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Shalnov [3]
3 years ago
6

Use the formula h=16t^2 to solve the problem . A diver dives from a cliff that has a height of 86.4 feet. Determine the time of

the dive . Round answer to the nearest tenth of a second
Mathematics
1 answer:
sdas [7]3 years ago
3 0
<span>2.3 seconds. Let's assign the known values to the equation and solve for t. h = 16t^2 86.4 = 16t^2 5.4 = t^2 2.323790008 = t Rounding to the nearest tenth of a second gives 2.3 seconds.</span>
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Given the sequence, 26, 13, 6.5, ..... find a) the 10th term and b) the sum of the first 18 terms
Hunter-Best [27]

Answer:

a) 10th term is 0.051

b) The sum of first 18 terms of given sequence is 51.48

Step-by-step explanation:

We are given the sequence 26, 13, 6.5, ..... we need to find

a) 10th term

b) Sum of first 18 terms

Before solving we need to determine if the sequence is arithmetic or geometric

The sequence is arithmetic if common difference d is same.

The sequence is geometric if common ratio r is same.

Finding common difference d: 13-26 = -13, 6.5-13= -6.5

As common difference is not same so, the sequence is not arithmetic.

Finding common ratio r : 13/26 =0.5, 6.5/13= 0.5

As common ratio is same so, the sequence is geometric.

a) Finding common difference: 13-26 = -13, 6.5-13= -6.5

As common difference is not same so, the sequence is not arithmetic.

a) 10th term

The formula to find 10th term is: a_n=a_1r^{n-1}

We have a₁=26 and r = 0.5 n=10

a_n=a_1r^{n-1}\\a_{10}=26(0.5)^{10-1}\\a_{10}=26(0.5)^{9}\\a_{10}=0.051

So, 10th term is 0.051

b) Sum of first 18 terms

The formula to find sum of geometric series is: S_n=\frac{a(1-r^n)}{1-r}

where a= 1st term, r = common ratio and n= number of terms

In the given sequence we have

a=26, r=0.5 and n=18

Finding sum of first 18 terms

S_n=\frac{a(1-r^n)}{1-r}\\S_{18}=\frac{26(1-(0.5)^{18}}{1-0.5}\\S_{18}=\frac{26(0.99)}{0.5}\\S_{18}=\frac{25.74}{0.5}\\S_{18}=51.48

So, sum of first 18 terms of given sequence is 51.48

6 0
3 years ago
Should be easy points!
Andru [333]

Answer:

Let x represent the number from the sentence.

Step-by-step explanation:

2(x) + 2(1/x) = 20/3

2x + 2/x = 20/3

multiply both sides of the equation by 3x

6x + 6 = 20x

6x - 20x + 6 = 0

6x - 18x - 2x + 6 = 0

6x(x-3 -2(x-3) = 0

(6x-2 = 0 or x-3 = 0

6x = 2 or x = 3

x = 2/6

x = 1/3

Since x represented the number

Therefore x = 1/3 or 3

4 0
3 years ago
The number 0.8 can be written as 8/9, so it is a irrational number true or false
lesya692 [45]
False//////////////////////////////////////////////////////////////////////////
5 0
3 years ago
Calculate the rf value for the reactant b spot. estimate the ruler to the nearest tenth, report the answer using two significant
Aliun [14]
<span>1. Measure the distance the solvent front traveled from the baseline (m1). 2. Measure the distance the reactant b spot traveled (the center of the spot) (m2). 3. To determine the rf, divide (m2/m1). 4. Significant figures- use 2 so the answer should be written to the hundredths place as the spot will not travel farther than the solvent front.</span>
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3 years ago
A rectangle has an area of 40 square units. The length is 6 units greater than the width.
vampirchik [111]
The length is 10
The width is 4
4 + 6 = 10
4 x 10 = 40
6 0
3 years ago
Read 2 more answers
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