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2 years ago

Help?

Mathematics

1 answer:

MAXImum [283]2 years ago

5 0

Answer:

$32.39

Step-by-step explanation:

She has a 15-gallon tank and it has 1/5 a tank of gas left (so about 3/15)

Because she needs to refill it and already has 1/5, she'll only need to pay for 4/5 a tank of gas (12/15).

So the equation should be 12 times $2.699.

12 × 2.699 = 32.388

Then, round to the nearest cent.

32.388 = $32.39

Hope this helped !

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Jessica owns 1/8 of a company worth $56,000. What is the value of

rosijanka [135]

7000

1/8th in percentage form is 12.5%
12.5% of 56000 is 7000

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2 years ago

Emily is adding 51 and 29 which steps can she use to add the numbers

frutty [35]

Answer:

51 + 29+ 80

Step-by-step explanation:

she got this by adding 51 + 29

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2 years ago

A triangular pyramid is formed from three right triangles as shown below.

Lady bird [3.3K]

ΔADC is a right angle triangle, we will use the Pythagorus Theorem to find the length CD.

Formula of the Pythagorus Theorem :

⇒ a² + b² = c²

⇒ AD² + CD² = AC²

The value of AD is 54 and the value of AC is 90:

54² + CD² = 90²

Solve for CD:

54² + CD² = 90²

CD² = 90² - 54²

CD² = 5184

CD = √5184

CD = 72

ΔADC is also a right angle triangle, we will use the Pythagorus Theorem to find the length BD.

Formula of the Pythagorus Theorem :

⇒ a² + b² = c²

⇒ BD² + CD² = BC²

The value of CD is 72 and the value of BC is 97:

BD² + 72² = 97²

Solve for BD:

BD² = 97² - 72²

BD² = 4225

BD = √4225

BD = 65

Answer: The length of BD is 65 units.

7 0

2 years ago

Two solutions to y'' – 2y' – 35y = 0 are yı = e, Y2 = e -5t a) Find the Wronskian. W = 0 Preview b) Find the solution satisfying

pashok25 [27]

Answer:

a. $w(t)=-12e^{2t}$

b. $y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}$

Step-by-step explanation:

We have a differential equation

y''-2 y'-35 y=0

Auxillary equation

$(D^2-2D-35)=0$

By factorization method we are finding the solution

$D^2-7D+5D-35=0$

$(D-7)(D+5)=0$

Substitute each factor equal to zero

D-7=0 and D+5=0

D=7 and D=-5

Therefore ,

General solution is

$y(x)=C_1e^{7t}+C_2e^{-5t}$

Let $y_1=e^{7t} \;and \;y_2=e^{-5t}$

We have to find Wronskian

$w(t)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}$

Substitute values then we get

$w(t)=\begin{vmatrix}e^{7t}&e^{-5t}\\7e^{7t}&-5e^{-5t}\end{vmatrix}$

$w(t)=-5e^{7t}\cdot e^{-5t}-7e^{7t}\cdot e^{-5t}=-5e^{7t-5t}-7e^[7t-5t}$

$w(t)=-5e^{2t}-7e^{2t}=-12e^{2t}$

a. $w(t)=-12e^{2t}$

We are given that y(0)=-7 and y'(0)=23

Substitute the value in general solution the we get

$y(0)=C_1+C_2$

$C_1+C_2=-7$ ....(equation I)

$y'(t)=7C_1e^{7t}-5C_2e^{-5t}$

$y'(0)=7C_1-5C_2$

$7C_1-5C_2=23$ ......(equation II)

Equation I is multiply by 5 then we subtract equation II from equation I

Using elimination method we eliminate $C_1$

Then we get $C_2=-\frac{5}{2}$

Substitute the value of $C_2$ in I equation then we get

$C_1-\frac{5}{2}=-7$

$C_1=-7+\frac{5}{2}=\frac{-14+5}{2}=-\frac{9}{2}$

Hence, the general solution is

b. $y(t)=-\frac{9}{2}e^{7t}-\frac{5}{2}e^{-5t}$

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2 years ago

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Step-by-step explanation: Simplify the expression.

I hope this helps you out. :)

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3 years ago