PLEASE HELP RIGHT AWAY

Mathematics

1 answer:

Rainbow [258]4 years ago

7 0

Answer:

Approximately 53

Step-by-step explanation:

This is a geometric progression, because each term is found by multiplying the previous one by a constant factor.

In our case, the first term is know (a1 = 3), and the growth factor is also known (q = 1.333333).

What we are tasked to do is to find the 11th (n=11) term of the series, since it asks for AFTER the 10th roll.. That's easy with the base formula:

$a_{n} = a_{1} q^{n-1}$

Let's place the values we have in the equation and solve it:

$a_{10} = 3 * (1.333333)^{11-1} = 3 * (17.758) = 53.3$

So, after the 10th roll, you should need 53 dice, approximately.

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the length of a rectangle is 4in more than its width, and its perimeter is 34in find the length and width of the rectangle

Anna [14]

Let $l$ and $w$ be, respectively, the length and the width of the rectangle.

If the length is 4 inches more than the width, we have

$l = w+4$

Moreover, the perimeter of a rectangle is given by

$2(l+w)$

And we can substitute $l=w+4$ to get

$2(w+4+w)=2(2w+4)=4w+8$

We know that the perimeter is 34 inches:

$4w+8=34 \iff 4w = 26 \iff w = \dfrac{26}{4}=6.5$

Which implies

$l=w+4=6.5+4=10.5$

5 0

4 years ago

Determine 2nd term and rth term of a.p.whose 6 th term is 12 and 8 th term is 22

mario62 [17]

Answer: $\bold{a_2=-8\qquad \qquad a_r=5r-18}$

Step-by-step explanation:

Given: a₆ = 12 a₈ = 22

$d=\dfrac{a_8-a_6}{8-6}\quad = \dfrac{22-12}{8-6}\quad =\dfrac{10}{5}\quad =\boxed{5}$

$a_n=a_0+d(n-1)\\\\\\\underline{\text{Use}\ a_6\ \text{to find}\ a_o}\\a_6=a_o+5(6-1)\\\\12=a_o+5(6-1)\\\\12=a_o+25\\\\a_0=\boxed{-13}\\\\\\\underline{\text{Equation:}}\\a_n=13+5(n-1)\\.\quad =-13+5n-5\\.\quad =5n-18\\\\\\\underline{2^{nd\ term:}}\\a_2=5(2)-18\\.\quad = 10-18\\.\quad =\boxed{-8}\\\\\\\underline{r^{th}\ term:}\\\boxed{a_r=5r-18}$