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3 years ago

Please explain how you got this answer

Mathematics

1 answer:

34kurt3 years ago

7 0

We have to determine how many different 3 vegetable combinations can be made from a selection of 10 vegetables.
We use the formula
combinations = 10! / [3! * (7!)]
combinations = 10 * 9 * 8 * 7! / 3!
combinations = 720 / 6
combinations = 120

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Sample Response: A linear function has a constant additive rate of change, while a nonlinear function does not. For a table of v

Leokris [45]

Answer:

The response that are true are:

linear function has a constant additive rate of change, while a nonlinear function does not.

Since in linear function the rate of change is always equal as for a linear function we get a equation of line such that the slope is same.

On a graph, the function must be a straight line to be linear.

Liner means there is a straight line of the function.

( Also it need not be true that the independent variable increases by 1.

There may be change of some other quantity in independent variable )

5 0

4 years ago

Read 2 more answers

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

Which statement is true about the discontinuities of the function f(x)?

Leno4ka [110]

Answer:

(a) There are asymptotes at x=3/2 and x=-1/3

Step-by-step explanation:

The denominator zeros can be found by factoring:

f(x) = (x +1)/((2x -3)(3x +1))

Neither of the denominator factors is cancelled by the numerator factor, so each represents a vertical asyptote, not a function hole.

The asymptotes are at the values of x where the denominator is zero:

2x -3 = 0 ⇒ x = 3/2

3x +1 = 0 ⇒ x = -1/3

8 0

2 years ago

Please can anyone help me please

yanalaym [24]

Answer:

700,000

Step-by-step explanation:

okay so to increase something by 7% you have to multiply it by 1.07

so if you divide it by 1.07, you'll find the original price

749,000 ÷ 1.07 = 700,000

5 0

3 years ago

Read 2 more answers

Donald spent half as much as Patricia did on presents this year, and Carl spent 3 times more than Donald. If the total spent bet

Nuetrik [128]

Answer:

Patricia spent $24 on presents, while Donald spent $12 and Carl spent $36.

Step-by-step explanation:

The problem is to solve how much money each person spent on presents in the year, through a series of equivalences. In order to determine how much money each one spent, the following equation must be proposed:

Patricia = X

Donald = 1 / 2X

Carl = 3/2 X

X + 1 / 2X + 3 / 2X = 72

1X + 0.5 X + 1.5 X = 72

3X = 72

X = 72/3

X = 24

Thus, Patricia spent $ 24 on presents, while Donald spent $ 12 (2/24) and Carl spent $ 36 (1.5 x 24).

4 0

3 years ago