Answer:
a. [tex]\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c[/tex]
b. [tex]x(t) = 6\frac{2}{3} \cdot c \cdot t[/tex]
c. [tex]c = \dfrac{3}{8} \ g/L[/tex]
Step-by-step explanation:
a. The volume of water initially in the fish tank = 15 liters
The volume of brine added per minute = 5 liters per minute
The rate at which the mixture is drained = 5 liters per minute
The amount of salt in the fish tank after t minutes = x
Where the volume of water with x grams of salt = 15 liters
dx = (5·c - 5·c/3)×dt = 20/3·c = [tex]6\frac{2}{3} \cdot c \cdot dt[/tex]
[tex]\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c[/tex]
b. The amount of salt, x after t minutes is given by the relation
[tex]\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c[/tex]
[tex]dx = 6\frac{2}{3} \cdot c \cdot dt[/tex]
[tex]x(t) = \int\limits \, dx = \int\limits \left ( 6\frac{2}{3} \cdot c \right) \cdot dt[/tex]
[tex]x(t) = 6\frac{2}{3} \cdot c \cdot t[/tex]
c. Given that in 10 minutes, the amount of salt in the tank = 25 grams, and the volume is 15 liters, we have;
[tex]x(10) = 25 \ grams(15 \ in \ liters) = 6\frac{2}{3} \times c \times 10[/tex]
[tex]6\frac{2}{3} \times c =\dfrac{25 \ grams }{10}[/tex]
[tex]c =\dfrac{25 \ g/L }{10 \times 6\frac{2}{3} } = \dfrac{25 \ g/L}{10 \times \dfrac{20}{3} } =\dfrac{3}{200} \times 25 \ g/L= \dfrac{75}{200} \ g/L = \dfrac{3}{8} \ g/L[/tex]
[tex]c = \dfrac{3}{8} \ g/L[/tex]
10. The GCD of two numbers is 8 and their
LCM is 360. If one of the numbers is 72,
what is the other number?
please help me pls ease
Answer:
8
Step-by-step explanation:
x = -2
the y to (-2,y) is 8
Two angles are supplementary. One angle is 36 degrees bigger than the other. What is the measure of the bigger angle
let the other angle be x degree
bigger angle = x +36°
According to the question,
x+36° + x° = 180°
=> 2x = 180–36
=> x = 144/2
=> x = 72°
Measure of the bigger angle = x + 36
= 72° + 36°
= 108°
Pls help :( :(((
Pls pls pls
Answer:
1.) a- 9,00
b-43,000
d-8,000
e-41,000
g-7,000
h-56,000
j-16,000
Step-by-step explanation:
2.)
a-5
b-17
c-21
Answer:
1)
a. 9,000 bytes
b. 43,000 bytes
c. 9,600 bytes
d. 8,000 kilobytes
e. 41,000 kilobytes f. 7,300 kilobytes
g. 7,000 MB h. 56,000 MB
i. 2,500 MB j. 16,000,000 Bytes
2)
a. 5
b. 17
c. 21
Why do people engage in various ?
Answer:
When and why do people engage in different forms of proactive behavior at work? We propose that as a result of a process of trait activation, employees with different types of self-construal engage in distinct forms of proactive behavior if they work in environments consistent with their self-construals. In an experimental Study 1 (n = 61), we examined the effect of self-construals on proactivity and found that people primed with interdependent self-construals engaged in more work unit–oriented proactive behavior when job interdependence was also manipulated. Priming independent self-construals did not enhance career-oriented proactive behavior, even when we manipulated job autonomy. In a field Study 2 (n = 205), we found that employees with interdependent self-construals working in jobs with high interdependence reported higher work unit commitment and higher work unit–oriented proactive behavior compared to employees in low interdependent jobs. Employees with independent self-construals working in jobs with high autonomy also exhibited stronger career commitment and more career-oriented proactive behavior than did those in jobs with low autonomy. This research offers a theoretical framework to explain how dispositional and situational factors interactively shape people’s engagement in different forms of proactive behavior.
Step-by-step explanation:
Which function BEST represents the graph?
Answer:
The last one
Step-by-step explanation:
K so first look at y intercept which is +5, so we eliminate A and C, then the graph opens up so the b in ax+bx+c has to be positive which is D
the point ( 0 ; 5 ) in on the curve
so f(0) = 5
choice between :
x² - 2x + 5 or x² + 2x + 5 then :
we have the point (1 ; 4)
with x² - 2x + 5
f(1) = 1² - 2*1 + 5 = 1 - 2 + 5 = 4
so it's correct
=> x² - 2x + 5 is the right one
Which of the following is an Expression
*
O 1+2 = 3
O x+3 = 9
O 8 = 9 x 5
O 12 +9
Please help me I don´t get it?
Find an equation of a line that is parallel to y = 3x - 9 and passes through
the point (1, 1). *
Answer:
y=3x-2
Step-by-step explanation:
For this problem, you can use the point-slope formula: y-y1=m(x-x1), with x1 and y1 being from the given coordinate, and m being the slope (which is 3 that can be seen in the equation). Since we're finding a line that is parallel to this line, the slopes of both equations are the same.
y-(1)=3(x-1)
y-1=3x-3
y=3x-2
Check:
(1)=3(1)-2
1=3-2
1=1
[tex]y=3x-2[/tex] is an equation of a line that is parallel to [tex]y = 3x - 9[/tex] and passes through the point [tex](1, 1).[/tex]
What is equation?
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
What is Parallel lines?
In geometry, parallel lines are coplanar straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet.
According to question, we have to write an equation of a line that is parallel to [tex]y = 3x - 9[/tex] and passes through the point [tex](1, 1)[/tex]
Since, the line passes through [tex](1,1)[/tex] and have slope[tex]=3[/tex]
So, [tex]y-(1)=3(x-1)[/tex]
⇒ [tex]y-1=3x-3[/tex]
⇒ [tex]y=3x-2[/tex]
Hence, we can conclude that [tex]y=3x-2[/tex] is an equation of a line that is parallel to [tex]y = 3x - 9[/tex] and passes through the point [tex](1, 1).[/tex]
Learn more about Parallel lines here:
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Two cylindrical vases have the same base, but one vase is twice as tall as the other one. Therefore, the taller vase will hold 8 times as much water as the shorter vase.
Answer:true
Step-by-step explanation:
If the ratio of a:b is 4:15 and the ratio of b:c is 5:9, what is the ratio of a:c?
Answer:
Your answer should be 4:9
Step-by-step explanation:
Good luck.
solve the simultanious equasion
8x+3y=45
2x+3y=27
pls pls pls help
Answer:
[tex]x=3,\:y=7[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}8x+3y=45\\ 2x+3y=27\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}x=\frac{45-3y}{8}[/tex]
[tex]\begin{bmatrix}2\cdot \frac{45-3y}{8}+3y=27\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\frac{45+9y}{4}=27\end{bmatrix}[/tex]
[tex]y=7[/tex]
[tex]\mathrm{For\:}x=\frac{45-3y}{8}[/tex]
[tex]\mathrm{Substitute\:}y=7[/tex]
[tex]x=\frac{45-3\cdot \:7}{8}[/tex]
[tex]x=3[/tex]
[tex]\mathrm{The\:solutions\:are}:[/tex]
[tex]x=3,\:y=7[/tex]
Foster is centering a photo that is 9 1/2 inches wide on a scrapbook page that is 14 inches wide. How far from each side of the page should he put the picture? Enter your answer as a mixed number.
Step-by-step explanation:
Given that he dimension is
9 1/2 inches wide
and 14 inches wide.
half way from 9.5 inches is
4.75in
half way from 14 inches is
7in
Therefore he put the picture at 4.75in from the top and 7in from the sides
15
The table below shows the lengths in
centimeters (cm) of a sample of 5 leaves
from a tree.
Leaf Length (cm)
14.2
2 13.8
12.6
13.4
5 11.5
WIN
3
4
?
A 6th leaf is added to the sample and its length is
measured. Its measure increases the mean value of
the sample of leaves but decreases the median value
of the sample of leaves. What is a possible
measurement for the length of the 6th leaf?
A) 13.1 cm
B) 13.3 cm
C) 13.4 cm
D) 13.7 cm
The mean measurement is the average value of the leaves
The possible measurement of the 6th leaf is 13.3
How to determine the possible value of the 6th sampleThe dataset is given as:
14.2, 13.8, 12.6, 13.4 and 11.5
Sort the data elements
11.5, 12.6, 13.4, 13.8 and 14.2
Calculate the mean
[tex]\bar x = \frac{11.5 + 12.6 + 13.4 + 13.8 + 14.2}{5}[/tex]
[tex]\bar x = \frac{65.5}{5}[/tex]
[tex]\bar x = 13.1[/tex]
So the mean is 13.1 and the median is 13.4
For the mean to increase, the 6th dataset must be greater than 13.1.
For the median to decrease, the 6th dataset must be less than 13.4
From the list of given options, the element that satisfy the above highlights is 13.3
Hence, the possible measurement of the 6th leaf is 13.3
Read more about mean and median at:
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HELP i need help quickly please
Answer:
c
Step-by-step explanation:
Hello Guys, I really need help with these questions. Here they are.
Solve each absolute value inequality and show its solution set.
(a) |x|<7
(b) |x+3|<9
(c) |y-8|>11
(g) |3x-1| greater or equal to 18
|4y+3| less than or equal to 13
Please help me with these. WIll give you 20 pts. I will award brainly for the best answer! Make the answers in numbers (inequalities)
Answer:
a.[tex]-7 < x < 7[/tex]
b.[tex]-12 < x < 6[/tex]
c. Two answers are: y < -3 or y > 19
d. Two answers are x ≤ -17/3 or x ≥ 19/3
e. -4 ≤ y ≤ 5/2
Step-by-step explanation:
Given the following questions:
Question one:
[tex]|x| < 7[/tex]
x is less than 7
[tex]=-7 < x < 7[/tex]
Question two:
[tex]|x+3| < 9[/tex]
[tex]x+3 > -9[/tex]
[tex]3-3=0[/tex]
[tex]-9+-3=-12[/tex]
[tex]x > -12[/tex]
[tex]x+3 < 9[/tex]
[tex]3-3=0[/tex]
[tex]9-3=6[/tex]
[tex]x < 6[/tex]
x is greater than -12, while less than 6
[tex]-12 < x < 6[/tex]
Question three:
[tex]|y-8| > 11[/tex]
[tex]y-8 < -11[/tex]
[tex]-8+8=0[/tex]
[tex]-11+8=-3[/tex]
[tex]y < -3[/tex]
[tex]y-8 > 11[/tex]
[tex]-8+8=0[/tex]
[tex]11+8=19[/tex]
[tex]y > 19[/tex]
Two answers are: y < -3 or y > 19
Question four:
|3x - 1| ≥ 18
3x - 1 ≤ -18
-1 + 1 = 0
-18 + 1 = -17
3x ≤ -17
x ≤ -17/3
3x - 1 ≥ 18
-1 + 1 = 0
18 + 1 = 19
3x ≥ 19
x ≥ 19/3
Two answers are: x ≤ -17/3 or x ≥ 19/3
Question five:
|4y + 3| ≤ 13
|4y + 3| ≤ 13 = -13 ≤ 4y + 3 ≤ 13
-13 ≤ 4y + 3 ≤ 13
4y + 3 ≥ -13
3 - 3 = 0
-13 + - 3 = -16
4y ≥ -16
4 ÷ - 16 = -4
y ≥ -4
4y + 3 ≤ 13
3 + -3 = 0
13 - 3 = 10
4y ≤ 10 = 10/4 ÷ 2 = 5/2
y ≤ 5/2
-4 ≤ y ≤ 5/2
Hope this helps.
1 If 3, p, q, 9 are in the geometric sequence, find the value of p and q. 9.
Answer:
Step-by-step explanation:
1/3 p, 9,9 are in the geometric sequence
9/ ( 1 1/3) = 27
3^3 = 27
So -- p = 1/3 x 3 = 1
q= 1 x 3 = 3
3 x 3=9
There is a pair of parallel sides in the following shape.
2 12 13 7
What is the area of the shape?
___units
The area of the shape is the amount of space on the shape
Using the assumed parameters, the area of the shape is 25 square units
How to determine the area?The question is incomplete, as the shape is not given.
Assume the shape is a trapezoid, the area of the shape would be:
A = 0.5 * (sum of parallels sides) * height
Using the assumed values, we have:
Area = 0.5 * (12 + 13) * 2
Evaluate the product
Area = 25
Using the assumed values, the area of the shape is 25 square units
Read more about areas at:
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Answer:
54
Step-by-step explanation:
I don't understand at all of how to do this
Answer:
17
Step-by-step explanation:
5x2=10
8 1/2x2=17
What is the error in the problem
Is 10, 24, 13 a Pythagorean Tripe? Explain
Answer:
car
Step-by-step explanation:
Lee wanted to visit his grandmother who lives 1,400 air miles
away. If Lee's plane travels 400 miles per hour, how many
hours would Lee's flight take?
Answer:
Lee's flight would take 3.5 hours.
Step-by-step explanation:
1400 ÷ 400 = 3.5
Please help! Will give brainliest!
Answer:
A. Martin was faster
Step-by-step explanation:
If you look at the graph, you can see that Martin is going faster.
For example: When George is at 2 weeks, he is almost at 3 kg. When Martin is at 2 weeks, he is at 4 kg exactly.
Brainliest?
i need help with this equation its confusing ASAP
Answer:
multiply both sides by 3
Step-by-step explanation:
i would multiply 3 on both sides to cancel the fraction out so i dont have to work with fractions
Answer:
multiply both 3 sides
Step-by-step explanation:
real simple m
532^7•532^-8•532^3
How do I do this it’s hard
Answer:
283024
Step-by-step explanation:
First do 532^7
The answer is 12060947473224100000
Next, do 532^-8
The answer is 1/6416424055755230000000
Multiply that number by the first number
(I don't want to type that all out again)
The answer is 1/532
Now, do the last problem. 532^3
The answer is 150568768
Multiply that number by 1/532
The answer is 283024
Hope I helped :)
Please consider Brainliest :)
(it took me so long to type that)
¿cuántos kilos de productos de primera necesidad ,ha consumido la familia de manuel en los tres meses?
En total, durante los últimos meses la familia de Manuel ha consumido 792 kilos de productos de primera necesidad.
¿Cómo calcular el total de comida consumida?Sumar la cantidad total de cada alimento.Sumar estos totales.¿Cuál es el total de cada comida?Arroz: 17+13+18= 48 kg
Fideos: 12+27+30 = 69 kg
Harina: 26+56+50= 132 kg
Aceite: 6+24+30= 60 kg
Avena: 8+16+20= 44 kg
Papa: 32+48+48= 128 kg
Frejol: 12+20+27= 59 kg
Alverja: 16+24+26= 66 kg
Pollo: 12+12+12= 36 kg
Carne de res: 8+10+10= 28 kg
Mazamorra: 8+25+28= 61 kg
Leche: 13+24+24=61 kg
¿Cuál es el total de comida consumida?48+69+132+60+44+128+59+66+36+28+61+61= 792 kilos
Nota: Esta pregunta está incompleta, a continuación se adjunta la parte faltante.
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What is the equation written in vertex form of a parabola with a vertex of (–1, 8) that passes through (1, 0)?
Answer:
y = -2(x + 1)^2 + 8
Step-by-step explanation:
The equation of a parabola can be written in the form;
y = a(x-h)^2 + k
where a is the multiplier (h,k) is the vertex
so h = -1 and k = 8
Plug in these values
y = a(x + 1)^2 + 8
So to get the value of a, we use the point where the parabola passes through which is the point (1,0)
Simply substitute the values of x and y
0 = a(1 + 1)^2 + 8
0 = a(2)^2 + 8
-8 = 4a
a = -8/4
a = -2
So therefore the equation of the parabola is ;
y = -2(x + 1)^2 + 8
The required equation of parabola with given vertex and point of passing is [tex]y=-2(x+1)^{2}+8[/tex].
Given data:
The vertex of parabola is, (-1, 8).
The vertex is passing through (1, 0).
We know that standard equation parabola is,
[tex]y=a(x-h)^{2}+k[/tex]
Here, a is any multiplier, h and k are the vertices.
From the given problem,
h = -1
k = 8
So substituting the values as,
[tex]y=a(x-(-1))^{2}+8\\y=a(x+1)^{2}+8[/tex]..............................................(1)
To obtain the value of a, we use the point where the parabola passes through which is the point (1,0). Here, x = 1 and y =0.
So,
[tex]0=a(1+1)^{2}+8\\\\a = -2[/tex]
Substitute the value of a in equation (1) as,
[tex]y=(-2)(x+1)^{2}+8\\\\y=-2(x+1)^{2}+8[/tex]
Thus, the required equation of parabola is [tex]y=-2(x+1)^{2}+8[/tex].
learn more about the parabola here:
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Two angles are complementary. One angle measures 28 What is the measure of the other angle?
the sum of two complementary angles is 90°
so 28 + ? = 90
? = 62°
here'
complementry angle means those whose sum is 90
here one angle is given so,
another angle =90-28
that is 72.ans
Find the product. −3y2(−5y3 + y − 6)
If O is an angle in standard position and its terminal side passes through the point
(-35,-12), find the exact value of sin 0 in simplest radical form.
[tex](\stackrel{a}{-35}~~,~~\stackrel{b}{-12})\qquad \impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c = \sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-35)^2+(-12)^2}\implies c=\sqrt{1225+144}\implies c=\sqrt{1369} \\\\\\ \underline{c=37}~\hspace{10em}sin(\theta )=\cfrac{\stackrel{opposite}{-12}}{\underset{hypotenuse}{37}}[/tex]