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Nutka1998 [239]

2 years ago

8

One of these scenarios represents a direct variation and one does not. How can you tell the difference? a) A large pizza with on

e topping costs $15.50. A large pizza with 4 toppings costs $20. Does the price vary directly with the number of toppings? b) A marathoner ran 5 miles in 40 minutes and 15 miles in 120 minutes. Does the number of minutes vary directly with the number of miles? Your answer:

1 answer:

babunello [35]2 years ago

3 0

Answer: See explanation

Step-by-step explanation:

a) A large pizza with one topping costs $15.50. A large pizza with 4 toppings costs $20.

A large pizza with one topping costs $15.50.

Using the formula for direct variation,

y = kx

where,

y = Cost of pizza

x = number of toppings

k = constant of proportionality

15.50 = 1k

k = 15.50

A large pizza with 4 toppings costs $20.

Using y = kx

20 = 4k

k = 20/4

k = 5

Here, the price does not vary directly with the number of toppings because the constant of proportionality is different.

b) A marathoner ran 5 miles in 40 minutes and 15 miles in 120 minutes.

Using y = kx

where,

y = 40

x = 5

y = kx

40 = 5k

k = 40/5

k = 8

Using y = kx

where,

y = 120

x = 15

y = kx

120 = 15k

k = 120/15

k = 8

The number of minutes vary directly with the number of miles. This is because the constant of proportionality is thesame in both cases.

Therefore, the second one(B) represents a direct variation and the first one (A) doesn't.

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Answer:

Shane had $240 at the beginning of his trip.

Step-by-step explanation:

Shane returned from a trip to Las Vegas with $420 and this is 75% more of at the beginning.

Let us assume the money he carried at the beginning of the trip was $x

At present he is having 75% more means total money he has = x+75% of x

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3 years ago

Use the Fundamental Theorem of Calculus to find the area of the region between the graph of the function x5 + 8x4 + 2x2 + 5x + 1

belka [17]

Answer:

The area of the region between the graph of the given function and the x-axis = 25,351 units²

Step-by-step explanation:

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15

If 'f' is a continuous on [a ,b] then the function

$F(x) = \int\limits^a_b {f(x)} \, dx$

By using integration formula

$\int{x^n} \, dx = \frac{x^{n+1} }{n+1} +c$

Given x⁵ + 8 x⁴ + 2 x² + 5 x + 15 in the interval [-6,6]

$\int\limits^6_^-6} (x^{5} + 8 x^{4} + 2 x^{2} + 5 x + 15) )dx$

<em>On integration , we get</em>

= $(\frac{x^{6} }{6} + \frac{8 x^{5} }{5} + 2 \frac{x^{3} }{3} +\frac{5 x^{2} }{2} + 15 x)^{6} _{-6}$

$F(x) = \int\limits^a_b {f(x)} \, dx = F(b) -F(a)$

= $(\frac{6^{6} }{6} + \frac{8 6^{5} }{5} + 2 \frac{6^{3} }{3} +\frac{5 6^{2} }{2} + 15X 6) - ((\frac{(-6)^{6} }{6} + \frac{8 (-6)^{5} }{5} + 2 \frac{(-6)^{3} }{3} +\frac{5 (-6)^{2} }{2} + 15 (-6))$

After simplification and cancellation we get

= $\frac{2 X 8 X (6)^{5} }{5} + \frac{2 X 2 X (6)^3}{3} + 2 X 15 X 6$

on calculation , we get

= $\frac{124,416}{5} + \frac{864}{3} + 180$

On L.C.M 15

= $\frac{124,416 X 3 + 864 X 5 + 180 X 15}{15}$

= 25 351.2 units²

<u><em>Conclusion</em></u>:-

<em>The area of the region between the graph of the given function and the x-axis = 25,351 units²</em>

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