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2 years ago

HCF of 2 numbers is 18 and product of 2 numbers is 648 . Find the LCM of 2 numbers

Mathematics

1 answer:

Alla [95]2 years ago

7 0

Answer:

what is HCF

but I will try

To sum up, the lcm of 2 and 8 is 8. In common notation: lcm (2,8) =

Step-by-step explanation:

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A cone has radius 9 and a height 12. A frustum of this cone has height 4.

Anettt [7]

Answer:

Part A)

The lower base has a radius of 9 units, and the upper base has a radius of 6 units.

Part B)

5 units.

Part C)

75π or about 235.62 square units.

Step-by-step explanation:

Please refer to the figure below.

The cone has a radius of 9 units and a total height of 12 units.

A frustum of the cone has a height of 4 units.

Part A)

The lower radius of the frustum will simply be 9 units.

For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:

$\displaystyle \frac{12}{8}=\frac{9}{x}$

Solve for <em>x.</em> Simplify:

$\displaystyle \frac{3}{2}=\frac{9}{x}$

Cross-multiply:

$18=3x\Rightarrow x=6$

The upper base has a radius of 6 units.

Part B)

We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:

$SH^2=12^2+9^2$

Simplify:

$SH^2=225\Rightarrow SH=15\text{ units}$

Now, find the slant height of the upper cone:

$(SH_\text{cone})^2=8^2+6^2=100$

So:

$SH_\text{cone}=10$

Then the slant height of the frustum will be the cone subtracted from the total. Thus:

$SH_{\text{frustum}}=15-10=5\text{ units}$

Part C)

We can first find the lateral area of the entire cone. The lateral area is given by:

$LA=\pi r\ell$

The lateral area of the entire cone will be:

$LA=\pi (9)(15)=135\pi$

The lateral area of the upper cone will be:

$LA_\text{cone}=\pi(6)(10)=60\pi$

Then the lateral area of the frustum is:

$LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2$

5 0

2 years ago

Suppose the Bainters purchase the $150,000.00 home with a 20% down payment, a 30-year mortgage, and an interest rate of 4.2%. An

Elden [556K]

Answer:

$809.32

Step-by-step explanation:

The loan amount is 80% of $150,000, or $120,000. The monthly payment of principal and interest is $586.82.

The total annual expense for taxes and insurance is $1920 +750 = $2670, so the monthly expense is $2670/12 = $222.50.

Then the total of payments for mortgage and escrow will be ...

$586.82 +222.50 = $809.32

The monthly P&I payment is given by ...

A = P(i/12)/(1 -(1 +i/12)^(-12t)) . . . . . where i is the annual interest rate, t is the number of years, and P is the amount financed.

A = $120,000(0.042/12)/(1 -(1 +0.042/12)^(-12·30)) ≈ $586.82

A spreadsheet or financial calculator can be useful for calculating payments, though the formula isn't difficult to use.

7 0

3 years ago

3e + 7 - e and 2e + 10 + 2e -3

ch4aika [34]

Answer:

The sum is

$6e + 14$

Step-by-step explanation:

Assuming we are finding the sum of :

3e + 7 - e and 2e + 10 + 2e -3

Then we set up the addition as follows:

$3e + 7 - e + 2e + 10 + 2e - 3$

We group similar try to get:

$3e - e + 2e + 2e - 3 + 7 + 10$

We now combine the similar terms to obtain:

$6e + 14$

Therefore the sum is

$6e + 14$

5 0

3 years ago

One bus leaves a stop every 9minutes. A second bus leaves the stop every 15 minutes. If they both leave at 1:25 P.M., AT what ti

jasenka [17]

1:40 because 25 plus 15 equals 40 and if it went over 60 it would 2:00 so the answer is 1:40

8 0

3 years ago

A cylinder has a radius of 5 cm and a height of 8 cm. How many cubic meters of fluid can fill this cylinder

Artist 52 [7]

V=bh
V=pi r^2*h
V=pi 5^2*8
V=pi 25*8
V=pi 200
V=200cubic meters

4 0

3 years ago