.

Hope this helped,
Loafly

4 0

3 years ago