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3 years ago

5. The length of a rectangle is 3 inches less than its width. If the

Mathematics

1 answer:

artcher [175]3 years ago

5 0

Answer:

length is 17 in, width is 20

Step-by-step explanation:

let's shape this as an algebraic equation, where x= the length of one side.

since the width is 3 inches longer than the length, x will be the length and x+3 will be the width.

the perimeter is 74 in, and the perimeter is the added length of all sides. in a rectangle, 2 sides are the length and 2 sides are the width, so:

74 = 2x + 2(x + 3)

let's distribute the 2.

74 = 2x + 2x + 6

now, we combine the x's.

74 = 4x + 6

after this step, subtract 6 from the right to add it to the left side.

68 = 4x

finally, divide both sides by 4.

17 = x

perfect! now that we know the length, we just have to add 3 to find the width.

17 + 3 = 20

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At what points does the curve r(t) = ti (4t − t2)k intersect the paraboloid z = x2 y2? (if an answer does not exist, enter dne.)

Aleonysh [2.5K]

$\mathbf r(t)=x(t)\,\mathbf i+y(t)\,\mathbf j+z(t)\,\mathbf k=t\,\mathbf i+(4t-t^2)\,\mathbf k$
$\implies \begin{cases}x(t)=t\\y(t)=0\\z(t)=4t-t^2\end{cases}$

So the paraboloid is given by

$z(t)=x(t)^2y(t)^2\iff 4t-t^2=0$

which holds for $t^2-4t=t(t-4)=0$ , i.e. when $t=0$ and $t=4$ .

To make sure this is correct, plug in $t=0$ and $t=4$ to find out the value of $\mathbf r(t)$ , and see if these points are on the paraboloid.

$\mathbf r(0)=0\,\mathbf i+0\,\mathbf j+0\,\mathbf k\implies (0,0,0)$
$0=0^2\times0^2$

$\mathbf r(4)=4\,\mathbf i+0\,\mathbf j+(4\times4-4^2)\,\mathbf k\implies (4,0,0)$
$0=4^2\times0^2$

Both of these hold, so the answer is correct.

8 0

4 years ago

5/x = 4/8?

photoshop1234 [79]

Answer:

Step-by-step explanation:

5/x = 4/8

Cross multiply

4*x = 5*8

4x = 40

x = 10

Answer is 10

You are correct

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3 years ago

Donovan can type 45 words per minute. He needs to type a report that is 9 pages long each page has about 300 words. What is a re

irinina [24]

Answer:

C.60

Step-by-step explanation:

Just multiply 300 by 9 and then divide by 45.

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Korvikt [17]

The answer I think is 12+16=20

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3 years ago

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