The vertex is the point where the graph is horizontal, which you can find by setting the first derivative to zero.

derivative: -4x + 8 = 0 => x=2
fill it in in the equation:

y=-2*2² + 8*2 - 5 = 3

So the answer is the point (2,3)

8 0

4 years ago

Read 2 more answers

HELP HELP HELP HELP<br> BEEN STUCK FOREVERRR

elena-s [515]

Answer:

r ≈ 31.5 cm

Step-by-step explanation:

The arc of a circle is calculated as

arc = circumference of circle × fraction of circle

Here arc = 22 , then

2πr × $\frac{40}{360}$ = 22

2πr × $\frac{1}{9}$ = 22 ( multiply both sides by 9 to clear the fraction )

2πr = 198 ( divide both sides by 2π )

r = $\frac{198}{2\pi }$ ≈ 31.5 cm

5 0

3 years ago

A hiker in Africa discovers a skull that contains 32% of its original amount of C-14. find the age of the skull.

ziro4ka [17]

Answer:

9419.3 years.

Step-by-step explanation:

Let the initial amount of C-14 be 100 units.

We have been given that a hiker in Africa discovers a skull that contains 32% of its original amount of C-14. We are asked to find the age of the skull.

We will use half life formula to solve our given problem.

$A=a\cdot(\frac{1}{2})^{\frac{t}{h}}$ , where,

A = Amount left after t years,

a = Initial amount,

t = time,

h = Half life.

We know that half-life of C-14 is 5730 years.

32% of 100 units would be 32.

$32=100\cdot(\frac{1}{2})^{\frac{t}{5730}}$

$\frac{32}{100}=\frac{100\cdot(\frac{1}{2})^{\frac{t}{5730}}}{100}$

$0.32=(0.5)^{\frac{t}{5730}}$

Now, we will take natural log of both sides.

$\text{ln}(0.32)=\text{ln}((0.5)^{\frac{t}{5730}})$

Using log property $\text{ln}(a^b)=b\cdot\text{ln}(a)$ , we will get:

$\text{ln}(0.32)=\frac{t}{5730}\cdot \text{ln}(0.5)$

$\frac{\text{ln}(0.32)}{\cdot \text{ln}(0.5)}=\frac{t\cdot \text{ln}(0.5)}{5730\cdot \text{ln}(0.5)}$

$1.64385618977=\frac{t}{5730}$

$\frac{t}{5730}=1.64385618977$

$\frac{t}{5730}*5730=1.64385618977*5730$

$t=9419.295967$

$t\approx 9419.3$

Therefore, the age of skull is approximately 9419.3 years.

5 0

3 years ago

Plz someone help with 2 and 4 I'll thank

11111nata11111 [884]

Answer:

A, C, and then B

Step-by-step explanation:

well 2 because it's the formulas and 4 because a triangular prism is like three triangles standing up hugging each other, so if you cut their heads off, it would be a triangle, because three sides.

6 0

3 years ago