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2 years ago

Which number is a perfect cube? 21 49 343 600

Mathematics

1 answer:

artcher [175]2 years ago

6 0

Answer:

343

Step-by-step explanation:

7 cubed = 7 x 7 x 7 = 343

so, 343 is a perfect cube.

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Laura, Scott, and Joe served a total of 104

umka21 [38]

9514 1404 393

Answer:

Joe: 57
Scott: 19
Laura: 28

Step-by-step explanation:

Let s represent the number of orders Scott served. Then we have Joe served 3s, and Laura served (s+9). The total of orders served is ...

3s +s +(s +9) = 104

5s = 95 . . . . . . . . . . . subtract 9 and collect terms

s = 19 . . . . . . . . . divide by 5

3s = 3×19 = 57

s+9 = 19+9 = 28

Joe served 57 orders, Scott served 19, and Laura served 28 orders.

3 0

3 years ago

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

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

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

7 0

2 years ago

Multiply the following<br>1)34/7×3<br>2)3/8×7<br>3)3/4×7

Gelneren [198K]

Answer:

1) 102/21

2) 21/51

3) 21/24

Step-by-step explanation:

7 0

3 years ago

Point K is between points H and J, HK=x-5, KJ=5x-12, and HJ=25. Find the value of x

bija089 [108]

X-5 + 5x-12 = 25
combine like terms
6x-17 = 25
add 17
25 + 17 =42
6x + 42
x = 7

7 0

3 years ago

Plz help me ill mark u brainliest

Ulleksa [173]

Answer:

c5=20

Step-by-step explanation:

in order to find the cost of one smoothie, you must multiply the cost by the amount of smoothies. when solved, the cost of one smoothie is $4

6 0

4 years ago