What is the vertex of the graph of the function y=-2x^2+16x-15

1 answer:

andrey2020 [161]2 years ago

8 0

X - Vertex
$Vertex = -\frac{b}{2a} \\Vertex = -\frac{16}{2(-2)} \\Vertex = -\frac{16}{-4} \\Vertex = 4$

Y - Vertex
$y = -2x^{2} + 16x - 15 \\y = -2(4)^{2} + 16(4) - 15 \\y = -2(16) + 64 - 15 \\y = -32 + 64 - 15 \\y = 32 - 15 \\y = 17$

Vertex:(4, 17)

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PLZ HELP!!! WILL MARK THE BRAINLIEST IF ANSWER IS CORRECT.

slavikrds [6]

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6 0

2 years ago

A small military base housing 1,000 troops, each of whom is susceptible to a certain virus infection. Assuming that during the c

slava [35]

Answer:

$I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}$

Step-by-step explanation:

The rate of infection is jointly proportional to the number of infected troopers and the number of non-infected ones. It can be expressed as follows:

$\frac{dI}{dt}=a*I*(1000-I)$

Rearranging and integrating

$\frac{dI}{dt}=a*I*(1000-I)\\\\\frac{dI}{I*(1000-I)}=a*dt\\\\\int\frac{dI}{I*(1000-I)}=\int a*dt\\\\-\frac{ln(1000/I-1)}{1000}+C=a*t$

At the initial breakout (t=0) there was one trooper infected (I=1)

$-\frac{ln(1000/1-1)}{1000}+C=0\\\\-0,006906755+C=0\\\\C=0,006906755$

In two days (t=2) there were 5 troopers infected

$-\frac{ln(1000/5-1)}{1000}+0,006906755=a*2\\\\-0,005293305+0,006906755=2*a\\a = 0,00161345 / 2 = 0,000806725$

Rearranging, we can model the number of infected troops (I) as

$-\frac{ln(1000/I-1)}{1000}+0,006906755=0,000806725*t\\\\-\frac{ln(1000/I-1)}{1000}=0,000806725*t-0,006906755\\-ln(1000/I-1)=0,806725*t-0.6906755\\\\\frac{1000}{I}-1=exp^{0,806725*t-0.6906755} \\\\\frac{1000}{I}=exp^{0,806725*t-0.6906755}+1\\\\I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}$