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3 years ago

A curve is describe by the following parametric equations:

Mathematics

1 answer:

soldi70 [24.7K]3 years ago

7 0

Answer:

A. The curve is a parabola with a vertex at (3,-4) and is traced from left to right for increasing values of t.

Step-by-step explanation:

x = 3 + t

y = t² − 4

Eliminating the parameter:

t = x − 3

y = (x − 3)² − 4

This is an upwards parabola with a vertex at (3, -4).

x = 3 + t, so as t increases, x increases.

So the curve is traced from left to right.

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At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,

mart [117]

Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

$f(x)=mx+b$

where

$m\rightarrow$ slope of line

$b\rightarrow$ y-intercept

Let linear function to calculate total cost of gym be:

$c(n)=mn+b$

where

$c\rightarrow$ total cost of gym

$m\rightarrow$ cost per month (slope)

$n\rightarrow$ number of months

$b\rightarrow$ start-up fee (y-intercept)

For Gym 1

$m=20$ , $b=12$

$c(n)=20n+12$

For Gym 2

$m=22$ , $b=4$

$c(n)=22n+4$

In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months $(n)$

$20n+12=22n+4$

$\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}$

So,

In 4 months the cost of both gyms will be the same.

5 0

3 years ago

Kevin can carry a basket 5 feet Rachel can carry it three feet farther than Kevin Daniel can carry the basket half as far as Rac

OlgaM077 [116]

Yes. Kevin can carry the basket 5 ft. Rachel can carry it 3 feet more than Kevin (5+3=8). Daniel can carry the basket half the length of Rachel (8/2=4). The total distance they can carry the basket is 5+8+4=17. 17 is greater than 15, so yes they can carry it 15 feet.

8 0

3 years ago

The 100-meter dash times in the girls track meet were normally distributed with a mean of 13 seconds and a standard deviation of

Svetllana [295]

Answer:

97.68 %

z(lower) = .0227

z(upper) = .999

Step-by-step explanation:

5 0

2 years ago

he wanted to make another quilt with an area of 42 square feet what are its possible dimensions if they must be whole numbers. W

Ostrovityanka [42]

Area=legnth times width
42=legnth times width
a quilt is normally for a big bed probably at leas 3 feet wide
factor 42
42=2 times 3 tiesm 7
possible values are
2 by 21
3 by 14
6 by 7
I would go with the 6 by 7 format

8 0

3 years ago

The Niagara Falls ferris wheel has a diameter of 48 meters, and one revolution takes 2.25 minutes to complete. Riders can see Ni

Yanka [14]

The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)

<h3>How to interpret Cycle Graphs?</h3>

From the diagram attached, we can say that;

Period = 2π/k

where;

k = 2π/2.25

k = 8π/9

Thus;

h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)

h(t) = -24cos (8π/9)t + 24.5

Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;

41 = -24cos (8π/9)t + 24.5

41 - 24.5 = -24cos (8π/9)t

16.5 = -24cos (8π/9)t

-0.6875 = cos (8π/9)t

cos⁻¹0.6875 = (8π/9)t

t = 0.834 min

Thus, time interval is between;

0.834 < t < (2.25 - 0.834)

⇒ 0.834 < t < 1.416 and

(2.25 + 0.834) < t < (2.25 + 1.416)

⇒ (3.084, 3.666)

Read more about Cycle Graphs at; brainly.com/question/24461724

#SPJ1

4 0

2 years ago