Answer:
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
Step-by-step explanation:
We are given the following differential equation:
[tex]\frac{dP}{dt} = kP - h[/tex]
Solving by separation of variables:
[tex]\frac{dP}{kP-h} = dt[/tex]
Integrating both sides:
[tex]\int \frac{dP}{kP-h} = \int dt[/tex]
On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then
[tex]\frac{1}{k} \ln{kP-h} = t + K[/tex]
In which K is the constant of integration.
[tex]\ln{kP-h} = kt + K[/tex]
[tex]e^{\ln{kP-h}} = e^{kt + K}[/tex]
[tex]kP - h = Ke^{kt}[/tex]
[tex]kP = Ke^{kt} + h[/tex]
[tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
3. Find the length of X (in the picture) plssss I need help.
Answer:
imagine the upper triangle as the same as the lower one, but rotated by 180° around the corner point they share, and resized.
the base of the smaller triangle is resized by a factor of 3/4.5, or reduced: 1/1.5
we just take the length from the hypotenuse of the bigger triangle and resize it to, either by multiplying with 1/1.5 or by dividing by 1.5
personally, I find the latter easier.
x = 7.5/1.5 = 5
If m and n are two rational numbers, then m+n lies between m and n
2
Answer:
19thuuzvdkedhddudhjdhdhfghfidhdhdhfheidhfjr9fddy6gqufgaqgxhrhrydudkydtdffyztstdtiztuytzmyrsyrststststsut0egjjefeigjeojokfzbkehfzifgihrxeudihxizhieg9zfjz9deffejfjiefeihfiefhiefhefiefh3fr3hi3jfhfhfkzdhf2ivuvdfuvuzfecfkfidyfl5a4
The length of a rectangle should be 8 meters longer than 7 times the width. If the length must be
between 43 and 106 meters long, what are the restrictions for the width, x?
Answer:
The restrictions for x would be 14 > x > 5.
Step-by-step explanation:
Let the length of the rectangle be y and the width be x.
That being said, the equation would be as follows:
[tex]y = 7x + 8[/tex]
[tex]y - 8 = 7x[/tex]
[tex]x = \frac{y-8}{7}[/tex]
Therefore, substituting the two values of y into the equations, we would get:
[tex]x = \frac{43-8}{7}[/tex]
[tex]x = \frac{35}{7}[/tex]
[tex]x = 5[/tex]
And:
[tex]x = \frac{106-8}{7}[/tex]
[tex]x = \frac{98}{7}[/tex]
[tex]x = 14[/tex]
Therefore, x would be between 5 and 14, and the restrictions for x would be 14 > x > 5.
Hope this helped!
PLEASE HELP ME WITH THIS ONE QUESTION
How many combinations with repetition are allowed if n = 6 and r = 3?
A) 27
B) 20
C) 18
D) 56
Answer:
D. 56
Step-by-step explanation:
The general solution for the number of combinations with repetition is represented by the following expression:
[tex]x = \frac{(n + r - 1)!}{r!\cdot (n-1)!}[/tex] (1)
Where:
[tex]n[/tex] - Total number of elements.
[tex]r[/tex] - Number of the sample.
If we know that [tex]n = 6[/tex] and [tex]r = 3[/tex], then the number of combinations with repetition:
[tex]x = \frac{(6+3-1)!}{3!\cdot (6-1)!}[/tex]
[tex]x = 56[/tex]
Hence, correct answer is D.
a bag contains 5white and 3red identical balls.if the balls are drawn at random after the other without replacement. what is the probability that the first red ball is picked at fifth draw
Answer:
2/7
Step-by-step explanation:
Use technology to help you test the claim about the population mean, mu, at the given level of significance, alpha, using the given sample statistics. Assume the population is normally distributed.
Claim: μ>1220;α=0.08; σ=211.67.
Sample statistics: x=1235.91,n=300
Identify the null and alternative hypotheses and calculate the standardized test statistic.
Answer:
H0 : μ = 1220
H1 : μ > 1220
Test statistic = 1.30
Step-by-step explanation:
Sample mean, x = 1235.91
Standard deviation, σ = 211.67
Sample size, n = 300
The hypothesis :
Null ; H0 : μ = 1220
Alternative ; H1 : μ > 1220
Tbe test statistic :
(x - μ) ÷ (σ/√(n))
(1235.91 - 1220) ÷ (211.67/√(300))
15.91 / 12.220773
= 1.3018
= 1.30
find slope from the pair of points (2,-2) (-5,4)
Answer:
-6/7
Step-by-step explanation:
If we have two points, we can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 4 - -2)/( -5 -2)
= ( 4+2) /(-5-2)
= 6/-7
= -6/7
Can anyone please help me
Answer:
The experiment shows the frequency of results derived from tossing a coin
Rachel is driving to visit her mother, who lives 250 miles away. How long will the
drive be, round-trip, if Rachel drives at an
average speed of 40 mph?
Answer:
Time for a round trip = 12.5 hours
Step-by-step explanation:
Mother's house = 250 miles
Total distance for the round trip = 250 + 250 = 500 miles
Given speed = 40 mph
Find time .
[tex]Speed = \frac{distance }{Time }\\\\Time = \frac{distance }{speed } = \frac{500}{40} \\\\Time = 12.5 \ hours[/tex]
Mrs. Smith bought 6.2 kg of cassava and 1 kg 250 g of bananas. What is the total weight in kg?
Step-by-step explanation:
my answer is in the image above
A landscaper is making a garden bed in the shape of a rectangle. The length of the garden bed is 2.5 feet longer than twice the width of the bed. The area of the garden bed is 62.5 square feet. What is the perimeter of the garden bed, in feet?
Answer:
I'll setup the problem, then you can do the calculations
Step-by-step explanation:
Perimeter = 2width(W) + 2length (L)
Area = LW
L = 2.5 + 2W
LW = 62.5
substitute L in equation for area
[tex]2.5W + {2W}^{2} = 62.5 \\ \\ {2W}^{2} + 2.5 - 62.5 \\ \\ use \: quadratic \: solution \\\frac{ - b ± \sqrt{ {b}^{2} - 4ac}}{2a} [/tex]
a = 2; b = 2.5; c = 62.5
send a comment if you have a question
The perimeter of a rectangle.
P = 2 ( length + width )
The area of a rectangle.
Area = length x width
The perimeter of the rectangle shape garden bed is 32 feet.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
A rectangular shape Landscaper:
Width = W
Length = 2.5 + W
Area = 62.5 square feet
The perimeter of a rectangle.
P = 2 ( length + width )
The area of a rectangle.
Area = length x width
Now,
Area = 62.5
length x width = 62.5
(2.5 + W) x W = 62.5
2.5W + W² = 62.5
W² + 2.5W = 62.5
W² + 2.5W - 62.5 = 0 ______(A)
The roots of this equation (A) are:
W = 6.75 and W = -9.25 (eliminated)
Now,
Length = 2.5 + 6.75 = 9.25 feet
Width = 6.75 feet
The perimeter of the rectangle.
P = 2 ( length + width )
P = 2 x (9.25 + 6.75)
P = 2 x 16
P = 32
Thus,
The perimeter of the rectangle shape garden bed is 32 feet.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ2
How do you find the surface area
Answer:
It depends on what shape you have. Here are some formulas for different shapes.
Step-by-step explanation:
Rectangular prism: 2lw + 2lh + 2wh
Cylinder: 2 pi r² + 2 pi rh
Sphere: 4 pi r²
Cone: pi r² + pi rl
Square-based pyrimid: 1/2lp +B
I hope this helps!
A bus travels at a constant speed. The following table shows the distance the bus travels (in kilometers) over a period of
time (in hours):
distance (d) 42 252 378
time (9 0.5 3
4.5
a. Use complete sentences to describe the relationship represented in the table.
b. Write an equation using variables that represents the relationship shown in the table.
c. Use your equation to find how far the bus travels in 6 hours.
Answer:
question is not clear
specify the table
I need help I’ll give u brainlest
Answer:
216 yd³
Step-by-step explanation:
Volume of a rectangular prism
= product of the three orthogonal sides
= 6yd * 6yd * 6yd
= 216 yd³
Answer:
216
Step-by-step explanation:
:)
Which represents where f(x) = g(x)
he speeds (in MPH) of automobiles traveling in a city are given below:
20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58
The mean speed of the cars is
Answer:
Mean speed = 41.3 mph
Step-by-step explanation:
Given that,
The speeds of an automobiles are given below:
20, 35, 42, 52, 65, 49, 24, 37, 23, 41, 50, 58
We need to find the mean speed of the cars.
Mean = sum of observations/ no. of observation
[tex]M=\dfrac{20+35+42+52+65+49+24+37+23+41+50+58}{12}\\\\M=41.3[/tex]
So, the mean speed of the cars is equal to 41.3 mph.
Find the probability
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Red: 2
Blue: 4
Yellow: 4
[tex]\frac{2}{10}[/tex]
[tex]\frac{2/2}{10/2}=\frac{1}{5}[/tex]
The volume of a right cylinder is 277 cubic centimeters, and the
height is 3 centimeters (cm). What is the radius of the cylinder?
Answer:
3cm
use the formula for the volume of a cylinder
and substitute
Solve the compound inequality 7x ≥ –56 and 9x < 54.
Answer: first one is x≥-8 second one is x<6
Step-by-step explanation: for the first one you divide both sides by 7 and the second won do the same except divide by 9 on each side
Hello,
7x ≥ -56
⇔ 7x / 7 ≥ -56 / 7
⇔ x ≥ -8
S = [-8 ; +∞[
9x < 54
⇔ 9x / 9 < 54 / 9
⇔ x < 6
S = ]-∞ ; 6]
:-)
Value of 140 degree in diagrams
Answer:
There are 360º in a circle. 140º has been allocated to one angle.
There are 360-140 = 220º left in the circle.
Step-by-step explanation:
Please help me esperas this!!
9514 1404 393
Answer:
tan(φ) = (x² -1)/(2x)
Step-by-step explanation:
In a right triangle, the tangent of one of the acute angles is the ratio of the opposite side to the adjacent side. Here, the length of the adjacent side is not given, but can be found from the Pythagorean theorem.
adjacent side = √((x² +1)² -(x² -1)²) = √((x⁴ +2x² +1) -(x⁴ -2x²+1))
adjacent side = √(4x²) = 2x
Then the tangent ratio is ...
tan(φ) = (opposite side)/(adjacent side)
tan(φ) = (x² -1)/(2x) . . . . . . for x > 0
HELP!!!!
Car Survey In a survey of 3,200 people who owned a certain type of car, 2,080 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
___% of the people surveyed were satisfied with the car.
Answer:
65%
Step-by-step explanation:
2080/3200times100%
simplify 4-x squared ÷2x-x squared
Answer:
4-[tex]\frac{x}{2}[/tex]-[tex]x^{2}[/tex]
Step-by-step explanation:
6 Write 89.4945 correct to (a) nearest whole number, [1] (b) two decimal places.
Answer:
a)89
b)89.45
Step-by-step explanation:
Evaluate if 8y + 4x – (2x + 3) if x = – 2 and y = 6
Answer:
41
Step-by-step explanation:
substitute x=-2 and y=6, we know
8×6 +4×(-2) -(2×(-2) +3) = 48-8-(-1) =41
Answer:
41
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
8y + 4x - (2x + 3)
x = -2
y = 6
Step 2: Evaluate
Substitute in variables: 8(6) + 4(-2) - (2 · -2 + 3)(Parenthesis) Multiply: 48 - 8 - (-4 + 3)(Parenthesis) Add: 48 - 8 - (-1)Subtract: 41Need help with this question
Answer:
cant see it
Step-by-step explanation:
just type it out
which of the following is the quotient of the rational expressions shown below? x/3x-1 divided by x-2/2x ?
Answer:
Below.
Step-by-step explanation:
x/3x-1 divided by x-2/2x
= x/3x-1 * 2x/x-2
= 2x^2/(3x-1)(x-2).
If we expand the denominator it is
2x^2/(3x^2-7x+2).
If I have 46 $ and the taxi cab charges 0.60$ plus 7$ fee how far can I ride
Answer:
65 miles
Step-by-step explanation:
costs = flat fee + cost per mile * miles
46 = 7+ .60m
Subtract 7 from each side
46-7 = 7+.6m-7
39 = .6m
Divide each side by .6
39/.6 = m
65 miles
When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps andfound that 1304 of them were not pumping accurately (within 3.3 oz when 5 gal ispumped),and 5689 pumps were accurate. Use a 0.01 significance level to test the claimof an industryrepresentative that less than 20% of the pumps are inaccurate.
Answer:
The p-value of the test statistic from the standard normal table is 0.0017 which is less than the level of significance therefore, the null hypothesis would be rejected and it can be concluded that there is sufficient evidence to support the claim that less than 20% of the pumps are inaccurate.
Step-by-step explanation:
Here, 1304 gas pumps were not pumping accurately and 5689 pumps were accurate.
x = 1304, n = 1304 + 5689 = 6993
The level of significance = 0.01
The sample proportion of pump which is not pumping accurately can be calculated as,
The claim is that the industry representative less than 20% of the pumps are inaccurate.
The hypothesis can be constructed as:
H0: p = 0.20
H1: p < 0.20
The one-sample proportion Z test will be used.
The test statistic value can be obtained as:
[tex]Z=\frac{\hat{p}-P}{\sqrt{\frac{P(1-P))}{n}}}\\\\Z=\frac{0.186-0.20}{6993}\\\\Z=-2.927[/tex]
PLS HELP ASAP!!!
THANK YOU.
9514 1404 393
Answer:
rectangular prism: 288 ft³triangular prism: 72 ft³total: 360 ft³Step-by-step explanation:
The volume of a rectangular prism is given by the formula ...
V = LWH . . . . . the product of length, width, height
This rectangular prism has a volume of ...
V = (12 ft)(6 ft)(4 ft) = 288 ft³ . . . . rectangular prism volume
__
The volume of a triangular prism is found from the formula ...
V = Bh
where B is the area of the triangular base, and h is the height of the prism (distance between the triangular bases). The triangular base area is found from ...
A = 1/2bh . . . . .where b is the base of the triangle, and h is its height.
Here, we have ...
B = 1/2(6 ft)(4 ft) = 12 ft²
V = Bh = (12 ft²)(6 ft) = 72 ft³ . . . . triangular prism volume
__
The total volume of the given geometry is the sum of the volumes of the parts:
aquarium volume = 288 ft³ +72 ft³ = 360 ft³