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3 years ago

5

You have 400 cards stored 3/5 of them are from family. 1/4 of them are from friends. The rest you made. How many cards did you m

ake?

1 answer:

omeli [17]3 years ago

5 0

You made 3/20 of the 400 cards, which is 60 cards.

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Let R = [ 0 , 1 ] × [ 0 , 1 ] R=[0,1]×[0,1]. Find the volume of the region above R R and below the plane which passes through th

Bond [772]

The three vectors $\langle0,0,1\rangle$ , $\langle1,0,8\rangle$ , and $\langle0,1,9\rangle$ each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,

$\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle$

$\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle$

Then the cross product of these two results is normal to the plane:

$\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle$

Let $(x,y,z)$ be a point on the plane. Then the vector connecting $(x,y,z)$ to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that

$\langle-7,-8,1\rangle\cdot(\langle x,y,z\rangle-\langle0,0,1\rangle)=0$

which reduces to the equation of the plane,

$-7x-8y+z-1=0\implies z=7x+8y+1$

Let $z=f(x,y)$ . Then the volume of the region above $R$ and below the plane is

$\displaystyle\int_0^1\int_0^1(7x+8y+1)\,\mathrm dx\,\mathrm dy=\boxed{\frac{17}2}$

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3 years ago

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Schach [20]

Answer:

Our free fall calculator can find the velocity of a falling object and the height it ... accelerating by 9.80665 m/s (approximately equal to 32.17405 ft/s ) every second.

Step-by-step explanation:

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3 years ago

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3 years ago

Which of the numbers below are divisible by 2?

joja [24]

286, 260, 124, 420, 286

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3 years ago

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A washing machine sells for $201 after being discounted by 40 percent. What was the original price of the washing machine?

olga_2 [115]

Step-by-step explanation:

Let original price be x

Price after 40% discount is $201

Therefore

x × 40% = $201

x = 201 ÷ (40/100)

x = 502.5

Therefore, the original price is $502.5

Hope it helps :)

5 0

3 years ago