!!!3 QUESTIONS!!!

Mathematics

1 answer:

RUDIKE [14]3 years ago

6 0

Answer:

1.) He still owes $100 of debt

2.) 1 rose would be .75 cents and 1 carnation would be .90 cents

3.) C 8 and 3/8

Step by Step explanation

(/ means divided by in the first 2 equations but / in the last question is for the fractions.)

1.) _(1,500 / 3 =500. 1,500 - 500 =1,000 / 5 =200 x 3 =600. 700 - 600 =$100)

2.)_(1.50/2 =.75 cents. 2.70/3 =.90 cents.)

3.) i first added the fractions ( i equalized them) then i added the whole numbers (the u in the equation was to separate the whole num. and fraction )

Before i equalized it: (6u3/4 + 1u1/8 = 7u1/8 + 1/8 = 8u3/8)

After i equalized it: (6u6/8 + 1u1/8 = 7u1/8 + 1/8 = 8u3/8)

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This robotic arm is made up of two cylinders with equal volume and two triangular prism hands. The volume of each hand is

BaLLatris [955]

Answer:

$\frac{r}{3\pi h+r}$

Step-by-step explanation:

Since the height isn't given, we assume it to be "h" (of cylinders). And the answer will be in terms of "r" and "h".

The area of 1 arm is given, so the area of 2 arms would be:

$A_{arm}=2*(\frac{1}{2}r*\frac{1}{3}r*2r)=\frac{2r^3}{3}$

Now, area of 2 cylinders would be the formula:

$A_{cyl}=2*(\pi r^2 h)=2\pi r^2 h$

So, total area is A_arm PLUS A_cyl. The fractional area the arms are would be gotten by taking expression A_arm divided by A_total.

Shown below:

$\frac{A_{arm}}{A_{total}}=\frac{\frac{2r^3}{3}}{2\pi r^2 h + \frac{2r^3}{3}}$

We simplify further:

$\frac{\frac{2r^3}{3}}{2\pi r^2 h + \frac{2r^3}{3}}\\=\frac{\frac{2r^3}{3}}{2r^2(\pi h + \frac{r}{3})}\\=\frac{r}{3(\pi h + \frac{r}{3})}\\=\frac{r}{3\pi h+r}$