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makkiz [27]
3 years ago
11

A vine maple grows fast when it is planted under the cover of cedar trees. One month after it is planted it has grown 12 inches,

and after eight weeks it had grown 19 inches. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks.
Mathematics
1 answer:
Goshia [24]3 years ago
5 0

Answer:

  y = (7/4)(x -4) +12

Step-by-step explanation:

The rate of growth is ...

  (19 in -12 in)/(8 wk -4 wk) = 7/4 in/wk

Using this slope in a point-slope form of the equation for a line, we get ...

  y = m(x -h) +k . . . . . line with slope m through point (h, k)

  y = (7/4)(x -4) +12 . . . . . line with slope 7/4 through the point (4 wk, 12 in)

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Doug hits a baseball straight towards a 15 ft high fence that is 400 ft from home plate. The ball is hit 2.5ft above the ground
Scorpion4ik [409]

Answer:

125.4\ \text{m/s}

Step-by-step explanation:

u = Initial velocity of baseball

\theta = Angle of hit = 30^{\circ}

x = Displacement in x direction = 400 ft

y = Displacement in y direction = 15 ft

y_0 = Height of hit = 2.5 ft

a_y = g = Acceleration due to gravity = 32.2\ \text{ft/s}^2

t = Time taken

Displacement in x direction

x=u_xt\\\Rightarrow x=u\cos\theta t\\\Rightarrow t=\dfrac{x}{u\cos\theta}\\\Rightarrow t=\dfrac{400}{u\cos30^{\circ}}\\\Rightarrow t=\dfrac{400}{u\dfrac{\sqrt{3}}{2}}\\\Rightarrow t=\dfrac{800}{u\sqrt{3}}

Displacement in y direction

y=y_0+u_yt+\dfrac{1}{2}a_yt^2\\\Rightarrow y=y_0+u\sin\theta t+\dfrac{1}{2}a_yt^2\\\Rightarrow 15=2.5+u\sin30^{\circ}(\dfrac{800}{u\sqrt{3}})+\dfrac{1}{2}\times -32.2\times (\dfrac{800}{u\sqrt{3}})^2\\\Rightarrow \dfrac{400}{\sqrt{3}}-\dfrac{10304000}{3u^2}-12.5=0\\\Rightarrow 218.44=\dfrac{10304000}{3u^2}\\\Rightarrow u=\sqrt{\dfrac{10304000}{3\times218.44}}\\\Rightarrow u=125.4\ \text{m/s}

The minimum initial velocity needed for the ball to clear the fence is 125.4\ \text{m/s}

5 0
3 years ago
PLEASE PLEASE HELP!!! Figure 1 is dilated to get figure 2. What is the scale factor? Figure 1 is the smaller figure and has a 6
Xelga [282]
The answer is 1.5

Hope this helps!!
6 0
3 years ago
One smartphone plan costs $52 per month for talk and messaging and $8 per gigabyte of data used each month. A second smartphone
valina [46]

Answer:

Both plans would cost $100 if 6 gigabytes of data are used.

Explanation:

From the question, the system of equation are correctly represented by using small letter c to represent the total cost in dollars for both equations as already assumed in the question as follows:

c = 52 + 8d ........................... (1)

c = 82 + 3d ........................... (2)

Since c is common to both, equations (1) and (2) can therefore be equated and d solved for as follows:

52 + 8d = 82 + 3d

8d - 3d = 82 - 52

5d = 30

d = 30 / 5

d = 6

Substituting d = 6 into equation (1), we have:

c = 52 + (8 * 6)

c = 52 + 48

c = 100

Since d = 6 and c = 100, it therefore implies that both plans would cost $100 if 6 gigabytes of data are used.

5 0
2 years ago
The points A, B, and C lie on a line so that AB = 12 cm and BC = 13.5 cm. Find the length of segment AC. Give all possible answe
natita [175]

Answer:

25.5 and 1.5

Step-by-step explanation:

AC = 12 cm

BC = 13.5 cm

12 + 13.5 = 25.5 cm

13.5 - 12 = 1.5 cm

4 0
2 years ago
I need a bit of help on this one: mr. james borrows money from the bank to buy a new car. he borrows 10,000 at 3% for 5 years. H
EastWind [94]

Answer:

Between $11,000-$11,500  

Between $10,500-$11,000  

Between $9,500-$10,000  

Between $9,000-$9,500  

Between $10,000-$10,500

Correct answer:

Between $10,000-$10,500

8 0
3 years ago
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