Owners of a recreation area are filling a small pond with water. They are adding water at a rate of
25
liters per minute. There are
600
liters in the pond to start.
Let
W
represent the amount of water in the pond (in liters), and let
T
represent the number of minutes that water has been added. Write an equation relating
W
to
T
, and then graph your equation using the axes below
Answers
The equation relating W to T is W = 600 + 25T.
Given:
The initial amount of water in the pond is 600 liters.
The water is being added at a rate of 25 liters per minute.
As time (T) increases, the amount of water in the pond (W) will increase due to the constant addition of 25 liters per minute.
The equation can be written as follows:
W = 600 + 25T
In this equation, 600 represents the initial amount of water in the pond (at T = 0), and 25T represents the additional water added for each minute of time (T).
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Related Questions
Rational irrational0.01π 100 π √100 √1100
Answers
What is the probability of spinning a 3 on a spinner numbered 1-5 and 2 on a spinner numbered 1-3?
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How do i find an angle that is complementary to theta?
...?
Answers
90 degrees minus theta is the complimentary angle.
You will need 120 feet of fencing to put all the way around a rectangular garden. the length of the garden is 40 feet. what is the width?
Answers
Plug in L = 40
2(40) + 2w = 120
Solve for w
2w = 120 - 80 = 40
w = 20
To find the width of a rectangular garden with a total perimeter of 120 feet and a known length of 40 feet, use the perimeter formula. Solving the equation, the width is determined to be 20 feet.
Explanation:To find the width of a rectangular garden when you know the total fencing needed and the length of the garden, you can use the perimeter formula for a rectangle. The formula for the perimeter P of a rectangle is P = 2l + 2w, where l is the length and w is the width. In your case, the total perimeter is 120 feet and the length l is 40 feet. Setting up the equation using the given perimeter:
120 = 2(40) + 2w
Solving for w, the width:
120 = 80 + 2w
120 - 80 = 2w
40 = 2w
w = 20 feet
So, the width of the garden is 20 feet.
If A is uniformly distributed over [-12,16] , what is the probability that the roots of the equation
x^2+Ax+A+3=0
are both real?
Answers
Final answer:
The probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real is approximately 0.6786. Then we calculate the length of the range [-3, 16] divided by the length of the entire interval [-12, 16].
Explanation:
To find the probability that the roots of the equation [tex]x^2+Ax+A+3=0[/tex] are both real, we need to determine the range of values for A that will result in real roots. For real roots, the discriminant (b^2-4ac) must be greater than or equal to 0. In this case, the equation can be rewritten as [tex]x^2+(1+A)x+(A+3)=0[/tex], so a = 1, b = (1+A), and c = (A+3). The discriminant is (1+A)^2 - 4(A+3), which must be greater than or equal to 0.
Expanding and simplifying, we get (A^2 + 2A + 1) - 4A - 12 ≥ 0. Combining like terms, we have [tex]A^2 - 2A - 11 > 0[/tex].
To solve the inequality, we can find the values of A that make the equation equal to 0. Factoring, we get (A - 4)(A + 3) ≥ 0. The solutions are A ≤ -3 or A ≥ 4.
Therefore, the probability that the roots of the equation are both real is the probability of A taking values in the interval [-12, -3] or [4, 16]. To find this probability, we divide the length of the interval [-3, 16] by the length of the entire interval [-12, 16].
P(A is in [-3, 16]) = (16 - (-3)) / (16 - (-12)) = 19 / 28 ≈ 0.6786.
Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. Which statement describes the number and nature of all roots for this function?
f(x) has two real roots and one imaginary root.
f(x) has three real roots.
f(x) has five real roots.
f(x) has three real roots and two imaginary roots.
Answers
The second imaginary root is the conjugate of the first. The third real root can be obtained by multiplying the two imaginary ones together.
Answer: The correct option is f(x) has three real roots and two imaginary roots.
Explanation:
It is given that the roots of fifth degree polynomial function are -2, 2 and 4+i.
Since he degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.
According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).
Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).
From the the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.
Therefore, the correct option is f(x) has three real roots and two imaginary roots.
A population of bacteria is introduced into a culture. the number of bacteria P can be modeled by P=500(1+4t/(50+t^2 )) where t is time in hours. Find the rate of change in population when t=2 ...?
Answers
P'(t) = 500 [(50+t^2).4 - 4t.2t]/(50+t^2)^2
by the quotient rule
500 (-4t^2 + 200)/(t^2 + 50)^2
Hence
P'(2) = 500 . (-16 + 200)/54^2 ~= 31.6
Which is greater one mile or one kilometer?
Answers
There relation are: 1 M = 1.6 Km
Hope this helps!
The solution to -16 + x = -30 is -14.
True
False
Answers
Answer:
True
Step-by-step explanation:
[tex]x = - 30 + 16 \\ \\ or \: \: x = - 14[/tex]
What is the derivative of cos(pi*t/4) ?
Answers
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{-\pi}{4} \sin \bigg( \frac{\pi t}{4} \bigg)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \cos \bigg( \frac{\pi t}{4} \bigg)[/tex]
Step 2: Differentiate
Trigonometric Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle y' = -\sin \bigg( \frac{\pi t}{4} \bigg) \cdot \frac{d}{dt} \bigg[ \frac{\pi t}{4} \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = -\sin \bigg( \frac{\pi t}{4} \bigg) \cdot \frac{\pi}{4} \frac{d}{dt}[t][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{-\pi}{4}\sin \bigg( \frac{\pi t}{4} \bigg)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
You roll a blue die and a yellow die. What is
P(the sum of the dice is at least 6 | the blue die shows a 3)?
Write fractions using the slash ( / ) key. Reduce fractions to their lowest terms. ...?
Answers
P(blue die shows a 3) = 6
P(the sum of the dice is at least 6 | the blue die shows a 3) = 4/6 = 2/3
56 is what percentage of 112
Answers
what is the multiple zero and multiplicity of x^3+2x^2+x
Answers
=x(x+1)^2
Single root at x=0
Double root at x=-1
Answer:
Step-by-step explanation:
It is 2x by the third power because i dont know lol
What is the mean median mode and range of the numbers 31 28 30 31 30 ...?
Answers
2. The median is the middle number in the list of numbers, so, the answer is 30 as well.
3. Mode is the number that appears most often, so here it is 30 and 31 because they both appear 2 times.
4. Range is the difference between the largest and smallest number, so 31 - 28 = 3.
Which is bigger 4.953 or 4.951?
Answers
Hope this helps!
4.953 is larger than 4.951 because when comparing the digits from left to right, the thousandths place is different, where 3 is greater than 1.
To determine which number is larger, we compare them digit by digit starting from the left:
Both numbers have the same digit in the units place: 4.
Both numbers have the same digit in the tenths place: 9.
Both numbers have the same digit in the hundredths place: 5.
In the thousandths place, 4.953 has a 3, and 4.951 has a 1.
Since 3 is greater than 1, 4.953 is larger than 4.951.
Which of the following is a solution to the equation c+(4-3c)-2=0
Answers
c+4-3c-2=0
Add 4 and -2: 4+-2=2
Add c and -3c: c+=3c=-2c
Now you have:
2-2c=0
Add the -2c to the other side so we can work on getting c alone:
2=2c
Divide by 2 so c will now be alone:
c=1
The answer is C
Hope this helps :)
Through: (-2,4), parallel to y = -3/2x+3
Answers
To find a line parallel to y = -3/2x+3 through the point (-2,4), we use the point-slope form of a line using the given slope and coordinates.
Explanation:To find a line parallel to a given line, we need to note that parallel lines have the same slope. The given equation is in the form y = mx + b, where m is the slope. In this case, the slope of the given line is -3/2. So, our parallel line will also have a slope of -3/2. Using the point-slope form of a line, we can substitute the slope and the coordinates of the given point (-2,4) to find the equation of the parallel line: y - y1 = m(x - x1). This gives us: y - 4 = -3/2(x - (-2)), which simplifies to y - 4 = -3/2(x + 2).
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Add.
3/4 + 7/10
Write your answer as a fraction in simplest form.
Answers
7/10*4/4 = 28/40
30/40+28/40 = 58/40=29/20 is the simplest form.
To add the fractions 3/4 and 7/10, you need to find a common denominator, which in this case is 20. Both fractions are then converted to have this common denominator and added together to get the result 29/20.
Explanation:The subject of your question is fraction addition. To add 3/4 and 7/10, first we need to find a common denominator. In this case, the common denominator is 20. Change 3/4 into a fraction with 20 as a denominator, you get 15/20. Change 7/10 to a fraction with denominator 20, you get 14/20. Add these two fractions together, we get (15+14)/20, which simplifies to 29/20.
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(6 points)
2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(a) 6x + 4x - 6 = 24 + 9x
(b) 25 - 4x = 15 - 3x + 10 - x
(c) 4x + 8 = 2x + 7 + 2x - 20
Answer:
Answers
A has only one solution , x= 30
B is an identity because if you combine like terms and add, you get
25-4x=25-4x
C has no solutions
g(x) = arcsin(4x + 8)
Find the domain of this function.
Answers
function f(x) = arcsin(x)
Domain of htis function question would be
1≤y≤1
And in our case y = (4x+8)
hence,
−1≤4x+8≤1
Help?
Which of the following equations represents a parabola that opens up and has a vertex with a positive x-value?
A. y=-x^2+8x-15
B. y=2x^2-16x+38
C. y=2x^2+16x+24
D. y=-4x^2-14x-12
Answers
not A or D
vertex witha positive x value
for y=ax^2+bx+c
the x value of the vertex is -b/2a
test b and c
B. 2x^2-16x+38
-b/2a=-(-16)/2=16/2=8, that is positive
C. 2x^2+16x+24
-b/2a=-16/2=-8, negative
B is the answer
Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 6 inches.
Answers
All angles are 60 degrees.
2/3h=r
2/3h=6
h=9
You have a right triangle therefore you can calculate the base as (9tan30)=sqrtof3 over 3
Area of triangle 1/2 bh = 1/2(sqrt3 over 3)
(9) As this is just 1 triangle you then need to multiply it by 2
bh = sqrt of 3 over 3 * 9
Brianna cut 351 fresh flowers to make bouquets if she wants to place an equal number of flowers and each bouquet how many groups should she use
a. 2 groups
b. 4 groups
c.6 groups
d. 9 groups
Answers
It is not 4 groups because that would be 87.5
It is not 6.
Your answer is d.9. 351/9=39
Use the Rational Zeros Theorem to write a list of all potential rational zeros
f(x) = x3 - 10x2 + 4x - 24
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
±1, ±, ±2, ±3, ±4, ±6, ±8, ±12, ±24
±1, ±2, ±3, ±4, ±24
±1, ±2, ±3, ±4, ±6, ±12, ±24
Answers
The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
Anthony's birthday, his mother is making cupcakes for his 12 friends at his daycare. the recipe calls for 3 cups of flour. this recipe makes 2 1/2 dozen cupcakes. anthony's mother has only 1 cup of flour. is there enough flour for each of his friends to get a cupcake? k
Answers
3/30=1/x
Cross multiply: 3x=30, so x=10
It would not be enough flour for each friend to get a cupcake.
Will upvote. What is the area of a circle whose radius is 4 ft
4TTft^2
8TTft^2
16TTft^2
64TTft^2
Answers
Area=pi.r^2
Area=pi.4^2
Area =16.pi
Write this function in vertex form, and Identify its vertex x^2-4x-17
Answers
It is in the form y = ax^2 + bx + c where
a = 1
b = -4
c = -17
To find the value of h, we use this formula
h = -b/(2a)
h = -(-4)/(2*(1))
h = 4/2
h = 2
Plug this back into the original function to find k
k = x^2-4x-17
k = (2)^2-4(2)-17
k = 4-8-17
k = -4-17
k = -21
So we know that a = 1, h = 2 and k = -21 making
y = a(x-h)^2 + k
turn into
y = 1(x-2)^2 - 21
which is now in vertex form. The vertex is (h,k) = (2,-21)
SERIOUSLY NEED HELP WITH THIS QUESTION.
The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?
800 cubic feet
1,000 cubic feet
1,200 cubic feet
2,000 cubic feet
Answers
The volume of a parallelepiped is the area of the base times the height (the perpendicular distance from the base to the top face).
Given that the second solid has the same base of the cube and the same height, then the volumes of two solids are the same.
Answer: 1000 cubic feet.
Answer: 1000 ft³.
Step-by-step explanation:
Since, The volume of a cube = ( side )³
⇒ 1000 = (side)³ ⇒ side = 10
Hence, the side of the given cube = 10 feet
Since, the base of a cube = square having side 10 feet.
When we tilted the cube by 2 units,
Then, the base of the new solid = Rhombus having height 10 meters and base 10 feet,
Since, the square and rhombus are lying in the same base ( Shown in diagram)
Area of rhombus (Base of new solid) = Area of square having side 10 feet = 100 ft²
Since, the height of new solid is also 10 feet. the volume of new solid = Area of its base × height
= 10 × 100
= 1000 ft
The data set represents the number of miles Mary jogged each day for the past nine days. 6, 7, 5, 0, 6, 12, 8, 6, 9 The outlier of the data set is
Answers
Your answer for this question is 0
rewrite each expression more simply 5x+4x