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Nadya [2.5K]
3 years ago
11

Rectangle ABCD has vertex coordinates A(1, -2), B(4,-2),

Mathematics
1 answer:
Tomtit [17]3 years ago
8 0

\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}

Actually Welcome to the concept of Locus of a shape.

Here, the left movement is in x direction and vertical or up movement is in the y direction.

so we get as,

A(1,-2) ==> 1 towards left => 0

and 3 units up => 1

hence the new co-ordinates are A(0,1)

hence, A(0,1) is correct option

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Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x2 + y2 = 25 and the sphere x2 + y2
Inessa05 [86]

Answer:

Step-by-step explanation:

we are asked to find the volume of solid that lies within both the cylinder

x^2 + y^2 = 25

and

the spherex^2 + y^2 + z^2 = 49.

Conversion from rectangular to cylindrical is

x=rcost\\y = rsint\\z=z

|J| =r

In cylindrical coordinates the volume is bounded by the cylinder r=5 and

r^2+z^2 =49

Hence we can write volume as

\int \int \int dxdydz\\=\\\int _0^5 \int_0^{2\pi} \int_{-\sqrt{49-r^2} } ^{\sqrt{49-r^2} rdzdtdr\\= 2\pi \int _0^5 (2\sqrt{49-r^2} rdr\\=4\pi (-(49-r^2) (2/3)\\= \frac{4\pi}{3} (343-48\sqrt{6} )

6 0
3 years ago
Let ​ x^2−12x=61 .​
Anuta_ua [19.1K]
The answer for the first blank is 36 and the answer for the second blank is 97.

To complete the square, we first take half of the value of b.  The value of b in this equation is -12; -12/2 = -6.

Next we square the value we just got: (-6)² = 36.

This is what we add to both sides of the equation, giving us:
x²-12x+36=61+36

Combining like terms on the right, we have
x²-12x+36=97
4 0
3 years ago
Read 2 more answers
what is the difference between the commutative distributive and associative properties when multiplying?
Fantom [35]
<span>The associative rule is a rule about when it's safe to move parentheses around. You can remember that because the parentheses determine which expressions you have to do first--which numbers can associate with each other. It looks like this:

For addition: (a + b) + c = a + (b + c)
For multiplication: (ab)c = a(bc)

The commutative property is about which operations you can do backward and forward. You can remember this by thinking of people commuting to work: they go to work every morning, then they repeat the same operation backward when they commute home. It looks like this:

For addition: a + b = b + a
For multiplication: ab = ba

Finally, the distributive property tells you what happens when you distribute one operation against another kind in parentheses. It looks like this:

a * (b + c) = ab + ac

In other words, the a is "distributed" over the b and c.

Of course, you can make these work together:

a * (b + (c + d))
= a * ((b + c) + d) (by the associative property)
= a * (d + (b + c)) (by the commutative property)
= ad + a (b + c) (by the distributive property)
= ad + ab + ac (by the distributive property again).

Hope this helps. </span>
6 0
3 years ago
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