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3 years ago

On a coordinate plane, line A has a negative slope, line b is horizontal, line c is vertical, and line d has a positive slope.

Mathematics

1 answer:

Digiron [165]3 years ago

4 0

Answer:

Line b

Step-by-step explanation:

It cannot be line a or line d because the line will have a constant rate of change. It cannot be line c because line c would be undifined. Therefore, it must be line b.

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A farmer wants to fence a rectangular garden next to his house which forms the northern boundary. The fencingfor the southern bo

Ivahew [28]

Answer:

10 ft x 10 ft

Area = 100 ft^2

Step-by-step explanation:

Let 'S' be the length of the southern boundary fence and 'W' the length of the eastern and western sides of the fence.

The total area is given by:

$A=S*W$

The cost function is given by:

$\$ 120 = \$3*2W+\$6*S\\20 = W+S\\W = 20-S$

Replacing that relationship into the Area function and finding its derivate, we can find the value of 'S' for which the area is maximized when the derivate equals zero:

$A=S*(20-S)\\A=20S-S^2\\\frac{dA}{dS} = \frac{d(20S-S^2)}{dS}\\0= 20-2S\\S=10$

If S=10 then W =20 -10 = 10

Therefore, the largest area enclosed by the fence is:

$A=S*W\\A=10*10 = 100\ ft^2$

5 0

3 years ago

What is the radius of a sphere with a volume of 1/6 pie

Yakvenalex [24]

Answer:

$\large\boxed{the\ radius\ R=\dfrac{1}{2}}$

Step-by-step explanation:

The formula of a volume of a sphere:

$V=\dfrac{4}{3}\pi R^3$

We have

$V=\dfrac{1}{6}\pi$

Substitute:

$\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi$ divide both sides by π

$\dfrac{4}{3}R^3=\dfrac{1}{6}$ multiply both sides by 3

$3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}$

$4R^3=\dfrac{1}{2}$ divide both sides by 4

$R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}$

3 0

3 years ago

Francium has a decay rate of 50% every 22 minutes. How much of an initial amount of 4.8 grams would be left after 88 minutes?

Jlenok [28]

Answer:

0.65g

Step-by-step explanation:

Decay rate = 50%

Decay rate = 0.5

$A = Aoe {}^{ - kt}$

where Ao = initial amount at start, k = rate of decay or growth, t = time, e = euler's number and A = value at time 't'

Ao = 4.8

t = 88/44 = 4

k = 0.5

substitute these values in the equation

$A = 4.8e {}^{ - 0.5 \times 4}$

$A = 0.6496$

$A = 0.65 \: (2dp)$

5 0

3 years ago

Use the figure below to answer the questions.

Pavlova-9 [17]

The transformation is a reflection in the line $y=x$ followed by a reflection in the line $x=1$ .

The mapping for a reflection in the line $y=x$ is $(x,y) \rightarrow (y,x)$ .

That is simply swapping the coordinates.

$A(-3,4) \rightarrow (4,-3)$

$B(-3,0) \rightarrow (0,3)$

$C(-1,3) \rightarrow (3,-1)$

Now we reflect the resulting coordinates in the line $x=1$ which has the mapping $(x,y) \rightarrow (2(1)-x,y)$

So we transform the resulting coordinates as follows:

$(4,-3) \rightarrow A'(2(1)-4,-3)$

$(0,-3) \rightarrow B'(2(1)-0,-3)$

$(3,-1) \rightarrow C'(2(1)-3,-1)$

Hence we have

$A'(-2,-3),B'(2,-3) \: and\: C'(-1,-1)$

7 0

3 years ago

Solve each system by graphing

Ne4ueva [31]

2,-4 is you awnser. good day to you

5 0

3 years ago