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3 years ago

43 Points

Mathematics

2 answers:

Anarel [89]3 years ago

8 0

Answer:

I and III only

Step-by-step explanation:

I and II only is correct. Exponential decay functions have the form f(x) = abx + c. Function I is already in this form, and function II can be rewritten by changing

to 2-1, and then getting 2-x.

MrRa [10]3 years ago

4 0

$f(x)=b(a)^x\\\\exponential\ decay\ for\ b>0\ and\ a\in(0,\ 1)\ or\ for\ b1.\\\\I.\ f(x)=3\cdot5^{-x}=3\cdot\left(\dfrac{1}{5}\right)^x\to b=3>0\ and\ a=\dfrac{1}{5}\in(0,\ 1)\ \ \boxed{!}\\\\II.\ f(x)=\left(\dfrac{1}{2}\right)^x\to b=1>0\ and\ a=\dfrac{1}{2}\in(0,\ 1)\ \ \boxed{!}\\\\III.\ f(x)=-7e^x+8\to b1\ \ \boxed{!}\\\\Answer:\ C)\ I,\ II\ and\ III.$

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Find the slope of a line that is PRRPENDICULAR to the line that goes between (3,-8) and (5,2).

LiRa [457]

Answer:

-1/5

Step-by-step explanation:

Slope of the line = (y2-y1)/(x2-x1)

(2-(-8)/(5-3)

10/2 = 5

Perpendicular line = the slope is opposite of the reciprocal

-1/5

7 0

3 years ago

An open metal tank of square base has a volume of 123 m^3

snow_lady [41]

Answer:

a) h = 123/x^2

b) S = x^2 +492/x

c) x ≈ 6.27

d) S'' = 6; area is a minimum (Y)

e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

123 = x^2·h

h = 123/x^2

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

$S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}$

c) The derivative of the area with respect to x is ...

$S'=2x-\dfrac{492}{x^2}$

When this is zero, area is at an extreme.

$0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583$

d) The second derivative is ...

$S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6$

This is positive, so the value of x found represents a minimum of the area function.

e) The minimum area is ...

$S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78$

The minimum area of metal used is about 117.78 m².

3 0

3 years ago

Find the length of AB

marishachu [46]

Answer:

55?

Step-by-step explanation:

........................

7 0

3 years ago

Read 2 more answers

Hi please help this is due today thank u so much.

KatRina [158]

Answer: 8.944272

Step-by-step explanation:

Distance formula

6 0

3 years ago

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podryga [215]

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Answer:

33, 27
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Step-by-step explanation:

The price difference is found by subtracting Emma's price from DeShawn's price. Each price is the product of the number of square feet and the price per square foot.

The number of square feet is already given in the answer form, so you only need to fill in the per square foot prices. Those are found in the table. Both the window name and the window area give clues as to which is the right price to choose.

The expression is (4² × 33) - (3² × 27).

For the second fill-in, you need to actually do this arithmetic. For many calculators, you can enter this expression directly.

DeShawn paid $285 more for his window than Emma.

5 0

3 years ago