A constant function is exactly that - constant - meaning it exhibits no change whatsoever with respect to any change in its input. If [tex]f(x) = 1[/tex], then it doesn't matter what value of [tex]x[/tex] I give you, the value of [tex]f(x)[/tex] will always be nothing other than 1.
That the derivative of such a function is zero follows immediately from the definition of the derivative. If [tex]c\in\Bbb R[/tex] and [tex]f(x) = c[/tex], then
[tex]f'(x) = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0} \frac{1 - 1}h = \lim_{h\to0}\frac0h = 0[/tex]
Which expression is equivalent to 7sqrtx^2/5sqrty^3? Assume y does not equal 0
Answer:
Option A) [tex]\bf{ x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]
Step-by-step explanation:
we have
[tex]\sf{\dfrac{\sqrt[7]{x^{2}}}{\sqrt[5]{y^{3}}}}[/tex]
we know that
[tex]\sf{\sqrt[7]{x^{2}}=x^{\frac{2}{7}}}[/tex]
[tex]\sf{\sqrt[5]{y^{3}}=y^{\frac{3}{5}}}[/tex]
substitute in the expression
[tex]\sf{\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]
Select which form to use when you know the slope of the line and one of the points on the line. a. horizontal line c. slope-intercept form b. vertical line d. point-slope form Please select the best answer from the choices provided
The form which should be used when you know the slope of a line and one of the points on the line is: d. point-slope form.
What is the point-slope form?The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.
Mathematically, the point-slope form of a line is given by:
y - y₁ = m(x - x₁)
Where:
m is the slope.x and y are the points.In conclusion, you should use the point-slope form when you know the slope of a line and one of the points on the line is given.
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Answer:
b
Step-by-step explanation:
{(3,-2), (4,-2),(5,-2), (6,-2)} is this a function
Answer:
{(3,-2), (4,-2),(5,-2), (6,-2)} this relation is not a function.
if the endpoints of ST are S (1,4) and T (5,2) then the midpoint is in Quadrant IV?
It is false that the midpoint is in quadrant IV
How to determine the midpoint location?The endpoints are given as:
S (1,4) and T (5,2
The midpoint is
(x, y) = 0.5 *(x1 + x2, y1 + y2)
So, we have:
(x, y) = 0.5 *(1 + 5, 4 + 2)
Evaluate the expression
(x, y) = (3, 3)
The point (3, 3) is located in the first quadrant
Hence, it is false that the midpoint is in quadrant IV
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A manufacturing company has a machine that can make 16,200 bolts during an 8-hour shift. What is the constant of proportionality between the number of bolts and the number of hours?
A
1,620
B
2,025
C
2,314
D
2,700
The constant of proportionality between the number of bolts and the number of hours is 2025.
Option B is the correct answer.
What is the constant of proportionality between the number of bolts and the number of hours?Proportional relationships are relationships between two variables where their ratios are equivalent.
Using a ∝ b then a = kb
Where k is the proportionality constant.
Given that;
Number of bolts a = 16200Number of hours b = 8proportionality constant k = ?We substitute into our equation.
a = kb
16200 = k × 8
k = 16200 / 8
k = 2025
The constant of proportionality between the number of bolts and the number of hours is 2025.
Option B is the correct answer.
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Answer:
B
Step-by-step explanation:
The sum of three numbers is 14. The sum of twice the first number, 4 times the second number, and 5 times the third number is 56. The difference between 4 times the first number and the second number is 14. Find the three numbers.
Answer: 4, 2, 8
Step-by-step explanation:
4 + 2 + 8 = 14
14 = 14
2(4) + 4(2) + 5(8) = 56
8 + 8 + 40 = 56
56 =56
| 4(4) - 2 | = 14
|16-2| = 14
14 = 14
Elizabeth company has 10,000 units of their new product in warehouse. They sold 10,000 in pre-order that will need to be shipped immediately. They are producing 1,000 units per week and they are receiving 700 order per week. How long will it take to fill the warehouse to maximum capacity at the current production rate?
Answer:
m = 300w OR w = m/300
Step-by-step explanation:
They start with 10k, but that's immediately sold, so they're back at a flat 0. Every week they gain 1000 but lose 700 for a net profit of positive 300.
Therefore, the maximum capacity would be 300 multiplied by the number of weeks. If we know the maximum, then the answer would be m (maximum) divided by 300.
A ladder leans against a wall. The foot of the ladder is 8 feet from the wall, and the top of the ladder is pulled 1 foot away from the wall. How far will the top of the ladder slide down the wall? (HINT: Draw the coordinate axes and place the
ladder up against the y-axis.)
Using Pythagoras theorem, the top of the ladder will slide down the wall 1.64 ft
What length will the ladder slide down the wall?The ladder leaning against the wall forms a right-angled triangle of sides 8 ft and 6 ft.
The length of the ladder is y.
Using Pythagoras theorem:
[tex]y = \sqrt{8^{2} + 6^{2}} = 10 \:ft[/tex]
When the ladder is pulled 1 foot away from the wall, the new height, h the ladder rises up the wall is given below:
[tex]h = \sqrt{10^{2} - 9^{2}} = 4.36 \:ft[/tex]
The top of the ladder will slide 6 - 4.36 ft = 1.64 ft
In conclusion, the length the ladder will slide down is obtained using Pythagoras theorem.
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The 3kg object in Figure is released from rest at a height of on a curved frictionless ramp.
At the foot of the ramp is a spring of force constant 400N/m. The object slides down the
ramp and into the spring, compressing it a distance before coming momentarily to rest.
a) Find
b) Describe the motion of the object (if any) after
the block momentarily comes to rest?
The object compresses the spring up to 0.8577m.
What is Potential Energy?Potential Energy is the energy possessed by an object at rest.
The object is falling from the rest and it is assumed that the friction on the ramp is zero and the air resistance is also considered to be zero so only the gravitational force acts and the total potential energy gets converted to Kinetic Energy.
The total amount of potential energy at the top of the ramp is given by
Ep=mgh
Ep=3 * 9.81 *5
Ep=147.15 Joules
This is equal to kinetic energy.
From the formula for elastic potential energy
The distance up to which the spring is compressed is determined
The force constant = 400N/m
147.15 =(1/2)k(x²)
294.3=(400)(x²)
0.73575=x²
x=0.8577 m
So, the object compresses the spring up to 0.8577m.
When the object compresses the spring, the potential energy of the spring is converted into Kinetic Energy so it will push the object back again.To know more about Potential Energy
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PLEASE HELP!
Which linear inequality is represented by the graph?
Oy< 2/3x + 3
Oy> 3/2x+3
Oy> 2/3x + 3
Oy< 3/2x+3
Answer:
y > 2/3x + 3
Step-by-step explanation:
It is first option because > because shaded above the line and 2/3x is rise/run so 2/3.
+3 is because y-intercept is 3
The system of linear inequalities represented by the graph is the option;
y ≥ (1/3)·x + 3 and 3·x - y > 2
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
The system of linear inequalities are given by the in the question, that
describes the inequalities.
The points on the given graph are;
(3, 4), and (-3, 2)
The slope is; (2 - 4)÷((-3) - 3) = 1/3
The equation is;
y - 4 = (1/3)·(x - 3)
y = (1/3)·x - 1 + 4 = (1/3)·x + 3
Therefore;
The graph is y ≥ (1/3)·x + 3
Point on the second graph are;
(0, -2) and (2, 4)
The slope is; (4 - (-2)) ÷ (2 - 0) = 3
The equation is; y - (-2) = 3·(x - 0)
y = 3·x - 2
The inequality is; y < 3·x -2
Which gives;
2 < 3·x - y
Therefore;
3·x - y > 2
The correct option is the first option;
y ≥ (1/3)·x + 3 and 3·x - y > 2
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Use the function below to find F(4).
Hello !
[tex]F(x) = 5 \times ( \frac{1}{3} ) {}^{x} [/tex]
[tex]F(4) = 5 \times ( \frac{1}{3}) {}^{4} = 5 \times \frac{1 {}^{4} }{3 {}^{4} } = 5 \times \frac{1}{81} = \frac{5}{81} [/tex]
Is full biology in 9th grade?
Answer:
I think so, but maybe if the schools are different they change.
HELP FASTqkefjiwgjhjgjtgth
(3x-5)/2 = 8
3x - 5 = 2 × 8
3x - 5 = 16
3x = 16 + 5
3x = 21
x = 21/3
x = 7
Answer:
Step-by-step explanation:
Equation
(3x - 5)/2 = 8 Multiply both sides by 2
2*(3x - 5)/2 = 8 * 2 Combine
3x - 5 = 16 The 2s on the left cancel. Add 5 to each side
3x - 5 + 5 = 16+5 Combine
3x = 21 Divide both sides by 3
3x/3 = 21/3
x = 7
Answer: x = 7
what is a turning point on a quadratic graph?
Answer:
A turning point is the highest or lowest point on a quadratic graph.
Step-by-step explanation:
A quadratic graph looks something like the graph below.
The equation of a quadratic graph would normally look like
+/- ax^2 + bx + c
An example might be -16x^2 + 5x + 4
Note the negative symbol in front of the 16. The negative means that the graph will be facing downwards, or that the turning point is the highest point. A positive graph will mean that the graph is facing upwards, or that the turning point is the lowest point.
Essentially, it is the location where a graph has its lowest or highest point and where the y-values (can include x-values in horizontal quadratics) "turn" to the direction they originated.
D=a/a+12*M. The adult weighs 75 kg. Calculate the adults weight in kilograms to pounds. Round final answer 2 decimal places
An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.
How to convert kilograms to pounds
Herein we have an application of unit conversions between weight units, from kilograms to pounds. Unit conversions follow this direct proportional formula:
y = k · x
Where:
x - Weight in kilograms
y - Weight in pounds
k - Conversion ratio
If we know that x = 75 kg and k = 2.208 lb/kg, then the weight of the adult in pounds is:
y = (2.208 lb/kg) · (75 kg)
y = 165.6 lb
An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.
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Solve the proportion.
2/3/4 = 10
LO
x = [?]
Answer:
x = 6
Step-by-step explanation:
We want to find x,
[tex]\frac{3}{5} = \frac{x}{10}[/tex]
to get x alone, we multiple both side by 10
[tex]\frac{3}{5} * 10 = \frac{x}{10} *10[/tex]
[tex]\frac{30}{5} = x[/tex]
30 divided by 5 is 6
Check:
We can see that 5 x ____ = 10 where ____ is 2
5 x 2 = 10
so 3 x 2 = 6
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what is the domain of f(x)-(1/4)^x?
A. y>0
B. x<0
C. x>0
D. All real numbers
Choose the equation that satisfies the data in the table.
HELP!!!!
The equation of the line represented by the table in slope intercept form is; y = ²/₁₅x + 2
How to solve equation in slope intercept form?The formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
The y-intercept will occur when x = 0. Thus, from the table, it is clear hat the y-intercept will be c = 2.
Let us find the slope using the first two points;
m = (2 - 0)/(0 - (-15))
m = 2/15
Thus, the equation is;
y = ²/₁₅x + 2
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Which formula do i use for this? it seems i used the wrong one.
The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.
How to calculate the payment?Mathematically, annuity can be calculated by using this formula:
[tex]A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }][/tex]
Given the following data:
Time, t = 11 years.Number of times compounded (quarterly), n = 4.Present value, A = $13,000.Interest rate, r = 3.6% = 0.036.Substituting the given parameters into the formula, we have;
[tex]13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P[/tex]
P = 13000/53.6932898522
P = $242.12.
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Complete Question:
The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?
If twice a number, added to 3 is divided by the number plus 5, the result is three halves. Find the number.
The number is…..
Answer:2
Step-by-step explanation:
(2x+5)/3 = 3/2
Multiply both sides by 3:
2x + 5 = 9/2
Subtract 5 from both sides:
2x = 9/2 - 5 = 9/2 - 10/2 = 3/2
Divide both sides by :
x = 3/4
Answer:
-1/3
Step-by-step explanation:
A number x is multiplied by 2, then has 3 added to it, then is divided by x+5, and the answer is 3 halves.
Or, as an equation:
[tex] \frac{2x + 3}{x + 5} = \frac{3}{2} [/tex]
Let's cross multiply:
[tex]4(2x + 3) = 2(x + 5)[/tex]
Expand:
[tex]8x + 12 = 2x + 10[/tex]
Now solve:
[tex]6x + 12 = 10[/tex]
[tex]6x = -2[/tex]
[tex]x = \frac{-1}{3} [/tex]
So the answer is -1/3
Find the principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.
Answer:
801.5625
Step-by-step explanation:
25.65×100/1.6×2=801.5625
The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.
What is simple interest?Simple interest is a method of calculating the interest charge.
Simple interest can be calculated as the product of principal amount, rate and time peroid.
Simple Interest = (Principal × Rate × Time) / 100
The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.
Simple Interest = (Principal × Rate × Time) / 100
25.65 × 100/(1.6 × 2 )
= 801.5625
Therefore, the principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.
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what are the angles of rotation less than 360 degrees for figure. sorry dont have a picture.
Shape; perfect pentagon, sides are all equal, no uneven sides
Line of symmetry; 5
think you can help me out a bit?
Thank you
The Angle of rotation of the given regular pentagon after undergoing rotational transformation is; 72°
How to find the angle of rotation?
We are told that the image is a perfect pentagon that all its' sides are all equal with no uneven sides.
Now, A figure is said to have rotational symmetry if it looks exactly the same after rotating it some angle less than 360° which is a full rotation.
Now, a regular pentagon will have a rotational symmetry of order 5 because it will look the same after 5 turns.
Thus;
Angle of rotation = 360/5
Angle of rotation = 72°
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana.
Explanation: Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.
Josiah and Chana travel at constant and different speeds.
The point F indicates that after 25 seconds Josiah is 60 meters from the starting line but behind Chana How can the what the the point F represent be known?Josiah's head start = 10 meters from the start
Josiah's speed = 2 m/s
Chana's speed = 3 m/s
Expressing the distance traveled as an equation, we have;
D = d + s × t
Where;
D = The distance covered
d = The distance from the starting line the runner starts
s = The speed of the runner
t = The time spent running
For Josiah, we have;
D = 10 + 2•t (line a)
For Chana, we have;
D = 0 + 3•t = 3•t (line b)
The above equations are straight line equations.
The point F is on line a, which shows Josiah distance after 25 seconds which is 60 meters. The corresponding point on line b, Chana's distance after 25 minutes is 75 meters.
Therefore;
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Answer:
Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah
Step-by-step explanation:
I got it right on khan.
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 5 digits long, and that each digit could be a number between 0 and 4. Assume that the hacker makes random guesses.
What is the probability that the hacker guesses the password on his first try? Please report the answer to four decimal places.
The probability that the hacker guesses the password in first go is
[tex]\dfrac{1}{5^5}[/tex]
While statistics examines the frequency of previous events, probability deals with estimating the possibility of future events.
The primary goal of the theoretical branch of mathematics known as the probability is the investigation of the consequences of mathematical concepts. At its core, statistics is a field of mathematics that seeks to explain observations in the actual world.
Both topics are significant, pertinent, and helpful. However, they are distinct, and appreciating this difference is essential to correctly assessing the applicability of mathematical evidence.
Since sample space has 5⁵ possibilities.
The event space has only one possibility which is to successfully hack the password perfectly.
Hence, the probability is
[tex]\dfrac{1}{5^5}[/tex]
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If n is an integer and 2^n is a factor of 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9, what is the greatest possible value of n?
A) 6
B) 7
C) 8
D) 9
Answer:
7
Step-by-step explanation:
2 = 2
4 = 2²
6 = 2 * 3
8 = 2³
adding the exponents of 2, we get 1+2+1+3 = 7
find the work done by a person pushing a 40 pound box up an incline that is 30 degrees above the horizontal and 100 feet long (ignore friction forces etc.- also remember Work is the inner product of Force and direction vectors. Furthermore remember gravity is a force acting in the downward direction)
The work done in pushing the box is 64000 lb-ft²/s²
How to calculate the work done by the person?Since person pushing a 40 pound box up an incline that is 30 degrees above the horizontal and 100 feet long, the work done, W is
W = mgh where
m = mass of box = 40 lb, g = acceleration due to gravity = 32 ft/s² and h = height of incline = LsinФ where L = length of incline = 100 ft and Ф = angle of incline = 30°So, W = mgh
W = mgLsinФ
So, substituting the values of the variables into the equation, we have
W = mgLsinФ
W = 40 lb × 32 ft/s² × 100 ftsin30°
W = 1280 lb-ft/s² × 100 ft × 0.5
W = 1280 lb-ft/s² × 50 ft
W = 64000 lb-ft²/s²
So, the work done in pushing the box is 64000 lb-ft²/s²
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Chloe’s Cafe bakes croissants that it sells to local restaurants and grocery stores. The average costs to bake the croissants are $0.40 for 2,000 and $0.35 for 4,000.If the total cost function for croissants is linear, what will be the average cost to bake 3,200?
Answer: First step is to determine the total cost
Total cost at 2,800
=$0.80 ×2,800
=$2,240
Total cost at 5,600
=$0.75 × 5,600
=$4,200
Second step is to determine the Variable cost per unit
Variable cost per unit=$4,200-$2,240
Variable cost per unit=$1,960
Variable cost per unit=5,600-2,800
Variable cost per unit=2,800
Variable cost per unit=$1,960/2,800
Variable cost per unit=$0.70
Now let determine the average cost
Average cost=$0.70×4,800+[($0.80×2800)-(2,800 ×$0.70)]
Average cost=$3,360+($2,240-$1,960)
Average cost=$3,360+$280
Average cost=$3,640
Average cost =$3,640/4,800
Average cost=$0.76
In conclusion What will be the average cost to bake 4,800 is $0.76
Step-by-step explanation:
Given sin a=−2/5 and cos b=1/3 with a and b both in the interval (3π/2,2π), find sin(a+b)
Answer:
[tex]-\frac{8\sqrt{2}+2}{15}.[/tex]
Step-by-step explanation:
1) sin(a+b)=sin(a)cos(b)+sin(b)cos(a);
2) if sin(a)=-0.4, then cos(a)=0.8; if cos(b)=1/3, then sin(b)=-√8/3;
3) finally, sin(a+b)=-0.4*1/3-√8/3*0.8=
[tex]=-\frac{8\sqrt{2}+2}{15}.[/tex]
A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).
Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+12πr . What is the domain of A(r) ? In other words, for which values of r is A(r) defined?
Part b: Continue to assume that the height of your cylinder is 6 inches. Write the radius r as a function of A . This is the inverse function to A(r) , i.e., to turn A as a function of r into r as a function of A .
r(A)=
Part c: If the surface area is 175 square inches, then what is the radius r ? In other words, evaluate r(175) . Round your answer to 2 decimal places.
The radius is ? inches if the surface area is 175 square inches
The domain of A(r) will be (0, ∞), the inverse function to A(r) will be r = 2π[A(r)]² + 12πA(r), and the radius will be 3.07 inches.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
A cylinder (round can) has a circular base and a circular top with vertical sides in between.
Let r be the radius of the top of the can and let h be the height.
The surface area of the cylinder (A) is given as
A=2πr² + 2πrh
Part A: Assume that the height of your cylinder is 6 inches.
Consider A as a function of r, so we can write that as
A(r) = 2πr² + 12πr
Then the domain of A(r) will be (0, ∞).
Part B: Continue to assume that the height of your cylinder is 6 inches.
Then the inverse function to A(r) will be
r = 2π[A(r)]² + 12πA(r)
Part C: If the surface area is 175 square inches.
Then the radius will be
175 = 2πr² + 12πr
r² + 6r – 27.866 = 0
r = 3.07, -9.07
Then the radius will be 3.07 inches.
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m% of n write a expression
The percentage of a given number in another implies the fraction of the given number to that other number with respect to 100%. Thus the required expression is: [tex]\frac{m}{100}[/tex] x n
When a given number is written in percentage, it implies that the fraction of the number to the total number in relation to 100%. For example, to determine the percentage of a number r in s, -we have:
[tex]\frac{r}{s}[/tex] x 100%
Therefore in the given question, the required expression is;
m% = [tex]\frac{m}{100}[/tex]
So that;
m% of n can be expressed as;
[tex]\frac{m}{100}[/tex] x n
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