Find the 70th term of the following arithmetic sequence. 12,17,22,27,...

2 answers:

8 0

Since it starts at 12 and is increasing by 5 each time, the 70th term will be;
12 + 5(70)
12 + 350
362

362 is the 70th term of the sequence.

Marta_Voda [28]3 years ago

5 0

303 is the 70th term

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Pls can someone help me. I m giving 10 pts . I may mark you as the braniliest

worty [1.4K]

100 notes were altogether

Solution:

Given that ratio of the number of $2 notes to the number of $5 notes was 4 : 1

number of $2 notes : number of $5 notes = 4 : 1

Let 4x be the number of $ 2 notes

Let 1x be the number of $ 5 notes

Given that total value of notes is $ 260

Therefore,

$ 2 (number of $ 2 notes ) + $ 5(number of $ 5 notes ) = $ 260

$ 2(4x) + $ 5(1x) = $ 260

8x + 5x = 260

13x = 260

x = 20

Thus number of notes altogether is given as:

4x + 1x = 4(20) + 1(20) = 80 + 20 = 100

Thus 100 notes were altogether

4 0

3 years ago

Evaluate the surface integral. s x ds, s is the part of the plane 18x + 9y + z = 18 that lies in the first octant.

IceJOKER [234]

In the first octant, the given plane forms a triangle with vertices corresponding to the plane's intercepts along each axis.

$(x,0,0)\implies 18x+9\cdot0+0=18\implies x=1$
$(0,y,0)\implies 18\cdot0+9y+0=18\implies y=2$
$(0,0,z)\implies 18\cdot0+9\cdot0+z=18\implies z=18$

Now that we know the vertices of the surface $\mathcal S$ , we can parameterize it by

$\mathbf s(u,v)=\langle(1-u)(1-v),2u(1-v),18v\rangle$

where $0\le u\le1$ and $0\le v\le1$ . The surface element is

$\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|\,\mathrm du\,\mathrm dv=2\sqrt{406}(1-v)\,\mathrm du\,\mathrm dv$

With respect to our parameterization, we have $x(u,v)=(1-u)(1-v)$ , so the surface integral is

$\displaystyle\iint_{\mathcal S}x\,\mathrm dS=2\sqrt{406}\int_{u=0}^{u=1}\int_{v=0}^{v=1}(1-u)(1-v)^2\,\mathrm dv\,\mathrm du=\frac{\sqrt{406}}3$

5 0

3 years ago

Does anyone know this?

weeeeeb [17]

Answer:

BC = 10.24

Step-by-step explanation:

You can use the Pythagoras theorem for this question

$a^{2}$ + $b^{2}$ = $c^{2}$