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2 years ago

3

The points (80, 20) and (120, 30) form a proportional relationship. What is the slope of the line that passes through these poin

ts? 14

1 answer:

Ray Of Light [21]2 years ago

4 0

Answer:

10 over 40

Step-by-step explanation:

y2-y1 over x2-x1

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(b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y =

frutty [35]

Answer:

Check attachment for complete question

Step-by-step explanation:

Given that,

y=Coskt

We are looking for value of k, that satisfies 4y''=-25y

Let find y' and y''

y=Coskt

y'=-kSinkt

y''=-k²Coskt

Then, applying this 4y'"=-25y

4(-k²Coskt)=-25Coskt

-4k²Coskt=-25Coskt

Divide through by Coskt and we assume Coskt is not equal to zero

-4k²=-25

k²=-25/-4

k²=25/4

Then, k=√(25/4)

k= ± 5/2

b. Let assume we want to use this

y=ASinkt+BCoskt

Since k= ± 5/2

y=A•Sin(±5/2t)+ B •Cos(±5/2t)

y'=±5/2ACos(±5/2t)-±5/2BSin(±5/2t)

y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t

Then, inserting this to our equation given to check if it a solution to y=ASinkt+BCoskt

4y''=-25y

For 4y''

4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))

-25A•Sin(±5/2t)-25B•Cos(±5/2t).

Then,

-25y

-25(A•Sin(±5/2t)+ B •Cos(±5/2t))

-25A•Sin(±5/2t) - 25B •Cos(±5/2t)

Then, we notice that, 4y'' is equal to -25y, then we can say that y=Coskt is a solution to y=ASinkt+BCoskt

4 0

2 years ago

The grades on a history midterm at Gardner Bullis are roughly symmetric with μ = 69 μ=69mu, equals, 69 and σ = 3.5 σ=3.5sigma, e

katrin2010 [14]

Answer:

-1.14

Step-by-step explanation:

The given information in statement is

mean=μ=69

standard deviation=σ=3.5

Let X be the Ishaan's exam score

X=65

The Z score can be computed as

$z=\frac{x-mean}{standard deviation}$

$z=\frac{65-69}{3.5}$

z=-1.1429

z=-1.14 (rounded to two decimal places).

Thus, the computed z-score for Ishaan's exam grade is -1.14.

4 0

2 years ago

Todd's friend Olivia is flying her stunt plane at an elevation of 6.3 km. From the ground, Todd's used to plane moving directly

Aloiza [94]

Can't understand the sentence where it says "<span>From the ground, Todd's used to plane moving directly toward him from the West at a 49 degree angle of elevation". Help me interpret it.</span>

5 0

2 years ago

mark has a cabinet door in his kitchen with the dimensions shown below. he creates a scale drawing where the width of the cabine

laiz [17]

Answer:

$h^{*} = 25\,in$

Step-by-step explanation:

Let consider that door has a height of 5 feet and a width of 3 feet. The scale factor is:

$n = \frac{15\,in}{3\,ft}$

$n = 5\,\frac{in}{ft}$

The height of the cabinet is:

$h^{*} = n \cdot h_{door}$

$h_{*} = \left(5\,\frac{in}{ft} \right)\cdot (5\,ft)$

$h^{*} = 25\,in$

6 0

2 years ago

Read 2 more answers

Identify the independent and dependent variables in the following hypothesis: "People who exercise regularly are more likely to

JulijaS [17]

Answer:

Independent

dependent

Step-by-step explanation:

The scenario illustrates that the weight for people who exercises regularly tends is normal or below normal. It means that the weight of a person depends on how much a person exercises i.e. if person exercises more the weight is reduced and if not then weight will be gained. Thus, exercise is the independent variable while weight is dependent variable.

7 0

2 years ago