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Alex Ar [27]
3 years ago
7

Write 2.161616 as a mixed number

Mathematics
1 answer:
balandron [24]3 years ago
4 0
I believe it's 2 16/99
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Convert the rectangular coordinates (-9, 3V3) into polar form. Express the angle
Whitepunk [10]

Answer:

(6\sqrt{3},\,\frac{5\pi}{6})

Step-by-step explanation:

The radius  r  can be found from the relationship

 r^2=x^2+y^2\\r^2=(-9)^2+(3\sqrt{3})^2\\r^2=81+27=108\\r=\sqrt{108}\\r=6\sqrt{3}

The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.

\cos{\theta}=\frac{x}{r}=\frac{-9}{6\sqrt{3}}\\\cos{\theta}=-\frac{9}{6\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\\\cos{\theta}=-\frac{9\sqrt{3}}{6\cdot3}\\\cos{\theta}=-\frac{\sqrt{3}}{2}\\\\\cos^{-1}\frac{-\sqrt{3}}{2}}=\frac{5\pi}{6}

See the attached image.

7 0
3 years ago
When a sprinkler is installed in the ground, the spray of water goes up and falls in the pattern of a parabola. The height, in i
poizon [28]

Answer:

96feet

Step-by-step explanation:

Given the height, in inches, of a spray of water is given by the equation ℎ(x)=160−16x^2

x is the number of feet away from the sprinkler head the spray

To get the height of the spray 2 feet away from the sprinkler head, we will simply substitute x =2 into the function and et the height h as shown;

From the equation

ℎ(x)=160−16x^2

h(2) = 160-16(2)²

h(2) = 160-16(4)

h(2) = 160-64

h(2) = 96feet

Hence the height will be 96feet if the spray is 2feet away from the sprinklers head

8 0
3 years ago
The hours of daylight,y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y=3.06sin(0.017x-1.40) + 12.23
defon
The month of January has 31 days, so from January 1st to February 14th, there are 31 + 14 or 45 days, namely x = 45.

y = 3.06 * sin[ 0.017(45) - 1.40 ] + 12.23.

make sure your calculator is in Degree mode.
8 0
3 years ago
Read 2 more answers
T.J. invests $8,100 in an account
QveST [7]

Answer:

I don't know

Step-by-step explanation:

if don't know

6 0
3 years ago
PLEASE HELP!!!
Svetllana [295]
Vertex form is
y = a {(x - h)}^{2}  + k
where (h,k) is the vertex.
We can see that the vertex of the graph is at (2,0), and that the graph opens downwards, but does not look stretched at all.
Therefore,
a = -1
h = 2
k = 0
and our vertex form equation is
y =  -  {(x - 2)}^{2}  + 0
which is answer A
7 0
3 years ago
Read 2 more answers
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