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3 years ago

Help Again Please Answer The Image

Mathematics

1 answer:

sashaice [31]3 years ago

6 0

The top is +2 so the blank would be 6. On the bottom, the rate is +10 is the first blank is 55, the second blank is 75

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Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?

Mashutka [201]

Answer:

He showed that f(n) ÷ f(n - 1) was a constant ratio.

Given that Jake has proved that a function f(x) is a geometric sequence.

GEOMETRIC SEQUENCE: A geometric sequence is a sequence of numbers where each term is found by multiplying the preceding term by a constant called the common ratio, r.

So, in Jame's proof, he showed that each term is multiplied by a constant to get the next term.

That is, if 'c' is the constant that was used in the proof, then we must have

This implies that

Therefore, he showed that f(n) ÷ f(n - 1) was a constant ratio.

8 0

3 years ago

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

Lara wants to inscribe a square in a circle using only a compass and straightedge. She will first construct a circle and locate

astraxan [27]

The answer is C. You can make a rectangle by putting the diagonals through the center anywhere, but if you want a square, you have to put the two diagonals perpendicular to each other and join their ends. See the diagram.

4 0

3 years ago

Through any two points there is exactly one?

N76 [4]

Through any two points there is exactly one line

5 0

4 years ago

PLZ PLZ PLZ PLZ HELP HELP HELP HELPFind the area of the shape.

Bingel [31]

Answer:

3.14

Step-by-step explanation:

The formula for the area of a circle is $\pi r^2$ , where r is the radius. In this circle, the area would therefore be $3.14\cdot 2^2=12.56$ . However, since this is only a quarter circle, you need to divide the area by 4, meaning that the area of this shape is 3.14 square units. Hope this helps!

5 0

3 years ago

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