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3 years ago

Can you help me with this?|a^2| if a<0

Mathematics

1 answer:

7nadin3 [17]3 years ago

3 0

Answer:

|(-a)²| = | a² | = a²

Step-by-step explanation:

absolute value is always positive number as well as any number squared so sign is positive no matter what

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What is the volume of the rectangular prism if the length is 3/4 the width is 2/3 and the hight is 1/2

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4 years ago

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3 years ago

Five years ago, Victor was twice as old as his daughter Anika. In 10 years, the sum of their ages will equal 90. Find their ages

frozen [14]

Answer: 45 and 25

Step-by-step explanation:

Given

Five years ago victor was twice as old as his daughter

Suppose the current age of victor and his daughter are x and y

For five years ago

$\Rightarrow (y-5)=2(x-5)\\\Rightarrow y-5=2x-10\\\Rightarrow y=2x-5\\\Rightarrow 2x-y=5\quad \ldots(i)$

In 10 years sum of their ages is 90

$\Rightarrow (y+10)+(x+10)=90\\\Rightarrow x+y=70\quad \ldots(ii)$

On solving (i) and (ii) we get

$\Rightarrow x=25,y=45$

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2 years ago

(a) Find parametric equations for the line through (1, 4, 4) that is perpendicular to the plane x − y + 2z = 7. (Use the paramet

Alex777 [14]

Answer:

$x=1+t\\y=4-t\\z=4+2t$

Step-by-step explanation:

A vector perpendicular to the plane ax+by+cz+d=0 is of the form $(a,b,c)$ .

So, a vector perpendicular to the plane x − y + 2z = 7 is $(1,-1,2)$ .

The parametric equations of a line through the point $(x_0,y_0,z_0)$ and parallel to the vector $(a,b,c)$ are as follows:

$x=x_0+at\\y=y_0+bt\\z=z_0+ct$

Put $(x_0,y_0,z_0)=(1,4,4)$ and $(a,b,c)=(1,-1,2)$

Therefore,

$x=1+t\\y=4-t\\z=4+2t$

xy-plane:

Put z = 0 ⇒ t = -2 ⇒x = - 1 , y = 6

So, at point (-1,6,0)

yz-plane:

Put x = 0 ⇒ t = -1 ⇒ y = 5, z =2

So, at point (0,5,2)

xz-plane:

Put y = 0 ⇒ t = 4 ⇒ x = 5, z = 12

So, at point (5,0,12)

5 0

3 years ago