Consider a vat that at time t contains a volume V (t) of salt solution containing an amount Q(t) of salt, evenly distributed throughout the vat with a concentration c(t), where c(t) = Q(t) / V(t). Assume that water containing a concentration k of salt enters the vat at a rate rin, and that water is drained from the vat at a rate rout > rin.
(a) If V (0) = V0, find an expression for the amount of solution in the vat at time t. At what time T will the vat become empty? Find an initial value problem that describes the amount of salt in the vat at time t <= T. You may assume that Q(0) = Q0.
(b) Solve the initial value problem in part (a). What is the amount of salt in the vat at time t? What is the concentration of the last drop that leaves the vat at time t = T
Answers
Answer:
a.i \(\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}\)
ii. time at which vat will be empty
\(T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}\) when dQ/dt = 0
b. i Amount of salt at time t
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
ii. Concentration at t = T
c(T) = [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Step-by-step explanation:
a.
i. We determine the differential equation for the solution in the vat at time,t.
Let Q be the quantity of salt in the vat at any time,t.
So, dQ/dt = rate of change of quantity of salt in the vat. = rate of change of quantity of salt into the vat - rate of change of quantity of salt out of the vat.
Now, since a concentration of salt, k enter the vat at a rate of rin, rate of change of quantity of salt into the vat = krin.
Let V(0) = V₀ be the volume of water int the vat at time t = 0. Now, the volume of water in the vat increases at a rate of (rin - rout). The increase in volume after a time t is (rin - rout)t. So the volume after a time, t is V(t) = V₀ + (rin - rout)t. The concentration of this liquid is thus Q(t)/V(t) = Q(t)/V₀ + (rin - rout)t. Now, the rate of change of quantity of salt out of the vat is thus [Q(t)/V₀ + (rin - rout)t]rin = Q(t)rout/[V₀ + (rin - rout)t].
So, dQ(t)/dt = krin - Q(t)rout/[V₀ + (rin - rout)t].
\(\frac{dQ(t)}{dt} = kr_{in} - \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t}\\\frac{dQ(t)}{dt} + \frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}\)
ii Time T at which vat will be empty
At time T, when the vat is empty, dQ(T)/dt = 0.
So
\(\\\frac{dQ(T)}{dt} + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\0 + \frac{Q(T)r_{out} }{V_{0} + (r_{in} - r_{out} )T} = kr_{in}\\T = \frac{Q(T)r_{out} }{[V_{0} + (r_{in} - r_{out} )]kr_{in}}\)
b. i
i. We solve the differential equation to find the amount of salt at time,t
The integrating factor is ex
\(exp(\int\limits {\frac{r_{out} }{V_{0} + (r_{in} - r_{out})t} } \, dt ) = exp(\frac{r_{out}}{(r_{in} - r_{out})} \int\limits {\frac{ (r_{in} - r_{out})}{V_{0} + (r_{in} - r_{out})t} } \, dt )\\= exp(\frac{r_{out}}{(r_{in} - r_{out})} ln [V_{0} + (r_{in} - r_{out})t} ]) \\\= [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\)
Multiplying both side of the equation by the integrating factor, we have
\([V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{dQ(t)}{dt} + [V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\frac{Q(t)r_{out} }{V_{0} + (r_{in} - r_{out} )t} = kr_{in}[V_{0} + (r_{in} - r_{out})t} ]exp(\frac{r_{out}}{(r_{in} - r_{out})})\)dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt = krin[V(0) + (rin - rout)texp(rout/(rin - rout))]
Integrating both sides we have
∫(dQ(t)[V(0) + (rin - rout)texp(rout/(rin - rout))]/dt)dt = ∫(krin[V(0) + (rin - rout)texp(rout/(rin - rout))])dt
Let exp(rout/(rin - rout) = A
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + C
At t = 0, Q(t) = Q(0),
So,
Q(0)[V(0) + A(rin - rout)×0] = AkrinV(0)t + A(rin - rout)×0²/2 + C
C = Q(0)V(0)
Q(t)[V(0) + A(rin - rout)t] = Akrin[V(0)t + A(rin - rout)t²/2 + Q(0)V(0)
Q(t) = [[exp(rout/(rin - rout)]krin[V(0)t + [exp(rout/(rin - rout)](rin - rout)t²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)t]
The above is the amount of salt at time ,t.
ii. The concentration of the last drop of salt at time, t = T
To find the concentration of the last drop of salt at time t = T, we insert T into Q(t) to find its quantity and insert t = T into V(t) = V₀ + (rin - rout)t.
So
Q(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]
Q(T) = [[exp(rout/(rin - rout)]krin[V(0)T + [exp(rout/(rin - rout)](rin - rout)T²/2 + Q(0)V(0)]/[V(0) + [exp(rout/(rin - rout)](rin - rout)T]
the volume at t = T is
V(T) = V₀ + (rin - rout)T.
The concentration at t = T is c(T) = Q(T)/V(T) = [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/[V(0) + A(rin - rout)T]/V₀ + (rin - rout)T.
= [Akrin[V(0)T + A(rin - rout)T²/2 + Q(0)V(0)]/([V(0) + A(rin - rout)T][V₀ + (rin - rout)T])
= [krin[(V(0)T + (rin - rout)T²/2)exp(rout/(rin - rout) + Q(0)V(0)]/([V(0) + exp(rout/(rin - rout)[(rin - rout)T]][V₀ + (rin - rout)T])
Related Questions
Solve 5(2x – 3) = 5x – 10 for x.
Answers
Answer:
x=1
Step-by-step explanation:
5(2x – 3) = 5x – 10
Distribute
10x -15 = 5x-10
Subtract 5x from each side
10x-15-5x = 5x-5x-10
5x -15 = -10
Add 15 to each side
5x-15+15 =-10+15
5x = 5
Divide by 5
5x/5 = 5/5
x=1
Answer and Step-by-step explanation:
To solve for x, first distribute the 5 to the 2x and 3.
10x - 15 = 5x - 10
Now, add 15 to both sides and subtract 5x to both sides of the equation.
5x = 5
Divide both sides of the equation by 5.
x = 1
The answer is x = 1
#teamtrees #PAW (Plant And Water)
Not a mf clue lololol
Answers
Answer:
3.75
Step-by-step explanation:
Not sure hehe.Sry for that.
Question 10 of 10
Check all that apply. If tane = 15/8,then:
A. csco =17/15
B. sece =17/8
C. cose =15/17
D. cote =8/15
Answers
If tan Ф = 15/8 then we have these trigonometric functions cosec Ф = 17/15, sec Ф = 17/8 and cot Ф = 8/15.
According to the question,
We have the following information:
Tan Ф = 15/8
We know that in this trigonometric function we have perpendicular divided by base.
Now, we can find the hypotenuse using the Pythagoras theorem:
Let's denote hypotenuse with h, perpendicular with p and base with b.
\(h^{2} =p^{2} +b^{2}\)
\(h^{2}\) = \((15)^{2} +(8)^{2}\)
\(h^{2} = 225+64\\h^{2} = 289\\h = \sqrt{289}\)
h = 17 units
Now, we have the following values:
Cosec Ф = 17/15 (Hypotenuse/perpendicular)
Sec Ф = 17/8 (h/b)
Cos Ф = 8/17 (b/h)
Cot Ф = 8/15 (b/p)
Hence, the correct options are A, B and D.
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I need help answering. Thanks.
Answers
Answer:
28
Step-by-step explanation:
C or B's so 30% + 40% = 70% so:
70/100 multiplied by 40 because 40 students
7/10 times 40 = 28
Which transformation is needed to be used on x^2, to get the graph of f(x) = 2x2 - 12x + 22?
Select one:
O a. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 13 units
O b. Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O c. Shift right by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units
O d. Shift right by 3 units and shift upwards by 4 units
Please I need help
Answers
Answer: A
Step-by-step explanation:
The required transformation is Shift left by 3 units, stretch vertically by a factor 2 and then shift upward by 4 units. Hence option B is correct.
What is graph?The graph is a demonstration of curves which gives the relationship between x and y axis.
Since, both curve of x² and 2x² - 12x + 22 is in the graph.
Now, the steps of transformation of x² into 2x² - 12x + 22 is as follows.
1) Shift left by 3 units.
2) Stretch vertically by a factor 2.
3) Shift upward by 4 units
Thus, the required result will be seen graph.
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how much is 6x x 3y? Plz help
Answers
Answer:
18xy
Step-by-step explanation:
Just multiply the coefficients and then put both the variables at the end.
Write the equation of each graph in standard form. Show all work.
Answers
The equation of the parabola is:
y = (x + 4)² - 3
How to write the equation for the graph?We can see that we have the graph of a parabola.
Remember that the vertex form of a parabola whose leading coefficient is a and whose vertex is (h, k) is:
y = a*(x - h)² + k
Here we can see that the vertex is at (-4, -3)
So we can write:
y = a*(x + 4)² - 3
We also can see that the function passes through (-3, -2), replacing that we will get:
-2 = a*(-3 + 4)² - 3
-2 = a - 3
-2 + 3 = a
1 = a
The equation is:
y = (x + 4)² - 3
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Solve: 2m³-5m² - 7m = 0
Answers
Answer:
m = - 1 , m = 0 , m = \(\frac{7}{2}\)
Step-by-step explanation:
2m³ - 5m² - 7m = 0 ← factor out common factor m from each term
m(2m² - 5m - 7) = 0
factorise the quadratic 2m² - 5m - 7
consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term
product = 2 × - 7 = - 14 and sum = - 5
the factors are + 2 and - 7
use these factors to split the m- term
2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )
2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term
(m + 1)(2m - 7)
then
2m³ - 5m² - 7m = 0
m(m + 1)(2m - 7) = 0 ← in factored form
equate each factor to zero and solve for m
m = 0
m + 1 = 0 ( subtract 1 from both sides )
m = - 1
2m - 7 = 0 ( add 7 to both sides )
2m = 7 ( divide both sides by 2 )
m = \(\frac{7}{2}\)
solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)
Consider the line y = 7x-1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answers
What is the slope of a line
parallel to this line?
What is the slope of a line
perpendicular to this line?
Hi, there!
______
\(\begin{tabular}{c|1} \boldsymbol{Things \ to \ Consider} \\\cline{1-3} \end{tabular}\)
How are the slopes of parallel lines related to each other?How are the slopes of perpendicular lines related to each other?(1)
- The slopes of parallel lines are identical.
{The line \(\sf{y=7x-1}\) has a slope of 7}
Thus,
{The slope of the line that is parallel to the aforementioned line (whatever its equation happens to be) is \(\sf{7}\).}
(2)
- The slopes of perpendicular lines are negative inverses of each other.
The negative inverse of 7 is
\(-\dfrac{1}{7}\).
Therefore,
\(\textsc{Answers:\begin{cases} \bf{7} \\ \bf{-\dfrac{1}{7}} \end{cases}}\)
Hope the answer - and explanation - made sense,
happy studying!! \(\tiny\boldsymbol{Frozen \ melody}\)
Can some one pls help me
Answers
Answer:
C
Step-by-step explanation:
You always start with the parenthesis in equations. I hope this helped!
ttttttttttttttttttttttthhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeerrrrrrrrrrrrrrrrrrrreeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
Step-by-step explanation:
(C)
The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
Answers
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
Determine the equation of the line below using the given slope and point.
Slope = m = 4 , Point (-3,-11)
Answers
\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)
The equation is:
⇨ y + 11 = 4(x + 3)Work/explanation:
Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),
where m is the slope and (x₁, y₁) is a point on the line.
Plug in the data:
\(\rm{y-(-11)=4(x-(-3)}\)
Simplify.
\(\rm{y+11=4(x+3)}\)
Hence, the point slope equation is y + 11 = 4(x + 3).Simplified to slope intercept:
\(\rm{y+11=4x+12}\)
\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation
Help please is for now
Answers
Steps:
5x - 2y = 30
5(8) - 2y = 30
40 - 2y = 30
-2y = 30 - 40
-2y = -10
y = -10/-2
y = 5
I would appreciate the brainliest if this answer was correct and the steps were clear and helpful! :)
The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of itsâ height, and inversely as the length of the beam. A beam feetâ long, with a width of inches and a height of inches can support a maximum load of pounds. If a similar board has a width of inches and a height of âinches, how long must it be to support âpounds?
Answers
The question is incomplete.Here is the complete question.
The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its length, and inversely as the length of the beam. A beam 13 feet long, with a width of 6 inches and a height of 4 inches can support a maximum load of 800 pounds. If a similar board has a width of 8 inches and a height of 7 inches, how long must it be to support 1300 pounds?
Answer: It must be 392 inches or approximately 33 feet.
Step-by-step explanation: According to the question, the measures (width, length and height) of a beam and the weight it supports are in a relation of proportionality, i.e., if divided, the result is a constant.
For the first load:
width = 6in
height = 4in
length = 13ft or 156in
weight = 800lbs
Then, constant will be:
\(\frac{6.4^{2}}{156} k = 800\)
\(k=\frac{800.156}{96}\)
k = 1300
For the similar beam:
\(\frac{8.7^{2}}{L}1300=1300\)
L = 49.8
L = 392in or 32.8ft
A similar board will support 1300lbs if it has 392 inches or 32.8 feet long.
Timmy has a square backyard with a width of (2x-5). he wants to lay new sod. what is the area of his yard?
Answers
Answer:
\( {4x}^{2} - 20x + 25\)
Step-by-step explanation:
\( {(2x - 5)}^{2} = {(2x)}^{2} - 2(2x)(5) + {5}^{2} = 4 {x}^{2} - 20x + 25\)
Is DEF = ABC? If so, type the reason, if not type no.
Answers
Answer:
Yes
Step-by-step explanation:
All you need to do is figure out the missing angles. We know that the three angles in a triangle add up to 180 degrees.
For angle B in ABC, 180-52-39= 89. So angle B = 89 degrees.
For angle D in DEF, 180-39-89= 52. So angle D = 52 degrees.
Then see if the order of the angles match up.
DEF = 52 degrees, 89 degrees, 39 degrees
ABC = 52 degrees, 89 degrees, 39 degrees
The order of the same angles match, so triangle DEF and triangle ABC are equal.
Answer:
Yes, triangle DEF is similar to triangle ABC because their corresponding angles are the same size.
Step-by-step explanation:
Interior angles of a triangle sum to 180°.
⇒ ∠A + ∠B + ∠C = 180°
⇒ 52° + ∠B + 39° = 180°
⇒ ∠B = 89°
⇒ ∠D + ∠E + ∠F = 180°
⇒ ∠D + 89° + 39° = 180°
⇒ ∠D = 52°
Two triangles are similar if their corresponding angles are the same size.
If ΔDEF ~ ΔABC then:
∠D = ∠A∠E = ∠B∠F = ∠CFrom inspection of the given diagram:
∠D = 52° and ∠A = 52° so ∠D = ∠A∠E = 89° and ∠B = 89° so ∠E = ∠B∠F = 39° and ∠C = 39° so ∠F = ∠CTherefore, the triangles are similar because their corresponding angles are the same size.
Enter the midpoint of the segment whose endpoints are (6,5) and (-8, 12).
Answers
the segment is defined by the coordinates (6,5) and (-8,12) so the midpoint will be:
\(\begin{gathered} x=\frac{6+(-8)}{2}=-\frac{2}{2}=-1 \\ y=\frac{5+12}{2}=\frac{17}{2}=8.5 \end{gathered}\)So the midpoint is (-1,8.5)
What is the equation of the vertical line that passes through the point (6, -2)
Answers
X= 6 (I believe they want it in this form)
HELP ASAP
will mark brainliest
Answers
m=1/4
(or m=0.25)
M= rise/run
= 1/4
Hope this helps!
Please answer the first question
Answers
Answer:
12 inches
Step-by-step explanation:
Given
Volume = 763 cubic inchesDiameter = 9 inches ⇒ Radius = 9/2 inchesFormula for Volume of a Cylinder
V = πr²hSolving
763 = 3.14 x (9/2)² x h763 = 3.14 x 81/4 x h763 = 3.14 x 20.25 x h763 = 63.585hh = 11.99 ≅ 12 inchesAnswer:
The height is 12 inches
Step-by-step explanation:
Step 1: Determine the knowns a formula
\(Volume = 764\ in^3\)
\(Diameter = 9\ in\)
\(Formula: V = \pi r^2h\)
Step 2: Input the values and solve
\(V = \pi r^2h\)
\(764\ in^3 = \pi (9/2\ in)^2h\)
\(764\ in^3 = \pi (20.25\ in^2)h\)
\(764\ in^3 =63.617\ in^2 * h\)
\(\frac{764\ in^3}{63.617\ in^2} = \frac{63.617\ in^2 * h}{63.617\ in^2}\)
\(12.0\ in = h\)
Answer: The height is 12 inches
answer all you get brainiest
Answers
Step-by-step explanation:
1. 44
2. 26 95
3. 294
4. 126
5. 36.04
6. 52.02
what is the nth term in a cube number sequence
Answers
Answer:
cube numbers: 1, 8, 27, 64, 125, ... - the nth term is. triangular numbers: 1, 3, 6, 10, 15, ... (these numbers can be represented as a triangle of dots).Step-by-step explanation:
IF IT HELPED UH PLEASE MARK ME A BRAINLIEST :-)Ephemeral services corporation (esco) knows that nine other companies besides esco are bidding for a $900,000 government contract. each company has an equal chance of being awarded the contract. if esco has already spent $100,000 in developing its bidding proposal, what is its expected net profit?
a. $10,000
b. $0
c. $100,000
d. $90,000
Answers
Answer:
c. $100,000
Step-by-step explanation:
Calculation of the expected net profit of Ephemeral services corporation
Since we are been told that 9 other companies besides esco are as well bidding for the $900,000 government contract, it means we have to find the expected net profit by dividing 1 by 9×$900,000 .Thus ESCO can only expect to cover its sunk cost.
Hence ,
E(X) = (1/9) × $900,000
E(X)=0.111111111×$900,000
E(X)= $100,000
Therefore the expected net profit would be $100,000
Question 2
No calculations are necessary to answer this question.
3/01
3/02
$1.7420 $1.7360
Date
July GBP Futures
Contract Price
O long; long
Based on the closing prices of July GBP Futures Contract over the 3-day period in March 20XX as shown above, you shou
position on 3/01 and a position on 3/02.
O long; short
O short; short
3/03
short; long
$1.7390
Answers
The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.
Find the probability of getting two numbers whose sum exceeds .
Answers
The probability that the sum exceeds 5 is P ( A ) = 0.6111
Given data ,
To find the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice, we need to count the number of outcomes where the sum of the two numbers is greater than 5, and then divide that by the total number of equally-likely outcomes.
The outcomes where the sum exceeds 5 are:
(2, 4), (2, 5), (2, 6)
(3, 3), (3, 4), (3, 5), (3, 6)
(4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 22 outcomes where the sum exceeds 5 out of a total of 36 equally-likely outcomes.
So, the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice is:
P(sum > 5) = 22 / 36 ≈ 0.6111 or approximately 61.11 %
Hence , the probability is P ( A ) = 0.6111
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The complete question is attached below :
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right.Find the probability of getting two numbers whose sum exceeds 5
is 6.24 greater or less than .624
Answers
Answer:
6.24 is greater than .624
Step-by-step explanation:
If you put them in a fraction, it would be 6 24/100 and 624/1000.
As you can see, 6.24 has a whole number while .624 doesn't therefore, 6.24 is greater than .624.
Hope this helps?
Greater. The place value is to the right more then the other number making it greater.
To clarify 6.24 is bigger then .624
For example lets say you had 6.00 Apples. Thats 6 whole apples!
Then let's say you had 0.600 Apples. Thats only half an apple!
So 6.00 Apples would be more. Thats why 6.24 is bigger.
Mrs. Smith made 6 ¼ dozen cookies for the birthday party. At the end of the party, there were 3 ½ dozen cookies left. How many cookies did the guests eat?
Answers
The guests in the birthday party ate 33 cookies.
How many cookies did the guests eat?We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.
Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.
6 1/4 dozen = 25/4 dozen
3 1/2 dozen = 14/4 dozen
Now we can subtract the number of cookies that were left from the number of cookies that were made:
25/4 - 14/4 = 11/4 dozen
To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.
There are 12 cookies in one dozen, so:
11/4 x 12 = 33
Therefore, the guests ate 33 cookies.
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A waterfall has a height of 1900 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 12 feet per second. The height, h, of the pebble after t seconds is given by the equation h=-16t^2+12t+1900. How long after the pebble is thrown will it hit the ground?
Answers
Answer:
Step-by-step explanation:
h is the height of the pebble after a certain amount of time has gone by. Since we are told to find that time when the pebble is on the ground, we say that h = 0 since the height of something on the ground has no height at all. Then factor the quadratic.
\(-16t^2+12t+1900=0\)
Throw that into the quadratic formula or however you were taught to factor irrational quadratics (maybe completing the square?) to get that
t = 11.27869 sec and t = -10.52869 sec
Since we all know that time will never carry a negative value, we will disregard it and go with 11.27869 seconds. Not sure to where you are told to round.
What else would need to be congruent to show that ABC DEF by SAS? E AA. А B OA. BC = EF B. CF OC. ZA ZD D. AC = OF F Given: AC = DF CE F
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The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.
Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)
Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).
Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).
Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).
What is SAS congruence property?Given:
\($&\overline{A B} \cong \overline{D E} \\\) and
\($&\overline{A C} \cong \overline{D F}\)
According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.
Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)
Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).
Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).
Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).
To learn more about SAS congruence property refer to:
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