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earnstyle [38]
3 years ago
7

Please someone answer asap

Mathematics
1 answer:
Rus_ich [418]3 years ago
8 0

Answer:

(-inf,6]

Step-by-step explanation:

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Ten subtracted from the quotient if a number and 7 is less than -6
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10-(x/7)<-6

Step-by-step explanation:

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3 years ago
Find the surface area of the part of the circular paraboloid z=x^2+y^2 that lies inside the cylinder X^2+y^2=1
hichkok12 [17]

Answer:

\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}

Step-by-step explanation:

Given that:

The surface area (S.A) z = x^2 +y^2

Hence the S.A is of form z = f(x,y)

Then the S.A can be represented with the equation

A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA

where :

D = cylinder x^2 +y^2 =1

In polar co-ordinates:

D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)

Similarly, \dfrac{\partial z}{\partial x} = 2x and \dfrac{\partial z}{\partial y} = 2y

Therefore;

S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA

= \iint_D \sqrt{1+4(x^2+y^2)} \ dA

= \int^{2 \pi}_{0} \int^{1}_{0}  \sqrt{1+4r^2} \ r \ dr \d \theta

= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0

= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1]

\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}

6 0
3 years ago
Lynnette went to the coffee shop to buy coffee beans. She purchased 2.5 pounds of her favorite blend. This blend cost $8.50 per
ElenaW [278]

Answer: $21.25

Step-by-step explanation:

Given

Lynnette purchased 2.5 Pounds of blent, which costs $8.50 per pound

total cost is the Product of the amount of blend and rate of coffee blend

\Rightarrow C=2.5\times 8.50=\$21.25

So, coffee beans cost $21.25

4 0
3 years ago
HELP ME WITH THIS QUESTION PLEASE
Shkiper50 [21]

Answer:

Step-by-step explanation:

1. 7x + 4

2. 3x - 2

8 0
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