All categories

2 years ago

Which expression is equivalent to (27.3 5.9)47

Mathematics

1 answer:

sattari [20]2 years ago

8 0

The correct answer is Option 4.

You might be interested in

Please help<br> What is the slope of the line?<br><br> m =

Nitella [24]

Answer:

1/4

Step-by-step explanation:

rise over run

6 0

3 years ago

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

HELP!!!!!!! I WIL MAKE MARK YOU BRAINLIAST

Finger [1]

Answer:

M is 1.5

Step-by-step explanation:

Use M = 1/O

Replace 1 with a letter such as K

So you use M = K/O

Substitute values

0.5 = K/6

To get K times 0.5 by 6

You get 3

So K=3

Use the equation from the start to find M

M=3/2

M IS 1.5

8 0

4 years ago

Alfonso bought 1/2 pound of raisins, 2/5 pound of walnuts, and 1/3 pound of almonds. Write a comparison statement comparing the

elixir [45]

2/5 lbs walnuts > 1/3 lbs almonds
Hope this helped ;)

5 0

3 years ago

Read 2 more answers

Item cost $490 before tax, and the sales tax is $24.50

Advocard [28]

Answer: 5%

Step-by-step explanation:

Item Cost - $490

Tax - $24.50

Tax/Price = 24.50/490.00 = 0.05

0.05 *100 (for percent) = 5%

Check your work:

490.00*0.05 = 24.50

7 0

3 years ago

Read 2 more answers