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2 years ago

The bucket is in the form of a cylinder whose radius is 5 feet and height is 8 inches. Find the volume of the cylinder.

Mathematics

1 answer:

ivann1987 [24]2 years ago

4 0

Answer:

k h098j0

Step-by-step explanation:

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Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

$x^4-(3m+2)x^2+m^2=0$

$x^4+0x^3-(3m+2)x^2+0x+m^2=0$

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

$a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}$

$=\frac{0}{1}=0$

$\implies a=0----(1)$

$(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}$

$=\frac{-3m-2}{1}$

$3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2$

$-10b^2=-3m-2$

$\implies b^2=\frac{3m+2}{10}-----(2)$

$(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2$

$9b^4=m^2$

$9(\frac{3m+2}{10})^2=m^2$

$9(\frac{9m^2+4+12m}{100})=m^2$

$81m^2+36+108m=100m^2$

$-19m^2+108m+36=0$

$19m^2-108m-36=0$

$19m^2-114m+6m-36=0$

$19m(m-6)+6(m-6)=0$

$(19m+6)(m-6)=0$

$\implies m=-\frac{6}{19}\text{ or }m=6$

But m > 0,

Hence, the value of m is 6.

4 0

3 years ago

List the elements in the set.<br> 1) {x 1 x is an integer between -7 and -3}

omeli [17]

Answer:

सामाजिक अध्ययन र जिवनोपयोगी शिक्षाको महत्व दसांउनुहोस

8 0

1 year ago

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 4 . If there were

Kamila [148]

If there were 5 yes votes for every 4 no votes, there were 5 yes votes for every 9 total votes, so 5/9 of the 7911 votes were yes. 5/9*7911=4395.

7 0

2 years ago

What are the next two numbers in this pattern? 3, â9, 27, â81, . . ?

hjlf

729, <span>â6561 is the answer</span>

4 0

3 years ago

Analyze the diagram below and complete the instructions that follow?

yan [13]

Answer:

The exact value of tan(M) is 5/12 ⇒ answer (C)

Step-by-step explanation:

* Lets revise the trigonometry functions

- In ΔABC

# m∠B = 90°

# Length of AB = a , length of BC = b and length of AC = c

# The trigonometry functions of angle C are

- sin(C) = a/c ⇒ opposite side to ∠C ÷ the hypotenuse

- cos(C) = b/c ⇒ adjacent side to ∠C ÷ the hypotenuse

- tan(c) = a/b ⇒ opposite side to ∠C ÷ adjacent side to ∠C

* Now lets solve the problem

- In ΔONM

∵ m∠N = 90°

∵ MN = 12

∵ ON = 5

∵ tan(M) = ON/NM ⇒ opposite side of ∠(M) ÷ adjacent side of ∠(M)

∴ tan(M) = 5/12

* The exact value of tan(M) is 5/12

6 0

3 years ago