The salt that is left after t minutes is y = 16e^[-t/100]
We have to mix problems we use:
dy / dt = (rate in) - (rate out)
The water entering the tank at a speed of 10 L / min but it has no salt, therefore
rate in = 0
The tank has 1000 liters of brine with 16 kg of salt initially, therefore the concentration of salt at time "t" is:
y (t) / 1000
then rate out would be:
rate out = y (t) / 1000 * 10 = y (t) / 100
The difference equation would then be:
dy / dt = 0 - y (t) / 100
1 / y (t) * dy = 1/100 * dt
We integrate from both sides and we have:
ln y = - (1/100) * t + C1
y = e ^ [- (1/100) * t + C1]
y = e ^ [- (1/100) * t] * e ^ [C1]
We assume that C = e ^ [C1]
Thus:
y = C * e ^ [- (1/100) * t]
now y = 16 to t = 0, replacing:
16 = C * e ^ [- (1/100) * 0]
16 = C, therefore we would have:
y = 16*e ^ [- t / 100]
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an 7.40-cm-diameter, 370 g solid sphere is released from rest at the top of a 2.00-m-long, 19.0 ∘ incline. it rolls, without slipping, to the bottom.
The angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.
What is angular velocity?In physics, angular velocity or angular speed, also recognized as angular frequency vector, is a pseudovector portrayal of how fast the angular position or orientation of an object changes over time.
So, angular velocity will be:
mg(h sinθ) = 1/2 Iω² + 1/2mv²
I of solid sphere = 2/5 mr²
Hence,
mg(h sinθ) = 1/2 (2/5 mr²) ω² + 1/2 mv²
Now remove the mass:
g h sin θ = 1/5 r² ω² + 1/2 v²
ω = v/r, v = ωr
Now, calculate angular velocity as follows:
g h sin θ = 1/5 r² ω² + 1/2 (ωr)²
g h sin θ = (7/10) r² ω²
ω² = 10 g h sin θ/7 r²
ω = √10 g h sin θ/7 r²
= √10 (9.8) (2.1) sin 25° / 7 (0.04)²
= 88.1 rad/s
Therefore, the angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.
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Complete question:
An 8.0 cm diameter, 400 g sphere is released from rest ta the tip of a 2.1 m long, 25-degree incline. It rolls, without slipping, to the bottom. What is the sphere's angular velocity at the bottom of the incline?
The length of a line is 12.3 cm, correct to 1 decimal place.
Write down the upper bound of the length of the line.
The upper bound of the length of the line is 12.34 cm
How to determine the upper bound of the length of the lineFrom the question, we have the following parameters that can be used in our computation:
Length of the line = 12.3 cm
From the question, we understand that
Time = rounded to the nearest one decimal place
The highest number that can be rounded to 12.3 to the nearest one decimal place is 12.34
This means that
Upper bound = 12.34
Hence, the upper bound is 12.34 cm
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Please check if ur able to help with these Segments OA and OB are radii ofthe semicircle above. Arc AB has length 3n and OA = 5. What is the value of x ?'
OA=5 and the length of arc AB is 3π. The x value is [tex]108[/tex]°.
The circle's radius and arc length are both provided. Finding the angle that the arc occupies on the center O is necessary.
The correct formula is
s=rФ
Where
arc length is measured in radians,
r is the radius, and
Ф is the angle (in radians)
If Ф is in degrees, we apply the formula.
s= Ф[tex]*\frac{\pi }{180} *r[/tex]
In order to determine the value of theta, we must enter the specified values of s and r into the formula above.
[tex]3\pi =[/tex]Ф[tex]*\frac{\pi }{180} *5[/tex]
[tex]3\pi *\frac{180}{\pi } *\frac{1}{5}=[/tex]Ф
Ф=[tex]108[/tex]°
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A resort manager is choosing a committee of four people to discuss employment issues. He'll choose from eight housekeepers, three desk clerks, and five maintenance workers. How many possible committees are there if there have to be at least two housekeepers?
Answer:
There are 1,680 possible committees if there have to be at least two housekeepers.
Step-by-step explanation:
Which column of elements is the most reactive?
The alkali metals, which are located in Group 1A of the periodic table, are the most reactive metals.
The blue column on the left of the periodic table contains the alkali metals, which are the most reactive metals. As we move down column (group) one, which is depicted in blue, their responsiveness improves.
What are Alkali metals ?
Alkali metals are those that react with water to produce strong bases.
It is composed of six elements collectively referred to as the lithium family. These metals have one electron in their outermost shell, making them extremely reactive elements of the periodic table.
A few instances of alkali metal
lithium (Li), sodium (Na), rubidium (Rb), potassium (K), francium (Fr) and Caesium (Cs).
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If y varies directly with x what is the equation when y=-64andx=16
Answer: when y = -64 and x = 16 is y = -4x. This equation states that for every value of x, the corresponding value of y is equal to -4 times the value of x.
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
S:{10}
S:{3}
S:{2}
S:{0}
Hence, when [tex]n=10[/tex] the given inequality is true.
What is the inequality?
An inequality is said to be sharp if it cannot be relaxed and still be valid in general.
Here given that,
Which integer will make the inequality [tex]2(n + 2) < 5(n -1)[/tex] true.
So,
[tex]2(n + 2) < 5(n-1)[/tex]
When
[tex]n=10\\\\\\2(10+2) < 5(10-1)\\\\2(12) < 5(9)\\\\24 < 45[/tex]
Hence, when [tex]n=10[/tex] the given inequality is true.
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You work at Mike's pizza shop. You have the following information about the 7 pizzas in the oven: 3 of the 7 have thick crust and 2 of the 3 thick crust pizzas have mushrooms. Of the remaining 4 pizzas, 2 have mushrooms. Choose a pizza at random from the oven. Make a two-way table to model this chance process.
make a Venn diagram to model this chance process.
4/7 is probability a two-way table to model this chance process.
What are examples and probability?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.
No events getting thick crust pizza and getting pizza with mushrooms are not disjoint as we can have pizza that has thick crust and mushroom both.
No events are not independent as
P(thick and having mushroom) is not equal to P(thick crust)*P(having mushroom)
P( thick and having mushroom) = 2/7
P(thick crust) = 3/7
P( having mushroom) = 4/7
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What is the slope of the line that passes through the points(3,−3) and(18,−3)? Write your answer in simplest form.
Answer: (3, -3) and (18, -3) is 0
Step-by-step explanation:
The slope of a line is a measure of the line's steepness, and it is calculated by taking the difference in the y-coordinates of two points on the line, divided by the difference in their x-coordinates. In this case, the line passes through the points (3, -3) and (18, -3), and the y-coordinates of both points are -3. Therefore, the difference in the y-coordinates is 0, and the slope of the line is 0.
To write this answer in simplest form, we can simply express the slope as 0/1, which can be simplified to 0. Therefore, the slope of the line that passes through the points (3, -3) and (18, -3) is 0.
Answer:
0
Step-by-step explanation:
We can find the slope of the line given two points
m= ( y2-y1)/(x2-x1)
= ( -3 - -3)/(18 -3)
= (-3+3)/(15
= 0/15
= 0
Which statement describes the graph of 4x7 40x6 100x5?O The graph crosses the x axis at x = 0 and touches the x axis at x = 5.O The graph touches the x axis at x = 0 and crosses the x axis at x = 5.O The graph crosses the x axis at x = 0 and touches the x axis at x = –5.O The graph touches the x axis at x = 0 and crosses the x axis at x = –5.
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.
Option (C) is correct.
What is a function in mathematics?
In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. The set of inputs is called the domain of the function, and the set of possible outputs is called the range of the function.
First, factorize the function f(x):
[tex]f(x)=4x^7+40x^6+100x^5\\\\f(x)=4x^5(x^2+10x + 25)\\\\f(x)=4x^5(x+5)^2[/tex]
When f(x)=0, you get that
[tex]4x^5(x+5)^2 = 0\\\\x=0 $ or $ x = -5[/tex]
This means that the graph intersects the x-axis at points (0,0) and (-5,0). But:
1. since the degree at term [tex]x^5[/tex] is odd, point (0,0) is x-intercept;
2. since the degree at term [tex](x+5)^2[/tex] is even, point (-5,0) is the tangent point (see the attached graph of the function).
Hence, The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.
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what is half of 7 3/4 on a tape measure
So, the half of [tex]7\frac{3}{4}[/tex] is [tex]3\frac{7}{8}[/tex]. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
A fraction is a numerical value that represents a part of a whole. It is typically written as a ratio of two numbers, with a line separating the numerator and the denominator. For example, the fraction one-half can be written as 1/2. Fractions are often used to represent a part of a whole number or a part of a whole object, such as a pie that has been cut into several pieces.
To find half of 7 3/4 on a tape measure, we need to follow these steps:
Convert the mixed number 7 3/4 to an improper fraction. This can be done by multiplying the whole number, 7, by the denominator of the fraction, 4, and adding the numerator, 3, to the product. This gives us 7 x 4 + 3 = 31. So, 7 3/4 is equal to 31/4.Divide the numerator of the improper fraction by 2 to find half of the original mixed number. In this case, we divide 31 by 2 to get 31/2.Convert the resulting improper fraction, 31/2, back into a mixed number. To do this, we divide the numerator, 31, by the denominator, 2, and write the remainder, 1, as the numerator of the fraction part of the mixed number. This gives us the final answer of 3 7/8.Learn more about improper fraction, here https://brainly.com/question/21449807
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i want the answer
fast
Answer:
original fraction = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
let the denominator of the fraction be x then the numerator is x - 1 , so
original fraction is
[tex]\frac{x-1}{x}[/tex]
if 1 is added to the numerator and 5 to the denominator , then fraction is
[tex]\frac{-1+1}{x+5}[/tex] = [tex]\frac{x}{x+5}[/tex]
equate this to [tex]\frac{1}{2}[/tex]
[tex]\frac{x}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = x + 5 ( subtract x from both sides )
x = 5
then original fraction is
[tex]\frac{x-1}{x}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]
Answer:
Below
Step-by-step explanation:
Original fraction (x-1) / x <====given (use in final step below)
Altered fraction (x-1 +1) / (x+5) = 1/2 <====solve this for 'x'
x / (x+5) = 1/2 cross multiply
2x = x+5
x = 5
So original fraction was 4/5
solve (x 1)2 – 4(x 1) 2 = 0 using substitution. u = x 4(x 1) x 1 (x 1)2 select the solution(s) of the original equation. x = 1 x = 2 x = 3 x = 1 - x = 2 - x = 3 -
The necessarily simplified answer to the provided experiment is given as x = 1 ± √2.
What is simplification?A mathematical expression is simplified when it is replaced with a simpler, usually shorter, equivalent expression.
So, for the given phrase (x + 1)2 - 4(x + 1) + 2 = 0, find the simple answer as follows:
The expression is: (x + 1)² – 4(x + 1) + 2 = 0
Replace x + 1 = u in the preceding equation:
u² - 4u + 2 = 0
u² - 4u +4 - 4 + 2 = 0
(u - 2)² = 2
u - 2 = ±√2
replace with u = x + 1:
x + 1 - 2 = ±√2
x - 1 = ±√2
x = 1 ± √2
Therefore, the necessarily simplified answer to the provided experiment is given as x = 1 ± √2.
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Correct question:
Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u = Select the solution(s) of the original equation.
Given: AABC-ADEF
Determine the measure of DF
A)3 cm
B)4 cm
C)5 cm
D)6 cm
The measurement of side DF is 4cm.
What is congruent triangle?The SSS congruence theorem tells us that the triangles are congruent because there are three pairs of congruent sides. The corresponding triangle sides are also in proportion, so they are similar according to the SSS similarity theorem.If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.Here in the figure attached below,
Given two triangles ΔABC and ΔDEF
Also given that,
ΔABC and ΔDEF are congruent to each other.
Given AC = 4cm
Since both triangles are congruent ,
Side AC is congruent to DF
Therefore DF = 4cm (based on SSS theorem).
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The measure of DF is 4cm.
What is congruent triangle?
When two triangles are congruent, their three sides and their three angles match precisely.
If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.
Here in the figure attached below,
There are two triangles ΔABC and ΔDEF and it is given that ΔABC and ΔDEF are congruent to each other.
From the figure, side AC = 4cm
The side DF = AC = 4cm, because the triangles ΔABC and ΔDEF are congruent to each other and based on Side-Side-Side Theroem, we can confirm that.
Hence, DF = 4cm.
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Please help me, really need help
The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.
What is vertical opposite angle ?
When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.
Main body:
1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.
2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.
Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.
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leaning ladder a -ft ladder is leaning against a building. if the base of the ladder is ft from the base of the building, what is the angle of elevation of the ladder? how high does the ladder reach on the building?
The angle of elevation is 72.5° and the height at which the ladder will elevate on the building is 19.06 ft.
Here we have to find the angle of elevation of the ladder and the height the ladder will reach on the building if the ladder is leaned against a building.
Data given:
length of the ladder = 20 ft
the base of the ladder = 6ft
we have to find the angle of elevation.
cos Ф = base/ hypotenuse
= 6/20
Ф = [tex]cos^{-1}[/tex] ( 6/20)Ф
= 72.5°
Now we have to find how high the ladder reaches on the building when leaned against a building.
sin(72.5°) = x/ 20
x = 0.953 ×20
x = 19.06 ft
Therefore the angle of elevation is 72.5° and the ladder will elevate to 19.06.
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Caroline babysit for two families-Nelsons and the smiths. use the information below to compare her earnings
Answer:
6.25h
Step-by-step explanation:
Point slope form (-8,2) m=-3/4
Answer:
y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 2 ) , then
y - 2 = - [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is
y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)
the shape of any uniform probability distribution is a. negatively skewed b. positively skewed c. rectangular d. bell shaped
The shape will be rectangular.
In statistics, uniform distribution refers to a type of probability distribution in which all outcomes are equally likely. A deck of cards has within it uniform distributions because the likelihood of drawing a heart, a club, a diamond, or a spade is equally likely. A coin also has a uniform distribution because the probability of getting either heads or tails in a coin toss is the same.The uniform distribution can be visualized as a straight horizontal line, so for a coin flip returning a head or tail, both have a probability p = 0.50 and would be depicted by a line from the y-axis at 0.50.
From the definition of a uniform probability distribution, since it has a constant probability across a given interval, then it has a rectangular shape. Note also that another term for the uniform probability distribution is the rectangular distribution. Therefore, the correct answer is c.
Thus, option (c) will be the correct option.
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suppose you have 1/6 chance of winning with a scratch-off lottery ticket. if you buy 30 ticket what is the probability of winning with all 3
Answer: 18%
Step-by-step explanation:
I gogled
Which values are solutions to the inequality?
3r≤4r−6
Select each correct answer.
Responses
r = 4
r = , 4
r = 5
r, = 5
r = 6
r, = 6
r = 7
The solution of the inequality 3r ≤ 4r - 6 is r ≥ 6.
How to solve inequality?In Mathematics, the relationship between two values that are not equal is defined by inequalities.
An inequality have the symbol <, >, ≤ and ≥. Hence, the inequality can be solved as follows:
3r ≤ 4r - 6
subtract 4r from both sides of the inequality,
3r ≤ 4r - 6
3r - 4r ≤ 4r - 4r - 6
3r - 4r ≤ - 6
- r ≤ -6
divide both sides of the inequality by -1
Therefore, the solution is r ≥ 6
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2) Ratio of basketballs to soccer balls
1)
2:1
OPEN ENDED QUESTION
In example #2, which quantity will you write first:
basketballs or soccer balls? Why?
The ratio of basketballs to soccer balls is 2 : 1
The quantity which would be written first if basketballs to soccer balls is 2 : 1 is basketball
What is ratio?This refers to a number representing a comparison between two or more named things.
If the ratio of basketballs to soccer balls = 2 : 1
This means,
Basketball : soccer ball = 2 : 1
Therefore, Basketball is the quantity which would be written first because it comes first in the given expression.
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a jet airliner travels 1680 miles in 3 hours with a tail wind. the return trip, into the wind, takes 3.5 hours. write a system of equations whose solution is the ground speed of the airplane and the wind speed.
A system of equation is 1680mi3hr = p−w×600×2hr -p + w for a jet airliner travels 1680 miles in 3hours with a tail wind.
Let p be the speed of the jet airliner
and w be the speed of the tail wind
It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get
1680mi3hr = p−w×600×2hr = p + w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation, we use
200mph = p - w
Add w to both sides:
p = 200mph + w
Using the value of x, we can found the value of w using system of equations.
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
On dividing by 2:
50mph = w
So the speed of the tail wind is 50mph.
Therefore, 200mph = p - 50mph
Add 50mph on both sides:
250mph = p
Hence, speed of jet airliner is 250mph.
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Angel Sum Theorem PLEASE HELP with explanation if possible
Answer:
y = 90°
Step-by-step explanation:
You want the value of y in the diagram showing y as the angle at the base where the isosceles triangle a.pex angle bisector meets the base.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
Consider the large outside triangle. The sum of its angles is ...
60° +2x +60° = 180°
2x = 60° . . . . . . . . . . . . subtract 120°
x = 30° . . . . . . . . . . divide by 2
Now, consider the left smaller triangle. The sum of its angles is ...
60° +x +y = 180°
60° +30° +y = 180° . . . . . . use the known value of x
y = 90° . . . . . . . . . . . . subtract 90°
__
Additional comment
The a.pex angle bisector of an isosceles triangle is always an altitude that meets the base at right angles. The meeting point is the midpoint of the base, so that segment is also a median.
The halves of the isosceles triangle are congruent right triangles, so the base angle is complementary to the angle marked x.
1. calculate the theoretical yield of the solid precipitate. show your work.
The Theoretical yield of solid precipitate is 1.42g/mol
Now, consider solid precipitate as cacl2
let us take the mass of cacl2 and calculate the moles of cacl2.
Mass of CaCl2 =2.0 g
By, default the molar mass of CaCl2 =110.98 g/mol
To calculate the Moles we have a formula:
Moles=Given mass*1 mol/Molar mass of a precipitate.-----(1)
substitute the values in equation (1)
Moles of CaCl2 =2.0 g * 1 mol/110.98g
= 0.018 mol
Take another solid precipitate:
Mass of K2Co3=2.0 g
The molar mass of K2Co3 =138.205 g/mol
Now calculating the moles of K2Co3
substitute the values in equation(1)
Moles of K2Co3 =2.0 g * 1 mol/ 138.205g
=0.0145 moles
According to balanced equation 1mole of CaCl2 reacts with 1 mole of K2CO
Thus, 0.018 moles of CaCl2 will react with 0.018 moles of K2CO3
And,0.0145 moles of K2CO3 will produce 0.0145 moles of CaCO3
Molar mass of CaCO3 =100.0869 g/mol
Theoretical yield of CaCO3 =moles of CaCO3 *molar mass of CaCO3
=0.0145 moles * 100.0869 g/mol
=1.45g/mol
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1. If the required reserve ratio is 10% and the Fed conducts an open market purchase of $100, what is the maximum possible change in the money supply?
100, 1,000, 10,000 or 10
The maximum possible change in the money supply is $1000.
In the given question, if the required reserve ratio is 10% and the Fed conducts an open market purchase of $100, we have to find the maximum possible change in the money supply.
The required reserve ratio is 10%.
The Fed conducts an open market purchase of $100.
So the maximum possible change in the money supply is
money multiplier=1/RRR
money multiplier=100/10
money multiplier=10
Open market purchase of $100
Change in money supply is 10*100=$1000
So, the maximum possible change in the money supply is $1000.
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Expand (2x-1) (x+5) fully
The full expansion of the expression (2x - 1) (x + 5) is 2x² + 9x - 5
How to fully expand the expression?From the question, we have the following parameters that can be used in our computation:
(2x - 1) (x + 5)
Combine the factors of the expression using the product sign
So, we have
(2x - 1) (x + 5) = (2x - 1)* (x + 5)
Evaluate the products
This gives
(2x - 1) (x + 5) = 2x² - x + 10x - 5
Evaluate the like terms in the expression
(2x - 1) (x + 5) = 2x² + 9x - 5
Hence, the expanded expression is 2x² + 9x - 5
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Which of the following is a factor of 2x² + 3x - 5?
Answer:
(x-1)(2x+5)
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Point A is at ( -3,4) and Point C is at ( 2,-6 )
Find the coordinates of point B on line AC suck as the ratio of AB to AC is 4:5
The required coordinates of point B will be (2/9, -14/9).
Point A is at ( -3,4) and Point C is at ( 2,-6 )
Given that point B on line, AC suck as the ratio of AB to AC is 4:5
The coordinates of point B will be,
{[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}
Breaking it down, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)
As per the question, m = 4 and n = 5
The coordinates of point B :
⇒ {[(4×-3+5×2)/(4+5)],[(4×4+5×-6)/(4+5)]}
⇒ {[(-12+10)/(9)],[(16-30)/(9)]}
⇒ (2/9, -14/9)
Thus, the required coordinates of point B will be (2/9, -14/9).
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Please help me. It’s not that hard I’m just in a rush and dont have time to do it myself
Answer:D
Step-by-step explanation: 610/488= 1.25 or 5/4
