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2 years ago

To find the distance an object has traveled, you use the formula D=RT; where D=distance, R=rate and T=time.

Mathematics

1 answer:

devlian [24]2 years ago

6 0

Answer:

52.25 MPH

Step-by-step explanation:

Using the formula given D=RT we simply plug in values,

313.5=6R

313.5/6=R

52.25=R

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Find the solution r(t)r(t) of the differential equation with the given initial condition: r′(t)=⟨sin9t,sin6t,9t⟩,r(0)=⟨4,6,3⟩

klemol [59]

$\mathbf r'(t)=\langle\sin9t,\sin6t,9t\rangle$

$\mathbf r(t)=\displaystyle\int\mathbf r'(t)\,\mathrm dt$

$\mathbf r(t)=\left\langle\displaystyle\int\sin9t\,\mathrm dt,\int\sin6t\,\mathrm dt,\int9t\,\mathrm dt\right\rangle$

$\displaystyle\int\sin9t\,\mathrm dt=\frac19\cos9t+C_1$

$\displaystyle\int\sin6t\,\mathrm dt=\frac16\cos6t+C_2$

$\displaystyle\int9t\,\mathrm dt=\frac92t^2+C_3$

With the initial condition $\mathbf r(0)=\langle4,6,3\rangle$ , we find

$\dfrac19\cos0+C_1=4\implies C_1=\dfrac{35}9$

$\dfrac16\cos0+C_2=6\implies C_2=\dfrac{35}6$

$\dfrac92\cdot0^2+C_3=3\implies C_3=3$

So the particular solution to the IVP is

$\mathbf r(t)=\left\langle\dfrac19\cos9t+\dfrac{35}9,\dfrac16\cos6t+\dfrac{35}6,\dfrac92t^2+3\right\rangle$

4 0

3 years ago

Amy and rob each improve thier yards by pmanting rose bushes and ivy. They brought thier supplies from the same store. Amy spent

Rzqust [24]

Answer: cost of 1 pot of ivy = $12

Cost of 1 rose bush =$ 10

Step-by-step explanation:

Step 1

Let rose bushes be represented as r

and pot of ivy be represented as p

such that Amy who spent 82 dollars on 7 rose bushes and 1 pot of ivy can be expressed as

7 r + p = 82----- eqn 1

Rob who spent 74 on 5 rose bushes and 2 pots of ivy can be expressed as

5r +2 p = 74----- eqn 2

Step 2

Solving

7 r + p = 82----- eqn 1

5r +2 p = 74----- eqn 2

By elimination method Multiply eqn 1 by 5 and eqn 2 by 7

35r+ 5p= 410--- eqn 3

35r+ 14p =518--- eqn 4

Subtracting eqn 4 from eqn 3

9p = 108

p = 108/9

p=12

p = pot of ivy = $12

therefore rose bush wll be ( from equation 1)

7r+ p= 82

7r=82-12

7r= 70 r= 70/7

r= rose bush =$ 10

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3 years ago

The high temperature one day was -1 °F. The low temperature was -5 °F. What was the difference between the high and low temperat

insens350 [35]

Answer:

The difference is 4 degrees

Step-by-step explanation:

If its difficult for you to subtract negatives just switch them to a positive 1 and 5 now subtract 1 from 5=4 and because the measure being used is degrees the final answer would be 4 degrees.

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2 years ago

Simplify. –abc + 7abc – 3bc – 8abc ------------- abc − ------------bc

NISA [10]

- abc + 7abc - 3bc - 8abc
= 6abc - 3bc - 8bc
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Therefore
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3 years ago

Please help asap 29 pts

Alexeev081 [22]

Answer:

C. 56 is the correct answer, my bad.

Step-by-step explanation:

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3 years ago

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