Answer:
as
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0[/tex]
so
[tex]y'=0[/tex]
Step-by-step explanation:
Given the function
[tex]y=\:1-x+\frac{x^2}{1}+x-x^2[/tex]
Taking derivative
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)[/tex]
[tex]\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'[/tex]
[tex]=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)[/tex]
as
[tex]\frac{d}{dx}\left(1\right)=0[/tex] ∵ [tex]\mathrm{Derivative\:of\:a\:constant}:\quad \frac{d}{dx}\left(a\right)=0[/tex]
[tex]\frac{d}{dx}\left(x\right)=1[/tex] ∵ [tex]\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1[/tex]
[tex]\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x[/tex] ∵ [tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}[/tex]
[tex]\frac{d}{dx}\left(x\right)=1[/tex] ∵ [tex]\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1[/tex]
[tex]\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x[/tex] ∵ [tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}[/tex]
substituting all the values in the expression
[tex]=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)[/tex]
[tex]=0-1+2x+1-2x[/tex]
[tex]=0[/tex]
Hence,
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0[/tex]
Therefore,
[tex]y'=0[/tex]
1.What is the length of the altitude of an equilateral triangle with side lengths of 34 inches?
2. The bottom of a ladder must be placed 10 feet from a wall and reach a height of 16 feet. How long is the ladder?
I need help pls
Answer:
Step-by-step explanation:
Remark
Question One
It's equilateral. All three sides are equal. The base is 34 as well. So two right angles can be formed on the base by dropping the altitude from the top vertex.
Givens
altitude = h
a = 34/2 = 17
hypotenuse = 34
Formula
a^2 + h^2 = c^2
Solution
17^2 + h^2 = 34^2
289 + h^2 = 1156
h^2 +289 =1156
h^2 = 1156 - 289
h^2 = 867
sqrt(h^2) = sqrt(867)
h = 29.444
==============
Question Two
Givens
b = 10 feet
c = ?
height = h = 16
Formula
c^2 = b^2 + h^2
Solution
c^2 = 10^2 + 16^2
c^2 = 100 + 256
c^2 = 356
sqrt(c^2) = sqrt(356)
c = 18.87
5)
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Answer:
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Step-by-step explanation:
8. Mary and Todd went on a bike trip. The first day they biked 17 miles, and the second
day they traveled 19 miles. Then they turned around and bicycled back home again by
the same route. How many miles did they travel in all?.
Answer:
They traveled 72 miles in all.
Step-by-step explanation:
Answer:
The answer is 72.
Step-by-step explanation:
217+229+314+215=975
Hope you have A Great day!
father bought 2kg 200g of potatoes and 1kg 500g of tomatoes.find the total weight of vegetables he bought
Answer:
3kg 700g
hope it helps:-) :-)
Triangle ABC has 3 medians drawn creating centroid D. If a centroid creates a 2:1 ratio and one median is 24 inches, what is the larger piece?
PLS HELP ASAP! WILL MARK BRAINLEST!! THX :)
Answer: The larger piece is 16 inches
Step-by-step explanation: Median of a triangle is a line segment uniting a vertex and the midpoint of the opposite side. A triangle has 3 medians and the point where these 3 intersect is called centroid.
The ratio of one median is 2:1, which means the line segment is divides by the centroid into two parts, one the double of the other. So:
2x + x = 24
3x = 24
x = 8
Then, the larger piece is
2x = 2(8) = 16
The larger part of the median measuring 24 inches is 16 inches
Can you guys help me please and thank you.
Answer:
Y intercept is 3 (the first one)
Step-by-step explanation:
Get this right and I'll give Brainlist!!!!!!
Step-by-step explanation:
So, we have f / -(2/3) = -(1/3), right?
Well, this means that f = -(1/3) * -(2/3) = positive 2/9 !
Your answer is f = 2/9 :)
Answer:
F = 2/9
Step-by-step explanation:
Ruby drank 4/5 liter of water Monday before jogging.She drank 2/3 liter of water after her jog.How much water did Ruby drink altogether?
Answer:
22/15, or Liters of Water
Step-by-step explanation:
First find a Common Denominator, which in this case would be 15. But, you have to make the numerators numbers that can be with the new common denominator, so multiply 2*5, and that's 10, and 4*3, which is 12. Since the problem is asking you to find out how much water she drank in total, you can just add the numbers up since the denominators the same. So with the new numbers 10/15, add that with 12/15, and you get 22/15. At this point you can either keep it as 22/15, or you can make it into a mixed number of 1 7/15 as your final answer.
PART III
You operate a local mortgage & loan business with two other partners. Your role is to adjust
the prime interest rate for variable & fixed mortgages for your customers, as well as deal
with the length of a mortgage.
1. A client comes in looking to apply for a mortgage, but does not have any prior knowledge.
Answer the following questions to help them decide which type of mortgage to get.
(a) At most banking institutions, there are two types of mortgages available: fixed
mortgages and variable mortgages. Describe the difference between the two main
types of mortgages. Give one positive and one negative aspect of each type of
mortgage
(b) Banks will often advertise interest rates using the terminology prime plus/minus
percent. For example, if prime is 1.5%, then 2.5% might be advertised as prime plus
1%. Express 1.45% and 4.35% using the terminology of prime plus/minus percent
using Canada's current prime interest rate.
2. How many years will it take for your client to pay off a mortgage of $250,000 if he makes
month-end payments of $1,500? Assume a fixed interest rate of prime minus 0.5% over
the term of the whole mortgage. You may answer either by hand, or using the calculators
TVM buttons. If you use the calculator, ensure you write down all of your inputs for
full marks. No time diagram is necessary.
3. Your client borrows $250,000 and agrees to pay $1,500 at the end of every month for
a 5-year term. At the end of years, there is $200,000 remaining on the mortgage.
Use the calculator's TVM buttons to determine the fixed interest rate on this mortgage
(you will be unable to do this any other way). Write down all of your inputs, paying
careful attention to negative signs, for full marks. Express your final answer using prime
plus/minus terminology. No time diagram is necessary
Answer:
liflifljfjchhjxnxnxjjxdkhdkudkud
use the number line to model the equation -5 + -3 = -3+ (-5)
Answer: I don’t have a number line, but...
Step-by-step explanation:
If you add -1 to any number, you lose one, right?
So, do that five times, and use the properties to show that there is no difference between them.
*
Solve this system of equations: 2x+3y =12 12y=48-8x
(3,2)
O (6,0)
no solution
infinitely many solutions
Answer: (3,2)
Step-by-step explanation: x=-3/2y+6
2x+3y=12
Step 1: Add -3y to both sides.
2x+3y+−3y=12+−3y
2x=−3y+12
Step 2: Divide both sides by 2.
2x/2=-3y+12/2
i'm not finna do a whole tutoring session today, it make long explanations
Help ASAP Find the measure of Z.
45°
75°
105
Answer:
75°
Step-by-step explanation:
m∠W = m∠Z = 180° - 105° = 75°
Answer:
75°
Step-by-step explanation:
Can someone help solve this please ?
Answer:
it's the third one bc I got it right
pls help ! will give brainliest ! the pattern of numbers below is a geometric sequence 2, 10, 50, a, b, c, ... find the values of a b and c
a=250 ,b=1250, c=6250
brainliest?
7. Lin is reading a 146-page book. She read the first 20 pages in 35 minutes. 1 point How many minutes does it take her to finish reading the book?
Answer:
255.5 minutes or 255 minutes and 30 seconds
Step-by-step explanation:
146 pages/ x minutes
20 pages/ 35 minutes
All you have to do is cross-multiply to find the answer.
146x35= 5110
5110/20=x
5110/20= 255.5
x= 255.5
Change 3 minutes 12 seconds to seconds?
Answer:
192
Step-by-step explanation:
Answer:
192 BECAUSE 3 MIN = 180 SECONDS + 12 SECONDS = 192 SECONDS
Step-by-step explanation:
5. A life insurance policy costs $16.00 for every $1,000.00 of insurance. At
this rate, what is the total policy cost for $50,000.00 of insurance.
Answer:
800.00
Step-by-step explanation:
so you give me a hint that was for every 16.00 it was 1000.00
i did 16x50=800
i got 50 from 50 in 50000 and the 16 from 16.00 so then i times 16 from 50 which is 800
Five kittens share 6 cups of milk equally. How much milk does each kitten get?
Answer:
They get .83 cup per.
Step-by-step explanation:
Divide 6 by 5. So do 6 / 5, which gets you 0.833333333
An electrician has a piece of wire that is 4 and 3/8 cm long. She divides the wire into pieces that are 1 and 2/3 cm long. how many pieces does she have? (Type out your work)
Answer:
She has approximately 3 pieces ( 2.625)
Step-by-step explanation:
To get the number of pieces, we need to divide the length of the wire by the individual length of the pieces.
To get the division done, it would be easier to convert what we have into improper fractions
For the piece of wire, the length which is 4 and 3/8 centimeters long will be 35/8 centimeters
while;
the individual length of each of the piece which is 1 and 2/3 centimeters long will be 5/3 centimeters
The number of pieces is thus 35/8 divided by 5/3 = 35/8 * 3/5 = 21/8 = 2.625 which is approximately 3 pieces
Hope this helped
Logan ate g out of 16 gumdrops. Write an expression that shows how many gumdrops Logan has left.
Answer:
16-g=x
Step-by-step explanation:
You know you need to subtract because it says ate out of. Next you don't know how many gumdrops Logan ate so they gave a the variable g. Since you don't know how many gumdrops he ate you don't know how many are left. You need another variable to represent how many gumdrops are left.
can someone help me please and thank you!!
Answer:
Perimeter: perimeter = (12 x 2) + (x-2 times 2)
Area: 12 x (x-2)
Step-by-step explanation:
I hope im right im only in grade 6 so wouldnt trust me with that :/
Write 6.384 correct to 1 decimal place ?
Answer:
Write 6.384 correct to 1 decimal place ?=6
Answer:
6.4
Step-by-step explanation:
Rounding 6.384 to one decimal place would be the same as rounding it to the nearest tenth. The tenth in this number is 3. To round a number up, look at the number to the right of it - if the number is 5 or greater, then you increase the value of the number you're rounding by 1. If the number to the right of it is 4 or less, then the value of the number you're rounding stays the same.
In this case, the number we're rounding is 3 and the number to the right of it is 8. Since 8 is greater than 5, we have to increase the value of 3 by 1, which means that the number in the tenths position is now 4.
The number rounded to one decimal place is 6.4.
HELP PLEASE ASAP!!! Please show work I’ll mark you brilliant!!!!
1. The ratio of women to men at a construction site is 2 to 4. There are a
total of 60 workers. How many of the workers are women?
3x?=90 Can somebody please help me
Answer: 30
Step-by-step explanation:
3 x 30 = 90
Hope this helps!!
Answer:
x = 30
Step-by-step explanation:
3x = 90
Divide both sides by 3.
x= 3/ 90
Divide 90 by 3 to get 30.
x=30
Classify the triangle shown below. Check all that apply.
equilateral and acute
Answer:
A, E, F
equilateral, acute, and isosceles
Step-by-step explanation:
Which equation has a slope of -3/4 and goes through the point (-3,4)?
Answer:
Step-by-step explanation:
First write a point-slope equation y−y1=m(x−x1) , where (x1,y1) is the given point, (4,2) , and m is the slope, −3 . For graphing, you can convert to the slope-intercept form, y=mx+b , by solving for y , where m is the slope and b is the y-intercept.
Need help with fractions? Comment here if you need help :) I would love to help. This is Math subject. Please don't report. I'm just trying to help :)
Answer:
yeah what is 122×321???
It's really nice of you to help people when they're struggling with their subjects. You're a smart person! Stay positive and stay safe during this pandemic! Have a beautiful splendid day!!!
what is the value of x in the eqation 5x+3=4x
Answer :x=-3
Step-by-step explanation:Solve for x by simplifying bothh sides of the equation then isoolating the variable
Answer:
x = -3
Step-by-step explanation:
5x + 3 = 4x
5x = 4x - 3
5x - 4x - 3
x = -3
What is the hexadecimal conversion of the decimal number 224?
Answer:
This is a little confusing to me this question but I think its "E0"
Step-by-step explanation:
a) Divide 224 by 16 and then separate what is on the left and right side of the decimal point.
b) Multiply the right side of the decimal point by 16 (and convert to hex if neccessary) and keep that number to the side.
c) Divide the left side of the decimal point by 16 and separate what is on the left and right side of the decimal point.
d) Repeat step b and c above until the value on the left side is 0.
e) Then simply enter the numbers you got in step b in reverse order to get the answer.
Following the instructions above, your math should look like this:
224 / 16 = 14
0 x 16 = 0
14 / 16 = 0.875
0.875 x 16 = E
Thus, 224 decimal converted to hex is as follows:
E0