All categories

3 years ago

What is 1 and 1/6 minus 7/12 ?

1 answer:

7 0

$1 \frac{1}{6} - \frac{7}{12} \\ 
 \\ 1 \frac{1}{6}= \frac{1x6+1}{6}= \frac{7}{6} \\ 
 \\ \frac{7x2}{6x2}= \frac{14}{12} \\ 
 \\ \frac{7x1}{12x1}= \frac{7}{12} \\ 
 \\ \frac{14}{12} - \frac{7}{12}= \frac{7}{12} \\ 
 \\ Solution: \frac{7}{12} 
$

You might be interested in

Thrice the product of two and "Y".

love history [14]

Answer:

Step-by-step explanation:

We need to solve the statement ' Thrice the product of two and "Y" '.

Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.

Let the result is R. It can be calculated as follows :

$R=3\times 2\times Y$

We know that, 3×2 = 6

So,

$R=6Y$

Hence, Thrice the product of two and "Y" is 6Y.

6 0

3 years ago

What is the true solution to the logarithmic equation below?<br> log₂ (6x)-log₂ (√x)=2

slega [8]

Answer:

The true solution is x=4/9

EXPLANATION

The logarithmic equation given to us is

We need to use the quotient rule of logarithms.

When we apply this law the expression becomes

We now take the antilogarithm of both sides to get

We square both sides to get,

We evaluate to obtain,

This simplifies to

We divide both sides by 36 to get

We simplify to get,

6 0

2 years ago

Read 2 more answers

What is the distance between the point (-7,3) and (4, -5) on a coordinate plane?

Evgesh-ka [11]

To find this, use the distance formula. D= square root over... (x2-x1)^2+ (y2-y1)^2. Now plug in your coordinates.
D= square root... (4- -7)^2+ (-5-3)^2. Simplify. 4- -7=11 (two neg= positive) -5 -3= -8. So,
D= square root... 11^2+ -8^2. Simplify. 11^2= 121. And -8^2=64. Now just take the square root after adding. 121+64= 185. And the square root of 185 isn’t a whole number, so your final answer is D= (square root over) 185. Hope this helps

7 0

3 years ago

Question 13

natali 33 [55]

Answer:

y - 7 = (x + 5)

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

Slope(m) = 1

Point: (-5, 7) = (x1, y1)

To write the equation in point-slope form, we need to know the slope and one point. Since we were already given the values of the slope and one point, all we have to do is input those values into the equation:

y - y1 = m(x - x1)

y - 7 = 1(x - (-5))

y - 7 = (x + 5)

The equation in point-slope form is: y - 7 = (x + 5)

7 0

2 years ago

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves

Vadim26 [7]

The expression on the left side describes a parabola. Factorize it to determine where it crosses the y-axis (i.e. the line x = 0) :

-3y² + 9y - 6 = -3 (y² - 3y + 2)

… = -3 (y - 1) (y - 2) = 0

⇒ y = 1 or y = 2

Also, complete the square to determine the vertex of the parabola:

-3y² + 9y - 6 = -3 (y² - 3y) - 6

… = -3 (y² - 3y + 9/4 - 9/4) - 6

… = -3 (y² - 2•3/2 y + (3/2)²) + 27/4 - 6

… = -3 (y - 3/2)² + 3/4

⇒ vertex at (x, y) = (3/4, 3/2)

I've attached a sketch of the curve along with one of the shells that make up the solid. For some value of x in the interval 0 ≤ x ≤ 3/4, each cylindrical shell has

radius = x

height = y⁺ - y⁻

where y⁺ refers to the half of the parabola above the line y = 3/2, and y⁻ is the lower half. These halves are functions of x that we obtain from its equation by solving for y :

x = -3y² + 9y - 6

x = -3 (y - 3/2)² + 3/4

x - 3/4 = -3 (y - 3/2)²

-x/3 + 1/4 = (y - 3/2)²

± √(1/4 - x/3) = y - 3/2

y = 3/2 ± √(1/4 - x/3)

y⁺ and y⁻ are the solutions with the positive and negative square roots, respectively, so each shell has height

(3/2 + √(1/4 - x/3)) - (3/2 - √(1/4 - x/3)) = 2 √(1/4 - x/3)

Now set up the integral and compute the volume.

$\displaystyle 2\pi \int_{x=0}^{x=3/4} 2x \sqrt{\frac14 - \frac x3} \, dx$

Substitute u = 1/4 - x/3, so x = 3/4 - 3u and dx = -3 du.

$\displaystyle 2\pi \int_{u=1/4-0/3}^{u=1/4-(3/4)/3} 2\left(\frac34 - 3u\right) \sqrt{u} \left(-3 \, du\right)$

$\displaystyle -12\pi \int_{u=1/4}^{u=0} \left(\frac34 - 3u\right) \sqrt{u} \, du$

$\displaystyle 12\pi \int_{u=0}^{u=1/4} \left(\frac34 u^{1/2} - 3u^{3/2}\right) \, du$

$\displaystyle 12\pi \left(\frac34\cdot\frac23 u^{3/2} - 3\cdot\frac25u^{5/2}\right) \bigg|_{u=0}^{u=1/4}$

$\displaystyle 12\pi \left(\frac12 u^{3/2} - \frac65u^{5/2}\right) \bigg|_{u=0}^{u=1/4}$

$\displaystyle 12\pi \left(\frac12 \left(\frac14\right)^{3/2} - \frac65\left(\frac14\right)^{5/2}\right) - 12\pi (0 - 0)$

$\displaystyle 12\pi \left(\frac1{16} - \frac3{80}\right) = \frac{12\pi}{40} = \boxed{\frac{3\pi}{10}}$

6 0

1 year ago