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liberstina [14]

1 year ago

9

What is the inequality shown

1 answer:

Arturiano [62]1 year ago

5 0

Answer:

one has (_) and another has (+)

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Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.

Vladimir [108]

$\mathbf r(t)=\displaystyle\int(5t^4\,\mathbf i+6t^5\,\mathbf j+t\,\mathbf k)\,\mathrm dt$
$\mathbf r(t)=(t^5+C_1)\,\mathbf i+(t^6+C_2)\,\mathbf j+\left(\dfrac12t^2+C_3\right)\,\mathbf k$

Given $\mathbf r(1)=\mathbf i+\mathbf j$ , we have

$\begin{cases}1^5+C_1=1\\\\1^6+C_2=1\\\\\dfrac121^2+C_3=0\end{cases}\implies C_1=0,C_2=0,C_3=-\dfrac12$

so that the particular solution is

$\mathbf r(t)=t^5\,\mathbf i+t^6\,\mathbf j+\dfrac12(t^2-1)\,\mathbf k$

8 0

3 years ago

All real numbers between −14 and 14 inclusive

Vladimir79 [104]

Answer:

-13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

6 0

2 years ago

Read 2 more answers

a boutique handmade umbrella factory currently sells 22500 umbrellas per year at a cost of 9 dollars each. in the previous year

sergij07 [2.7K]

Answer:

The maximum revenue of the two years is $ 394,500 .

Step-by-step explanation:

Given as :

The current number of selling of umbrellas = 22500

The price of each umbrellas = $ 9

So, The Total price of 22500 umbrellas at $ 9 per umbrellas = $ 9 × 22500

I.e The Total price of 22500 umbrellas at $ 9 per umbrellas = $ 202,500

Again ,

The total number of umbrellas sold previous year = 12000

The price of umbrellas = $ 16

So, The Total price of 12000 umbrellas at $ 16 per umbrellas = $ 16 × 12000

I.e The Total price of 12000 umbrellas at $ 16 per umbrellas = $ 192,000

So, The maximum revenue of the two years = $ 202,500 + $ 192,000

I.e The maximum revenue of the two years = $ 394,500

Hence The maximum revenue of the two years is $ 394,500 . Answer

3 0

3 years ago

During the half time of a basketball game, a sling shot launches T-shirts at the crowd. The T-shirt is launched with an initial

kumpel [21]

Step-by-step explanation:

The T-shirt is launched with an initial upward velocity of 60 ft/s from a height of 5 feet. Its equation of motion is given by :

$f(x) = -12x^2 + 60x + 5$ ....(1)

(a) For maximum height, put $\dfrac{df(x)}{dt}=0$

So,

$\dfrac{ d(-12x^2 + 60x + 5)}{dt}=-24x+60$

Now put,

$-24x+60=0\\\\x=2.5\ s$

So, the time taken for the T-shirt to reach maximum height is 2.5 seconds.

(b) Put x = 2.5 s in equation (1)

$f(x=2.5) = -12(2.5)^2 + 60(2.5) + 5\\\\f(x)=80\ \text{feet}$

8 0

2 years ago

How do I convert 50% to an improper fraction?

densk [106]

50% =
0.5 =
50/100 =
1/2

This cannot be written as an improper fraction

6 0

2 years ago