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RUDIKE [14]
3 years ago
8

Due to gravity, an object falls 16t² feet in t seconds. You drop a backpack from a window that is 100 feet above the ground. Wil

l the backpack hit the ground in 3 seconds?
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
8 0

Answer:

the backpack will be on the ground in 3 seconds but it will first make contact with the ground in 2.5 seconds

Step-by-step explanation:

the equation would be:  y = -16t² + 100

if you solve for 't' then you will find the amount of time until it lands

0 = -16t² + 100

-100 = -16t²

100/16 = t²

t = √100/16

t = 10/4 = 2.5

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Tom [10]

We are given statement " gained 20 pounds and loses 15 pounds".

<em>Note: We take plus or positive sign for gain word and we take minus or negative sign for the loses word.</em>

Gained 20 means +20.

Loses 15 mean -15.

Therefore, we can setup an expression as:

<h3>+20 -15.</h3>

20 is a positive number and 15 is a negative number.

Because we have opposite signs of numbers, we would subtract them.

20-15 = 5 pounds.


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3 years ago
Whats 4/5 as a decmal?
Rashid [163]

Answer:

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Step-by-step explanation:


5 0
3 years ago
QUESTION IN THE ATTACHMENT
eimsori [14]

Answer:

A. The sum of the first 10th term is 100.

B. The sum of the nth term is n²

Step-by-step explanation:

Data obtained from the question include:

Sum of 20th term (S20) = 400

Sum of 40th term (S40) = 1600

Sum of 10th term (S10) =..?

Sum of nth term (Sn) =..?

Recall:

Sn = n/2[2a + (n – 1)d]

Sn is the sum of the nth term.

n is the number of term.

a is the first term.

d is the common difference

We'll begin by calculating the first term and the common difference. This is illustrated below:

Sn = n/2 [2a + (n – 1)d]

S20 = 20/2 [2a + (20 – 1)d]

S20= 10 [2a + 19d]

S20 = 20a + 190d

But:

S20 = 400

400 = 20a + 190d .......(1)

S40 = 40/2 [2a + (40 – 1)d]

S40 = 20 [2a + 39d]

S40 = 40a + 780d

But

S40 = 1600

1600 = 40a + 780d....... (2)

400 = 20a + 190d .......(1)

1600 = 40a + 780d....... (2)

Solve by elimination method

Multiply equation 1 by 40 and multiply equation 2 by 20 as shown below:

40 x equation 1:

40 x (400 = 20a + 190d)

16000 = 800a + 7600. ........ (3)

20 x equation 2:

20 x (1600 = 40a + 780d)

32000 = 800a + 15600d......... (4)

Subtract equation 3 from equation 4

Equation 4 – Equation 3

32000 = 800a + 15600d

– 16000 = 800a + 7600d

16000 = 8000d

Divide both side by 8000

d = 16000/8000

d = 2

Substituting the value of d into equation 1

400 = 20a + 190d

d = 2

400 = 20a + (190 x 2)

400 = 20a + 380

Collect like terms

400 – 380 = 20a

20 = 20a

Divide both side by 20

a = 20/20

a = 1

Therefore,

First term (a) = 1.

Common difference (d) = 2.

A. Determination of the sum of the 10th term.

First term (a) = 1.

Common difference (d) = 2

Number of term (n) = 10

Sum of 10th term (S10) =..?

Sn = n/2 [2a + (n – 1)d]

S10 = 10/2 [2x1 + (10 – 1)2]

S10 = 5 [2 + 9x2]

S10 = 5 [2 + 18]

S10 = 5 x 20

S10 = 100

Therefore, the sum of the first 10th term is 100.

B. Determination of the sum of the nth term.

First term (a) = 1.

Common difference (d) = 2

Sum of nth term (Sn) =..?

Sn = n/2 [2a + (n – 1)d]

Sn = n/2 [2x1 + (n – 1)2]

Sn = n/2 [2 + 2n – 2]

Sn = n/2 [2 – 2 + 2n ]

Sn = n/2 [ 2n ]

Sn = n²

Therefore, the sum of the nth term is n²

6 0
3 years ago
A property was assessed at 25% of value with a tax rate of $12 per hundred. if the taxes totaled $11,400, what was the value? 1
shusha [124]

11400 ÷12 = 950 hundreds

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4 0
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3 years ago
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