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3 years ago

2/3 + 1/4 what is a simplified expression?

Mathematics

1 answer:

Anna35 [415]3 years ago

5 0

Answer:

11/12

Step-by-step explanation:

We need to get a common denominator of 12

2/3 *4/4 = 8/12

1/4 *3/3 = 3/12

2/3 +1/4

8/12+3/12

11/12

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The radius of the base of a cylinder is 38 mm and its height is 51 mm. Find the surface area of the cylinder in terms of π.

KIM [24]

C 6764
You need to find the total surface area which is 21249.73271
Then times each option (a,b,c,d) by pi to see if you get 21249.7321

6 0

4 years ago

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Use a triple integral to find the volume of the tetrahedron T bounded by the planes x+2y+z=2, x=2y, x=0 and z=0

Tanzania [10]

Answer:

Volume of the Tetrahedron T = $\frac{1}{3}$

Step-by-step explanation:

As given, The tetrahedron T is bounded by the planes x + 2y + z = 2, x = 2y, x = 0, and z = 0

We have,

z = 0 and x + 2y + z = 2

⇒ z = 2 - x - 2y

∴ The limits of z are :

0 ≤ z ≤ 2 - x - 2y

Now, in the xy- plane , the equations becomes

x + 2y = 2 , x = 2y , x = 0 ( As in xy- plane , z = 0)

Firstly , we find the intersection between the lines x = 2y and x + 2y = 2

∴ we get

2y + 2y = 2

⇒4y = 2

⇒y = $\frac{2}{4} = \frac{1}{2}$ = 0.5

⇒x = 2( $\frac{1}{2}$ ) = 1

So, the intersection point is ( 1, 0.5)

As we have x = 0 and x = 1

∴ The limits of x are :

0 ≤ x ≤ 1

Also,

x = 2y

⇒y = $\frac{x}{2}$

and x + 2y = 2

⇒2y = 2 - x

⇒y = 1 - $\frac{x}{2}$

∴ The limits of y are :

$\frac{x}{2}$ ≤ y ≤ 1 - $\frac{x}{2}$

So, we get

Volume = $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}\int\limits^{2-x-2y}_{z=0} {dz} \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{[z]}\limits^{2-x-2y}_0 {} \, \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{(2-x-2y)} \, \, dy \, dx$

= $\int\limits^1_0 {[2y-xy-y^{2} ]}\limits^{1-\frac{x}{2}} _{\frac{x}{2} } {} \, \, dx$

= $\int\limits^1_0 {[2(1-\frac{x}{2} - \frac{x}{2}) -x(1-\frac{x}{2} - \frac{x}{2}) -(1-\frac{x}{2}) ^{2} + (\frac{x}{2} )^{2} ] {} \, \, dx$

= $\int\limits^1_0 {(1 - 2x + x^{2} )} \, \, dx$

= ${(x - x^{2} + \frac{x^{3}}{3} )}\limits^1_0$

= 1 - 1² + $\frac{1^{3} }{3}$ - 0 + 0 - 0

= 1 - 1 + $\frac{1 }{3}$ = $\frac{1}{3}$

So, we get

Volume = $\frac{1}{3}$

7 0

3 years ago

A. True/False

ra1l [238]

Answer:

True

Step-by-step explanation:

$x^{2} -6x=9$

subtract $9$ from both sides

$x^{2} -6x-9$

<em>plz mark me brainliest.</em> ;)

5 0

3 years ago

Evaluate the expression. 108÷9⋅(−12)÷6−(100÷5)

nata0808 [166]

108/9 * (-12) /6 -(100/5) simplifies to

12*-2-20 which is -44.

7 0

3 years ago

Read 2 more answers

For each function below, find its domain and then determine if the function increasing, decreasing, or constant on each piece of

VashaNatasha [74]

Answer:

Domain: all real numbers

The interval on which the function is increasing is : (0 , infinity)

The interval on which the function is decreasing is : (-infinity , 0)

The interval on which the function is constant is : ( 0,0 )

Step-by-step explanation:

f(r)=5r^2−4

This is a quadratic function.

vertex at (0, -4) and with positive coefficient for r^2

The interval on which the function is increasing is : (0 , infinity)

The interval on which the function is decreasing is : (-infinity , 0)

The interval on which the function is constant is : ( 0,0 )

8 0

4 years ago