Ask question

Ask question

All categories

3 years ago

10

The length of a iron-sheet and copper-sheet is 672 cm and 960 cm respectively.what will be the length of the highest piece of eq

ual size cut from the two sheets?
determine the numbers of pieces of those two sheets.
please explain

2 answers:

marissa [1.9K]3 years ago

8 0

In order to calculate the length of highest piece, You need to calculate the Greatest common divisor of 672 & 960 which is 96

So, the length of highest piece would be 96 cm

Now, Number of pieces of Iron-sheet = 672 / 96 = 7
Number of pieces of Copper-sheet = 960 / 96 = 10

Hope this helps!

gulaghasi [49]3 years ago

3 0

To determine length of the highest number of EQUAL pieces from both, you have to find HCF of 672 and 960, which is 96 !

So numbers are 672 ÷96 = 7 for iron sheet !

And 960/96 = 10 for copper sheet !

You might be interested in

Tirzah wants to put a fence around her garden. She has 22 yards Of fence material. Does she have enough to go all the way around

CaHeK987 [17]

No. She needs at least 31 yards of material.

3 0

3 years ago

F is a twice differentiable function that is defined for all reals. The value of f "(x) is given for several values of x in the

nadezda [96]

The correct answer is actually the last one.

The second derivative $f''(x)$ gives us information about the concavity of a function: if $f''(x)$ then the function is concave downwards in that point, whereas if $f''(x)>0$ then the function is concave upwards in that point.

This already shows why the first option is wrong - if the function was concave downwards for all x, then the second derivate would have been negative for all x, which isn't the case, because we have, for example, $f''(8)=5$

Also, the second derivative gives no information about specific points of the function. Suppose, in fact, that $f(x)$ passes through the origin, so $f(0)=0$ . Now translate the function upwards, for example. we have that $f(x)+k$ doesn't pass through the origin, but the second derivative is always $f''(x)$ . So, the second option is wrong as well.

Now, about the last two. The answer you chose would be correct if the exercise was about the first derivative $f'(x)$ . In fact, the first derivative gives information about the increasing or decreasing behaviour of the function - positive and negative derivative, respectively. So, if the first derivative is negative before a certain point and positive after that point. It means that the function is decreasing before that point, and increasing after. So, that point is a relative minimum.

But in this exercise we're dealing with second derivative, so we don't have information about the increasing/decreasing behaviour. Instead, we know that the second derivative is negative before zero - which means that the function is concave downwards before zero - and positive after zero - which means that the function is concave upwards after zero.

A point where the function changes its concavity is called a point of inflection, which is the correct answer.

7 0

3 years ago

Solve for x<br>2/x -2 = 3/2x +3

jenyasd209 [6]

Step-by-step explanation:

5 0

2 years ago

A certain college graduate borrows 7864 dollars to buy a car. The lender charges interest at an annual rate of 13%. Assuming tha

White raven [17]

Answer:

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = =$1573.17

Step-by-step explanation:

Consider A represent the balance at time t.

A(0)=$ 7864.

r=13 % =0.13

Rate payment = $k

The balance rate increases by interest (product of interest rate and current balance) and payment rate.

$\frac{dB}{dt} = rB-k$

$\Rightarrow \frac{dB}{dt} - rB=-k$ .......(1)

To solve the equation ,we have to find out the integrating factor.

Here p(t)= the coefficient of B =-r

The integrating factor $=e^{\int p(t) dt$

$=e^{\int (-r)dt$

$=e^{-rt}$

Multiplying the integrating factor the both sides of equation (1)

$e^{-rt}\frac{dB}{dt} -e^{-rt}rB=-ke^{-rt}$

$\Rightarrow e^{-rt}dB - e^{-rt}rBdt=-ke^{-rt}dt$

Integrating both sides

$\Rightarrow \int e^{-rt}dB -\int e^{-rt}rBdt=\int-ke^{-rt}dt$

$\Rightarrow e^{-rt}B=\frac{-ke^{-rt}}{-r} +C$ [ where C arbitrary constant]

$\Rightarrow B(t)=\frac{k}{r} +Ce^{rt}$

Initial condition B=7864 when t =0

$\therefore 7864= \frac{k}{r} - Ce^0$

$\Rightarrow C= \frac{k}{r} -7864$

Then the general solution is

$B(t)=\frac{k}{r}-( \frac{k}{r}-7864)e^{rt}$

To determine the payment rate, we have to put the value of B(3), r and t in the general solution.

Here B(3)=0, r=0.13 and t=3

$B(3)=0=\frac{k}{0.13}-( \frac{k}{0.13}-7864)e^{0.13\times 3}$

$\Rightarrow- 0.48\frac{k}{0.13} +11614.98=0$

⇒k≈3145.72

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = ${(3145.72×3)-7864}

=$1573.17

4 0

3 years ago

A body travels 10 meters during the first 5 seconds of its travel, and it travels a total of 30 meters over the first 10 seconds

meriva

The answer is 4 m/s.

In the first 5 seconds, a body travelled 10 meters. In the first 10 seconds of the travel, the body travelled a total of 30 meters, which means that in the last 5 seconds, it travelled 20 meters (30m + 10m).
The relation of speed (v), distance (d), and time (t) can be expressed as:
v = d/t

We need to calculate the speed of the second 5 seconds of the travel:
d = 20 m (total 30 meters - first 10 meters)
t = 5 s (time from t = 5 seconds to t = 10 seconds)

Thus:
v = 20m / 5s = 4 m/s

5 0

3 years ago

Read 2 more answers