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sergiy2304 [10]

2 years ago

5

Daniel is drawing a plan for a new animal pen for his farm. The rectangle plotted in the coordinate plane represents the pen, me

asured in feet. How many feet of fencing does he need to surround the pen? 10 feet 11 feet 20 feet 22 feet.

1 answer:

Nat2105 [25]2 years ago

3 0

Answer:

22ft

Step-by-step explanation:

I just did the edge.

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A table costs $350. There is also a sales tax of 7%. How much does the table cost, including sales tax?

IrinaVladis [17]

Tax
$350x0.07
=$24.50

(0.07 is the 7% tax in decimal form)

Total cost
$350+$24.50
=$374.50

OR

$350x107%
=$374.50

1.07 is the table cost (100%) plus the sales tax (7%)

The table costs $374.50 with tax.

7 0

3 years ago

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Marshall baked two kinds of cakes. Each cake was the same size. He served 1 half of the marble cake. He served 1 third of the le

Assoli18 [71]

Answer:

He served 3/6 of the lemon cake and 2/6 of the marble cake. He served 1 more piece of the lemon cake than marble cake.

Step-by-step explanation:

A third of 6 is 2 and half of six is 3.

8 0

2 years ago

Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(0) = 2.8 y(t) = 0 Preview

mario62 [17]

Answer: The required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

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

$5y^{\prime\prime}+3y^\prime-2y=0,~~~~~~~y(0)=0,~~y^\prime(0)=2.8~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

$5m^2e^{mt}+3me^{mt}-2e^{mt}=0\\\\\Rightarrow (5m^2+3y-2)e^{mt}=0\\\\\Rightarrow 5m^2+3m-2=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow 5m^2+5m-2m-2=0\\\\\Rightarrow 5m(m+1)-2(m+1)=0\\\\\Rightarrow (m+1)(5m-1)=0\\\\\Rightarrow m+1=0,~~~~~5m-1=0\\\\\Rightarrow m=-1,~\dfrac{1}{5}.$

So, the general solution of the given equation is

$y(t)=Ae^{-t}+Be^{\frac{1}{5}t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-Ae^{-t}+\dfrac{B}{5}e^{\frac{1}{5}t}.$

According to the given conditions, we have

$y(0)=0\\\\\Rightarrow A+B=0\\\\\Rightarrow B=-A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

and

$y^\prime(0)=2.8\\\\\Rightarrow -A+\dfrac{B}{5}=2.8\\\\\Rightarrow -5A+B=14\\\\\Rightarrow -5A-A=14~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{Uisng equation (ii)}]\\\\\Rightarrow -6A=14\\\\\Rightarrow A=-\dfrac{14}{6}\\\\\Rightarrow A=-\dfrac{7}{3}.$

From equation (ii), we get

$B=\dfrac{7}{3}.$

Thus, the required solution is

$y(t)=-\dfrac{7}{3}e^{-t}+\dfrac{7}{3}e^{\frac{1}{5}t}.$

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2 years ago

What 2 numbers multiply to -18 and add up to -4

ivann1987 [24]

Answer:

-9 x 1 x 1 x 1 x 2 = (-18)

-9 + 1 + 1 + 1 + 2 = (-4)

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2 years ago

Theo has a balence of $-4 in his savings account. After making a deposit, he has $25 in his account.What is the overall change t

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The has a +$29 change in his account

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2 years ago

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