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Juli2301 [7.4K]
2 years ago
12

I'm struggling on calculus. PLEASE HELP ASAP. use red writing to help out.​

Mathematics
1 answer:
andre [41]2 years ago
6 0

Step-by-step explanation:

1. Given: a = 4t + 4

We know that

a =  \frac{dv}{dt}  \:  \:  or \: dv = adt

By definition, the integral of a power function x^n is

\int {x}^{n} dx =  \frac{ {x}^{n + 1} }{n + 1}  + k

Integrating the acceleration <em>a</em>, we get

v = \int adt = \int(4t + 4)dt = 2 {t}^{2}  + 4t + k

where k = constant of integration. We know that v = 10 when t = 0 so when we do the substitution, we get k = 10 therefore, the final expression for v is

v = 2 {t}^{2}  + 4t + 10

To find s, we need to integrate v. Knowing that

v = \frac{ds}{dt}  \:  \: or \: s = \int v \: dt

s = \int(2 {t}^{2}  + 4t + 10)dt

=  \frac{2}{3}  {t}^{3}  + 2 {t}^{2}  + 10t + k

where k once again is the constant of integration. We know that s = 2 when t = 0, which gives us k = 2. Therefore, the final expression for <em>s</em> is

s =  \frac{2}{3}  {t}^{3}  + 2 {t}^{2}  + 10t + 2

2. The potential difference <em>V</em> between two boundaries <em>a</em> and <em>b</em> is given by

V = \frac{q}{2\pi \epsilon_0 \epsilon_r} \int_{b}^{a} \frac{dr}{r}

Note that the integral in the expression above can be rewritten and the integrated as

\int_{b}^{a} \frac{dr}{r}  =\int_{b}^{a}  {r}^{ - 1} dr = \ln |a|  -  \ln |b|

so the potential difference <em>V</em> is then J

V = \frac{q}{2\pi \epsilon_0 \epsilon_r} \int_{b}^{a} \frac{dr}{r}

= \frac{2 \times  {10}^{ - 6} }{2\pi (8.85\times {10}^{ - 12}) (2.77)}( \ln |20|  -  \ln |10| )

= 9000  \: V

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Question 4 pleaseeeeeee
arsen [322]

Answer:

B

Step-by-step explanation:

Unit rate means one quantity in terms of another unit quantity. In the answer choices, we see that the denominator is always in terms of UNIT LITERS (1 L), so that means, we have to find gallons in terms of UNIT LITERS.

It means, we have to divide gallons by liters to get in terms of unitary liters.

Let's check the first line:

19.5/75 = 0.26 Gallons / 1 Liter

Now, checking 2nd:

39/150 = 0.26 Gallons / 1 Liter

So, yes, they are the same and other 2 lines would be the same as well. The unit rate is:

0.26 gal/1L

That's answer choice B

7 0
3 years ago
How do you. Get the answers for 72 ounces in 6 steaks =
laila [671]
You divide the answer and it will equal 12
4 0
3 years ago
Please help soon I need it​
Gekata [30.6K]

Answer:

ok

Step-by-step explanation:

4 0
2 years ago
QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the nu
Andru [333]

Answer:

(a)Revenue=580x-10x²,

Marginal Revenue=580-20x

(b)Fixed Cost, =900

Marginal Cost,=300+50x

(c)Profit Function=280x-900-35x²

(d)x=4

Step-by-step explanation:

The price, p = 580 − 10x where x is the number of cakes sold per day.

Total cost function,c = (30+5x)²

(a) Revenue Function

R(x)=x*p(x)=x(580 − 10x)

R(x)=580x-10x²

Marginal Revenue Function

This is the derivative of the revenue function.

If R(x)=580x-10x²,

R'(x)=580-20x

(b)Total cost function,c = (30+5x)²

c=(30+5x)(30+5x)

=900+300x+25x²

Therefore, Fixed Cost, =900

Marginal Cost Function

This is the derivative of the cost function.

If c(x)=900+300x+25x²

Marginal Cost, c'(x)=300+50x

(c)Profit Function

Profit, P(x)=R(x)-C(x)

=(580x-10x²)-(900+300x+25x²)

=580x-10x²-900-300x-25x²

P(x)=280x-900-35x²

(d)To maximize profit, we take the derivative of P(x) in (c) above and solve for its critical point.

Since P(x)=280x-900-35x²

P'(x)=280-70x

Equate the derivative to zero

280-70x=0

280=70x

x=4

The number of cakes that maximizes profit is 4.

5 0
2 years ago
Takev0.7 from 1.3 answer please
torisob [31]
- - Let's solve:

0.7-1.3


- - Solve for that:

&#10;-0.6 &#10;

(-.6)
4 0
3 years ago
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