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pogonyaev
3 years ago
6

Solve each system by graphing. If the solution is not unique, identify the system as “inconsistent” or “dependent”

Mathematics
1 answer:
lapo4ka [179]3 years ago
6 0

Answer:

therefore the solution of the system of equations is (x,y) = (4,2)

the solution is unique and therefore the the system is neither "inconsistent" nor "dependent"

Step-by-step explanation:

i) x + 2 = 6   \Rightarrow  x = 4

ii) x - y = 2 \Rightarrow  4 - y = 2 ,  therefore  y  = 4 - 2 ,   therefore y = 2

iii) therefore the solution of the system of equations is (x,y) = (4,2)

iv) the solution is unique and therefore the the system is neither "inconsistent" nor "dependent"

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What is the solution of 5sin2θ=3 for 0≤θ≤2π? Please help.
grigory [225]

Answer:

C) \theta\approx\{0.3218,1.249,3.463,4.3908\}

Step-by-step explanation:

5\sin2\theta=3;\: 0\leq\theta\leq 2\pi\\\\\sin2\theta=\frac{3}{5}\\ \\2\theta\approx\{0.6436,2.498,6.926,8.7816\}\\\\\theta\approx\{0.3218,1.249,3.463,4.3908\}

7 0
2 years ago
The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t2 where d equals the
ohaa [14]

Answer:

A.48

Step-by-step 789333

6 0
3 years ago
A prism, bases of which are equilateral triangles, circumscribes a sphere of radius 6. What is the volume of the prism?
koban [17]

Answer:

  1296√3 cubic units

Step-by-step explanation:

The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.

The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...

  B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units

The volume of the prism is then ...

  V = Bh = (108√3)(12) = 1296√3 . . . cubic units

_____

<em>Comment on the geometry</em>

The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.

6 0
3 years ago
A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1200 feet, what are the dimensions of
boyakko [2]

Answer:

width=60     length=540

Step-by-step explanation:

(w+9w)*2=1200

5 0
3 years ago
The 15th term of an arithmetic series is
RSB [31]

Answer:

-1557

Step-by-step explanation:

a+14d=143

a+12d=183

--------------------

2d= -40

d= -20

a=183+240=423

a(100th)= 423+99*-20=423-1980= -1557

I hope that help =)

7 0
2 years ago
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