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vagabundo [1.1K]

3 years ago

14

A scuba diver descends slowly into the ocean at a constant rate. His depth is recorded for the first minutes in the following ta

ble:
a) how much deeper does the diver descend each minute?

b) what is the diver’s depth at minute 7?

c) how long will it take the scuba diver to reach a coral reef that is 120 feet deep?

d) Interpret the meaning of d8 = 96

1 answer:

vaieri [72.5K]3 years ago

7 0

Answer:

a) 12 feet per minute

b) 84 feet

c) 10 minutes

d)

Step-by-step explanation:

a) find the slope using furmula: y1 - y2/x1 - x2

24 - 12/2 - 1

12/1

12

12 feet per minute

b) 12 feet per minute so multiply the slope, 12 by 7

12 * 7 = 84

c) 12 * time, t, = feet deep

12 * t = 120

12t = 120

/12 /12

t = 10

10 minutes

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Read 2 more answers

Find number a and k so that x-2 is afactor<br>OF F(x)=x4-2ax tax-<br>X+k and F(-1)=3

Slav-nsk [51]

Question:

Find numbers a and k so that x-2 is a factor of

$f(x)=x^4-2ax^3+ax^2- x+k$

and

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$k = -2$ and $a=1$

Step-by-step explanation:

Given

$f(x)=x^4-2ax^3+ax^2- x+k$

$Factor:\ x - 4$

$f(-1)=3$

Required

Find a and k

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Substitute -1 for x

$f(x)=x^4-2ax^3+ax^2- x+k$

$f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k$

$f(-1) = 1 - 2a *-1 + a*1 +1 + k$

$f(-1) = 1 +2a + a +1 + k$

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Substitute 3 for f(-1)

$3 = 2 +3a + k$

Collect Like Terms

$3 - 2 = 3a + k$

$1 = 3a + k$

Also:

If $x - 2$ is a factor, then

$f(2) = 0$

Substitute 2 for x and 0 for f(x)

$f(x)=x^4-2ax^3+ax^2- x+k$

$0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k$

$0 = 16 - 2a * 8 + a * 4 - 2 + k$

$0 = 16 - 16a + 4a - 2 + k$

$0 = 16 - 12a - 2 + k$

Collect Like Terms

$2 - 16 = - 12a + k$

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$k = 12a - 14$

Substitute 12a - 14 for k in $1 = 3a + k$

$1 = 3a + 12a - 14$

$1 = 15a - 14$

Collect Like Terms

$15a = 1 + 14$

$15a = 15$

Solve for a

$a = \frac{15}{15}$

$a=1$

Substitute 1 for a in $k = 12a - 14$

$k = 12 * 1 - 14$

$k = 12 - 14$

$k = -2$

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3 years ago