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2 years ago

Which function is shown in the graph below?

Mathematics

2 answers:

Alexandra [31]2 years ago

7 0

Answer:

Option C.

Step-by-step explanation:

There are three points which are passing through the logarithmic function shown in the graph.

The points are (0.4, -0.6), (1, 0) and (3, 1).

Now we will plug in the values (3, 1) in all the options to get the correct answer.

a). $y=log_{0.4}x$

We can rewrite the equation as

$(0.4)^{y}=x$ [If $a^{b}=c$ then $b=log_{a}c$ ]

For (3, 1)

$(0.4)^{1}=3$

Which is not true so option A is not the answer.

b). $y=log_{1}x$

We can rewrite the equation as

$(1)^{y}=x$

For (3, 1)

$(1)^{3}=3$

1 = 3

Which is not true.

Therefore, Option B is not the answer.

c). $y=log_{3}x$

We can rewrite the equation as

$(3)^{y}=x$

For (3, 1)

$(3)^{1}=3$

3 = 3

Therefore, option C is the answer.

d). $y=log_{10}x$

We can rewrite the equation as

$(10)^{y}=x$

For (3, 1)

$(10)^{1}=3$

Not true. Therefore, option D is not the answer.

Stolb23 [73]2 years ago

3 0

The annswer is y=log3x

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A special shape is 2.02 m long and 1.22 m wide. A double row of tiles makes a border . Each tile is 2cm by 2cm. How many tiles a

Alex787 [66]

Answer:

6.48

Step-by-step explanation:

The computation of tiles are needed to make the border is shown below:-

$= 2 \times (length + breadth)$

where,

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Now placing these values to the above formula

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2 years ago

The rectangle below has an area of 6n^4+20n^3+14n^26n 4 +20n 3 +14n 2 6, n, start superscript, 4, end superscript, plus, 20, n,

Sindrei [870]

Given:

Area of rectangle = $6n^4+20n^3+14n^2$

Width of the rectangle is equal to the greatest common monomial factor of $6n^4, 20n^3,14n^2$ .

To find:

Length and width of the rectangle.

Solution:

Width of the rectangle is equal to the greatest common monomial factor of $6n^4, 20n^3,14n^2$ is

$6n^4=2\times 3\times n\times n\times n\times n$

$20n^3=2\times 2\times 5\times n\times n\times n$

$14n^2=2\times 7\times n\times n$

Now,

$GCF(6n^4, 20n^3,14n^2)=2\times n\times n=2n^2$

So, width of the rectangle is $2n^2$ .

Area of rectangle is

$Area=6n^4+20n^3+14n^2$

Taking out GCF, we get

$Area=2n^2(3n^2+10n+7)$

We know that, area of a rectangle is the product of its length and width.

Since, width of the rectangle is $2n^2$ , therefore length of the rectangle is $(3n^2+10n+7)$ .

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2 years ago

(1 point) Let P(t) be the performance level of someone learning a skill as a function of the training time t. The derivative dPd

monitta

Answer:

$P(t)=M+Ce^{-kt}$

Step-by-step explanation:

Given the differential model

$\dfrac{dP}{dt}=k[M-P(t)]$

We are required to solve the equation for P(t).

$\dfrac{dP}{dt}=kM-kP(t)\\$Add kP(t) to both sides\\\dfrac{dP}{dt}+kP(t)=kM\\$Taking the integrating factor\\e^{\int k dt} =e^{kt}\\$Multiply all through by the integrating factor\\\dfrac{dP}{dt}e^{kt}+kP(t)e^{kt}=kMe^{kt}\\\dfrac{dP}{dt}e^{kt}=kMe^{kt}\\(Pe^{kt})'=kMe^{kt} dt\\$Take the integral of both sides with respect to t\\\int (Pe^{kt})'=\int kMe^{kt} dt\\Pe^{kt}=kM \int e^{kt} dt\\Pe^{kt}=\dfrac{kM}{k} e^{kt} + C_0, C_0$ a constant of integration$

$Pe^{kt}=Me^{kt} + C\\$Divide both side by e^{kt}\\P(t)=M+Ce^{-kt}\\P(t)=M+Ce^{-kt}\\$Therefore:\\P(t)=M+Ce^{-kt}$

4 0

2 years ago

As part of Kayla's exercise program,she either runs 6miles/day or rides her bike 10 miles/day.Her new goal is to cover a minimum

poizon [28]

6(15) + 10b > = 200
90 + 10b > = 200
10b > = 200 - 90
10b > = 110
b > = 110/10
b > = 11

so she can do 15 days of running plus 11 days of biking....which totals 26 days

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2 years ago

Solve. A power outage affected all homes and businesses within a 3 mile radius of the power station. If the power station is loc

Aneli [31]

Answer:

$\left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 9$

Step-by-step explanation:

The power station is located 5 miles west and 6 miles north of the center of town. So if we try to locate the above points on a Cartesian plane. The co-ordinates of these points will be (-5,6).

And it is also mentioned that a power outage affected all homes and businesses within a 3 mile radius of the power station. So if we plot all the furthest points from the station affected by the power outage it will be a circle of radius 3 miles and center at (-5,6).

The equation of a circle with center (a,b) and radius r is given by :

$\left ( x-a \right )^{2}+\left ( y-b \right )^{2}= r^{2}$

Hence the equation of the resulting circle will be: $\left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 3^{2}$

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2 years ago