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noname [10]
3 years ago
11

I need to know if 93 is a multiple of 9×

Mathematics
1 answer:
iris [78.8K]3 years ago
5 0
93 is not a multiple of 9. Multiple of 9 would be 90 or 99. These are multiples of 9 in a range from 0 up to 100:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
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A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ
jonny [76]

Let \vec r(t),\vec v(t),\vec a(t) denote the rocket's position, velocity, and acceleration vectors at time t.

We're given its initial position

\vec r(0)=\langle0,0,10\rangle\,\mathrm m

and velocity

\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}

Immediately after launch, the rocket is subject to gravity, so its acceleration is

\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}

where g=9.8\frac{\rm m}{\mathrm s^2}.

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}

\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}

and

\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m

\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m

\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}

b. The rocket stays in the air for as long as it takes until z=0, where z is the z-component of the position vector.

10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}

c. The rocket reaches its maximum height when its vertical velocity (the z-component) is 0, at which point we have

-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)

\implies\boxed{z_{\rm max}=125,010\,\rm m}

7 0
3 years ago
72 tokens/12 games, tokens/10 games
Dmitry [639]

Answer:

60 tokens/ 10 games?

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Please help i keep getting the wrong answers
Mrrafil [7]

Answer:

10 inches

Step-by-step explanation:

Surface Area = π R² + π R L [ L is Slant Height ]

200 π = π (10)² + π (10) L

200 π = π (100) + π (10) L

200 π - 100 π = 10 π L

100 π = 10 π L

100 π / 10 π = L

10 = L

L = 10 inches

Hope this Helps......

3 0
3 years ago
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VashaNatasha [74]

Answer:

(0,1)- y intercept (1,0) x intercept

Step-by-step explanation:

first lets write this equation in slope intercept form: y=mx+b

m=slope

b=y intercept

so

slope formula:

(y2-y1)/(x2-x1)

y2=-3

y1=9

x2=4

x1=-8

so

(-3-9)/(4--8)=-12/12=-1

slope=-1

hence

y=-1x+b

substitute "x" as 4 and "y" as -3

so

-3=-1(4)+b

-3=-4+b

1=b

so

y=-x+1

1=y intercept

and

0=-x+1

-1=-x

1=x

1=x intercept

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3 years ago
The dot plot below shows the number of wings contestants in a wing-eating contest ate.
Stolb23 [73]

A.18 is the absolute deviation

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3 years ago
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