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3 years ago

The width of the vegetable garden is 1/4 it's length. If the length of the garden is 12 feet, what is the width?

Mathematics

2 answers:

kogti [31]3 years ago

7 0

12 times 1/4 = 3 (feet)

Kitty [74]3 years ago

5 0

Answer:3 feet

Step-by-step explanation:

12/4=3 which mean 3 feet is the width

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There are 5 red marbles, 15 blue marbles, and 5 green marbles in a bag. If you reach in and randon

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Step-by-step explanation:

It is very likely that you will pick a blue marble because the bag is mostly filled with blue marbles so even if it is random it is more probable

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D) change decimal to a fraction 0.078125.

Y_Kistochka [10]

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Step-by-step explanation:

not sure but I think the answer is 5/64

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3 years ago

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Solve the initial value problems.

slavikrds [6]

Both equations are linear, so I'll use the integrating factor method.

The first ODE

$xy' + (x+1)y = 0 \implies y' + \dfrac{x+1}x y = 0$

has integrating factor

$\exp\left(\displaystyle \int\frac{x+1}x \, dx\right) =\exp\left(x+\ln(x)\right) = xe^x$

In the original equation, multiply both sides by eˣ :

$xe^x y' + (x+1) e^x y = 0$

Observe that

d/dx [xeˣ] = eˣ + xeˣ = (x + 1) eˣ

so that the left side is the derivative of a product, namely

$\left(xe^xy\right)' = 0$

Integrate both sides with respect to x :

$\displaystyle \int \left(xe^xy\right)' \, dx = \int 0 \, dx$

$xe^xy = C$

Solve for y :

$y = \dfrac{C}{xe^x}$

Use the given initial condition to solve for C. When x = 1, y = 2, so

$2 = \dfrac{C}{1\cdot e^1} \implies C = 2e$

Then the particular solution is

$\boxed{y = \dfrac{2e}{xe^x} = \dfrac{2e^{1-x}}x}$

The second ODE

$(1+x^2)y' - 2xy = 0 \implies y' - \dfrac{2x}{1+x^2} y = 0$

has integrating factor

$\exp\left(\displaystyle \int -\frac{2x}{1+x^2} \, dx\right) = \exp\left(-\ln(1+x^2)\right) = \dfrac1{1+x^2}$

Multiply both sides of the equation by 1/(1 + x²) :

$\dfrac1{1+x^2} y' - \dfrac{2x}{(1+x^2)^2} y = 0$

and observe that

d/dx[1/(1 + x²)] = -2x/(1 + x²)²

Then

$\left(\dfrac1{1+x^2}y\right)' = 0$

$\dfrac1{1+x^2}y = C$

$y = C(1 + x^2)$

When x = 0, y = 3, so

$3 = C(1+0^2) \implies C=3$

$\implies \boxed{y = 3(1 + x^2) = 3 + 3x^2}$

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2 years ago

Dylan is moving and must rent a truck. There is an initial charge of $35 for the rental plus an additional fee per mile. If Dyla

SashulF [63]

Answer:

An equation for the function is C(m) = 35 + 2.5m

Step-by-step explanation:

Given:

Initial charge of the truck = $35

Dylan Drove = 2 miles

Total Cost after Driving 2 miles = $40

To Find:

Equation for the function C(m), representing the total cost of renting the truck if Dylan were to drive m miles.

Solution:

Let

The additional cost be x

Then

Total cost of renting will be = Initial charge of the truck + (number of miles X additional charge per mile)

We have

Total cost of renting = C(m)

number of miles = m

additional charge per mile = x

$C(m) = 35 + (m \times x)$ ---------------------------------(1)

But After 2 miles

$40 = 35 + (2\times x)$

$40 = 35 + 2x$

$40 - 35 = 2x$

$5 = 2x$

$x= \frac{5}{2}$

x = 2.5

Additional charge per mile = $2.5

$C(m) = 35 + (m \times 2.5)$

C(m) = 35 + 2.5m

3 0

3 years ago

If 8 pounds of bananas cost $3.68, what is the cost per<br> pound?

12345 [234]

Answer:0.46

Step-by-step explanation

3.68 divided by 8 = 0.46

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