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3 years ago

Which is NOT true about a direct proportion? (15 points)

Mathematics

2 answers:

Karo-lina-s [1.5K]3 years ago

8 0

The answer is D.
Its graph must be steeper than 0

vfiekz [6]3 years ago

6 0

Answer:

Step-by-step explanation:

IIDKXKD

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Find the solution of the given initial value problem: y''- y = 0, y(0) = 2, y'(0) = -1/2

igor_vitrenko [27]

Answer: The required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Step-by-step explanation: We are given to find the solution of the following initial value problem :

$y^{\prime\prime}-y=0,~~~y(0)=2,~~y^\prime(0)=-\dfrac{1}{2}.$

Let $y=e^{mx}$ be an auxiliary solution of the given differential equation.

Then, we have

$y^\prime=me^{mx},~~~~~y^{\prime\prime}=m^2e^{mx}.$

Substituting these values in the given differential equation, we have

$m^2e^{mx}-e^{mx}=0\\\\\Rightarrow (m^2-1)e^{mx}=0\\\\\Rightarrow m^2-1=0~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mx}\neq0]\\\\\Rightarrow m^2=1\\\\\Rightarrow m=\pm1.$

So, the general solution of the given equation is

$y(x)=Ae^x+Be^{-x},$ where A and B are constants.

This gives, after differentiating with respect to x that

$y^\prime(x)=Ae^x-Be^{-x}.$

The given conditions implies that

$y(0)=2\\\\\Rightarrow A+B=2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$y^\prime(0)=-\dfrac{1}{2}\\\\\\\Rightarrow A-B=-\dfrac{1}{2}~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Adding equations (i) and (ii), we get

$2A=2-\dfrac{1}{2}\\\\\\\Rightarrow 2A=\dfrac{3}{2}\\\\\\\Rightarrow A=\dfrac{3}{4}.$

From equation (i), we get

$\dfrac{3}{4}+B=2\\\\\\\Rightarrow B=2-\dfrac{3}{4}\\\\\\\Rightarrow B=\dfrac{5}{4}.$

Substituting the values of A and B in the general solution, we get

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Thus, the required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

4 0

3 years ago

a minivan can hold up to 7 people. How many minivans are needed to take 45 people to a basketball game?

DaniilM [7]

Answer=7 minivans

45/7=6.4

since you can't have 0.4 minivans, we round up 6.4 to 7

5 0

3 years ago

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Find the solution of this system of equations.

Kay [80]

Answer:

x=y

x+12x=-26

13x=-26

x=-2

y=-2

Step-by-step explanation:

6 0

3 years ago

Darrin lives in Washington, D.C., which has a sales tax of 6%. He just bought a video camera whose full price was $620, but afte

marshall27 [118]

562.20 So the answer is A.

7 0

3 years ago

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What is the equation of the line that began with a y-intercept of (0,4), was shifted up 3 units, and is perpendicular to y = 3/4

timama [110]

Answer:

Option A

y=-4/3x+7

Step-by-step explanation:

To solve this, we need to understand the various components of the equation of a straight line.

A straight line has the equation: y =mx + c

m is the slope and c is the intercept on the y-axis. If we can get these two components, we can figure out the equation for the new line.

Calculating the slope, m

To obtain the slope of the new line, we use the fact that it is perpendicular to the slope of the line y = 3/4x-2.

This means that

3/4 X m = -1

m = -4/3

To obtain the intercept, c

The intercept can be obtained by adding 3 to the y-component of (0, 4).

This will give (0, 7). Hence the intercept c will be 7.

Therefore, the equation of the line will be y = -4/3x+7. Option A

7 0

3 years ago