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3 years ago

Factor out 10d^7 + 2d^5

Mathematics

1 answer:

alexdok [17]3 years ago

7 0

Answer:

$2 {d}^{5} (5 {d}^{2} + 1)$

Step-by-step explanation:

$10d^7 + 2d^5 \\ \\ = 2 {d}^{5} (5 {d}^{2} + 1)$

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Juan has $120 in his checking account. He buys 4 equally priced shirts and pays with a check. If Juan now has -$60 in his accoun

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

Step 1. 120+60=180

Step 2. 120-180=-60

Step 3. 180 divded by 4

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3 years ago

Question 6 (0.5 points)

Sunny_sXe [5.5K]

Answer:

Step-by-step explanation:

(9-6)/2 = 3/2 = 1.5

(-8-3)/2 = -11/2 = -5.5

(1.5, -5,5)

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3 years ago

The zoo charges $4 admission fee

Andrews [41]

Answer:

Intial Value; $4 (charged)

Rate of change: $2 every exhibit visited

Admission: $4

1 exhibit visited: $6

2 exhibits visited: $8

3 exhibits visited: $10

4 exhibits visited: $12

5 exhibits visited: $14

6 exhibits visited: $16

7 exhibits visited: $18

8 exhibits visited: $20

etc.

Step-by-step explanation:

4+2x = C

C= Cost

X = amount of exhibits visited

To find the total cost.

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3 years ago

13. A test had four challenging questions (7 points each) and twenty-four easy questions

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Answer:

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3 years ago

Find a solution to the initial value problem, y′′+18x=0,y(0)=5,y′(0)=1.

Serga [27]

We want to find a solution to the initial value problem:

$y'' + 18x = 0 \qquad,\qquad y(0) = 5 \qquad,\qquad y'(0)=1.$

We can start by integrating the equation once:

$\dfrac{\textrm{d}^2 y}{\textrm{d}x^2} + 18 x = 0 \iff \dfrac{\textrm{d}^2 y}{\textrm{d}x^2} = -18 x \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -18\displaystyle\int x\textrm{ d}x \iff \dfrac{\textrm{d}y}{\textrm{d}x}=-18\dfrac{x^2}{2} + C \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + C.$

Using the initial condition $y'(0) = 1$ , we can determine the integration constant $C$ :

$\dfrac{\textrm{d}y}{\textrm{d}x}\Big\vert_{x= 0} = 1 \iff -9 \times 0^2 + C = 1 \iff C = 1.$

Therefore, we have:

$\dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + 1$

We can now integrate again:

$y(x) = \displaystyle\int\dfrac{\textrm{d}y}{\textrm{d}x}\textrm{ d}x = \int\left(-9x^2+1\right)\textrm{d}x = -9\int x^2\textrm{ d}x + \int\textrm{d}x =\\\\= -9\dfrac{x^3}{3} + x + K = -3x^3 + x + K.$

The integration constant $K$ is determined by using $y(0) = 5$ :

$y(0) = 5 \iff -3 \times 0^3 + 0 + K = 5 \iff K = 5.$

Finally, the solution is:

$\boxed{y(x) = -3x^3 + x + 5}.$

7 0

3 years ago