All categories

3 years ago

Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning.

Mathematics

1 answer:

shusha [124]3 years ago

6 0

Start with the parentheses first

4.6 -4.4+7.8 then calculate from left to right
= 0.2+7.8 = 8

You might be interested in

Which of the following is a good way to quickly determine whether 3⁄12 and ¼ are equal? A. Inverse multiplication B. Reciprocal

IRINA_888 [86]

D. , this is a good way because this way you can easily multiply and then you'll see your answer right in front of you.

** This is an opinionated question so you don't have to listen to my answer but please rate my answer. Thanks!

4 0

3 years ago

Read 2 more answers

Find the volume of the figure. A) 33 in^3 B) 150 in^3 C) 233 in^3 D) 425 in^3

Nikolay [14]

5x5x5=125
12x3=36
36x3=108
108+125=233
233in^3 is the answer

8 0

3 years ago

Read 2 more answers

What is the area of the sector with a central angle of 97 degrees and a diameter of 10cm

vampirchik [111]

Answer:

21. 162 (rounded to nearest thousandth)

Step-by-step explanation:

Area of a sector: (degree/360) (pi*radius^2)

degree given= 97

radius= diameter/2 = 5

(97/360) (pi*5^2)

(97/360) (pi*25) = 21.16211718

4 0

3 years ago

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

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

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

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

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

o decorate his bedroom, Mike spent $41.64 on new bedding, $36.84 on paint, and $72.49 on accessories. About how much did he spen

FromTheMoon [43]

He spent 150.97 hope this helps :) have a good day

3 0

3 years ago

Read 2 more answers