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3 years ago

If a car with an average speed of 50 miles per hour drives for 90 minutes, how far will it have gone?

Mathematics

2 answers:

gayaneshka [121]3 years ago

5 0

90 minutes = 1,5 hours
Distance = speed * time = 50 * 1.5 = 75 miles (answer).

Irina-Kira [14]3 years ago

5 0

Answer:

Total distance covered by the car is 75 miles.

Step-by-step explanation:

Given information:

Average speed of car = 50 miles per hour

Time = 90 minutes

We know that, 1 hour = 60 minutes

Using this conversion, convert the time in hours.

$Time=\frac{90}{60}=1.5\text{ hours}$

The formula for distance is

$Distance=Speed\times Time$

$Distance=50\times 1.5$

$Distance=75$

Therefore total distance covered by the car is 75 miles.

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B(n)=1 (-2)^n-1 What is the 4th term in the sequence

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Answer:

The fourth term of the sequence B(4) =-8

The sequence is 1,-2,4,-8...

Step-by-step explanation:

Explanation:-

Given that the sequence

B(n) = 1(-2)ⁿ⁻¹

Put n=1

B(1) = 1(-2)¹⁻¹ = 2⁰ =1

Put n=2

B(2) = 1(-2)²⁻¹ = (-2)¹ =-2

Put n=3

B(3) =1(-2)³⁻¹ = (-2)² =4

Put n=4

B(4) = 1(-2)⁴⁻¹ =(-2)³ =-8

The sequence

1,-2,4,-8...

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Answer:

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Which sum will be neither positive nor negative? 07+(-6) 0 3+2 0-6 + 6 0-4-(-4)

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3 years ago

Use sigma notation to represent the sum of the first seven terms of the following sequence -4,-6,-8.....

lina2011 [118]

Answer:Answer:

$\sum\left {{7} \atop {1}} \right -n(3+n)$

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as $S_n = \frac{n}{2}[2a+(n-1)d]$

n is the number of terms

a is the first term of the sequence

d is the common difference

Given parameters

n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2

Required

Sum of the first seven terms of the sequence

$S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70$

The sum of the nth term of the sequence will be;

$S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)$

The sigma notation will be expressed as $\sum\left {{7} \atop {1}} \right -n(3+n)$ . The limit ranges from 1 to 7 since we are to find the sum of the first seven terms of the series.

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