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3 years ago

Solve the seperable equation: dx/dt=3xt^2

1 answer:

5 0

$\displaystyle
\dfrac{dx}{dt}=3xt^2\\
\dfrac{dx}{x}=3t^2 \, dt\\
\int \dfrac{dx}{x}=\int 3t^2 \, dt\\
\ln x=3\dfrac{t^3}{3}+C\\
\ln x=t^3+C\\
x=e^{t^3+C}\\
x=e^{t^3}\cdot e^C\\
\boxed{x=Ce^{t^3}}$

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Emerson has $120. Each week, he saves an additional $15. Write a function f(x) that models the total amount of money Emerson has

Nastasia [14]

Answer:

f(x) = 120 + (15 * x)

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3 years ago

Read 2 more answers

A rectangle has a perimeter of 58 inches. The length is five more than twice the width. Write and solve an equation to determine

Ymorist [56]

Answer:

The width is 8 inches.

Step-by-step explanation:

Let the width be x. Per the question, the length should be 2x + 5. Set up a perimeter equation and solve for x.

I have attached the work to your problem.

Please see the attachment below.

I hope this helps!

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3 years ago

Use synthetic division and remainder theorem p(x) = 3x^3 - 5x^2 - x + 2. p(-1/3)=

Alik [6]

Answer:

5/3

Step-by-step explanation:

-1/3 goes on the outside and since we have our polynomial in standard form with no in between terms missing, 3,-5,-1,2 go inside because they are the coefficients of our polynomial.

-1/3 | 3 -5 -1 2

-------------------------------------

First step bring the 3 down inside. (3+0=3)

-1/3 | 3 -5 -1 2

-------------------------------------

Whatever goes below the bar, must be multiplied by outside number and put directly below next number inside.

-1/3 | 3 -5 -1 2

| -1

-------------------------------------

The numbers lined up vertically are added to get the numbers underneath the bar.

-1/3 | 3 -5 -1 2

| -1

-------------------------------------

3 -6

Again any number below the bar gets multiply to the number outside.

-1/3 | 3 -5 -1 2

| -1 2

-------------------------------------

3 -6

Again the numbers lined up vertically above the bar get added to get the number that goes underneath the bar there.

-1/3 | 3 -5 -1 2

| -1 2

-------------------------------------

3 -6 1

Multiply to outside number 1(-1/3)=-1/3.

This goes under the 2 inside.

-1/3 | 3 -5 -1 2

| -1 2 -1/3

-------------------------------------

3 -6 1

The last number we are fixing to be put is the remainder of (3x^3-5x^2-x+2)/(x+1/3) or you could say it is the value of p(-1/3) since:

P(x)/(x-c)=Q(x)+R/(x-c)

Multiply both sides by (x-c):

P(x)=Q(x)(x-c)+R

If you evaluate P at x=c, we get R:

P(c)=Q(c)(c-c)+R

P(c)=Q(c)*0+R

P(c)=R.

Let's finish:

-1/3 | 3 -5 -1 2

| -1 2 -1/3

-------------------------------------

3 -6 1 5/3

This means p(-1/3)=5/3.

We could have also got this by directly plugging in (-1/3) for x into 3x^3-5x^2-x+2.

7 0

3 years ago

A shoe store advertises that all shoes are on sale for 25% off the regular price. find the sale price of a pair of shoes that ha

DENIUS [597]

100-25=75
find 75% of the 85

percent means parts out of 100
75%=75/100=0.75

'of' means multiply

75% of 85 means
0.75 times 85=63.75

sale price is $63.75

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3 years ago

A group of students weighs 500 US pennies. They find that the pennies have normally distributed weights with a mean of 3.1g and

inysia [295]

Question 1

probability between 2.8 and 3.3

The graph of the normal distribution is shown in the diagram below. We first need to standardise the value of X=2.8 and value X=3.3. Standardising X is just another word for finding z-score

z-score for X = 2.8
$z= \frac{2.8-3.1}{0.41} =-0.73$ (the negative answer shows the position of X = 2.8 on the left of mean which has z-score of 0)

z-score for X = 3.3
$z= \frac{3.3-3.1}{0.41}=0.49$

The probability of the value between z=-0.73 and z=0.49 is given by
P(Z<0.49) - P(Z<-0.73)

P(Z<0.49) = 0.9879
P(Z< -0.73) = 0.2327 (if you only have z-table that read to the left of positive value z, read the value of Z<0.73 then subtract answer from one)

A screenshot of z-table that allows reading of negative value is shown on the second diagram

P(Z<0.49) - P(Z<-0.73) = 0.9879 - 0.2327 = 0.7552 = 75.52%

Question 2
Probability between X=2.11 and X=3.5

z-score for X=2.11
$z= \frac{2.11-3.1}{0.41}=-2.41$

z-score for X=3.5
$z= \frac{3.5-3.1}{0.41} =0.98$

the probability of P(Z<-2.41) < z < P(Z<0.98) is given by
P(Z<0.98) - P(Z<-2.41) = 0.8365 - 0.0080 = 0.8285 = 82.85%

Question 3
Probability less than X=2.96

z-score of X=2.96
$z= \frac{2.96-3.1}{0.41}=-0.34$
P(Z<-0.34) = 0.3669 = 36.69%

Question 4
Probability more than X=3.4
$z= \frac{3.4-3.1}{0.41}=0.73$
P(Z>0.73) = 1 - P(Z<0.73) = 1-0.7673=0.2327 = 23.27%

7 0

3 years ago