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2 years ago

You are choosing between two different cell phone plans. The first plan charges a rate of

Mathematics

1 answer:

Zolol [24]2 years ago

3 0

Answer:

at least 450 minutes

Step-by-step explanation:

Find an expression for the cost of each plan as a function of the number of minutes. Set the expressions equal to each other, and solve for the number of minutes.

Let x = number of minutes.

First plan:

cost (in dollars) = 0.21x

Second plan:

cost (in dollars) = 0.11x + 44.95

Set the expressions equal:

0.21x = 0.11x + 44.95

Subtract 0.11x from both sides.

0.1x = 44.95

Divide both sides by 0.1

x = 44.95/0.1

x = 449.5

Since you cannot have a fraction of a minute, the answer is 450 minutes.

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Let f(x)=4x-1 and g(x)=2x^2+3. Perform each function operations and then find the domain.

Triss [41]

F(x) = 4x - 1
g(x) = 2x² + 3

1. (f + g)(x) = (4x - 1) + (2x² + 3)
(f + g)(x) = 2x² + 4x + (-1 + 3)
(f + g)(x) = 2x² + 4x + 2
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

2. (f - g)(x) = (4x + 1) - (2x² + 3)
  (f - g)(x) = 4x + 1 - 2x² - 3
(f - g)(x) = -2x² + 4x + 1 - 3
(f - g)(x) = -2x² + 4x - 2
Domain: {x|-∞ < x < ∞}, (-∞, ∞)
3. (g - f)(x) = (2x² + 3) - (4x - 1)
(g - f)(x) = 2x² + 3 - 4x + 1
(g - f)(x) = 2x² - 4x + 3 + 1
(g - f)(x) = 2x² - 4x + 4
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

4. (f · g)(x) = (4x + 1)(2x² + 3)
(f · g)(x) = 4x(2x² + 3) + 1(2x² + 3)
(f · g)(x) = 4x(2x²) + 4x(3) + 1(2x²) + 1(3)
(f · g)(x) = 8x³ + 12x + 2x² + 3
(f · g)(x) = 8x³ + 2x² + 12x + 3
Domain: {x| -∞ < x < ∞}, (-∞, ∞)

5. $(\frac{f}{g})(x) = \frac{4x - 1}{2x^{2} + 3}$
Domain: 2x² + 3 ≠ 0
- 3 - 3
2x² ≠ 0
2 2
  x² ≠ 0
x ≠ 0
(-∞, 0) ∨ (0, ∞)

6. $(\frac{g}{f})(x) = \frac{2x^{2} + 3}{4x - 1}$
Domain: 4x - 1 ≠ 0
+ 1 + 1
4x ≠ 0
4   4
x ≠ 0
  (-∞, 0) ∨ (0, ∞)

6 0

3 years ago

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) A

julsineya [31]

Answer:

a) -13.9 ft/s

b) 13.9 ft/s

Step-by-step explanation:

a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:

$D^{2} = (90 - x)^{2} + 90^{2}$ (1)

$\frac{d(D^{2})}{dt} = \frac{d(90 - x)^{2} + 90^{2})}{dt}$

$2D\frac{d(D)}{dt} = \frac{d((90 - x)^{2})}{dt}$

$D\frac{d(D)}{dt} = -(90 - x) \frac{dx}{dt}$ (2)

Since:

$D = \sqrt{(90 -x)^{2} + 90^{2}}$

When x = 45 (the batter is halfway to first base), D is:

$D = \sqrt{(90 - 45)^{2} + 90^{2}} = 100. 62$

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

$100.62 \frac{d(D)}{dt} = -(90 - 45)*31$

$\frac{d(D)}{dt} = -\frac{(90 - 45)*31}{100.62} = -13.9 ft/s$

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.

b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

$D^{2} = 90^{2} + x^{2}$

$\frac{d(D^{2})}{dt} = \frac{d(90^{2} + x^{2})}{dt}$

$D\frac{dD}{dt} = x\frac{dx}{dt}$ (3)

We have that D is:

$D = \sqrt{x^{2} + 90^{2}} = \sqrt{(45)^{2} + 90^{2}} = 100.63$

By entering x = 45, dx/dt = 31 and D = 100.63 into equation (3) we have:

$\frac{dD}{dt} = \frac{45*31}{100.63} = 13.9 ft/s$

Therefore, the rate of the batter when he is from third base increasing at the same moment is 13.9 ft/s.

I hope it helps you!

4 0

3 years ago

Read 2 more answers

Help please and show the steps! thank you!

san4es73 [151]

Answer:

#1. x = -1

Answer = 8

#2. x = 1/5

Answer = 344/25

#3. x = 14

Answer = 13328

Step-by-step explanation:

#1. a. plug in -1

f(-1)= (5(-1)^3) - (2(-1)^2 - (-1) + 14

b. Solve the exponents.

(5(-1)^3)

(5x-1)

(-5) - (2(-1)^2) - (-1) + 14

(2(-1)^2)

(2x1)

(-5) - (2) - (-1) +14

c. simplify.

(-5) - (2) + 1 + 14

-7 + 15

#2.

f(1/5)= (5(1/5)^3) - (2(1/5)^2 - (1/5) + 14

(5(1/5)^3)

(5 x 1/125)

(1/25) - (2(1/5)^2)

(2 x 1/25)

(2/25)

(1/25) - (2/25) - (1/5) +14

(-1/25) - (1/5) +14

Note: (1/5) turns into (5/25) so it can be subtracted.

-6/25 + 14

Note: 14 turns into 350/25 so it can be added.

350/25 - 6/25 = 344/25

#3.

f(14)= (5(14)^3) - (2(14)^2 - (14) + 14

Note: Normally you do the exponents first but I'm just going to casually take out the two 14s at the end cause they cancel each other out.

f(14)= (5(14)^3) - (2(14)^2)

( 5 (14^3))

(5 x 2744)

(13720) - (2(14^2))

(2 (14^2))

(2x196)

392

(13720) - 392

13328

Good Luck!

3 0

3 years ago

A collector is selling antique coins from a collection. Currently, each coin is worth $11.50. the value of each coin is expected

Phoenix [80]

The answer to your question is 4657.50

4 0

3 years ago

Determine the effective monthly growth rate for a population that grows at a rate of 23% each year.

ivolga24 [154]

Answer:B.) 1.74%

Step-by-step explanation:

3 0

3 years ago