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3 years ago

Does the point (2,3) satisfy the inequality 4x+3y> 20

Mathematics

1 answer:

adell [148]3 years ago

5 0

No, (2 , 3) does not satisfy the inequality 4x + 3y > 20.

See attached picture:

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A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these

Vinvika [58]

Answer:

133 fishes

Step-by-step explanation:

Units of food A = 400 units

Units of food B = 400 units

Fish Bass required 2 units of A and 4 units of B.

Fish Trout requires 5 units of A and 2 units of B.

i. For food A,

total units of food A required = 2 + 5

= 7 units

number of bass and trout that would consume food A = 2 x $\frac{400}{7}$

= 114.3

number of bass and trout that would consume food A = 114

ii. For food B,

total units of food B required = 4 + 2

= 6 units

number of bass and trout that would consume food B = 2 x $\frac{400}{6}$

= 133.3

number of bass and trout that would consume food B = 133

Thus, the maximum number of fish that the lake can support is 133.

4 0

3 years ago

Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 = 36.

rewona [7]

Answer:

Step-by-step explanation:

From the given information:

The domain D of integration in polar coordinates can be represented by:

D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;

The partial derivates for z = xy can be expressed as:

$y =\dfrac{\partial z}{\partial x} , x = \dfrac{\partial z}{\partial y}$

Thus, the area of the surface is as follows:

$\iint_D \sqrt{(\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2 +1 }\ dA = \iint_D \sqrt{(y)^2+(x)^2+1 } \ dA$

$= \iint_D \sqrt{x^2 +y^2 +1 } \ dA$

$= \int^{2 \pi}_{0} \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr \ d \theta$

$=2 \pi \int^{6}_{0} \ r \sqrt{r^2 +1 } \ dr$

$= 2 \pi \begin {bmatrix} \dfrac{1}{3}(r^2 +1) ^{^\dfrac{3}{2}} \end {bmatrix}^6_0$

$= 2 \pi \times \dfrac{1}{3} \Bigg [ (37)^{3/2} - 1 \Bigg]$

$= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ]$

3 0

2 years ago

If 70% is £14 what is the full price

Veseljchak [2.6K]

70℅ = 14
100 = X

70X = 1400

X = 1400/70

X = 20

20 Euros is the full price

6 0

3 years ago

1. In which number does the 6 have a value that is one-tenth the value of the 6 in 34,7612

DiKsa [7]

I think it's C, I could be wrong though

8 0

3 years ago

What is a shorter way to write 10 divided by 5?

Alekssandra [29.7K]

Answer:

see below

Step-by-step explanation:

10/5

(10 over five)

Which is 2

4 0

2 years ago

Read 2 more answers