Answers
Answer:
1. "a" [tex]u'=6x[/tex]
2. "d" [tex]v'=15x^2[/tex]
3. "b" [tex]y'=75x^4+30x^2+6x[/tex]
Step-by-step explanation:
General outline:For parts 1 & 2, apply power ruleFor part 3, apply product rulePart 1.
Given [tex]u=3x^2+2[/tex], find [tex]\frac{du}{dx} \text{ or } u'[/tex].
[tex]u=3x^2+2[/tex]
Apply a derivative to both sides...
[tex]u'=(3x^2+2)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]u'=(3x^2)'+(2)'[/tex]
Scalars factor out of derivatives...
[tex]u'=3(x^2)'+(2)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]u'=3(2x)+0[/tex]
Simplify...
[tex]u'=6x[/tex]
So, option "a"
Part 2.
Given [tex]v=5x^3+1[/tex], find [tex]\frac{dv}{dx} \text{ or } v'[/tex].
[tex]v=5x^3+1[/tex]
Apply a derivative to both sides...
[tex]v'=(5x^3+1)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]v'=(5x^3)'+(1)'[/tex]
Scalars factor out of derivatives...
[tex]v'=5(x^3)'+(1)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]v'=5(3x^2)+0[/tex]
Simplify...
[tex]v'=15x^2[/tex]
So, option "d"
Part 3.
Given [tex]y=(3x^2+2)(5x^3+1)[/tex]
[tex]\text{Then if } u=3x^2+2 \text{ and } v=5x^3+1, y=u*v[/tex]
To find [tex]\frac{dy}{dx} \text{ or } y'[/tex], recall the product rule: [tex]y'=uv'+u'v[/tex]
[tex]y'=uv'+u'v[/tex]
Substituting the expressions found from above...
[tex]y'=(3x^2+2)(15x^2)+(6x)(5x^3+1)[/tex]
Apply the distributive property...
[tex]y'=(45x^4+30x^2)+(30x^4+6x)[/tex]
Use the associative and commutative property of addition to combine like terms, and rewrite in descending order:
[tex]y'=75x^4+30x^2+6x[/tex]
So, option "b"
Related Questions
F10) How many Solutions Does this
System Have?
y=2X
y = -x + 2
Answers
Answer:
See below.
Step-by-step explanation:
Problem:
Solve y=2x;y=−x+2
Steps:
I will solve your system by substitution.
y=2x;y=−x+2
Step: Solve y=2 x for y:
Step: Substitute 2x for y in y=−x+2:
y=−x+2
2x=−x+2
2x+x=−x+2+x(Add x to both sides)
3x=2
3x/3 = 2/3 (Divide both sides by 3)
x=2/3
Step: Substitute 2/3 for x in y = 2x
y=2x
y = 2(2/3)
y = 4/3 (Simplify both sides of the equation)
Answer:
x = 2/3 and y = 4/3
Answer:
only one at x = 2/3 y = 1 1/3
Step-by-step explanation:
At the same solution point Y = Y so
2x = -x + 2
3x = 2
x = 2/3
A line passes through (-9,-6) and has an undefined slope. Write an equation of the line satisfying the given conditions.
A. x= -9
B. y= -9
C. y= -6
D. x= -6
Answers
The equation of the line is x = -9 , Option is the correct answer
What is the equation of a line ?The equation of a line is given by y = mx+c
where m is the slope and c is the intercept
It is given that
A line passes through (-9,-6) and has an undefined slope.
undefined slope means it is a vertical line at -9
Therefore the equation of the line is x = -9 , Option is the correct answer
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This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answers
Step-by-step explanation:
[tex]29 {}^{ \frac{x}{2} } [/tex]
[tex]((29) {}^{ \frac{1}{2} } ) {}^{x} [/tex]
The answer is A
Someone do this please, ty.
Answers
5 is the missing value.
Step-by-step explanation:
12x = 60
x = 60/12
x = 5
Answer:
[tex]\boxed{\rm x = 5}[/tex]
Step-by-step explanation:
[tex] \rm \cfrac{12}{20} = \cfrac{3}{x} [/tex]
Find the missing value.
Solution with work shown:
Use criss-cross multiplication:
[tex]12 \times x = 3 \times 20[/tex][tex]12x = 60[/tex]Divide both sides by 12:
[tex] \cfrac{12x}{12} = \cfrac{60}{12} [/tex][tex]x = 5[/tex]Hence,the missing value is 5.
Based on the graph of g(x), on which intervals
are the function's values negative? Select all that
applv.
Answers
Answer:
[tex]\text{B}) \text{ } -3 < x < -1\\\text{D}) \text{ } 2 < x < \infty[/tex]
Step-by-step explanation:
The graph lies below the x-axis.
Determine the domain of (g ∘ f)(x) if f (x) = x2 + x − 3 and g of x is equal to 1 over the quantity x plus 1 end quantity period {x ∈ ℝ| x ≠ −1} {x ∈ ℝ| x ≠ −2, 1} {x ∈ ℝ| x ≠ −2, −1, 1} {x ∈ ℝ}
Answers
The domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .
What is domain?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
given function:
f(x) = x² + x -3
g(x) = 1/x+1
Now, solving the equation
gof = g(f(x))
=g( x² + x -3)
=1/(x² + x -3)+1
=1/ x² + x -2
= 1/ x² +2x - x -2
= 1/ x( x+ 2) - (x +2)
=1/ (x+2)(x-1)
Hence, the domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .
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Identify one pair of vertical angles in the diagram below,
Answers
Answer:
b and d
Step-by-step explanation:
there are two
but only one is an answer choice
b and d
the other which is not an answer choice is
a and c
gathmath
(c) Nicole has a part-time job entering data in a computer. Her pay at the end of the week C
is affected by the amount of data she enters each hour. What is the dependent
variable?
Answers
Answer:
the dependent variable is the data because it's the one that changes
Need help finding the quadratic function...15 pts for your help
Answers
The function is [tex]y = (x +2)^2 + 5.[/tex]
we use the vertex form of the quadratic equation
We have given a graph,
What is the vertex form of the quadratic equation?y = a(x - h)^2 + k.
Therefore the vertex of the given graph is
See the vertex at (-2, 5)
Since the general way to write the vertex is (h, k), we compare (h, k) to (-2, 5).
[tex]y = a(x - (-2))^2 + 5.\\y=a(x+2)^2+5......(1)[/tex]
Now we have given that (-4,1) use this value in the above equation so we get,
[tex](1)=a(-4+2)^2+5[/tex]
[tex]1=a(-2)^2+5[/tex]
[tex]1=4a+5[/tex]
[tex]1-5=4a[/tex]
[tex]-4=4a[/tex]
[tex]a=-4/4[/tex]
[tex]a=-1[/tex]
Using the value of an in equation (1) we get,
Therefore the function is [tex]y = (x +2)^2 + 5.[/tex]
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I also dont get this :(
Answers
An equation is formed of two equal expressions. If x is increased by 5 then the value of y is increased by 10.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that y=2x+1, now if the value of x increased by 5. then the value of y will be,
[tex]y_1=2(x+5)+1\\y_1 = 2x + 11[/tex]
Now if we compare y and y₁, then it can be said that if x is increased by 5 then the value of y is increased by 10.
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Another job is advertising leaflets printed on sheets of A4 paper (210 x 297 mm).
The sheets are then folded into thirds as shown.
What are the measurements in millimetres of each folded leaflet?
Answers
5%3×4+14-15 answers thes questions
In the following month 10% savings on other costs are expected. What is the total other costs target for next month for the five locations
Answers
Answer:
The given question is incomplete. The graphs for the question are attached below.
Total savings on other costs expected in the following month is 13,950.
Total other costs targeted for next month for the five locations:
Washington Place = 14,850
Lincoln Square = 9,900
Millienium Concourse = 18,000
The old mill = 13,500
CWG Tenton = 0
Step-by-step explanation:
According to the graphs, there are two parts to this question
1. In the following month, 10% savings on other costs are expected.
The graph is attached below for reference
10% savings on other costs are expected in the following month:
=> (4,000 + 2,000 + 5,000 + 2,000 + 2,500) * (1-10%)
=> 15,500 * [tex](1-\frac{10}{100})[/tex]
=> 15,500 * [tex]\frac{90}{100}[/tex]
=> 13,950
Total savings on other costs expected in the following month is 13,950
2. Total other costs target for next month for the five locations are:
Washington Place = 6,000+3,000+3,500+ 4,000 = 16,500 * 0.9 = 14,850
Lincoln Square = 5,000+ 2,000+ 2,000+2,000= 11,000 * 0.9 = 9,900
Millienium Concourse =7,000+3,000+5,000+5,000= 20,000 * 0.9 = => 18,000
The old mill = 6,000+ 5,000+ 4,000=15,000 * 0.9 = 13,500
CWG Tenton = 0 * 0.9 = 0
Total other costs target for next month for the five locations:
Washington Place = 14,850
Lincoin Square = 9,900
Millienium Concourse = 18,000
The old mill = 13,500
CWG Tenton = 0
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Dedi had a combination lock.To open the lock he started at 37.He made 3 half turns clockwise and 3 quarter turns anticlockwise
What number did he end up at?
Answers
Therefore your answer is 37 + (3*1/2)-(3*1/4)
= 37.75
Hope this helped :)
roger contracts childrens playhouses all the top of each house he places an isosceles triangle to from the roof the largest angle measures 146 what are the measurement of the other two angles
Answers
Step-by-step explanation:
there are clearly some typos in the question.
so, to summarize what I understood :
the roof of each playhouse is an isoceles triangle, with the largest angle being 146°.
we need to find the other 2 angles.
"isoceles" means that both legs are equally long.
that means automatically that both side angles (bottom left and bottom right) are equally large too.
and now, this please burn into your brain forever :
the sum of all angles in a triangle (no matter what type) is always 180°.
so, if we call a side angle x, we have here
180 = 146 + x + x = 146 + 2x
34 = 2x
x = 17°
so, both missing angles are 17°.
a pretty flat triangle roof.
What is the inverse of f(x)=9x-3
Answers
Answer:
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x9+13 f - 1 ( x ) = x 9 + 1 3 is the inverse of f(x)=9x−3 f ( x ) = 9 x - 3
Answer:
y = x + 3/9
Step-by-step explanation:
Change f(x) y = 9x-3Solve for y +3 +3
x+3 = 9y = y=x+3/9
what are the solutions in the following equations?
Answers
Answer: (0, -6) and (1, -5)
Step-by-step explanation:
If [tex]x-y=6[/tex], then [tex]y=x-6[/tex]. Substituting this into the second equation,
[tex]x-6=x^{2}-6\\\\x^{2}-x=0\\\\x(x-1)=0\\\\x=0, 1[/tex]
If x=0, y=-6.
If x=1, y=-5.
So, the solutions are (0, -6) and (1, -5)
Your Uncle Malcolm has a honeybee colony that consists of a single queen, hundreds of male drones and roughly 60,000 female worker bees. His beehive produced 200
pounds of honey last year. If Uncle Malcolm continues beekeeping with the same
number of bees, how many pounds of honey will his hive produce after 10 years? Write
your answer in scientific notation.
Answers
In scientific Notation , After 10 years he will have in total 2 x 10 ³ pounds.
What is Scientific Notation ?Scientific Notation is a way of writing very large or small quantities.
It is written in the form of x 10ˣ
It is given that
The colony of bees has a single queen, hundreds of male drones and roughly 60,000 female worker bees.
The quantity of honey produced is 200 pounds.
After 10 years he will have in total
200 * 10 = 2000 pounds
In scientific Notation it will be written as
2 x 10 ³ pounds.
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What is the reciprocal of (10xyz)/(40xyz)
Answers
Answer:
4
Step-by-step explanation:
10xyz/40xyz
the xyz would cancel out
leaving 10/40.
10/40 would then simplify to 1/4 (divide by 10)
1/4
The reciprocal of 1/4 is 4
To check:
1/4 * 4 = 1
Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)
2. Jay Smith deposited $5,000 into an annuity due at the beginning of each quarter for 3 years at 6%
compounded quarterly.
Answers
Answer:
value: $66,184.15interest: $6,184.15Step-by-step explanation:
The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.
__
formulaThe formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...
FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148
FV ≈ 66,184.15
calculatorThe attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.
__
a)The future value of the annuity due is $66,184.15.
b)The total interest earned is the difference between the total of deposits and the future value:
$66,184.15 -(12)(5000) = 6,184.15
A total of $6,184.15 in interest was earned by the annuity.
The surface area of a cone is 250 square centimeters. The height of the cone is double the length of its radius.
What is the height of the cone to the nearest centimeter?
A.
10 centimeters
B.
20 centimeters
C.
15 centimeters
D.
5 centimeters
Answers
Answer: C
Step-by-step explanation:
just took it
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
Given that, the surface area of a cone is 250 square centimetres. The height of the cone is double the length of its radius.
We need to find what is the height of the cone to the nearest centimetre.
What is the surface area of a cone?The area occupied by the surface/boundary of a cone is known as the surface area of a cone. It is always measured in square units. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as a curved surface area.
If the radius of the base of the cone is "r" and the slant height of the cone is "l", the surface area of a cone is given as total surface area, T = πr(r + l) square units
Now, let the radius of a cone be x.
Then the height of the cone is 2x.
Slant height=√x²+4x²
=√5x
So, the surface area of cone=πx(x+2.24x)
⇒250=3.14 × 3.24x²
⇒x²=24.57
⇒x=4.95≈5 centimetre
So, height=2x=10 centimetre
The height of the cone to the nearest centimetre is 10 centimetres. Therefore, option A is the correct answer.
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I’m so confused on what numbers l should put into the boxes
Answers
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The lines for the given statements can be plotted as shown below.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The lines for the given statements can be plotted as shown below.
The coordinate grid can be filled as,
1)
x 0 3 1
y 3 0 2
2.)
x 0 1 -1
y 1 0 2
3.)
x 0 4 -1
y -2 0 2
4.)
x 0 1 1
y -2 0 -2
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little melinda has nickels and quarters in her bank she has 8 fewer than nickels she has 5.60 in the bank how many coins of each type does she have
Answers
Answer:
She has 20 coins in her bank, where she has 12 nickels and 8 quarters
Step-by-step explanation:
A quarter is 25 centsA nickel is 5 centsSince she has 8 fewer than nickels, we add 8 to the number of nickelsQ = N + 8, 25Q + 5N = 560
25(N + 8) + 5N = 560
25N + 200 + 5N = 560
25N + 200 - 200 + 5N = 560 - 200
30N = 360
30N / 30 = 360 / 30
N = 12 nickels
Finding amount of Quarters:
Q = N + 8 → Q = 12 + 8
Q = 20 quarters
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P is a polynomial of degree 4 with three zeros: -1 and 2 are zeros of multiplicity one, and 3 is a zero with multiplicity two. If P(0) = 90, what is the lead coefficient of P ?
Answers
Answer:
[tex]P(x) = (x+1)(x-2)(x-3)^2 + 108[/tex]
Step-by-step explanation:
let me know if you want an explanation
The segments shown below could form a triangle.
A
C
B
8
O
B
A. True
B. False
15
A
Answers
Answer:
False
Step-by-step explanation:
these lines are unable to form a triangle, the longest line (BA) is 15. The other small lines (AC and CB) if added together, need to be longer than 15, otherwise if you were trying to form a triangle, they would not be able to connect completely with eachother while creating a triangle shape
The number 900 is increased by 20% and then decreased by 20%. Find the new number.(the ans is 864 apparently:/ I need steps)
Answers
Step-by-step explanation:
if 900 is increased by 20% then
120/100×900=1080
Decreasing it by 20% then
80/100×1080=864
patulong po,thankyou
Answers
1.8 x 1.2 = 2.16
2.16 x 12.5 = 27
Because we just multiplied all three numbers by each other, we have identified our missing volume. The volume of the rectangular box is 27 cubic meters.
Your final answer: A.
What expression is equivalent to ten square root five
Answers
The expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
= 10√5
We can write the above equation:
= √(10×10×5)
Because √(10×10) = 10
= √(100×5)
= √500
Thus, the expression 10√5 can be written as √500 because √(10×10) = 10 option (A) √500 is correct.
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9 is subtracted from 3 times the sum of 4 and 2.
Answers
Answer:
9
Step-by-step explanation:
This problem is represented below.
=3(4+2)-9
=3(6)-9
=18-9
=9
Your final answer: 3 x (4 + 2) - 9 = 9.
Sum of 1/2*3 +1/3*4 +1/4*5 ..1/99*100
Answers
Answer:
11∗2+13∗4+15∗6+⋯+199∗100=?
=(1−12)+(13−14)+(15−16)+⋯+(199−1100)
=(1+13+15+17+⋯+199)−(12+14+16+⋯+1100)
=(1+13+15+17+⋯+199)−12(1+12+13+⋯+150)
=∑k=15012k−1−∑k=15012k
Continue further.
area of a trapezium base 8 top6 height 4
Answers
The area of a trapezium with base 8 top 6 height 4 is 28 cm².
Given that, base of trapezium (b)=8 cm, top of trapezium (a)=6 cm and height of trapezium = 4 cm.
What is the area of a trapezium?
The trapezium is a quadrilateral with pair of sides parallel. The area of a trapezium is the area enclosed within its four sides.
We know that area of a trapezium [tex]=\frac{1}{2}(a+b) \times h[/tex]
Where a and b are parallel sides of a trapezium.
Now, the area of a given trapezium [tex]=\frac{1}{2}(6+8) \times 4[/tex] cm²
=14×2=28 cm²
Therefore, the area of a trapezium with base 8 top 6 height 4 is 28 cm².
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