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3 years ago

8

In a recent year, the price of a gallon of heating oil in a New England town rose 5 cents, dropped 2 cents, and then rose 4 cent

s. By how much did the price change during that period?

2 answers:

erma4kov [3.2K]3 years ago

5 0

What do you think it is

Leona [35]3 years ago

4 0

it changed by 1 cent, the price went up

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Share $600 between Anna and Raman in the ratio 3:7 and 1:4

Ulleksa [173]

Answer:

3 : 7 =>

Anna = $180

Raman = $420

1 : 4 =>

Anna = $120

Raman = $480

Step-by-step explanation:

<u>Shares when ratio is 3 : 7</u>

Anna : Raman = 3 : 7

Sum of ratio 10

Anna's share=

$\frac{3}{10} \times 600 = \$ 180$

Raman 's share=

$\frac{7}{10} \times 600 = \$ 420$

<u>Shares when ratio is 1 : 4</u>

Anna : Raman = 1 : 4

Sum of ratio = 5

Anna 's share =

$\frac{1}{5} \times 600 = \$ 120$

Raman's share =

$\frac{4}{5} \times 600 = \$ 480$

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scZoUnD [109]

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2 years ago

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xxTIMURxx [149]

Answer:

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Step-by-step explanation:

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3 years ago

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

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

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

Help me out hunnys ❤️

Alenkinab [10]

Answer:

g(x)=3(x+3)^2-8

Step-by-step explanation:

You can solve by using these acronyms.

H. orozontal.

I. nside.

O. pposite.

Meaning that a horozontal translation would be written inside the parenthesis and the poopsite sigh you would usually (Ex. Left is usually negitave but in this case it is positive).

The other acronym is,

V. erticle.

O. utside.

S. ame.

Meaning for a vrerticle translation the number would go on the outside of the parenthesis and tha sign would be normal (Ex. Negitave would be left and positive would be right).

For this one use H.I.O sinse you are moving on a horozontal plain. You are only working with the (x-2) nothing else matters.

Since you are moving left the number will move up 3 hence the O.

<h2><u>This transformation leaves you with g(x)=3(x+3)^2-8</u></h2>

3 0

3 years ago