Lets check if the three conditions hold.
1 : Continuity of g on the interval [0,2]
First, g(x) is a continuous function on R, as the sum of a cubic function wich is continuous on R, and a linear polynomial of the form ax + b which is also continuous on R. Finally g is also continuous on the interval [0,2]
2 : Differentiable on the same interval
Since the cubic function and the linear polynomial one are differentiable on R, g also is differentiable and particularly on the interval [0,2]
Also we have g'(x) = 2*3*x² - 3 = 6x² - 3
3 : Do we have g(0) = g(2) ?
Lets compute g(0) = 2*0^3 - 3*0 + 1 = 1
And g(2) = 2*2^3 - 3*2 + 1 = 2 * 8 - 6 + 1 = 16 - 6 + 1 = 11
Since g(0) ≠ g(2), Rolle's theorem is not applicable. Thus unfortunately, we can not conclude that there exist c ∈ (0,2) such that f'(c) = 0
Help!! I’m not sure what to do
Answer:
h=23
Step-by-step explanation:
triangle equals 180 degrees
180-40=140
140/4=35
g An employee joined a company in 2017 with a starting salary of $50,000. Every year, the employee receives a raise of $1,000 plus 5% of the salary of the previous year. (a). Set up a recurrence relation for the salary of the emplyee n years after 2017. A recurrence relation of a sequence is an equation that express a subscript n using one or more of previous terms. (b). What will be the salary of the employee in 2025
Answer:
a) s[n] = 1.05s[n-1] +1000; s[0] = 50,000
b) $83,421.88
c) s[n] = 70000·1.05^n -20000
Step-by-step explanation:
a) Let s[n] represents the employee's salary in dollars n years after 2017. The salary in 2017 is given as $50,000, so ...
s[0] = 50000 . . . . the recursion relation initial condition
The next year, the salary is multiplied by 1.05 and 1000 is added:
s[1] = 1.05·s[0] +1000
This pattern repeats, so the recursion relation is ...
s[n] = 1.05·s[n-1] +1000
__
c) It is convenient to find a formula for the salary before trying to compute the salary 8 years on. So, we work part (c) before part (b).
The base salary gets multiplied by 1.05 each year, so can be described by the exponential function ...
base salary after n years = 50,000·1.05^n
The add-on to the raise becomes a geometric sequence whose common ratio is 1.05. The sum can be described by the formula for the sum of such a sequence:
sum = a1(r^n -1)/(r -1) . . . . . (see note below)
sum of add-ons = 1000(1.05^n -1)/(1.05 -1) = 20000(1.05^n -1)
So, the total salary after n years is ...
s[n] = 50000·1.05^n + 20000(1.05^n -1)
The exponential terms can be combined, so we have the explicit formula ...
s[n] = 70000·1.05^n -20000
__
b) The year 2025 is 8 years after 2017, so we want to find s[8].
s[8] = 70000·1.05^8 -20000 = 70000·1.4774554 -20000
= 103,421.88 -20000 = 83,421.88
In 2025, the employee's salary will be $83,421.88.
_____
Note on the sum of the add-ons
A geometric sequence starts with term a1 and gets multiplied by a ratio r to make the next term: a2=r·a1; a3=r²·a1, ....
The sum of such a geometric sequence has the formula
Sn = a1·(r^n -1)/(r -1)
Here, the sequence starts in year 1 with a1=1000 and has a common ratio r=1.05. The denominator of the sum is r-1 = 0.05 = 1/20, so the sum can be written as
Sn = 20000·(1.05^n -1).
what is 240.50 x 19.54
Answer:
240.50 x 19.54= 4699.37
Mikael has a loan of $40 000.
He pays 1.6% simple interest for six months
How much interest does he pay altogether?
Step-by-step explanation:
Based on the given conditions,
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}[/tex]
[tex]Reduce the fraction: 2 \times320
[tex]Reduce the fraction: 2 \times320Calculate the product orquotient: 640[tex]
Answer 640
Answer:
[tex]\sf\longmapsto \: 640[/tex]
Step-by-step explanation:
Based on given cases:
[tex] \sf \: Formulate: 1.6\% \times 40000 \times 12 \div 12[/tex]
Reduce the fraction:
[tex] \sf \longmapsto \: \dfrac{2 \times 40000}{125}[/tex]
[tex] \sf \longmapsto \: 320 \times 2[/tex]
Calculate the product/quotient:
[tex] \sf\longmapsto \: 640[/tex]
Find the Area of the figure below, composed of an isosceles trapezoid and one semicircle. Rounded to the nearest tenths place
Step-by-step explanation:
the area =
[½(8+2)×4] + [½×3.14×1²]
= 20 + 1.57
= 21.57
= 21.6
Simplify this expression 5xy - x2 + 2xy + 3x2
Answer: 5xy-x2t+2xy+3x2t Final result : x • (2xt + 7y) Step by step solution : Step 1 :Equation at the end of step 1 : ((5xy-((x2)•t))+2xy)+(3x2•t) Step 2 : Step 3 :Pulling out like terms : ...
Step-by-step explanation:
Answer:
2 [tex]x^{2}[/tex] + 7 x y
Step-by-step explanation:
Quickly answer number 10 text only no fonts (100 points) mark brainliest
25
have a great day! :3
Answer:
Hello again the square root of 625 is 25
5 3/4 as an improper fraction
Answer:
23/4
Step-by-step explanation:
Answer:
A mixed number is an addition of its whole and fractional parts.
[tex]5 \frac{3}{4} [/tex]
Add:
[tex]5 \: and \: \frac{3}{4} [/tex]
To write 5 as a fraction with a common denominator, multiply by
[tex] \frac{4}{4} [/tex]
Combine:
[tex]5 \: and \: \frac{4}{4} [/tex]
Combine the numerators over the common denominator.
[tex] \frac{5.4 + 3}{4} [/tex]
Simplify the numerator.
Multiply 5 by 4.
Add 20 and 3.
[tex] \frac{23}{4} [/tex]
Step-by-step explanation:
Thanks!!!!!!
Please help hurry ,,,.€.£\’smsmmsms
12(x-2×4-2x-5)
Solve...
Answer:
=−12x−156
Step-by-step explanation:
=(12)(x+−8+−2x+−5)
=(12)(x)+(12)(−8)+(12)(−2x)+(12)(−5)
=12x−96−24x−60
=−12x−156
Step-by-step explanation:
= 12(x - 8 -2x - 5)
= 12(-x - 13)
= -12x - 156
please give me a brainliest answer
Find x Please Help Thank You
uhhhhhhhhhhhhhhhhh i have no clue so sorry
The given diagram shows a construction completed using a straightedge and a compass.
B
À
E
The diagram shows the construction
If m ABC is 249, then m FDE is
Answer:
angle bisected of angle abc
24 degrees
Step-by-step explanation:
Answer:
Step-by-step explanation:
Tell me if im right
Jeffrey makes 3% commission on
his sales. If his sales total $1800
this week, how much money will he
make?
Answer:
He will make $54
Giải giúp mình với ạ
Answer:
answer is b
Step-by-step explanation:
Is is possible to divide Pi aka : 3.14159
Answer:
If you WANT to divide pi, there is half a pi left.
Step-by-step explanation:
There are 2pi radians in a circle. So one quarter of the circle corresponds to half of pi (If you want to divide to get half of pi) . So it would then be: one quarter corresponds to a half.
(if that makes sense! sorry if it doesn't :\ )
what is the value of x when y is 31
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Direct variation
y = kx
16 = k*8
Divide each side by 8
16/8 = 8k/8
2 = k
The equation is y =2x
y =2x
Let y =32
32 = 2x
Divide by 2
32/2 = x
16 =x
lost on what to do here.
Answer:
x = 45
Step-by-step explanation:
180-136 = 44
x - 1 = 44
x = 44 + 1
x = 45
x = 45°
Step-by-step explanation:
The two angles are supplementary so
[tex]136° + (x-1) = 180°[/tex]
[tex]\Rightarrow x - 1 = 44°[/tex]
or
[tex]x = 45°[/tex]
what is the slope of the line containing the points (3,-7) and (-3,7)
Answer:
-7/3
Step-by-step explanation:
To find the slope, we use the slope formula
m= ( y2-y1)/(x2-x1)
= ( 7 - -7)/(-3 -3)
= ( 7+7)/( -6)
= 14/-6
= 7/-3
= -7/3
Step-by-step explanation:
m = y2-y1 / x2-x1
= 7+7 / -3-3
= 14/-6
= -7/3
Answer quickly! [tex]x^{2} = 6[/tex]
[tex]x = \pm \sqrt{6}[/tex]
rational function f(x)=5-x/x^2+5x+6 f(x)=3
Answer:
jgfjfhjhjbnbvmnfnmf
Step-by-step explanation:
Simplify 12 to the power of 3 over 12 to the power of 7
A). 12 to the power of 4
B). 12 to the power of 10
C). 1 over 12 to the power of 4
D). 1 over 12 to the power of -4
Answer:
The correct answer I think is D
Step-by-step explanation:
The explanation of the other person is right, but you do 3-7, which gives u -4
Write the equation for the line that passes through ( - 8, - 4 ) and ( -6, - 1 ) in slope-intercept form.
Step-by-step explanation:
y=(3/2)x +8
that is the answer
The equation of the line is y = (3/2)x + 8 if the line that passes through ( - 8, - 4 ) and ( -6, - 1 ).
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The line that passes through (-8, - 4 ) and ( -6, - 1)
The standard form of the line in slope-intercept form:
y = mx + c
Here m is the slope of the line
c is the y-intercept.
As we know, the ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{-1-(-4)}{-6-(-8)}[/tex]
m = 3/2
y = (3/2)x + c
Plug x = -8, y = -4
-4 = (3/2)(-8) + c
c = 8
y = (3/2)x + 8
Thus, the equation of the line is y = (3/2)x + 8 if the line that passes through ( - 8, - 4 ) and ( -6, - 1 ).
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ2
I need the answer for this
Answer:
it is either f or h
lily cleaned the coin fountain at the mall and found 20 coins consisting of nickels and quarters. Her collection totaled $2.60 . How many quarters did she find
Answer:
10
Step-by-step explanation:
eight quarters in $2.00, 2 quarters in .50 cents = 10 quarters.
a line passes through the point of (4,2) and has a slope of -5/4
Answer:
y = -5/4x + 7
Step-by-step explanation:
y = -5/4x + b
2 = -5/4(4) + b
2 = -5 + b
7 = b
ok this is stressin me out anyone know this
hello please help me
Answer:
perimeter is 9+7.5+6=22.5cmwe know that area is(1/2* base *height)=1/2*9*4.2
=18.9square cm
Answer:
Perimeter: 6 + 7.5 + 9 = 22.5
area: 18.9
Step-by-step explanation:
Students were asked to find an equivalent value of the expression 13 divided by 19/100 which could a student use?
Answer:
68.4210526316
you first divide 19/100 and then you divide the out put 13/ 0.19
Step-by-step explanation:
helppppppppppppppppppppppppppppppppppppp
Answer:
(m÷3)+2in
Step-by-step explanation:
(m÷3) represents the division of Myron's height and 3
+2 is the extra 2 inches
Hope this helps! :)
Tom purchased international calling cards before traveling abroad. He bought a 60-minute card for $9.99, a 90-minute card for $14.29, a 100-minute card for $17.99, and a 200-minute card for $29.49. After using all of his calling cards, Tom used his mobile phone for 38 minutes at a rate of $2.99/minute.
The amount spent on calls per minute is an illustration of unit rates.
The amount spent on the 38-minute call is $113.62
The given parameters are:
[tex]\mathbf{Rate = \$2.99/minute}[/tex]
[tex]\mathbf{Time = 38\ minutes}\\[/tex]
So, the amount spent on call is:
[tex]\mathbf{Amount = Rate \times Time}[/tex]
This gives
[tex]\mathbf{Amount = \$2.99/minute \times 38\ minutes}[/tex]
Cancel out minutes
[tex]\mathbf{Amount = \$2.99 \times 38}[/tex]
[tex]\mathbf{Amount = \$113.62}[/tex]
Hence, the amount spent on the 38-minute call is $113.62
Read more about unit rates at:
https://brainly.com/question/18065083
