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3 years ago

What is the product of Three-fourths and Negative StartFraction 6 over 7 EndFraction? -9/14

Mathematics

1 answer:

Brums [2.3K]3 years ago

3 0

Answer:

The product is : $-\frac{9}{14}$

Step-by-step explanation:

First term given to us is = $\frac{3}{4}$

Second term given to us = $-\frac{6}{7}$

We have to find product for term 1 and term 2

Which means that we have to find : $(\frac{3}{4})\cdot(-\frac{6}{7})$

Calculating the product of fraction is pretty simple. To calculate the product of any two fractions. We have to multiple the numerator of 1st term with numerator of 2nd which serves as the the numerator of the product. Similarly we have to multiply denominator with denominator.

$(\frac{3}{4})\cdot(-\frac{6}{7}) = \frac{3\cdot(-6)}{4\cdot7} = -\frac{18}{28}$

Reduce the fraction

$-\frac{18}{28}= -\frac{9}{14}$

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Step-by-step explanation:

According to the Question,

Given, A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours.

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4 years ago

The displacement of a particle from a reference point at any instant is given by s = 3 t 2 - 4 t + 5 , where s is in metres and

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The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.

How to determine average velocity and instantaneous velocity?
Average velocity is defined as the body's overall displacement divided by its time of motion. While instantaneous velocity is defined as a body's speed at a certain instant in time, or its displacement at that instant. When the velocity is constant, average and instantaneous velocities will equalize at just one condition.
The definition of instantaneous velocity is the rate of change of position over a relatively brief time period (almost zero). Simply said, the speed of an object at that precise moment. The definition of instantaneous velocity is "The velocity of an item in motion at a certain point in time." The instantaneous velocity of an object may be equal to its standard velocity if it has uniform velocity.
Mathematically, average velocity = [s(t₂) - s(t₁)]/[t₂ - t₁]
Instantaneous velocity at time, t is = (ds/dt) at time = t

Given, the displacement for the particle is given by s = 3t² - 4t + 5
Time interval, t₁ = 5s and t₂ = 3s;
Using formula in literature, average velocity of the particle in the time interval between 3s and 5s is:
Average velocity = (s(5) - s(3))/(5 - 3) = (60 - 20)/2 = 20 ms⁻¹
Instantaneous velocity at t = 4 is ds/dt at that time-frame:
Now, v = ds/dt = 6t -4
Now, v(4) = 6(4) - 4 = 20 ms⁻¹
The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.

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