The domain of the function to know the number of cars remaining on any day during the month is [0, 40]. The maximum and minimum values are 120 and 0 respectively.
The domain is the all inputted value for which the function is defined. All the x values are domain of a function.
Now, finding the domain of the function,
We know that, the number of cars cannot be negative, so
[tex]f(x)\geq0\\120-3x\geq0\\3x\leq120\\x\leq40[/tex]
The number of cars should be greater than 0, so x > 0.
So, the domain will be [0, 40].
The maximum value is given by putting x = 0,
[tex]f(0)=120-3(0)\\=120[/tex]
The minimum value is given by putting x = 40,
[tex]f(40)=120-3\times40\\=120-120\\=0[/tex]
Therefore, the domain of the function f(x)=120-3x to know the number of cars remaining on any day during the month is [0, 40]. The maximum and minimum values are 120 and 0 respectively.
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Match the word to know with its definition
Expanded form
Product
Place value
Digit
A number that is written as a sum of single digit multiples of powers of 10
Any of the symbols ( 0 to 9 ) that are used to write a number
The result of multiplying two or more numbers together
The value of where a digit is located in a number
write an equation for a line parallel to: y = -3x + 2.
Answer:
y = 1/3x + 2
Step-by-step explanation:
convert 100110 base two to a number in base three
Convert to base 10:
10 0110₂ = 2⁵ + 2² + 2¹ = 38
Convert to base 3:
38 = 27 + 11 = 27 + 9 + 2 = 3³ + 3² + 2×3⁰ = 1102₃
What is the possible answer?
Standard form of a quadratic equation: ax^2 + bx + c = 0
3x - 4 = -x^2
x^2 + 3x - 4 = 0
Hope this helps!
Hello again! This is another Calculus question to be explained.
The prompt reads that "If f(x) is a twice-differentiable function such that f(2) = 2 and [tex]\frac{dy}{dx}[/tex] = [tex]6\sqrt{x^2 + 3y^2}[/tex], then what is the value of [tex]\frac{d^2y}{dx^2}[/tex] at x = 2?"
My initial calculation lead to 12, but then I guessed 219 as the answer and it was correct. Would any kind soul please explain why the answer would be 219? Thank you so much!
Answer:
See explanation.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Functions
Function NotationExponential Property [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Property [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(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:
We are given the following and are trying to find the second derivative at x = 2:
[tex]\displaystyle f(2) = 2[/tex]
[tex]\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}[/tex]
We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:
[tex]\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}[/tex]
When we differentiate this, we must follow the Chain Rule: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big][/tex]
Use the Basic Power Rule:
[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')[/tex]
We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:
[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big][/tex]
Simplifying it, we have:
[tex]\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big][/tex]
We can rewrite the 2nd derivative using exponential rules:
[tex]\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}[/tex]
To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:
[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}[/tex]
When we evaluate this using order of operations, we should obtain our answer:
[tex]\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Find the number of bit strings that satisfies the given conditions. The bit strings of length 11 having at least four 1s
Answer:
Step-by-step explanation:
Find a degree 3 polynomial having zeros 1,4 and 2 leading coefficient equal to 1
The degree 3 polynomial with the zeros {1, 4, 2} and a leading coefficient equal to 1 is:
p(x) = x^3 -7x^2 + 14x - 8
We know that for a polynomial of degree n, with a leading coefficient "a" and the zeros {x₁, x₂, ..., xₙ} can be written as:
p(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Knowing that here we have a polynomial of degree n = 3, with a leading coefficient a = 1, and the zeros {1, 4, 2}
Replacing these in the above form, we get:
p(x) = 1*(x - 1)*(x - 4)*(x - 2)
Now we can expand that to get:
p(x) = (x^2 - x - 4x + 4)*(x - 2) = (x^2 - 5x + 4)*(x - 2)
p(x) = x^3 - 5x^2 + 4x - 2x^2 + 10x - 8
p(x) = x^3 -7x^2 + 14x - 8
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What is the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)?
= –216+616–4116
= –216+616–4116
=216–616+4116
=216–616+4116
Answer: y= x^2/16-6x/16+41/16
Step-by-step explanation:
The equation of a parabola will be; y = x^2/16 - 6x/16 + 41/16
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
y=a(x-h)^2 + k
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
Otherwise, we had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.
This point (h,k) is called the vertex of the parabola that quadratic equation represents.
WE need to find the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)
Thus, the equation of a parabola will be;
y = x^2/16 - 6x/16 + 41/16
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Find m angle AFE.
Please I need help badly
The measure of the angle AFE or m∠AFE is 173 degrees option (B) 173 is correct if the angle AFB = 25 degrees, Angle BFC = 57 degrees, Angle CFD = 34 degrees, and Angle DFE = 57 degrees.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have angles shown in the picture.
Angle AFB = 25 degrees
Angle BFC = 57 degrees
Angle CFD = 34 degrees
Angle DFE = 57 degrees
Angle AFE is the sum of the angle AFB, Angle BFC, Angle CFD, and Angle DFE.
Angle AFE = Angle AFB + Angle BFC + Angle CFD + Angle DFE
Angle AFE = 25 + 57 + 34 + 57
Angle AFE = 173 degrees
Thus, the measure of the angle AFE or m∠AFE is 173 degrees option (B) 173 is correct if the angle AFB = 25 degrees, Angle BFC = 57 degrees, Angle CFD = 34 degrees, and Angle DFE = 57 degrees.
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Determine if the following conjecture is valid.
Given: If a computer sales person sells at least 15 computers in a week, then she gets a bonus. Mandy sells 12 computers in a week.
Conclusion: Mandy gets a bonus.
Answer:
Not valid
Step-by-step explanation:
Because 12 is minor than 15
The conjecture is not valid.
Mandy not gets a bonus.
Given that:
If a computer sales person sells at least 15 computers in a week, then she gets a bonus.
Maddy sells 12 computers in a week.
Conclusion: Maddy gets a bonus.
We have to check the conjecture is valid or not.
What is Conjecture?
A conjecture is a conclusion or proposition that is proffered on the tentative basis without the proof.
Now,
Here, if a person sells 15 or more computers in a week, she gets a bonus.
Maddy sells 12 computers in a week, which is less than 15.
So, Maddy did not get a bonus.
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Select the correct answer from each drop-down menu. The simplest form of the expression has in the numerator and in the denominator.
Answer:
Numerator is 7 and denominator is (m+4)
Step-by-step explanation:
(4m-17)/(m^2-16)+(3m-11)/(m^2-16)=(7m-28)/(m^2-16)=7/(m+4)
e Reasons Y...
SIVARI Leaming su...
Solve for 2. Round to the nearest tenth, if necessary.
х
K
J
63°
I
PLS HELP
Answer:
x = .5
Step-by-step explanation:
Since we have a right triangle, we can use trig functions
tan theta = opp / adj
tan 63 = 1/x
x tan 63 = 1
x = 1/ tan 63
x=0.50952
Rounding to the nearest tenth
x = .5
Solve the system of equations and choose the correct ordered pair.
4x - 2y = -2
6x + 3y = 27
A. (2,5)
B. (3,7)
C. (0, -1)
D. (0,9)
Answer:
(2,5)
Step-by-step explanation:
4x - 2y = -2
6x + 3y = 27
Divide the first equation by 2 and the second equation by 3
2x - y = -1
2x + y = 9
Add the equations together
2x - y = -1
2x + y = 9
-------------------
4x = 8
Divide by 4
4x/4 = 8/2
x =2
2x+y = 9
2(2) +y = 9
4+u = 9
y = 9-4
y=5
(2,5)
Escribe una situacion quese represeten con los 60 -4 0 -10 cual es el resultado
Answer:
Sorry I didn't knowIf f(x) = x2 + 1, what is the ordered pair for x =
-4.?
Answer:
(-4,17)
Step-by-step explanation:
y = f(x)
f(-4) = (-4)^2+1 = 17
y-coordinate = 17
Answer:
D). (-4, 17)
Step-by-step explanation:
Plug in -4 for x.
[tex]f(-4)=(-4)^2}+1[/tex]
Solve.
[tex]f(-4)=16+1[/tex]
[tex]f(-4)=17[/tex]
We already know that the x-coordinate is -4. (-4, y)
f(x) stands for y, so y=17.
(-4, 17)
I hope this helps!
Write each function in parametric form, using the given equation for x.
x^2+y^2=9, x= cos t
SOMEONE PLEASE HELP ME OUT THIS IS DUE In 20 MINUTES (PICTURE)
What is the y-intercept of the line shown?
1
0
10
2
4
-10
ОО
01
03
3.5
Answer:
y-intercept = 3
Step-by-step explanation:
value that's on the y - axis
The sine of angle θ is 0.3.
What is cos(θ)?
The answer:
[tex]\sqrt{9}1 /10[/tex]
Explanation to your question:
Since the sin of theta is 0.3, we can reasonably deduct that the opposite side to theta has a ration of 3 to 10 to that of the hypotenuse. Thus, the adjacent side to theta, using the pythagorean theorem, will be root91. Therefore, since the cosine of theta is the adjacent/hypotenuse, we get root 91/10
what is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (-3, 1)?
Answer:
y -1 = 3/ 2( x + 3)
Step-by-step explanation:
m = (2 +4)/( 2+2)
m = 3/2
In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x
ax – 2 = 12.5
Answer:
x = 14.5/a
Step-by-step explanation:
ax – 2 = 12.5
Add 2 to each side
ax – 2+2 = 12.5+2
ax = 14.5
Divide by a
ax/a = 14.5/a
x = 14.5/a
I NEED HELP ASAPPP!!!! It’s urgentttttt!!!!
Answer: (x - 2)² + (y - 14)² = 1
Step-by-step explanation:
Concept:
Here, we need to know the idea of the circle formula.
Circle formula: (x - h)² + (y - k)² = r²
Center = (h, k)
Radius = r
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
Center = (2, 14)
Radius = 1
Given formula
(x - h)² + (y - k)² = r²
Substitute the value into the formula
(x - 2)² + (y - 14)² = (1)²
Simplify
(x - 2)² + (y - 14)² = 1
Hope this helps!! :)
Please let me know if you have any questions
solve for why please.
Answer:
[tex]sin {45}^{ \circ} = \frac{x}{2} \\ = > x = 2 \: sin {45}^{ \circ} \\ = > x = 2 \times \frac{1}{ \sqrt{2} } \\ = > \green{x = \sqrt{2} }[/tex]
[tex]tan {45}^{ \circ} = \frac{x}{y} = \frac{ \sqrt{2} }{y} \\ = > y = \frac{ \sqrt{2} }{tan {45}^{ \circ} } \\ = > y = \frac{ \sqrt{2} }{1} \\ = > \pink{ y = \sqrt{ 2 } }[/tex]
plssssssss helpppppppppppp i want it now pls
3/5kg + 760g
3/5kg = 3/5×1000
= 600g
Now
600g + 760g = 1360g
Or 1.36kg
Answered by Gauthmath must click thanks and mark brainliest
A number is raised to the 4 th power, then divided by half the of the original number, and finally increased by 141/2. If the result is 100, what was the orginal number
Answer:
the number is 2.45
Step-by-step explanation:
let the original number = n
[tex]\frac{n^4}{n/2} = \frac{2n^4}{n} = 2n^3\\\\2n^3 + \frac{141}{2} = 100\\\\4n^3 + 141= 200\\\\4n^3 = 200 - 141\\\\4n^3 = 59\\\\n^3 = \frac{59}{4} \\\\n^3 = 14.75\\\\n = \sqrt[3]{14.75} \\\\n = 2.45[/tex]
Therefore, the number is 2.45
Joe worked for three days. On the first day, he completed 1/2 of his work. On the second day, he completed 1/3 of the remaining work. What fraction of the work was left for the third day?
Answer:
1/3
Step-by-step explanation:
first day work=1/2
work left=1-1/2=1/2
second day finished=1/3 ×1/2=1/6
work left =1/2-1/6=3/6-1/6=2/6=1/3
Jeremy is buying a new car. The total cost, including tax, is $18275. If the tax rate is 7.5% , what is the sticker price of the car?
Answer:
$17000
Step-by-step explanation:
Given
[tex]Total = 18275[/tex]
[tex]Tax = 7.5\%[/tex]
Required
The original price
This is calculated using:
[tex]Price(1 + Tax) = Total[/tex]
Make Price the subject
[tex]Price = \frac{Total}{(1 + Tax)}[/tex]
So, we have:
[tex]Price = \frac{18275}{(1 + 7.5\%)}[/tex]
[tex]Price = \frac{18275}{1.075}[/tex]
[tex]Price = 17000[/tex]
In a sports club of 150 members, 88 play golf, 63 play bowls, and 45 play golf and bowls. Find the probability that:
a) a member plays golf only.
b) a member doesn't play golf or bowls.
pls explain too if u could. thanks!
Answer:
a) .287
b) .293
Step-by-step explanation:
The answers are boxed in red in the picture.
First I found how many people only golfed. Then I did the same for the people that only bowled. Next I found how many members didn't golf or bowl.
From there I found the probabilities by dividing
a.) # of members that only golf / total # of members
b.) # of members that don't bowl or golf / total # of members
a. $30
b. $60
c. $40
d. $50
Answer:
it should be $30 so letter a
A line passes through the point (8,9) and has a slope of 3/4
What is the equation in slope intercept form for this line
Answer: [tex]y=\frac{3}{4}x+3[/tex]
Step-by-step explanation:
Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. Since we are given slope, we can plug that into m, and use the given point to find the y-intercept.
[tex]y=\frac{3}{4}x+b[/tex] [plug in (8,9)]
[tex]9=\frac{3}{4}(8)+b[/tex] [multiply]
[tex]9=6+b[/tex] [subtract both sides by 6]
[tex]b=3[/tex]
Now that we have b, we can complete the equation to [tex]y=\frac{3}{4}x+3[/tex].
