Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
Answers
The derivative of the function f(x) = -5x²+3x-2 is -10x+3.
Given the function is f(x) = -5x²+3x-2
Differentiate with respect to x.
d/dx -5x²+3x-2 = d/dx (-5x²) + d/dx(3x) - d/dx(2)
using the power rule d/dx [xⁿ] = nxⁿ⁻¹
⇒ d/dx -5x²+3x-2 = -5(2)x²⁻¹ + 3(1) - 0
⇒ d/dx -5x²+3x-2 = -10x+3
The power rule states that the derivative of xn is nx(n-1) for every x if n is a positive integer, regardless of whether you are thinking of derivatives at a point (numbers) or derivatives on an interval (functions).
Hence we get the derivative as -10x+3.
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Related Questions
A ladder resting on a vertical wall makes an angle whose tangent is 2.5 with the ground of the distance between the foot of the ladder and the wall is 60cm what is the length on the ladder
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If AC denote the ladder and B be foot of the wall the length of the ladder AC be x metres then the length of the ladder exists 5 m.
What is meant by trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
Let AC denote the ladder and B be foot of the wall. Let the length of the ladder AC be x metres.
Given that ∠ CAB = 60° and AB = 2.5 m In the right Δ CAB,
cos 60° = AB / AC
simplifying the above equation, we get
⇒ AC = AB / (cos 60°)
x =2 × 2.5 = 5 m
Therefore, the length of the ladder exists 5 m.
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I need help on answering 3. (d) I have two choices it can be which is false and sometimes true.
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Question:
Solution:
If x represents a positive integer, then the point x is a natural number, that is, x is greater than zero, in particular, if x is a number greater than zero it can be a number greater than any number after zero. For example, it can be greater than 1.
Then the question d is ALWAYS TRUE.
do you know the north Zone at the football stadium has 95 Rose there are 48 seats in a row how many people will the North end zone seat
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The North zone at the football stadium has 95 rows.
There are 48 seats in a row.
How many people will the North end zone seat?
Since there are 95 rows and each row has 48 seats, multiply them to get the total number of seats.
[tex]\begin{gathered} total\: seats=rows\times seats \\ total\: seats=95\times48 \\ total\: seats=4560 \end{gathered}[/tex]Therefore, there are 4560 people sitting in the North zone.
What is the y-intercept of f(x) =(3/5)^x?
Answers
Answer:
the y intercept is -1.
Step-by-step explanation:
the y intercept is -1 because it goes through the point (0,-1)
Trini Cars break down on the highway.show me estimates that she is 20 to 30 miles from the nearest car repair shop she calls a towing company that charges a fee of $80 plus $3 per mile to tow a car.if training uses this towing company, which is the best estimate for the amount of money,m,she will pay for the company to tow her car.a .103 greater than sign and greater than sign 113 b.140 greater than sign M greater than sign 150 c.114 greater than 5 m greater than 170 d. 560 greater than 10 m > 70
Answers
We have that the cost is $80 plus $3 per mile, and also we now that the car is 20 to 30 miles from the car repair shop. So we have that Trini have to pay
[tex]\begin{gathered} 80\text{ + 3(20) }\leq\text{ M }\leq\text{ 80 + 3(30)} \\ 80\text{ + 60 }\leq\text{ M }\leq\text{ 80 + 90} \\ 140\text{ }\leq\text{ M }\leq170 \end{gathered}[/tex]So the answer is: b.140 greater than sign M greater than sign 150.
To find the area of a shape region:Find the area of the entire region:Fimd the area of the unshaded region(s)Subtract the area of the unshape region from the area of the entire region
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IN order to find the area of the shaded region, proceed as follow:
calculate the area of the right triangle:
A = b·h/2
A = (21 yd)(34 yd)/2 = 357 yd²
next, calculate the area of the circle:
A' = π r²
A' = (3.1415)(7 yd)² = 153.93 yd²
next, subtract the area of the circle to the area of the rectangle:
AT = A - A' = 357 yd² - 153.93 yd²
AT = 203.07 yd²
Hence, the area of the shaded region is 203.07 yd²
The students of a school were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard.Each penholder was to be radius of 3cm and height 10.5 cm. The school was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be brought for the competition. Assume: pi = 22/7
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Recall the surface area for the following figures.
[tex]\begin{gathered} \text{Cylinder}=2\pi rh+2\pi r^2 \\ \\ \text{The term }2\pi r^2\text{ includes a cover both the top and bottom of the cylinder} \\ \text{Since we will be using only the bottom modify the formula such that it only} \\ \text{includes the bottom part} \\ \\ \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \end{gathered}[/tex]Given that
height = h = 10.5 cm
radius = r = 3 cm
π = 22/7
Substitute the following given and we have the surface area for the pen holder
[tex]\begin{gathered} \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \\ \text{Pen Holder Surface Area}=2(\frac{22}{7})(3\operatorname{cm})(10.5\operatorname{cm})+(\frac{22}{7})(3\operatorname{cm})^2 \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+(\frac{22}{7})(9\operatorname{cm}) \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+\frac{198}{7}\operatorname{cm} \\ \text{Pen Holder Surface Area}=\frac{1584}{7}\operatorname{cm}^2 \end{gathered}[/tex]Now that we have the surface area, multiply it by 35 since there are 35 competitors in the competition
[tex]undefined[/tex]Which of these numbers is irrational?
✍️Record your work/explanation on your document or paper
Which of these numbers is irrational?
✍️Record your work/explanation on your document or paper
\sqrt{5}
5
\frac{3}{5}
5
3
-3.5
3.\overline{5}3.
5
Answers
See attachment for problem
Answers
The liters in the tank when it is filled to a height of 3.70 is 5,580 liters
The liters that needs to be added to 100% capacity is 480 liters
What is the volume?A right circular cone is a three dimensional object has a flat circular base that tapers to a vertex. The volume of a right circular cone is the amount of space in the right circular cone.
Volume of a cone = 1/3(πr²h)
Where:
π = pi = 3.14r = radius h = heightVolume of the right circular cone when its filled to a height of 3.70 = 1/3 x 3.14 x 3.70 x 1.20² = 5.58 m³
5.58 x 1000 = 5,580 liters
Volume of the right circular cone when it is full = 1/3 x 3.14 x 4 x 1.20² = 6.03 m³
6.03 x 1000 = 6030 liters
Liters that needs to be added to 100% capacity = 6030 liters - 5,580 liters = 480 liters
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The functions f(x) and g(x) are shown on the graph.f(x)=x^2What is g(x)?A. g(x)=(x+3)^2B. g(x)=(x-3)^2C. g(x)=(1/3x)^2D. g(x)=3x^2
Answers
Given:
[tex]f(x)=x^2[/tex]Let's find g(x).
From the given graph, we can see the graph of g(x) is compressed horizontally from f(x).
Thus, to find g(x) aply the transformation rules for function.
We have:
Horizontal compression of b units ==> f(bx)
Given the point on g(x):
(x, y) ==> (2, 12)
Let's solve for the value of the compressed factor.
We have:
[tex]\begin{gathered} 12=b(2)^2 \\ \\ 12=b4 \\ \\ \text{Divide both sides by 4:} \\ \frac{12}{4}=\frac{b4}{4} \\ \\ 3=b \\ \\ b=3 \end{gathered}[/tex]This means the graph of f(x) was compressed horizontally by a factor of 3 to get g(x).
Thus, to write the function for g(x), we have:
[tex]g(x)=3x^2[/tex]ANSWER:
[tex]D\text{.}g(x)=3x^2[/tex]5. Joseph Cheyenne is earning an annual salary of $24,895. He has been offered the job in the ad. How much more would he earn per month if he is paid: a. the minimum? b. the maximum
Answers
Joseph has an annual salary of $24895 dollars and she get the new job that is between 28000-36000 dollars so:
the minimum will be:
[tex]24895+28000=52000[/tex]and the maximun will be:
[tex]24895+36000=60895[/tex]Find the circumference of a circle with a diameter of centimeters. Round your answer to the nearest centimeter.
Answers
Circumference = 2* pi * r
r = radius
r = diameter/2
r = 50/2
r = 25 cm
Circumference = 2*3.14 * 25
Circumference = 157 cm
Result = 157 cm
The second choice
4y+3+6xWhat is the numerical coefficient of the first term?What is the constant term?
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We are given the following expression:
[tex]4y+3+6x[/tex]The numerical coefficient is the number that multiplies a variable, in this case, the first variable is "y" and the numerical coefficient is 4.
The constant in an expression is the number that does not multiply any variable, in this case, the constant is 3.
Quadrilateral PQRS is plotted in the coordinate plane. The quadrilateral is dilated by a scale factor of 3/4. What are the new ordered pairs for P'Q'R'S'?
Answers
Explanation:
The first thing is to state the coordinates of Quadrilateral PQRS
P (5, 5), Q (3, 5), R (3, 1), S (5, 1)
Then we find the distance between two points using the distance formula
[tex]dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} P(5,5),Q(3,5)\text{ = (x1, y1) and (x2, y2)} \\ \text{distance PQ = }\sqrt[]{(5-5)^2+(3-5)^2}\text{ = }\sqrt[]{0+(-2)^2}\text{ =}\sqrt[]{4} \\ \text{distance PQ = }2 \end{gathered}[/tex][tex]\begin{gathered} Q(3,5),R(3,1)\text{= (x1, y1) and (x2, y2)} \\ \text{distance QR = }\sqrt[]{(1-5)^2+(3-3)^2}\text{ = }\sqrt[]{(-4)^2+0}\text{ = }\sqrt[]{16} \\ \text{distance QR = 4} \end{gathered}[/tex]It is a quadrilateral, meaning the two lengths are equal. Like wise the two widths are equal.
length PQ = length SR = 2
Length QR = length PS = 4
Scale factor = 3/4
Scale factor = corresponding side of new image/ corresponding side of original image
PQRS = original image, P'Q'R'S' = new image
3/4 = P'Q'/PQ
3/4 = P'Q'/2
P'Q' = 2(3/4) = 6/4 = 3/2
Since P'Q' = S'R'
S'R' = 3/2
3/4 = Q'R'/QR
3/4 = Q'R'/4
Q'R' = 3/4 (4) = 12/4 = 3
Since Q'R' = P'S
P (5, 5), Q (3, 5), R (3, 1), S (5, 1)
PQRS to P'Q'R'S' = 3/4(
P' = 3/4 (5, 5) = (15/4, 15/4)
Q' = 3/4 (3, 5) = (9/4, 15/4)
R' = 3/4 (3, 1) = (9/4, 3/4)
S' = 3/4 (5, 1)
what's the difference between two whole number 1/2 percent of 36 and 30% of 10
Answers
Here, we proceed step by step, to obtain our answer,
[tex]\frac{1}{2}[/tex] % of 36 can be written as ,
0.5 % of 36 , which means,
100 % refers to 36, then
0.5 % refers to what, thus, by cross multiplication we get,
0.5 % of 36 = [tex]\frac{0.5 X 36}{100}[/tex] = 0.18 ___(1), which can be expressed in whole numbers as 0.
Now, 30 % of 10 means,
100 % refers to 10, then
30 % refers to what, thus, by cross multiplication we get,
30 % of 10 = [tex]\frac{30 X 10}{100}[/tex] = 3 __(2)
From equations (1) and (2),
the whole numbers that we obtain are 0 and 3, respectively,
Thus the difference between these two whole numbers is,
= 3 - 0 = 3.
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The path of the baseball follows the equation h= -4.9t^2 + 60t + 1.5 where h represents the height of the baseball, t seconds after the baseball was hit. How long will it take the baseball to return to the ground?
Answers
SOLUTION
Given the question in the question tab, the following are the steps to solve the problem:
Step 1: Write out the equation for the path of the baseball where h is height and t is time in seconds
[tex]h=-4.9t^2+60t+1.5[/tex]Step 2: Rewrite the new equation
The height of the baseball when it returns to the ground is zero(0). Therefore, at that point where the baseball returns to the ground, the function becomes:
[tex]0=-4.9t^2+60t+1.5[/tex]Step 3: We solve the quadratic equation to get the value of t:
[tex]\begin{gathered} 0=-4.9t^2+60t+1.5 \\ u\sin g\text{ quadratic formula which states that:} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=-4.9,b=60,c=1.5 \\ \text{Substituting the values, we have:} \\ \frac{-60\pm\sqrt[]{60^2-4(-4.9)(1.5)}}{2(-4.9)} \\ =\frac{-60\pm\sqrt[]{3600+29.4}}{-9.8} \\ =\frac{-60\pm60.2445}{-9.8} \\ =\frac{-60+60.2445}{-9.8}\text{ or }\frac{-60-_{}60.2445}{-9.8} \\ =\frac{0.2445}{-9.8}or\frac{-120.2445}{-9.8} \\ t=-0.024948979\text{ or }12.26984184 \\ t\approx-0.0249\text{ or 12.270} \end{gathered}[/tex]Since the value for time cannot be negative, hence the time it will it take the baseball to return to the ground is approximately 12.270 seconds
Solve this system of equations by elimination. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer. If your answer is no solution, type "no solution". If your answer is infinitely many solutions, type "infinitely many solutions".
Answers
5x + 2y = -12 (a)
3y + 5x =-8 (b)
First, write (b) in the ax+by=c form:
5x + 3y = -8 (b)
Now, subtract (b) to (a) to eliminate x
5x + 2y = -12
-
5x + 3y = -8
__________
-y = -4
solve for y:
Multiply both sides by -1
y=4
Replace y=4 on (a) and solve for x:
5x + 2 (4) = -12
5x + 8 = -12
5x = -12-8
5x = -20
x = -20/5
x = -4
Solution: (-4,4)
Let w be defined as 2 more than the number of digits in the integer w. For example, 15* = 4 (2 digits in 15 + 2). If whas 7000 digits, then what is the value of (w)*?
Answers
The number of digits in 7000 is 4
The number of digits in w=7000
[tex](w)^{\cdot}=\text{ the number of digits in w+2}[/tex][tex](w)^{\cdot}=\text{7000+2}[/tex][tex](w)^{\cdot}=7002[/tex]Hence the required value is 7002.
Could you please help with
Answers
The angle measures
m WXZ = 180 - 90 - 24
mWXZ = 66°
Sophia spent $40 on supplies to make 20 bracelets. She plans to sell them at a craft show for $5 each. Let y represent the amount of her profit. Is it discrete or continuous? And what are the domain and range?
Answers
we have that
y ------> the amount of her profit
x -----ghe number of bracelets
REmember that
Profit is equal to sell minus cost
so
y=5x-40
the domain is the interval (0,1,2,3,4,5) ------> is a discrete
the range is equal to
For x=
2) Add or subtract the following polynomials: (5pts each) 1) (98-7x' +5x-3)+(2x* +4x'-6x-8) = ii) (8x* +6x - 4x2 -2)-(3x* – 5x – 7x+9)=
Answers
When we are adding/subtracting polynomials, we add or subtract like terms.
For example,
x^2 added with x^2 terms
x^4 added with x^4 terms
numbers (constants) added with numbers etc.
2 i)[tex](9x^5-7x^2+5x-3)+(2x^4+4x^3-6x-8)[/tex]Since we are "adding" the 2nd parenthesis polynomial, we can take out the parenthesis and put them in order and them simply add/subtract(!) The steps are shown below:
[tex]\begin{gathered} (9x^5-7x^2+5x-3)+(2x^4+4x^3-6x-8) \\ =9x^5-7x^2+5x-3+2x^4+4x^3-6x-8 \\ =9x^5+2x^4+4x^3-7x^2+5x-6x-3-8 \\ =9x^5+2x^4+4x^3-7x^2-x-11 \end{gathered}[/tex]Note: there were like terms with "x's" and "constants". We added/subtracted them only.
Is 1/4 n - 16 equivalent to 4(n - 4)?
Answers
Answer:
[tex]\frac{1}{4}n-16[/tex]is not equivalent to:
[tex]4(n-4)[/tex]Explanation:
The expression
[tex]\frac{1}{4}n-16[/tex]can be written as:
[tex]\frac{1}{4}(n-64)[/tex]It is not equivalent to:
[tex]4(n-4\text{)}=4n-16[/tex]Peri earned $55 for 5 dog walks. If Peri earned $22, how many times did she walk her neighbor's dog?
Answers
Answer:
2
Step-by-step explanation:
55÷5=11
22÷11=2
how many apples are in 4 dozen
Answers
There are 48 apples in 4 dozen
Explanations:1 dozen = 12
This means that:
1 dozen of apples = 12 apples
4 dozen = 12 x 4
4 dozen = 48 apples
What is the probability that a data value in a normal distribution is between a Z score of -1.52 and Z score of -.34
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We are asked to find the probability that a data value in a normal distribution is between a Z score of -1.52 and -0.34
[tex]P(-1.52First, we need to find out the probability corresponding to the given two Z-scoresFrom the Z-table, the probability corresponding to the Z-score -1.52 is 0.0643
From the Z-table, the probability corresponding to the Z-score -0.34 is 0.3669
So, the probability is
[tex]\begin{gathered} P(-1.52Therefore, the probability that a data value in a normal distribution is between a Z score of -1.52 and a Z score of -0.34 is 30.3%Option A is the correct answer.
The endpoints are a side of a rectangle ABCD in the coordinate plane at A(3,4), B(6,1) Find the equation of the line the given segment The line segment is line Segment AB
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The endpoints are a side of a rectangle ABCD in the coordinate plane at A(3,4), B(6,1) Find the equation of the line the given segment
The line segment is line Segment AB
step 1
Find the slope of segment AB
m=(1-4)/(6-3)
m=-3/3
m=-1
step 2
Find the equation of the line in slope intercept form
y=mx+b
we have
m=-1
point (3,4)
substitute
4=(-1)*(3)+b
4=-3+b
b=4+3
b=7
therefore
the equation of segment AB is
y=-x+7the probability he chooses orange fruit
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Consider that the total number of fruits are 10. The probability to get some fruit is given by the quotient in between the number of suc a fruit and the total number of fruits.
Then, at the first time, the probability of getting a kiwi is:
p1 = 1/10 = 0.1 (becasue there is one kiwi)
After the kiwi is taken out, the number of fruits are 9. In this case, the probability of getting one orange is:
p2 = 3/9 = 0.33 (because there are three oranges)
THe probability of the two previous events, that is, to obtain one kwi and then one orange is the product of the probabilities p1 and p2:
P = p1*p2 = (0.1)(0.33) = 0.03
Hence, the probabilty is approximately 0.03
IN Date OUT IN OUT Employee Time Card: 7:30 10/1 11:30 4:15 12:00 John Apple 10/2 8:15 11:00 5:15 11:45 10/3 11:15 3:55 7:00 12:10 Dept: Cust. Serv. 4:30 10:55 12:00 6:25 10/4 NOTE: NO OVERTIME 1:30 5:00 12:45 10/5 6:00 TOTAL HOURS RATE per hour: $13.75 What is John's total pay for the week? deneaker notes
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I can see it now
thank you
11:30-7:30= 4h
11:00-8.15=2:45h
11:15-7:00=4:15h
10:55-6:25=4:30h
10:45-6:00=4:45h
Total = 4+2.75+4.25+4.5+4.75=20.25
4:15-12:00=4:15h
5:15-11:45=5:30h
3:55-12:10=3:45h
4:30-12:00=4:30h
5:00-1:30=3:30h
Total = 4.25+5.5+3.75+4.5+3.5=21.5
Total hours = 21.5+20.25=41.75
ok, the total pay would be:
Rate per hour * total hours:
[tex]13.75\times41.75=574.0625[/tex]Did you get the same value? hello? are you still with me? ok
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Solve the inequality and write the solution using:
the inequality
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Determine the missing coordinates in the ordered pair (-1,?) so that it will satisfy the given equation
Answers
we have the equation
2x-3y=4
Remember that
if the ordered pair is a solution of the given equation, then the ordered pair must satisfy the given equation
we have the ordered pair (-1,a)
substitute the given coordinates in the equation
2(-1)-3(a)=4
-2-3a=4
solve for a
3a=-2-4
3a=-6
a=-2
therefore
the missing coordinate is -2
