How many pints are in6 1/2quarts? A: 3 1/4pt B: 13 pt C:19 1/2pt D: 26 pt

What are the solutions to the equation x2 + 3 = 124? A. –3 and 3 B. –11 and 11 C. The equation has no solutions. D. –10

Ronch [10]

$x^2 + 3 = 124 \ \ |-124\\ \\x^2+3-124 = 124 -124 \\ \\ x^2-121 =0\\ \\x^2-11^2=0 \\ \\ (x-11)(x+11)=0\\ \\x-11=0 \ \ or \ \ x+11 =0\\ \\x=11 \ \ or \ \ x=-11 \\ \\Answer : B. \ \ -11 \ and \ \ 11 \\ \\ \\ a^2-b^2=(a-b)(a+b) 
$

3 0

4 years ago

Mr. Lin received a box of books in the shape of a rectangular prism. The volume of the box is 486 in 3. What is the width of the

GREYUIT [131]

Answer:

W = 9 inches.

Step-by-step explanation:

The volume of a rectangular prism is given by

$V=whl$

Where

w,h and l re width, height and length of rectangular prism

It is not mentioned that a box has a length of 18 inches and a height of 3 inches.

Using above formula.

$486=w\times 18\times 3\\\\486=54w\\\\w=9\ \text{inches}$

So, the width of the box is 9 inches.

5 0

3 years ago

Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Anestetic [448]

Answer:

Step-by-step explanation:

Let the rectangle have (x,y,z) as vertex in positive octant. The rectangular box has to be necessarily symmetrical about all the three axes.

Then the sides of the box would be

$2x,2y,2z$

Volume = $8xyz$

Maximize volume subject to

$x^2+y^2+z^2 =1$

i.e. $g(x,y,z) = x^2+y^2+z^2 -1=0$

Use Lagrangian multipliers , we have

$∇f(x,y,z)=λ∇g(x,y,z)$ at the maximum

$∇f(x,y,z)=λ∇g(x,y,z) =(8yz,8xz,8xy)\\∇g(x,y,z)=(2x,2y,2z)$

$8yz=2λx8xz=2λy8xy=2λz$

Dividing we get

$\frac{y}{x} =\frac{x}{y} \\x^2=y^2$

Similarly $y^2=z^2$

Thus we get $3x^2 =1\\x = \frac{1}{\sqrt{3} }$

Hence dimensions are

(2x,2y,2z)

So dimensions are

$\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } ,\frac{2}{\sqrt{3} } )$

3 0

3 years ago

What should we subtract from 50/29 to get 24

Scrat [10]

Answer:

-22.28

Step-by-step explanation:

Let the number to be subtracted from 50/29 to get 24 to be x

So this can be written as : 50/29 - x =24 ----collect like terms as

50/29 - 24 = x

1.72 -24 = x

-22.28 = x

So to check the answer;

50/29 -{x} = 24

50/29 - {- 22.28} = 24

1.72+ 22.28 = 24 ---correct.

7 0

3 years ago

How many years will it take an account to double in value, assuming a 5.2% interest rate compounded quarterly? Round your answer

zhuklara [117]

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years.

<h3>How to determine the doubling time of money account</h3>

The compound interest takes into account the change of money deposited in time in contrast with the simple interest, which only takes the initial amount of money into account. Please notice that four quarters equals a year.

The compound interest formula is described below:

C = C' · (1 + r/100)ⁿ (1)

Where:

r - Interest rate
n - Number of periods
C' - Initial money amount
C - Current money amount

If we know that C = 2 · C' and r = 5.2, then the doubling time is:

n = /㏒ C/C'/㏒ (1 + r/100)

n = ㏒ 2/㏒ 1.052

n ≈ 13.674

The money account is doubled at an interest rate of 5.2 % compunded quarterly, that is, under the model of compound interest in a time period of about 3.5 years. $\blacksquare$

To learn more on compound interests, we kindly invite to check this verified question: brainly.com/question/14295570

7 0

2 years ago

How many pints are in​6 1/2​quarts? A: 3 1/4​pt B: 13 pt C:19 1/2​pt D: 26 pt

How many pints are in6 1/2quarts? A: 3 1/4pt B: 13 pt C:19 1/2pt D: 26 pt