Need help Please math

A 2-column table with 7 rows. Column 1 is labeled Power of 3 with entries 3 cubed, 3 squared, 3 Superscript 1, 3 Superscript 0,

Masja [62]

Answer:

a=1, b=1/3, c=1/27

Step-by-step explanation:

The table is given below:

$\left|\begin{array}{c|c}$Powers of 3&Value\\----&---\\3^3&27\\3^2&9\\3^1&3\\3^0&a\\3^{-1}&b\\3^{-2}&\frac{1}{9} \\3^{-3}&c\end{array}\right|$

(a)As the exponents decrease, the next term is gotten by a division of the previous term by 3.

$f_n=f_{n-1}\div 3$

(b)

$f_n=f_{n-1}\div 3\\I.a=f_n, f_{n-1}=3,\\a=f_n=3\div 3=1\\II. b=f_n, f_{n-1}=1,\\b=f_n=1\div 3=\frac{1}{3}\\III. c=f_n, f_{n-1}=\frac{1}{9},\\c=f_n=\frac{1}{9}\div 3=\frac{1}{27}$

a=1, b=1/3, c=1/27

7 0

3 years ago

Read 2 more answers

Jade used Fraction 3 over 4 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 4 over 5 yards o

aksik [14]

Answer:

Yes, because the quotient of Fraction 1 and 4 over 5 ÷ Fraction 3 over 4 is 2 and 2 over 5

Step-by-step explanation:

Jade used Fraction 3 over 4 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 4 over 5 yards of fabric, and why?

Representing the above expression Mathematically

3/4 yard = 1 scarf

1 4/5 yards of fabric = x

Cross Multiply

3/4x = 1 4/5 × 1

x = 9/5/ 3/4

x = 9/5 ÷ 3/4

x = 9/5 × 4/3

x = 12/5 scarves

x = 2 2/5 scarves

Hence, the correct option is :

Yes, because the quotient of Fraction 1 and 4 over 5 ÷ Fraction 3 over 4 is 2 and 2 over 5

6 0

3 years ago

Read 2 more answers

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

lubasha [3.4K]

First find a parameterization for the curve of intersection.

Given the equation of a cylinder, a natural choice for a parameterization would be one utilizing cylindrical coordinates. Here,

$16x^2+y^2=16\implies x^2+\left(\dfrac y4\right)^2=1$

which suggests we could use

$\begin{cases}x(t)=\cos t\\y(t)=4\sin t\\z(t)\end{cases}$

with $0\le t\le2\pi$ , and we get $z(t)$ from the equation of the plane,

$x+y+z=12\implies z(t)=12-x(t)-y(t)=12-\cos t-4\sin t$

Now use the arc length formula:

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt$

$\displaystyle\ell=\int_0^{2\pi}\sqrt{\sin^2t+16\cos^2t+(\sin t-4\cos t)^2}\,\mathrm dt$

$\displaystyle\ell=\sqrt2\int_0^{2\pi}\sqrt{\sin^2t-4\cos t\sin t+16\cos^2t}\,\mathrm dt\approx\boxed{24.0878}$

4 0

4 years ago

Which equation represents the line that is perpendicular to the graph of 4x + 3y = 9 and passes through (-2, 3)? RE A 3x - 4y =

Keith_Richards [23]

Answer:

15279

Step-by-step explanation:

6 0

3 years ago

A grapefruit has a peel that is 1cm thick and a total diameter of 12cm. What percentage of volume of the grapefruit is the peel?

ira [324]

Answer:

0.3056 or 30.56%

Step-by-step explanation:

The volume of the grapefruit with the peel is:

$V_p=\frac{4 \pi (d/2)^2}{3}\\V_p=\frac{4 \pi (12/2)^2}{3}\\V_p=48 \pi$

When removing the peel, the grapefruit diameter becomes 10 cm (take out 1 cm of peel from each side). The volume of the grapefruit without the peel is:

$V_n=\frac{4 \pi (d/2)^2}{3}\\V_n=\frac{4 \pi (10/2)^2}{3}\\V_n=33.333 \pi$

The percentage of the volume correspondent to the peel is given by the difference between both volumes, divided by the total volume:

$\%P = \frac{48\pi - 33.333\pi}{48\pi}\\ \%P =0.3056 = 30.56\%$

30.56% of volume of the grapefruit is the peel.

4 0

4 years ago