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Sunny_sXe [5.5K]
3 years ago
7

What is -3/2 - 7/4 + 1/8

Mathematics
1 answer:
Eddi Din [679]3 years ago
3 0

Answer:

3/8

Step-by-step explanation:

-3/2 can change to -12/8

7/4 can change to 14/8

1/8 stays the same

-12/8 + 14/8 = 2/8 + 1/8 = 3/8

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Someone plsss help me quick
Marina CMI [18]

Answer:

15b + 30

Step-by-step explanation:

By expansion (6 x 2.5b) + (6 x 5)

= 15b + 30

5 0
3 years ago
The coordinates of the community center are (5, −1). Who has a house in the same quadrant as the community center?
WINSTONCH [101]
(5,-1) is located in quadrant IV......quadrant IV has (+ x, -y).....so any points that have (+ x, - y) are in this quadrant. 
Example : (6,-3) is in this quadrant......(2,-4) is also in this quadrant. 
So whoever has the house with (+ x, -y) is going to be in the same quadrant as the community center.
3 0
3 years ago
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Does (3,5) and (-3,-5) lie in the same quadrant
Arlecino [84]

Answer:

no they don't one lies in  quadrant 1 while the other is in quadrant 3

Step-by-step explanation:

4 0
3 years ago
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Find an equation of the tangent plane to the given parametric surface at the specified point.
Neko [114]

Answer:

Equation of tangent plane to given parametric equation is:

\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}

Step-by-step explanation:

Given equation

      r(u, v)=u cos (v)\hat{i}+u sin (v)\hat{j}+v\hat{k}---(1)

Normal vector  tangent to plane is:

\hat{n} = \hat{r_{u}} \times \hat{r_{v}}\\r_{u}=\frac{\partial r}{\partial u}\\r_{v}=\frac{\partial r}{\partial v}

\frac{\partial r}{\partial u} =cos(v)\hat{i}+sin(v)\hat{j}\\\frac{\partial r}{\partial v}=-usin(v)\hat{i}+u cos(v)\hat{j}+\hat{k}

Normal vector  tangent to plane is given by:

r_{u} \times r_{v} =det\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]

Expanding with first row

\hat{n} = \hat{i} \begin{vmatrix} sin(v)&0\\ucos(v) &1\end{vmatrix}- \hat{j} \begin{vmatrix} cos(v)&0\\-usin(v) &1\end{vmatrix}+\hat{k} \begin{vmatrix} cos(v)&sin(v)\\-usin(v) &ucos(v)\end{vmatrix}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u(cos^{2}v+sin^{2}v)\hat{k}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u\hat{k}\\

at u=5, v =π/3

                  =\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k} ---(2)

at u=5, v =π/3 (1) becomes,

                 r(5, \frac{\pi}{3})=5 cos (\frac{\pi}{3})\hat{i}+5sin (\frac{\pi}{3})\hat{j}+\frac{\pi}{3}\hat{k}

                r(5, \frac{\pi}{3})=5(\frac{1}{2})\hat{i}+5 (\frac{\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}

                r(5, \frac{\pi}{3})=\frac{5}{2}\hat{i}+(\frac{5\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}

From above eq coordinates of r₀ can be found as:

            r_{o}=(\frac{5}{2},\frac{5\sqrt{3}}{2},\frac{\pi}{3})

From (2) coordinates of normal vector can be found as

            n=(\frac{\sqrt{3} }{2},-\frac{1}{2},1)  

Equation of tangent line can be found as:

  (\hat{r}-\hat{r_{o}}).\hat{n}=0\\((x-\frac{5}{2})\hat{i}+(y-\frac{5\sqrt{3}}{2})\hat{j}+(z-\frac{\pi}{3})\hat{k})(\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k})=0\\\frac{\sqrt{3}}{2}x-\frac{5\sqrt{3}}{4}-\frac{1}{2}y+\frac{5\sqrt{3}}{4}+z-\frac{\pi}{3}=0\\\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}

5 0
3 years ago
Identify which of the following statement(s) is always true?
julia-pushkina [17]

Answer:

Statement 3

Step-by-step explanation:

<u>Statement 1:</u> For any positive integer n, the square root of n is irrational.

Suppose n = 25 (25 is positive integer), then

\sqrt{n}=\sqrt{25}=5

Since 5 is rational number, this statement is false.

<u>Statement 2:</u> If n is a positive integer, the square root of n is rational.

Suppose n = 8 (8 is positive integer), then

\sqrt{n}=\sqrt{8}=2\sqrt{2}

Since 2\sqrt{2} is irrational number, this statement is false.

<u>Statement 3:</u> If n is a positive integer, the square root of n is rational if and only if n is a perfect square.

If n is a positive integer and square root of n is rational, then n is a perfect square.

If n is a positive integer and n is a perfect square, then square root of n is a rational number.

This statement is true.

8 0
3 years ago
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