Find the average rage of change of each of the following functions over the interval 1 < ×

A shopkeeper sold a watch for Rs 810 at 10% loss. How much did he pay to buy the watch ?

Svetlanka [38]

Answer:

Rupees 891

Step-by-step explanation:

If you multiply 810 times 0.1 which is the decimal of 10%, you get 81 which you can add to 810 to get 891 which is the price the shopkeeper payed to buy the watch.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

7 0

3 years ago

Convert. 4600 g = _____ kg

faltersainse [42]

Answer:

4.6 Kilograms.

Step-by-step explanation:

6 0

3 years ago

which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!

coldgirl [10]

9514 1404 393

Answer:

(a) -(x+7)/y

(b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

$\dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}$

Likewise, the expression of (b) with the minus sign factored out is ...

$\dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}$

On the other hand, simplifying expression (c) gives something different.

$\dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}$

__

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

Given: (-x-7)/y = (-x/y) +(-7/y)

(a) -(x+7)/y = (-x/y) +(-7/y)

(b) (x+7)/(-y) = (-x/y) +(-7/y)

(c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.

__

Of course, you need to know the use of the distributive property and the rules of signs.

a(b+c) = ab +ac

-a/b = a/(-b) = -(a/b)

-a/(-b) = a/b

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Summary: The given expression matches (a) and (b).

_____

Additional comments

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

$\left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0$

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

(c) evaluates to (-1-7)/-2 = 4, different from given

3 0

3 years ago

A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t) = 6cos(t). At

Rom4ik [11]

a. By the fundamental theorem of calculus, the velocity function is

$v(t)=v(0)+\displaystyle\int_0^ta(u)\,\mathrm du$

The particle starts at rest, so $v(0)=0$ , and we have

$v(t)=\displaystyle\int_0^t6\cos u\,\mathrm du=6\sin u\bigg|_0^t=6\sin t$

Then the position function is

$x(t)=\displaystyle x(0)+\int_0^tv(u)\,\mathrm du$

with $x(0)=6$ , so

$x(t)=6+\displaystyle\int_0^t6\sin u\,\mathrm du=6-6\cos u\bigg|_0^t=12-6\cos t$

b. The particle is at rest whenever $v(t)=0$ ; this happens for

$6\sin t=0\implies \sin t=0\implies t=n\pi$

where $n$ is any integer.

3 0

3 years ago

52% of ______ days is 13 days.

abruzzese [7]

'of' in mathematics means multiplication
'is' in mathematics means equal

52% * x = 13

52/100 * x = 13

0.52x = 13

x = 13/0.52

x = 25

52% of 25 days is 13 days.

8 0

3 years ago

Find the average rage of change of each of the following functions over the interval 1 < × < 5.