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3 years ago

Suppose that a varies inversely with b^2. If a=9 when b=2, find the value of a when b=3.

Mathematics

1 answer:

Archy [21]3 years ago

4 0

Answer:

a = 4

Step-by-step explanation:

We can set up an equation to model this:

a = $\frac{k}{b^2}$

Now, we can plug in the information given to find the value of k:

9 = $\frac{k}{2^2}$

9 = $\frac{k}{4}$

36 = k

Now, we can find the value of a when b = 3.

a = $\frac{36}{3^2}$

a = $\frac{36}{9}$

a = 4

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A spherical fish bowl is half-filled with water. The center of the bowl is C and the length of segment AB is 16 inches as shown

NNADVOKAT [17]

Segment AB is a diameter of the sphere.

diameter = AB = 16 in.

radius = r = (16 in.)/2 = 8 in.

Volume of a sphere:

V = (4/3) * pi * r^3

V = (4/3) * (22/7) * (8 in.)^3

The water inside the bowl occupies half of the bowl, so the volume of the water is half the volume of the bowl.

Volume of water:

V = (1/2)(4/3)(22/7)(8^3) in.^3

Answer: Second choice.

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3 years ago

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The area of a rectangular wall of a barn is 85 square feet. Its length is 12 feet longer than the width. Find the length and wid

MaRussiya [10]

Answer:

Length = 17 feet, Width = 5 feet

Step-by-step explanation:

Given:

The area of a rectangular wall of a barn is 85 square feet.

Its length is 12 feet longer than the width.

Question asked:

Find the length and width of the wall of the barn.

Solution:

Let width of a rectangular wall of a barn = $x$

As length is 12 feet longer than the width.

Length of a rectangular wall of a barn = $12+x$

As we know:

$Area\ of\ rectangle=length\times breadth$

$85=(12+x)x\\\\85=12x+x^{2} \\$

Subtracting both sides by 85

$x^{2} +12x-85=0\\x^{2} +17x-5x-85=0\\Taking\ common\\x+(x+17)-5x(x+17)=0\\(x+17)(x-5)=0\\x+17=0, x-5=0\\x=-17,x=5$

As width can never be in negative, hence width of a rectangular wall of a barn = $x$ = 5 feet

Length of a rectangular wall of a barn = $12+x=12+5=17\ feet$

Therefore, length and width of the wall of the barn is 17 feet and 5 feet respectively.

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3 years ago

(5/8 x - 10) - (1/8 x - 12)

nikklg [1K]

Answer: 16x-25 over 4(4x-5)(2x-3)

Step-by-step explanation:

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3 years ago

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ANSWER ASAP PLEASE!!!!!!!!!!!! THANKS!!!!!!!!! :)

krok68 [10]

Answer: the answer is A

Step-by-step explanation:

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3 years ago

X - y = -2 y = -x - 2 What is the solution

LenKa [72]

Answer:

x = -2

y = 0

Step-by-step explanation:

Pretty hard process, but let me explain:

First, solve for y.

Substitute -x - 2 for y in x - y = -2:

Then, simplify both sides of the equation.

x - y = -2

x - (-x - 2) = -2

After, add -2 to both sides of the equation.

2x + 2 = -2

2x + 2 + -2 = -2 + -2

Next, divided both sides by 2.

2x/2 = -4/2

After that, substitute -2 for x in y = -x - 2:

You must simplify both sides of the equation.

y = -x - 2

y = -(-2) - 2

y = 0

Sorry if this is long and confusing, but I hope this helps!!

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3 years ago