Cullen Banks

2023-03-03

A small block slides, without friction, down an inclined plane starting from rest. Let ${S}_{n}$ be the distance travelled from time t=(n-1) to t=n. If $\frac{{S}_{n}}{{S}_{n+1}}$ is found to be 5/7, then value of n is?

Elliot Watson

Beginner2023-03-04Added 1 answers

Distance travelled in t sec $={S}_{t}$

$\therefore {S}_{t}=u+at-a/2$

as u=0

$\frac{{S}_{n}}{{S}_{n+1}}=\frac{an-a/2}{a(n+1)-a/2}=\frac{a(2n-1)\times 2}{2a(2n+1)}\phantom{\rule{0ex}{0ex}}=\frac{2n-1}{2n+1}=\frac{5}{7}\phantom{\rule{0ex}{0ex}}\Rightarrow 14-7=10n+5\phantom{\rule{0ex}{0ex}}\Rightarrow 4n=12\phantom{\rule{0ex}{0ex}}\Rightarrow n=3$

$\therefore {S}_{t}=u+at-a/2$

as u=0

$\frac{{S}_{n}}{{S}_{n+1}}=\frac{an-a/2}{a(n+1)-a/2}=\frac{a(2n-1)\times 2}{2a(2n+1)}\phantom{\rule{0ex}{0ex}}=\frac{2n-1}{2n+1}=\frac{5}{7}\phantom{\rule{0ex}{0ex}}\Rightarrow 14-7=10n+5\phantom{\rule{0ex}{0ex}}\Rightarrow 4n=12\phantom{\rule{0ex}{0ex}}\Rightarrow n=3$

Find the volume V of the described solid S

A cap of a sphere with radius r and height h.

V=??

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

?

$d)f\left(x\right)={x}^{5}+1$In how many different orders can five runners finish a race if no ties are allowed???

State which of the following are linear functions?

a.$f(x)=3$

b.$g(x)=5-2x$

c.$h\left(x\right)=\frac{2}{x}+3$

d.$t(x)=5(x-2)$ Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

A square is also a

A)Rhombus;

B)Parallelogram;

C)Kite;

D)none of theseWhat is the order of the numbers from least to greatest.

$A=1.5\times {10}^{3}$,

$B=1.4\times {10}^{-1}$,

$C=2\times {10}^{3}$,

$D=1.4\times {10}^{-2}$Write the numerical value of $1.75\times {10}^{-3}$

Solve for y. 2y - 3 = 9

A)5;

B)4;

C)6;

D)3How to graph $y=\frac{1}{2}x-1$?

How to graph $y=2x+1$ using a table?

simplify $\sqrt{257}$

How to find the vertex of the parabola by completing the square ${x}^{2}-6x+8=y$?

There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?

Write 18 thousand in scientific notation.