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Vanyuwa [196]
3 years ago
10

Estimate the following sum by clustering.

Mathematics
2 answers:
alexdok [17]3 years ago
5 0

Answer: 390 Anyway. God bless :D I love you guys! <3 have a great day.

Step-by-step explanation:

Lostsunrise [7]3 years ago
3 0
Answer is 390 . mark me brainiest please that helps a lot
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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
What is the sign of addend with greater absolute value
Nady [450]

Answer:

8

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
242 X 38 1 9 36 9,1 96 Which digits belong in the blue boxes shown on the multiplication problem?
babymother [125]

Answer:

C. 726

Step-by-step explanation:

9196-1936=7260 and take away the 0 so your answer will be 726

4 0
2 years ago
Read 2 more answers
Abcd is a rectangle if DB=26 and DC=24 find bc
Anettt [7]
Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

Let's first establish that triangle BCD is a right-angle triangle.

Therefore, we can use Pythagoras theorem to find BC and solve this problem. Pythagoras theorem is displayed below:

a^2 + b^2 = c^2

Where c = hypotenus of right-angle triangle

Where a and c = other two sides of triangle

Now we can solve the problem by substituting the values from the problem into the Pythagoras theorem as displayed below:

Let a = BC

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

a^2 + 24^2 = 26^2

a^2 = 26^2 - 24^2

a = square root of ( 26^2 - 24^2 )

a = square root of ( 676 - 576 )

a = square root of ( 100 )

a = 10

Therefore, as a = BC, BC = 10.

If we want to check our answer, we can substitute the value of ( a ) from our answer in conjunction with the values given in the problem into the Pythagoras theorem. If the left-hand side is equivalent to the right-hand side, then the answer must be correct as displayed below:

a = BC = 10

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

10^2 + 24^2 = 26^2

100 + 576 = 676

676 = 676

FINAL ANSWER:

Therefore, BC is equivalent to 10.

Please mark as brainliest if you found this helpful! :)
Thank you and have a lovely day! <3
7 0
2 years ago
What is the 72nd term of -27, -11, 5
FinnZ [79.3K]

Answer:

1109

Step-by-step explanation:

The first term is -27, and the common difference is 16.

The nth term is:

a = a₁ + d (n − 1)

a = -27 + 16 (n − 1)

a = -27 + 16n − 16

a = 16n − 43

The 72nd term is:

a = 16(72) − 43

a = 1109

5 0
3 years ago
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