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3 years ago

Given f(x) = -x^2 - 2x + 4, find each of the following,

Mathematics

2 answers:

tankabanditka [31]3 years ago

7 0

Answer:

Symmetric point: x = -1; (-1, 5)

Minimum of f: None; approaches -∞.

Maximum of f: y = 5.

Is f(x) a one-to-one: No, it fails the horizontal line test and is not injective.

Increasing from: -∞ to -1; (-∞, -1)

Decreasing from: -1 to ∞. (-1, ∞)

chubhunter [2.5K]3 years ago

6 0

Answer:

Given f(x) = -x^2 - 2x + 4, find each of the following,

Step-by-step explanation:

f(x) = -x²-2x+4

f(2) = (-2)²-2×2+4

f(2) = 4-4+4

f(2) = 4

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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

Find the product. Write your answer in scientific notation. (3 x 10^2)×(4×10^5)

suter [353]

Answer:

12 * 10 ^ 7

Step-by-step explanation:

3 * 10 ^ 2 * 4 * 10 ^5

= 12 * 10^ 2 + 5

= 12 * 10 ^ 7

Hope it will help :)

7 0

3 years ago

There are 6 roses, 8 carnations, and 12 tulips. Write the ratio of carnations to all flowers in all three forms (simplify first,

Norma-Jean [14]

Your answer is 8 to 26

the number of carnations is 8 and the total number of flowers is 26. since you said carnations to flowers it is 8 to 26.

here are the 3 ways to write the ratio:

8 to 26 8:26 8/26

3 0

3 years ago

sarah is 27 years old and is retiring at the age of 65. when she retires, she estimates that she will need a semiannual income f

hichkok12 [17]

<span>In order for you to be able to solve this problem you have to first identify what the questions is asking. In this case it wants to know the approximation of what the semiannual income that Sarah will be able to draw.

To solve this you simply have to find the future value of her investment prior to retirement and use the as her investment amount upon retirement.

<span>I hope it helps, Regards. </span></span>

5 0

3 years ago

Someone please help!!

klasskru [66]

Answer:

All the values smaller than or equal 3

Step-by-step explanation:

Any function has domain and rang, the domain is the values of x and the range is the values of y so when ask about the range that means all the values of y which including the graph the graph is downward starting from 3 on the y-axis and go to negative infinity so the answer is all the values smaller than or equal 3

6 0

3 years ago