Find the general or particular​ solution, as​ indicated, for the following differential equation.
dydx=−0.3y
​y(0)=60
Question content area bottom
Part 1
y=enter your response here

Answer: 2

Step-by-step explanation:

If there are three times as many students when there are 6 students you do 6 divided by three to give you two.

Answer:

he last ratio is written incorrectly.

Mandy reversed the input and output in the numerator and denominator.

The correct ratio is 50/10.

The relationship is proportional.

Answer:

35.53

Step-by-step explanation:

19.00x 87%=16.53

16.53+19.00= 35.53

Step-by-step explanation:

all can come

better to take 1,2,3

because triangle is of only three sides and we can construct a triangle according to the angle which we want

Answer:

7,24,25

Step-by-step explanation:

i got it right. i may be a little too late. but thats the answer

There are several theorems that are necessary for AP Calculus BC including: Fundamental Theorem of Calculus, Mean Value Theorem, Intermediate Value Theorem, Extreme Value Theorem, and Rolle's Theorem.

Calculus is a branch of mathematics associated with the study of instantaneous rates of change (differential calculus) and the summation of infinitely smaller factors to calculate some whole (integral calculus). The theorems that are necessary for AP Calculus BC are:

1. The Fundamental Theorem of Calculus: This theorem relates the derivative and the integral of a function. It is used to calculate definite integrals and is a crucial part of calculus.

2. The Mean Value Theorem: This theorem states that if a function is continuous on a closed interval and differentiable on an open interval, then there exists a point in the interval where the derivative is equal to the average rate of change of the function over the interval.

3. The Intermediate Value Theorem: This theorem states that if a function is continuous on a closed interval, then it takes on every value between its minimum and maximum values on that interval.

4. The Extreme Value Theorem: This theorem states that if a function is continuous on a closed interval, then it has both a maximum and minimum value on that interval.

5. Rolle's Theorem: This theorem is a special case of the Mean Value Theorem and states that if a function is continuous on a closed interval, differentiable on an open interval, and has the same value at the endpoints of the interval, then there exists a point in the interval where the derivative is zero.

These theorems are essential for understanding and solving problems in AP Calculus BC.

Learn more about Theorem:

https://brainly.com/question/28167439

#SPJ11

Answer:

distance from P to the plane  = 8957.6 m

Step-by-step explanation:

sin23 = 3500 / distance from P to the plane

distance from P to the plane  = 8957.6 m

To find the rate of change of y with respect to time t, we need to take the derivative of the function y = 500(1-0.2)^t with respect to t:

dy/dt = 500*(-0.2)*(1-0.2)^(t-1)

Simplifying this expression, we get:

dy/dt = -100(0.8)^t

Therefore, the rate of change of y with respect to t is given by -100(0.8)^t. This means that the rate of change of y decreases exponentially over time, and approaches zero as t becomes large.

Answer:

y=2x-7

2(2x-7)=4x-14

4x-14=4x-14

therefore,this has no solutions

Answer:

255.75ft/inch

Step-by-step explanation:

s (scale) = 12,276/4

s = 3069 ft

s = 3069/12

s = 255.75

answer.)s=255.75

explanation:

•divide 12,276' by 4'

•3069'/1'

• 1'=12"

• 3069' divided by 12"

•255.75

a) The mean for the given data is 11.44

b) The median for the given data is 11

c) The mode for the given data is 11

d) The maximum score received by a student is 18

e) The minimum score received by a student is 3

f) The range for the given data is 15

g) The interquartile range for the given data set {12, 6, 9, 5, 11} is 6

h) The third quartile for the given data set  {0, 8, 14, 17, 7} is 15.5

i) The third quartile for the given data set {14, 11, 9, 3, 12} is 13

j) The interquartile range for the given data set {3, 8, 9, 11, 5}  is 6

The interquartile range is a measure of statistical dispersion in descriptive statistics, which is the spread of the data. The IQR is also known as the middle 50% spread, the fourth spread, or the H-spread.

a) Mean=(12+8+11+10+6+7+10+13+14+15+9+18+17+15+3+11+11)/18

=11.44

Therefore, mean=11.44

b) Median= n is even

Then,

((n/2 )th +((n/2)+1)th)/2

=(11+11)/2

=11

Therefore, median=11

c) Mode= The number that is repeated highest number of times

Mode=11

Therefore, mode=11

d) The maximum score received by a student is 18

e) The minimum score received by a student is 3

f) Range=maximum-minimum

=18-3

=15

Therefore, Range=15

g) Median=9

Q₁=(5+6)/2=5.5

Q₃=(11+12)/2=11.5

Interquartile range=|Q₃-Q₁|

=|11.5-5.5|

=6

The interquartile range for the given data set {12, 6, 9, 5, 11} is 6

h) Median=10

Q₃=(14+17)/2=15.5

The third quartile for the given data set  {0, 8, 14, 17, 7} is 15.5

i) Median=11

Q₃=(12+14)/2=13

The third quartile for the given data set {14, 11, 9, 3, 12} is 13

j) Median=8

Q₁=(3+5)/2=4

Q₃=(9+11)/2

Interquartile range=|Q₃-Q₁|

=|10-4|

=6

The interquartile range for the given data set {3, 8, 9, 11, 5}  is 6

To know more about interquartile range, visit:

https://brainly.com/question/4135956

#SPJ1

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

Learn more on law of sine here;

https://brainly.com/question/30401249

#SPJ1

Answer:

ok, so the answer would be 27 hot dogs and 53 tacos salads

Step-by-step explanation:

The total cost of gas in December is $6088.55.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Given that, the rate per unit is $0.65.

Number of units of gas used in December is 9367 units.

Now, the total cost = 9367×0.65

= $6088.55

Therefore, the total cost of gas is $6088.55.

To learn more about the unit rate visit:

https://brainly.com/question/11258929.

#SPJ9

"Your question is incomplete, probably the complete question/missing part is:"

Find how many units of gas were used each month. Then find the total bill for each month. Assume the rate per unit is $0.65

December, 9367

When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when the advances are not given for shows. This is to ensure that the performer is fully committed to performing at the event and to cover any expenses that may be incurred in the process.

The advance fee is usually non-refundable and is paid by the promoter or venue operator to the booking agent. This is to show their commitment to the performer and to demonstrate that they are serious about booking them for the event. The remaining balance is then usually paid on the day of the performance or shortly after.

The booking agent should also ensure that all parties involved in the booking are aware of the terms and conditions and have signed a contract or agreement to confirm their agreement.

To know more about advance fee, refer

https://brainly.com/question/32729770

#SPJ11

Answer:

diagonally, both numbers on top, both numbers on bottom.

Step-by-step explanation:

Diagonally, because cross-multiplying. And the other two are obvious.

Answer:

base = 10cm and height = 10cm

Step-by-step explanation:

base + height = 20

base = height = 20/2= 10cm

The original retail price is $42.15, which is the solution to the equation 0.65x = 27.30. In other words, when Jennifer paid $27.30, that was 65% of the original retail price of $42.15.

The original retail price can be found by solving the equation 0.65 x = 27.30 for x. To do this, we need to isolate the variable x on one side of the equation.

0.65 x = 27.30

Divide both sides of the equation by 0.65:

x = 27.30 / 0.65

Simplify the right side of the equation:

x = 42.15

So, the original retail price was $42.15

In summary, if the sale price Jennifer paid was $27.30, then the original retail price was $42.15

Learn more about original retail price: https://brainly.com/question/7459025

#SPJ11

Answer:

3 3/4 or 3/75

Step-by-step explanation:

Answer:

3 3/4 or 3.75

We get: y'[(2x - x² - 1)e^(-x)(y² + 2y + 2) + 2(2x - x² - 1)e^(-x)y] = (2x - x² - 1)(y² + 2y + 1) - y Now, we can substitute the values of T₁ = 15, T2 = 916 and T3 = 917 .

As per the given problem, we need to calculate an approximate value for V0.7 using the first three terms of the √0.7√1-0.3 binomial expansion which is given by:√0.7 = √(1 - 0.3)

We know that the binomial expansion of the above expression is given by:(1 - x)^n = 1 - nx + n(n - 1)x^2 / 2! - n(n - 1)(n - 2)x^3 / 3! + ...

Applying the same formula, we get:√(1 - 0.3) = 1 - 0.3/2 + (0.3*0.7)/(2*3)√(1 - 0.3) = 1 - 0.15 + 0.0315√(1 - 0.3) = 0.8815 .

Therefore, the approximate value of V0.7 is 0.8815 using the first three terms of the √0.7√1-0.3 binomial expansion.

Now, we need to determine all the critical coordinates (turning points/extreme values) of y = (x² + 1)e¯*

The given function is y = (x² + 1)e^(-x)Let's first determine its first derivative, which is given by: y' = (2x - x² - 1)e^(-x)

Setting this first derivative equal to 0 to get the critical values: (2x - x² - 1)e^(-x) = 0(2x - x² - 1) = 0x² - 2x + 1 = 0

Solving the above quadratic equation, we get: x = 1, 1 For the second derivative, we get: y'' = (x² - 4x + 3)e^(-x)

Now, let's check the nature of the critical points using the second derivative test: When x = 1: y'' > 0, which means that this is a local minimum . When x = 1: y'' > 0, which means that this is a local minimum .

Therefore, the critical coordinates are (1, e^(-1)) and (1, e^(-1)).

Now, we need to find the expression for dx= y'r [1+y]²-x+y=4.

Differentiating with respect to x, we get: d/dx (dx/dx) = d/dx [(2x - x² - 1)e^(-x)][1 + y]² - d/dx y = d/dx (x - 4)1 = [(2x - x² - 1)(1 + y)^2 - 2(1 + y)(2x - x² - 1)e^(-x)y'] - y'

Therefore, we get: y' = [(2x - x² - 1)(1 + y)² - 2(1 + y)(2x - x² - 1)e^(-x)y' - y] / [(2x - x² - 1)e^(-x)(1 + y)² - 1]y'[(2x - x² - 1)e^(-x)(1 + y)² - 1] = (2x - x² - 1)(1 + y)² - 2(1 + y)(2x - x² - 1)e^(-x)y' - y

Simplifying, we get: y'[(2x - x² - 1)e^(-x)(1 + y)² - 1 + 2(1 + y)(2x - x² - 1)e^(-x)] = (2x - x² - 1)(1 + y)² - y

Therefore, we get: y'[(2x - x² - 1)e^(-x)(y² + 2y + 2) + 2(2x - x² - 1)e^(-x)y] = (2x - x² - 1)(y² + 2y + 1) - y

Now, we can substitute the values of T₁ = 15, T2 = 916 and T3 = 917 in the above expression to get the final answer.

To know more about Values  visit :

https://brainly.com/question/30145972

#SPJ11

Answer:

b+8≥12.4

Step-by-step explanation:

Here, we want to select the correct option

From what we have here;

b ≥12.4-8

b ≥ 4.4

Looking at the range of values in the set

We can see that the smallest of values is 4.4

This tells exactly the correctness of the last option as the values of b are 4.4 or greater

a).The bearing of point A from B is 234°.

b). The bearing of point B from point A is 054°.

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

The bearing of point A from B is the angle measured from the north of B to the straight line distance between A and B which is 234°. While the bearing of point B from point A is the angle measure starting from the north of A to the straight line distance between A and B which is 054°.

Therefore, the bearing of point A from B is 234° while the bearing of point B from point A is 054°.

Read more about bearing here:https://brainly.com/question/22518031

#SPJ1

The if statement assigns a value of 10000 to the variable "bonus" if the value of the variable "goodssold" exceeds 500000.

To achieve this, we can use an if statement in programming. An if statement allows us to conditionally execute a block of code based on a specified condition. In this case, the condition is whether the value of the variable "goodssold" is greater than 500000. If the condition evaluates to true, the code inside the if statement will be executed, and the variable "bonus" will be assigned a value of 10000.

Here's an example of how the if statement can be written in Python:

if goodssold > 500000:

   bonus = 10000

In this code snippet, the variable "goodssold" represents the number of goods sold, and we compare its value to 500000 using the greater than operator (>). If the condition is true, the code inside the if statement is executed, and the variable "bonus" is assigned a value of 10000. If the condition is false, the code inside the if statement is skipped, and the variable "bonus" retains its previous value (if any).

By using this if statement, we can dynamically assign a bonus of 10000 to the variable "bonus" based on the value of the variable "goodssold" being greater than 500000. This allows for flexible and conditional handling of the bonus calculation in the program.

Learn more about statement here:

https://brainly.com/question/30483936

#SPJ11

Answer:

8.5 ft (nearest tenth)

Step-by-step explanation:

To find the depth of the pool at the deep end, we need to find the height of the right triangle with angle 16.5° and add it to 4.5 ft

Base of the triangle = 35 - 9 - 12.5 = 13.5 ft

Use the tan trig ratio:

\(\tan(x)=\dfrac{O}{A}\)

where x is the angle, O is the side opposite and angle and A is the side adjacent to the angle in a right triangle.

Given:

\(\implies\tan(16.5)=\dfrac{h}{13.5}\\\\\implies h= 13.5\tan(16.5)\\\\\implies h = 4.0 \textsf{ ft (nearest tenth)}\)

Therefore, the depth of the pool at the deepest end = 4 + 4.5 = 8.5 ft (nearest tenth)

Now

\(\\ \rm\Rrightarrow tan\theta=\dfrac{P}{B}\)

\(\\ \rm\Rrightarrow tan16.5=\dfrac{P}{13.5}\)

\(\\ \rm\Rrightarrow P=13.5tan16.5\)

\(\\ \rm\Rrightarrow P=13.5(0.3)\)

\(\\ \rm\Rrightarrow P\approx 4ft\)

The most appropriate unit to weigh a single medical pill is the kilogram.

In Physics, the term unit directs to the quantity of a constant magnitude, utilized to estimate the magnitudes of other quantities of an identical class.

Tons stand massive and are utilized to weigh very heavy objects, usually in manufacturing and vehicular measures.

Ounces exist as a member of the imperial system of measurement, which stands as the least popular utilized in medicine worldwide.

Cups exist as a measurement of volume, not mass.

Therefore, the correct answer is option B: kilogram.

To learn more about a kilogram

https://brainly.com/question/21091217

#SPJ2

The volume of the cone in this problem is given as follows:

V = 48π units³.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

From the image given in this problem, the parameters are given as follows:

r = 6 mm, h = 4 mm.

Hence the volume is given as follows:

V = π x 6² x 4/3

V = 48π units³.

More can be learned about the volume of a cone at brainly.com/question/12004994

#SPJ1

The allowable child and dependent care credit considering their pre-credit tax liability is $0

The following chart illustrates how their authorized child and dependent care credit was calculated:

If the revenue is less than $22,000, the full 22% would be permitted.

However, the eligible kid expense would only be allowed up to $7,000.

Consequently, the sum would be

= $7,000 × 22%

= $1,540

Since there is already a pre-credit tax liability, $0 should be taken into account because there would be no credit.

Due to their pre-credit tax liability, the available child and dependent care credit is therefore $0.

To learn more about tax liability click here:

brainly.com/question/15394738

#SPJ4

Answer:

the blue one <3

Step-by-step explanation:

the black one has slope of 1

the blue one has slope of 4/2 which is also 2

Georgia  takes 24 minutes to clean the espresso machine by herself.

The correct answer is an option D.

The equation for the situation is:

\(\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8}\)

here, x is the number of minutes it takes Georgia to clean the machine by herself.

We need to find the value of x.

Consider the equation,

\(\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8} \\\\\frac{(x -12)+x}{x(x-12)}=\frac{1}{8}\\\\\frac{x -12+x}{x^2-12x}=\frac{1}{8}\)

(2x - 12) × 8 = x² - 12x

16x - 96 =  x² - 12x

x² - 12x -16x + 96 = 0

x² - 28x + 96 = 0

x²-24x-4x+96 = 0

(x - 24)(x - 4) = 0

x = 24 or x = 4

If x = 4, then x - 12 would be negative which is not possible.

Thus, it takes 24 minutes for Georgia.

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Find the complete question below.

The answer to the given binary operation is 10012. The binary operation of adding 1112 and 102 will be solved by converting the binary numbers to base 10, performing the addition in base 10, and then converting the result back to base 2.

Converting the binary numbers to base 10, we have 1112 = 7 and 102 = 2. Adding 7 and 2 in base 10 gives us 9. To convert the result back to base 2, we divide 9 by 2 repeatedly until the quotient becomes 0. The remainder in each division gives us the binary digits of the answer. In this case, 9 divided by 2 is 4 with a remainder of 1, and 4 divided by 2 is 2 with a remainder of 0. Therefore, the binary representation of 9 is 1001. Hence, the answer to the given binary operation is 10012.

Learn more about binary here:
brainly.com/question/33333942

#SPJ11

Answer:

A. 85  B. 87  C. 60

Step-by-step explanation:

As shown in the shapes, A, is a full circle making 360 degrees full. B, a half circle making 180 degrees half. C, a full circle again making 360 degrees full.

A: [360-(132+63+80)]

360 - 275

=85

B: [180(60+33)]

180 - 93

=87

C: [360(120+60+120)]

360 - 300

=60