MATHEMATICS COLLEGE

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Answers

Answer 1

Answer:

Answer:

1.7

Step-by-step explanation:

1 + 7/10

= 1 + 0.7

= 1.7

Answer 2

Answer: 1.7 is the correct answer

Solution :

Let's solve by using Pythagoras theorem,

$\hookrightarrow \: (10) {}^(2) = {(x})^(2) + (x + 2) {}^(2)$

$\hookrightarrow \: 100 = {x}^(2) + {x}^(2) + 4x + 4$

$\hookrightarrow \: 100 - 4 = 2 {x}^(2) + 4x$

$\hookrightarrow \: 96 = 2 {x}^(2) + 4x$

$\hookrightarrow \: 2 {x}^(2) + 4x - 96 = 0$

$\hookrightarrow \: 2( {x}^(2) + 2x - 48) = 0$

$\hookrightarrow \: {x}^(2) + 2x - 48 = 0$

$\hookrightarrow \: {x}^(2) + 8x - 6x - 48 = 0$

$\hookrightarrow \: x(x + 8) - 6(x + 8) = 0$

$\hookrightarrow \: (x + 8)(x - 6) = 0$

now there are two cases

Case 1 : when (x + 8) = 0

$\hookrightarrow \: x + 8 = 0$

$\hookrightarrow \: x = - 8$

but the value of x can't be negative, since side of a triangle isn't a negative value .

Case 2 : when (x - 6) = 0

$\hookrightarrow \: x - 6 = 0$

$\hookrightarrow \: x = 6$

therefore the measure of other two sides are :

$\hookrightarrow \: x = 6 \: units$

$\hookrightarrow \: x + 2 = 6 + 2 = 8 \: units$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathrm{TeeNForeveR }$

11/5 divided by 51/4 equals

Answers

When 11/5 is divided by 51/4 then the quotient will be equal to 44/255.

To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

So, to calculate (11/5) ÷ (51/4), we can do the following:

(11/5) ÷ (51/4)

= (11/5) × (4/51)

Now, multiply the numerators and denominators:

Numerator: 11 × 4 = 44

Denominator: 5 × 51 = 255

Therefore, (11/5) ÷ (51/4) = 44/255.

Hence, when 11/5 divided by 51/4 equals to 44/255.

To learn more on Division click:

brainly.com/question/21416852

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Answer:

44/255

Step-by-step explanation:

Since you you are dividing fraction you have to multiply by the reciprocal.

11/5 x 4/51

11 x 4 = 44

51 x 5 = 255

= 44/255

If leah has 22 boxes she gives 12 boxes to her mom how many boxes does leah have left

Answers

Subtract the amount she gives her mom from the total amount she has:

22 - 12 = 10

She has 10 boxes left.

Find the slope of the line that passes through the point (0,-3) and (4,5)

Slope=?

Answers

It depends which pair goes first but the formula is Y2-y1 over x2-x1

Answer: $m=2$

(0,-3) = (x1,y1)

(4,5) = (x2,y2)

Slope = $(y2-y1)/(x2-x1)$

= $(5-(-3))/(4-0)$

= $(5+3)/(4)$

= $(8)/(4)$

= $2$

Which ordered pairs are solutions to the inequality −2x+y≥−4 ?Select each correct answer.

(0, −5)

(3, −1)

(1, −2)

(0, 1)

(−1, 1)

Answers

Answer:

(0,-5) , (1,-2) , (0,1) and (-1,1)

Step-by-step explanation:

-2x + y ≥ -4

y ≥ 2x - 4

Taking a point (0,-5):

-5 ≥ 0 - 4 , 5 ≥ -4

This situation is true.

Taking a point (3,-1):

-1 ≥ 2(3) - 4 , -1 ≥ 2

This situation is not true.

Taking a situation (1,-2):

-2 ≥ 2(1) - 4 , -2 ≥ -2

This situation is true.

Taking a point (0,1):

1 ≥ 0 - 4 , 1 ≥ -4

This situation is true.

Taking a point (-1,1):

1 ≥ 2(-1) - 4 , 1 ≥ -6

This situation is true.

The correct answers are

(−1, −1)

(5, −12)

(0, 1)

Have a nice day!

Let C be the unit circle in the xy-plane, oriented counterclockwise as seen from above. The divergence of the vector field F~ = (z, x, y) is zero, and as a result the flux through every surface with boundary C should be the same. Confirm that this is the case with the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane

Answers

Upper half of the unit sphere (call it $S_1$ ): parameterize by

$\vec s(u,v)=(\cos u\sin v,\sin u\sin v,\cos v)$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to be

$(\partial\vec s)/(\partial v)*(\partial\vec s)/(\partial u)=(\cos u\sin^2v,\sin u\sin^2v,\cos v\sin v)$

Then the flux of $\vec F$ over this surface is

$\displaystyle\iint_(S_1)\vec F\cdot\mathrm d\vec S=\int_0^(\pi/2)\int_0^(2\pi)(\cos v,\cos u\sin v,\sin u\sin v)\cdot(\cos u\sin^2v,\sin u\sin^2v,\cos v\sin v)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^(\pi/2)\int_0^(2\pi)\cos u\sin^2v\cos v+\cos u\sin u\sin^3v+\sin u\cos v\sin^2v=\boxed{0}$

Lower half of the sphere (call it $S_2$ ): all the details remain the same as above, but with $\frac\pi2\le v\le\pi$ . The flux is again $\boxed{0}$ .

Unit disk (call it $D$ ): parameterize the disk by

$\vec s(u,v)=(u\cos v,u\sin v,0)$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to be

$(\partial\vec s)/(\partial u)*(\partial\vec s)/(\partial v)=(0,0,u)$

Then the flux across $D$ is

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^(2\pi)\int_0^1(0,u\cos v,u\sin v)\cdot(0,0,u)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^(2\pi)\int_0^1u^2\sin v\,\mathrm du\,\mathrm dv=\boxed{0}$

Final answer:

The flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same and it is zero.

Explanation:

The divergence of the vector field F~ = (z, x, y) is zero. Therefore, the flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same.

This can be confirmed by considering that the electric flux through a closed surface is zero if there are no sources of electric field inside the enclosed volume. Since there are no charges inside the surfaces mentioned, the flux through each surface is zero.

Therefore, the flux through the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane is the same, and it is zero.