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pochemuha
3 years ago
7

Abbie decides to start doing crunches as part of her daily workout. She decides to do 15 crunches the first day and then increas

e the number 4 each day after that. Write an explicit formula for the number of crunches Abbie will do on day n.
Mathematics
1 answer:
Pavlova-9 [17]3 years ago
3 0
For this case, the first thing we must do is define a variable.
 We have then:
 n: number of days.
 We now write the explicit formula that represents the problem.
 We have then:
 an = 4n + 15
 Where,
 15: crunches the first day
 4: increase the number 4 each day
 Answer:
 
An explicit formula for the number of crunches Abbie will do on day n is:
 
an = 4n + 15
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A golfball is hit from the ground with an initial velocity of 200 ft/sec. The horizontal distance that the golfball will travel,
algol13

Answer:

The golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of \pi/4.

Step-by-step explanation:

The formula from the maximum distance of a projectile with initial height h=0, is:

d(\theta)=\frac{v_i^2sin(2\theta)}{g}

Where v_i is the initial velocity.

In the closed interval method, the first step is to find the values of the function in the critical points in the interval which is [0, \pi/2]. The critical  points of the function are those who make d'(\theta)=0:

d(\theta)=\frac{v_i^2\sin(2\theta)}{g}\\d'(\theta)=\frac{v_i^2\cos(2\theta)}{g}*(2)\\d'(\theta)=\frac{2v_i^2\cos(2\theta)}{g}

d'(\theta)=0\\\frac{2v_i^2\cos(2\theta)}{g}=0\\\cos(2\theta)=0\\2\theta=\pi/2,3\pi/2,5\pi/2,...\\\theta=\pi/4,3\pi/4,5\pi/4,...

The critical value inside the interval is \pi/4.

d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\d(\pi/4)=\frac{v_i^2sin(2(\pi/4))}{g}\\d(\pi/4)=\frac{v_i^2sin(\pi/2)}{g}\\d(\pi/4)=\frac{v_i^2(1)}{g}\\d(\pi/4)=\frac{(200)^2}{32}\\d(\pi/4)=\frac{40000}{32}\\d(\pi/4)=1250ft

The second step is to find the values of the function at the endpoints of the interval:

d(\theta)=\frac{v_i^2sin(2\theta)}{g}\\\theta=0\\d(0)=\frac{v_i^2sin(2(0))}{g}\\d(0)=\frac{v_i^2(0)}{g}=0ft\\\theta=\pi/2\\d(\pi/2)=\frac{v_i^2sin(2(\pi/2))}{g}\\d(\pi/2)=\frac{v_i^2sin(\pi)}{g}\\d(\pi/2)=\frac{v_i^2(0)}{g}=0ft

The biggest value of f is gived by \pi/4, therefore \pi/4 is the absolute maximum.

In the context of the problem, the golfball launched with an initial velocity of 200ft/s will travel the maximum possible distance which is 1250 ft when it is hit at an angle of \pi/4.

4 0
3 years ago
1+1 PLEASE PLEASE PLEASE LPEASE PLEASAE PLEASE
arlik [135]

Answer:

2

Step-by-step explanation:

1+1=2 so the answer is 2

5 0
2 years ago
Read 2 more answers
Chelsea records the number of quarts of water she gives her garden over 444 days. She rounds the measurements to the nearest \df
geniusboy [140]

Answer:

33

Step-by-step explanation:

Total=7

8

4

​

+7

8

4

​

+8

8

6

​

+9

8

2

​

start text, T, o, t, a, l, end text, equals, 7, start fraction, 4, divided by, 8, end fraction, plus, 7, start fraction, 4, divided by, 8, end fraction, plus, 8, start fraction, 6, divided by, 8, end fraction, plus, 9, start fraction, 2, divided by, 8, end fraction

Hint #22 / 3

Let's add the whole numbers then add the fractions.

\begin{aligned} \text{Total}&=(7+7+8+9)+\left(\dfrac{4}{8}+\dfrac{4}{8} +\dfrac{6}{8}+\dfrac{2}{8}\right)\\\\ &= 31+\dfrac{16}{8}\\\\ &=31+2\\\\ &=33 \end{aligned}

Total

​

 

=(7+7+8+9)+(

8

4

​

+

8

4

​

+

8

6

​

+

8

2

​

)

=31+

8

16

​

=31+2

=33

​

Hint #33 / 3

Chelsea used 33 quarts of water on her garden.

6 0
2 years ago
Whats the surface area of a cylinder with height of 12in.and the radius is 4in​
emmainna [20.7K]

Answer:

401.92 in²

Step-by-step explanation:

S.A. = 2πr²+2πrh

S.A. = 2π4²+2π4·12

S.A. = 100.48 + 301.44

S.A. = 401.92 in²

7 0
3 years ago
A patient is given a solution containing 0.625 g of calcium carbonate. If the calcium carbonate solution contains 1250 mg per 5
Dmitrij [34]

Answer: 2.5 mL

Step-by-step explanation:

Given : A patient is given a solution containing 0.625 g of calcium carbonate.

i.e. Patient required calcium carbonate = 625 mg  [∵ 1 g = 1000 mg]

Let x be the amount of solution ( in millimeters) given to the patients.

Ratio of amount of calcium carbonate (mg) to amount of solution (ml) =\dfrac{625}{x}

If the calcium carbonate solution contains 1250 mg per 5 mL,

Then, Ratio of amount of calcium carbonate to amount of solution =\dfrac{1250}{5}

By using proportion we have :-

\dfrac{625}{x}=\dfrac{1250}{5}\\\\\Rightarropw\ x=\dfrac{5\times625}{1250}=2.5

Hence, 2.5 mL solution were given to the patient.

3 0
3 years ago
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