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3 years ago

Enter your answer and show all the steps that you use to solve this problem.

Mathematics

1 answer:

slamgirl [31]3 years ago

3 0

Answer:

h = -t+20

After 8 hours the candle will be 12 inches

Step-by-step explanation:

We have 2 points (time, inches)

(3,17) and (5,15)

We can find the slope

m = (y2-y1)/(x2-x1)

= (15-17)/(5-3)

= -2/2

= -1

We can use point slope form

y-y1 = m(x-x1)

Replace y with h and x with t

h-17 = -1 (t-3)

Distribute

h-17 = -t+3

Add 17 to each side

h-17+17 = -t+3+17

h = -t+20

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2 years ago

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Hey There!

To find the rate of change, simply use the following formula.

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3 years ago

(csc x - 1) (csc x + 1)

victus00 [196]

<h2>Explanation:</h2>

Here we have the following expression:

$(csc x - 1) (csc x + 1)$

So we need to extend this. Remember that the difference of squares tells us:

$(a-b)(a+b)=a^2-b^2$

So here:

$a=cscx \\ \\ b=1$

Thus:

$(csc x - 1) (csc x + 1)=csc^2x-1 \\ \\ \\ But: \\ \\ cscx=\frac{1}{sinx} \\ \\ \\ Then: \\ \\ csc^2x-1=\frac{1}{sin^2x}-1=\frac{1-sin^2x}{sin^2x}=\frac{cos^2x}{sin^2x}=cot^2x \\ \\ \\ Finally: \\ \\ \boxed{(csc x - 1) (csc x + 1)=cot^2x}$

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3 years ago

Given f(x)= 2x²+4x-6 and g(x)=2x-2, find each function

valkas [14]

F(x)= 2x²+4x-6 and g(x)=2x-2, find each function
1. (f/g) (x) = f(x)÷g(x) = (2x²+4x-6)÷(2x-2)
First factor both top and bottom:
(2x-2)(x+3)÷(2x-2) = x+3

2. f(a + 2) = plug (a+2) in anywhere there is an x in f(x)=2x²+4x-6 -->
2(a+2)^2 +4(a+2)-6 = 2(a^2+4a+4)+4a+8-6, now distribute:
2a^2+8a+8+4a+2, combine like terms
2a^2+12a+10

3. g(a/2) = plug (a/2) in anywhere there's an x in g(x)=2x-2:
2(a/2)-2 = a-2

5 0

3 years ago

Question: How long does it take an investment to quadruple in value if it earns 4% simple interest per year?

Assoli18 [71]

Answer:

It takes 75 years for the investment to quadruple in value

Step-by-step explanation:

Simple Interest

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

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After t years, the total amount of money is:

$T = E + P$