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2 years ago

Are 3:5and 1:2 equivalent

Mathematics

2 answers:

german2 years ago

6 0

Answer:

No. They are not equivalent.

Step-by-step explanation:

$\frac{3}{5} \neq \frac{1}{2}$

=> $\frac{6}{10} \neq \frac{5}{10}$

Therefore, 3/5 and 1/2 are not equivalent.

Hoped this helped.

seropon [69]2 years ago

6 0

Answer:

yes

Step-by-step explanation:

they are equivalent

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Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi

Liono4ka [1.6K]

Answer:

a) $f (x,y,z)= xy^2\sin(z)$

b) $\int_C F \cdot dr =0$

Step-by-step explanation:

Recall that given a function f(x,y,z) then $\nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})$ . To find f, we will assume it exists and then we will find its form by integration.

First assume that F = $\nabla f$ . This implies that

$\frac{\partial f}{\partial x} = y^2\sin(z)$ if we integrate with respect to x we get that

$f(x,y,z) = xy^2\sin(z) + g(y,z)$ for some function g(y,z). If we take the derivative of this equation with respect to y, we get

$\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}$

This must be equal to the second component of F. Then

$2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)$

This implies that $\frac{\partial g}{\partial y}=0$ , which means that g depends on z only. So $f(x,y,z) = xy^2\sin(z) + g(z)$

Taking the derivative with respect to z and making it equal to the third component of F, we get

$xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)$

which implies that $\frac{dg}{dz}=0$ which means that g(z) = K, where K is a constant. So

$f (x,y,z)= xy^2\sin(z)$

b) To evaluate $\int_C F \cdot dr$ we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

$\int_C F \cdot dr = f(r(\pi))-f(r(0))$

Recall that $r(\pi) = (\pi^2, 0, \pi)$ so $f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0$

Also $r(0) = (0, 0, 0)$ so $f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0$

So $\int_C F \cdot dr =0$

5 0

3 years ago

Solve question 10 using substitution or elimination. Show all work.

BlackZzzverrR [31]

Solid paper costs 1.75 each
Printed paper costs 2.50 each

Given:
Ben = $43.50 (12 rolls solid paper and 9 rolls of
printed paper)
Joel = $51.50 (8 rolls solid paper and 15 rolls of
printed paper)
Let x = solid paper
Let y= printed paper
12x + 9y = 43.50
8x + 15y = 51.50

Find X:
8x + 15y = 51.50
8x = 51.50 - 15y
x= (51.50 - 15y)8

Substitute X:
12x + 9y = 43.50
12(51.50 - 15y)/8 + 9y = 43.50
(618 - 180y)/8 + 9y = 43.50
8 (618 - 180y)/8 + 8*9y = 43.50 * 8
618-180y + 72y =348
-108y = 348 - 618
-108y =-270
-108y/-108=-270/-108

Y= 2.50

x = (51.50 - 15y)/8
x = (51.50 - 15(2.5) /8
x= (51.50 - 37.50\8
X = 14/8

X = 1.75

To check: x = 1.75; y = 2.5
12x + 9y = 43.50
12(1.75) + 9(2.5) = 43.50
21 + 22.50 = 43.50
43.50 = 43.50
8x + 15y = 51.50
8(1.75) + 15(2.5) = 51.50
14 + 37.50 = 51.50
51.50 = 51.50

Hope that helps! Have a good day :)

5 0

2 years ago

What is the total surface area of this square pyramid?

slamgirl [31]

Answer:

The total surface area of this square pyramid is $297\ mm^{2}$

Step-by-step explanation:

we know that

The surface area of a square pyramid is equal to

$SA=b^{2} +4[\frac{1}{2}(b)(h)]$

we have

$b=9\ mm$ ----> the length side of the square base

$h=12\ mm$ ----> the height of the triangular faces

substitute the values

$SA=9^{2} +4[\frac{1}{2}(9)(12)]=297\ mm^{2}$

4 0

3 years ago

A manufacturing company with 450 employees begins a new product line and must increase their number of employees by 18%. How man

nika2105 [10]

The answer would <span>531. You would add 18% more employees to the company so the answer is 531. I really hope this helped you. Have a nice day!</span>

4 0

3 years ago

The thirrdgrade Class Is GOING ON A FIELD TRIP BY BUS TO THE MUESUEM THE BUS LEAVES THE SCHOOL AT 9;45 A.M. THE BUS RIDE TAKES 4

torisob [31]

9:60 is one hours
it takes 15 mins to get to 60
47-15=32

9:45+47=9:45+15:32=10:00+32=10:32 AM

7 0

3 years ago