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sasho [114]
4 years ago
14

at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 whe

n gas cost $2.20 per gallon on average
Mathematics
1 answer:
Lina20 [59]4 years ago
8 0
The average cost represents the slope of the line of the graph.
Increasing the slope of the graph increases the steepness of the line.
Therefore, increasing the average cost of gas from $1.50 to $2.20 will increases the steepness of the line. (i.e. the line becomes closer to the vertical line).
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Differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².​
Liula [17]

Step-by-step explanation:

Let y(x)=f(x)g(x)h(x) where

f(x) = x^4

g(x)= (1 -2x^5)^6

h(x)= (5 - 8x^3)^2

so that

y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2

Recall that the derivative of the product of functions is

y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)

so taking the derivatives of the individual functions, we get

f'(x) = 4x^3

g'(x) = 6(1 - 2x^5)^5(-10x^4)

h'(x) = 2(5 - 8x^3)(-24x^2)

So the derivative of y(x) is given by

y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 +  x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 +  x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)

or

y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2

\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2

\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)

3 0
3 years ago
Heidi Muir, a sporting goods wholesaler, purchased goods from a supplier for $3,400. The
Lena [83]

Answer:

56.44%

Step-by-step explanation:

From the question, we have the following values

% Discount = 3%

Full allowed payment days = 30 days

Discount days = 10 days

1 year = 365 days

The formula for Effective Annual rate or Annual rate in effect =

Discount %/(1-Discount %) x (365 days/(Full allowed payment days - Discount days))

= 3%/(1 - 3%) × (365 days/30 days - 10 days)

= 0.03/(1 - 0.03) × (365/20)

= 0.03/0.97 × (365/20)

= 0.5644329897

Converting to percentage

0.5644329897 × 100

= 56.44329897%

Approximately = 56.44%

Therefore, the annual rate Heidi, in effect, is paying the supplier if she fails to pay the invoice at the end of the discount period is 56.44%

7 0
3 years ago
What is the 100th term in the sequence 15, 22, 29, 36, 43,...
oksano4ka [1.4K]

Answer

Step-by-step explanation:

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Wittaler [7]
Answer : 1 3/5 yds
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Tell whether each triangle with the given sides is a right triangle.
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