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2 years ago

Solve for y a. 7 cmb. 20 cmc. 14 cmd. 10 cm

Mathematics

1 answer:

Rainbow [258]2 years ago

7 0

Answer:

20 cm

Step-by-step explanation:

We can use ratios to solve

We know x = 7 since they are of equal length

x x+7

----- = -------

10 y

7 7+7

----- = -------

10 y

Using cross products

7y = 14*10

7y = 140

Divide by 7

7y/7 = 140/7

y = 20

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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the

m_a_m_a [10]

Answer:

Required volume is $\frac{4864\pi}{3}$ unit.

Step-by-step explanation:

Given equations of curves,

$y=32-x^2$ , $y=x^2$

substitute second in first we will get,

$x^2=36-x^2\implies x^2=16\implies x=\pm 4$

When $x=4, y=16$ and $x=-4, y=16$ . Thus both curves intersect at the points (4,16),(-4,16). And thus $-4$ .

Considering width of the representative rectangle as $\Delta x$ which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,

$V_{Shell}=(\textit{Length of box})\times (\textit{Width of box})\times (\textit{Thikness of box})$

Now,

Length of generating box=Length of $\Delta x$ from line x=4(axis of revolution)=circumference of the shell=(4-x)

Width of box= $(36-x^2)-x^2$

Hence,

$V_{Shell}$

$=\int_{-4}^{4}2\pi (4-x)(36-2x^2)dx$

$=2\pi\int_{-4}^{4}(144-36x-8x^2+2x^3)dx$

$=2\pi\{144\big[x\big]_{-4}^{4}-18\big[x^2\big]_{-4}^{4}-\frac{8}{3}\big[x^3\big]_{-4}^{4}+\frac{1}{2}\big[x^4\big]_{-4}^{4}\}$

$=\frac{4864\pi}{3}$

which is required volume of generating area.

3 0

2 years ago

Chris uncle from japan promised to give him 42 g of gold .The local jewelry exchange will buy gold for $1286 per once.How much m

Tanzania [10]

Answer:

Chris will make $1905.22 by selling gold.

Step-by-step explanation:

Amount of gold Chris will have = 42 g

Current rate of gold = $1286 per ounce

We need to find the amount Chris will make after selling the gold.

Now we will first find Current rate of gold in grams.

We know that 1 ounce = 28.3495 grams.

So we can say that

28.3495 g = $1286

So 1 g = Rate of gold for 1 gram.

By Using Unitary method we get;

Rate of gold for 1 gram = $\frac{1286}{28.3495} \approx \$45.3624$

Now we will find the amount for 42 g of gold

if 1 g = $45.3624

so 42 g = Amount of money for 42 g

Again by using Unitary method we get;

Amount of money for 42 g = $42 \times 45.3624 \approx \$1905.22$

Hence Chris will make $1905.22 by selling gold.

4 0

3 years ago

Solve for y a. 7 cmb. 20 cmc. 14 cmd. 10 cm​

Solve for y a. 7 cmb. 20 cmc. 14 cmd. 10 cm