First, let me do the Mathematical part of that, and then I shall explain the theory behind it.
Mathematical part:
We are going to multiply 513 with 46. So the two partial products that we are going to choose are 40 and 6.
Multiply 513 with 6 first.
513
x46
--------------------------
18 (as 6*3 = 18)
60 (as 6*10 = 60; In 513, the digit at tenths place is 1, so 1*10=10)
3000 (as 6*500 = 3000; In 513, 5 is at hundredth place, so 5*100=500)
120 (as 40*3 = 120; since 4 is at the tenth place, so 4*10=40)
400 (as 40*10 = 400)
20000 (as 40*500 = 20000)
--------------------------
23598 (Add all of them)
Theory:
As you can see above that we have chosen the two partial products individually which are 6 and 40. Since 4 in 46 is in tenth place, we have to consider it 40 (since 4*10 = 40). One by one, we first multiply 6 with 513. Then we move to the tenth place, and multiply 513 with 40. At the end, we have added all the results we found after multiplication.
Check: If we check the multiplication result by using the calculator, we would get the same result (23598).
Another Method (instant):
513 * (40+6) = (513*40) + (513*6) = 23598.
Solve for x by cross multiplying and the answer is x=6
hope this helps and plz rate below :)
Distribute and combine like-terms!
-4x + 12x - 2x - 2
6x - 2
Answer:
So the exchange rate is that each dollar is worth 70.4 yens.
Step-by-step explanation:
We have that:
1 euro is priced at $1.25
1 euro will also buy 88 Japanese yen
This also means that:
$1.25 is priced at 88 Japanese yen
How much is the cross rate between the yen and the dollar (yen per dollar exchange rate)?
How much yens is 1 dollar?
This can be solved by a simple rule of three.
$1.25 - 88 yen
$1 - x yen
![1.25x = 88](https://tex.z-dn.net/?f=1.25x%20%3D%2088)
![x = \frac{88}{1.25}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B88%7D%7B1.25%7D)
![x = 70.4](https://tex.z-dn.net/?f=x%20%3D%2070.4)
So the exchange rate is that each dollar is worth 70.4 yens.
Answer: 890.12 cm^3
Step-by-step explanation:
The formula for the volume of a cylinder is
![V=\pi *r^2*h](https://tex.z-dn.net/?f=V%3D%5Cpi%20%2Ar%5E2%2Ah)
V=628.3185307 cm^3
or simply
V=628.32 cm^3
Since, you know the radius of the hemisphere on top, you also know the radius since the height of the hemisphere is the same as it is wide.
Next, the formula for the volume of a sphere is
![V=\frac{4}{3} \pi *r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2Ar%5E3)
so the volume of a hemisphere is half of that or:
![V=\frac{2}{3} *\pi *r^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%7D%7B3%7D%20%2A%5Cpi%20%2Ar%5E3)
V= 261.7993878 cm^3
or simply
V=261.80 cm^3
Finally, you add both of the volumes together to get
V= 890.1179185 cm^3
or simply
V=890.12 cm^3