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2 years ago

A rectangular beam will be cut from a cylindrical log of radius 10 inches.

Mathematics

1 answer:

QveST [7]2 years ago

4 0

Answer:

Step-by-step explanation:

pls mark me brainless pls

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Find the area enclosed by x2=2y and y2=16x

jekas [21]

Answer: $\dfrac{32}{3}$

Step-by-step explanation:

Given

The parabolas are $x^2=2y$ and $y^2=16x$

Find the point of intersection of two parabolas

$\Rightarrow \left(\dfrac{x^2}{2}\right)^2=16x\\\\\Rightarrow x^4=64x\\\Rightarrow x(x^3-64)=0\\\Rightarrow x=0,4$

Obtain y using x

$(x,y)\rightarrow (0,0)\ \text{and }(4,8)$

Area enclosed between the two is

$\Rightarrow I=\int\limits^4_0 ({4\sqrt{x}-\dfrac{x^2}{2}}) \, dx\\\\\Rightarrow I=\left ( 4\times \dfrac{2}{3}x^{\frac{3}{2}}-\dfrac{x^3}{2\times 3} \right) _0^4\\\\\Rightarrow I=\left ( \dfrac{8}{3}\times 8-\dfrac{4^3}{6} \right )-0\\\\\Rightarrow I=\dfrac{128-64}{6}\\\\\Rightarrow I=\dfrac{64}{6}\\\\\Rightarrow I=\dfrac{32}{3}$

Thus, the area bounded by the two parabolas is $\dfrac{32}{3}$ sq. units.

4 0

3 years ago

Prove that : 1/1-secA + 1/1+secA = -2cot^2A

irina1246 [14]

Answer:

Step-by-step explanation:

LHS = 1/1-secA + 1/1+secA

$= \frac{1*(1+Sec A)}{(1-Sec A)(1+Sec A)}+\frac{1*(1-Sec A)}{(1+Sec A)*(1-Sec A)}\\\\=\frac{(1+Sec A)}{1-Sec^{2} A}+\frac{(1-Sec A)}{1-Sec^{2} A}\\\\=\frac{1+Sec A+1-Sec A}{(1-Sec^{2} A)}\\\\= \frac{2}{(1-Sec^{2} A)}\\\\=\frac{2}{-(Sec^{2} A - 1)}\\\\= \frac{-2}{Tan^{2} A}\\\\= -2Cot^{2} A$

7 0

3 years ago

Can you answer these please? Show all work

Ganezh [65]

Answer:

i) Sally' s grocery bill = c - $\frac{5}{100}$ c = 0.95c

Therefore the correct option is B.)

ii) Therefore the expression which represents the expected population

next year is given by :

= p + $\dfrac{7.5}{100}$ p = 1.075p

Therefore the correct option is B.)

Step-by-step explanation:

Sally has a discount card that reduces the price of her grocery bill in a certain grocery store by 5%.

Let c represent the cost of Sally's groceries.

therefore the expression which represents Sally's grocery bill is given by :

Sally' s grocery bill = c - $\frac{5}{100}$ c = 0.95c

Therefore the correct option is B.)

The population of a city is expected to increase by 7.5% next year If p represents the current population, which expression represents the expected population next year?

Let p = current population of a city.

Therefore the expression which represents the expected population next year is given by :

= p + $\dfrac{7.5}{100}$ p = 1.075p

Therefore the correct option is B.)

8 0

3 years ago

Plz help; look at the picture

Ksenya-84 [330]

All the linear functions in form y = mx + b where m ≠ 0 has the inverse in form
y = x/m - b/m.
Answer: The inverse of f exist.

4 0

3 years ago

Shiva bought a second hand motorcycle for rupees 153200 his spent to 1200 to repair it and sold it to vishnu at 8% loss. how muc

Alecsey [184]

Answer:

142048

Step-by-step explanation:

8 0

3 years ago