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
A loan used for buying a home is called a mortgage. The Fortunato family is borrowing $430,000 to buy a home. They are taking out a 30-year mortgage at a rate of 3.55%. a. Compute the monthly payment to the nearest cent. fill in the blank 1 b. Find the total of all of the monthly payments for 30 years. fill in the blank 2 c. What is the total interest? fill in the blank 3 d. Which is greater, the interest or the original cost of the home?
Using compound interest, it is found that:
a) The monthly payments are of $3,401.49.
b) The total of all monthly payments for 30 years is of $1,224,536.
c) The total interest is of $794,536.
d) The total interest is greater.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.For the parameters, we have that:
The Fortunato family is borrowing $430,000 to buy a home, hence P = 430000.30-year mortgage, hence t = 30.Rate of 3.55%, hence r = 0.0355.Yearly compounding, hence n = 1.For practicality, first we are going to solve item b.
Item b:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(30) = 430000\left(1 + \frac{0.0355}{1}\right)^{30}[/tex]
[tex]A(30) = 1224536[/tex]
The total of all monthly payments for 30 years is of $1,224,536.
Item a:
$1,224,536 is paid in 30 x 12 = 360 months, hence:
1224536/360 = $3,401.49.
The monthly payments are of $3,401.49.
Item c:
The interest is the total subtracted from the principal, hence:
1224536 - 430000 = $794,536.
The total interest is of $794,536.
Item d:
Loan of $430,000, interest of $794,536, hence the total interest is greater.
You can learn more about compound interest at https://brainly.com/question/25781328
How do I Graph 2y=-8
Hey can someone help please hurry it’s important
[tex]\large\underline{\sf{Solution-}}[/tex]
Given info:
6885 ÷ 46
Here, we have given divisor (43) & dividend (6885). And in problem they asked to find quotient & remainder.
Let's solve!!
[tex] \sf{46 \overline{\bigg)68885 \bigg(}149← \red{Quotient}} \\ \sf \underline{ 46 \: \: \: \: \: \: \: \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf{228 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf{ \underline{ - 184 \: \: \: \: \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \sf0445 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \underline{ \sf - 414 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf{031 \red{←Remainder}} \\ [/tex]
[tex] \therefore \: \sf{Quotient = 149 \: and \: Remainder \: = 31} \\ [/tex]
[tex] \sf{Now,} \\ [/tex]
[tex] \sf{Divisor \times Quotient + Remainder } \\ [/tex]
[tex] \sf = 46 \times 149 + 31 \\ [/tex]
[tex] \sf = 6854 + 31 \\ [/tex]
[tex] \sf{ = 6885} \\ [/tex]
[tex] \sf = \red{ Dividend}. \\ [/tex]
Choose the pythagorian triplet with the smallest number as 10.
a) 24, 26, 10
b) 10, 6, 8
c) 10, 16, 18
d) 10, 18, 20
Answer:
b
Step-by-step explanation:
pls give brainliest hope helpful
Find the x-intercept and y-intercept of the line and then graph the equation
-4x+2y=-4
Answer:
x-intercept is 1 and y-intersect is -2
Step-by-step explanation:
To find the x-intercept let y = 0 and to find the y-intercept let x = 0 and solve each equation.
-4x + 2y = -4 Let x = 0 and solve for y
-4(0) +2y = -4
0 + 2y = -4
2y = -4
y = -4/2 ; y = -2 y- intercept is -2
Let y = o and solve
-4x + 2y = -4
-4x + 2(0) = -4
-4x + 0 = -4
-4x = -4
x = -4/-4 ; x = 1 x-intercept is 1
Circle each input value. Underline each output value. 1. {(1, 1), (2, 3), (3,5)} 2. {(6,2), (5, 3), (4,8)}
Answer:
The first numbers in the sets are input and the second numbers are outputs.
1. {(1, 1), (2, 3), (3,5)}
Input = 1, 2, 3Output = 1, 3, 52. {(6,2), (5, 3), (4,8)}
Input = 6, 5, 4Output = 2, 3, 8Hello, please be honest, is this correct?
Answer:
Yes that is correct you got keep up good work
i am just completely lost at this point so pls just answer properly
Answer:
$80
Step-by-step explanation:
192÷12=16
16•5=80
Answer:
Elena puts in $80 into her savings account
Step-by-step explanation:
You need to multiply 5/12 and 192. Think of "5/12 x 192" as "5/12 of 192." If you don't know how to multiply a fraction with a whole number, you can convert the fraction to a decimal. Hope this helps!
Homework help!!!!!!!
Answer:
r = -9
Step-by-step explanation:
the less the negative number is the more it is .
Help or don’t eiether way you’re amazing
Answer:
267 (please double check this!!!)
Step-by-step explanation:
Separate the block into sections that you can find the volume for easily and figure out the measurements for each
the two smaller blocks on top will be symmetrical
the bottom area is 5 high and 3 deep and you get the length by adding 4+5+4 because that's the length of the whole thing
so 13*3*5 = 195
The two smaller blocks is just adding a *2 once you figure out the one
it's 3 deep still and 4 wide, if you subtract the total height from the height given of the bottom part you get 3
3*4*3 = 36
you have another one of those blocks so it'd be 36*2
then you add them both 72+195 = 267
please be super quick 3 minutessssss
Answer:
im pretty sure its B
Step-by-step explanation:
I THINK SOOO AHH
Complete the following.Write the answers in your journal
I learned filtering of solid and liquid mixtures can be saperated with the use of____ or____ as a medium in which_______material in the medium
Sieving is a method in which ________of ________sizes are separated from a mixture on the basis of the _____
Answer:
1.FILTER WATER 2.FILTER CLOTH
3.LIQUIDS
4.INSOLUBLE
5.DIFFERENCE
please help with this algebra ii question
Answer:
Second Choice
Step-by-step explanation:
The vertex form can be expressed as:
[tex] \displaystyle \large{f(x) = a {(x - h)}^{2} + k}[/tex]
We know that the vertex is (h,k) which we are given (-3,-1). Substitute h = -3 and k = -1 in:
[tex] \displaystyle \large{f(x) = a {(x - ( - 3))}^{2} - 1} \\ \displaystyle \large{f(x) = a {(x + 3)}^{2} - 1}[/tex]
Now we know that the parabola passes through (-2,1). Substitute x = -2 and f(x) = 1 then solve for a.
[tex] \displaystyle \large{1= a {( - 2 + 3)}^{2} - 1} \\ \displaystyle \large{1= a {(1)}^{2} - 1} \\ \displaystyle \large{1= a - 1} \\ \displaystyle \large{1 + 1= a } \\ \displaystyle \large{2 = a}[/tex]
Therefore a = 2.
Hence:-
[tex] \displaystyle \large{f(x) = 2{(x + 3)}^{2} - 1}[/tex]
the ratio 4:2 is equivalent to 2
To make pastry for an apple pie, you need 4 oz flour and 2 oz fat. The ratio of flour to fat is
4 : 2 .
But this ratio can be simplified in the same way that two fractions can be simplified. We just
cancel by a common factor. So
4 : 2 = 2 : 1 .
4. Which values are solutions of
2x – 1= 7? Select all that apply.
A) X=-4
(B) x = -3
C=3
D= 4
Answer:
D. x = 4
Step-by-step explanation:
2x – 1= 7
add 1 to both sides:
2x=8
divide both sides by 2:
x=4
One solution.
What percent of the hours were billed by Jon, Roy, or Dean?
Write your answer using a percent
sign (%).
Answer:
10%
Step-by-step explanation:
please tell me if im right or wrong
Helpppppppp meeeeeeee
Answer:
Step-by-step explanation:
solution 1:
570 not man = 15% (cause 100% - 85%)
15% = 570
100% = w (for "whole package")
15w = 100 * 570
15w = 57000
w = 57000 / 15
w = 3800
solution 2:
15% = 570
85 = m (for "men)
15m = 570 * 85
15m = 48450
m = 48450 / 15
m = 3230
100% = 85% + 15%
100% = b (for "buch of people")
b = 3230 + 570
b = 3800
is -5.25 greater than -3
Answer:
False -5.25 is < (less than) -3
Step-by-step explanation:
A truck can be rented from Company A for $80 a day plus $0.40 per mile. Company B charges $40 a day plus $0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same. At nothing miles, the rental costs are the same from either company
Please help. I will give brainly. Thank you
Answer:
1.
a = 1.96
( 1.4 x 1.4)
b= 3750
c= 1/48
2.
a= 2?
dont take my word on that but here.( An arithmetic sequence is any list of numbers that differ, from one to the next, by a constant amount. For example, the list of even numbers, 0,2,4,6,8… is an arithmetic sequence, because the difference from one number in the list to the next is always 2.[1] If you know you are working with an arithmetic sequence, you may be asked to find the very next term from a given list. You may also be asked to fill in a gap where a term is missing. Finally, you might want to know, for example, the 100th term, without actually writing out all 100 terms. A few simple steps can help you do any of these.
b= 3
c= 16-4a
( IM NOT SO CONFIDENT ABOUT 2)
3.
a= 17
b= ( 2squared - 1)
Step-by-step explanation:
Answer:
thank you for the points bozzo
how do I determine what a function is for a line graph
Answer: Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Step-by-step explanation:
In a group of 97 students, the number of students taking programming is twice the number of students taking math. There are 53 students taking exactly one of these subjects, and 15 are taking neither of these subjects. How many students are taking math? How many students are taking programming? In a group of 97 students, the number of students taking programming is twice the number of students taking math. There are 53 students taking exactly one of these subjects, and 15 are taking neither of these subjects. How many students are taking math? How many students are taking programming?
The number of student taking math is 37 while the number of students taking programming is 74
Universal set = 97
let
The number taking math = x
The number taking programming = 2x
The number of students that take exactly one subject = 53
The student taking neither of the subject = 15
The number of students taking only maths will be
x - n(m ∩ p)The number of students taking only programming will be
2x - n(m ∩ p)let
n(m ∩ p) = y
Therefore,
x - y + 2x - y = 53
3x - 2y = 53
Also,
97 = x + 2x - y + 15
3x - y = 82
Therefore,
3x - 2y = 53
3x - y = 82
-y -(-2y) = 82 - 53
y = 29
3x - 29 = 82
3x = 82 + 29
3x = 111
x = 111/3
x = 37
Finally,
number of students taking maths = 37
number of student taking programming = 37×2 = 74
Check similar problem on sets: https://brainly.com/question/16132324?referrer=searchResults
what is the total surface area of the prism in square inches
Answer:
Surface area of a square prism = 4 × (s × h) = 4sh, where, s is the length of the side of the square and h is the height of the square prism.
Identify the angles that each have a measure of 60\degree
Answer:
parrelel
Step-by-step explanation:
Fatima drove 100 miles in 4 hours. What is the constant of proportionality for 100 miles in 4 hours and 200 miles in 8 hours? Please answer ASAP.
Answer:
25
Step-by-step explanation:
4 hours goes into 100 miles 25 times.
Dùng kí hiệu toán học để viết mệnh đề sau:
Định nghĩa : tam giác ABC gọi là tam giác cân nếu có hai góc bằng nhau
Answer:
g vs lhnkdeugyvsvjxbd shall
What is an equation of the linethat passes through the points (3,-8) and (1,-2)
Answer:
y=3x+1
Step-by-step explanation:
m= [tex]\frac{-2-(-8)}{1-3} =\frac{-6}{2}[/tex] or -3
-8= -3(3) + b
-8= -9 + b
+9 +9
1=b
Then put in slope intercept form:
y= 3x+1
Hope this helps! :)
Is this relation a function? Justify your answer.
Answer:
Yes
Step-by-step explanation:
(I can only read the graph).
Since for each dot, a vertical line drawn through it only intersects that dot, we conclude that the relation is a function.
Explain why there is not enough information to state that CP is the perpendicular bisector of AB.
Answer:
First, we need to know if AP is equal to PB. We don't really know that CP passed through the midpoint of AB. We also don't know if CPA is equal to CPB. This is why there is not enough information to state that CP is the perpendicular bisector of AB.
Step-by-step explanation:
A perpendicular bisector is a segment that passes through a midpoint of a segment and is perpendicular to it.
-kiniwih426
HELP!
A group of activists wants to raise money for a good cause, so they decide to sponsor a bicycle race. It receives $60 per cyclist entry and $15,000 in donations, but it must spend $18 per entry to cover the cost of the race.
Write and solve an inequality to determine the number of cyclists the group needs to raise at least $57,000.
9514 1404 393
Answer:
60x +15000 ≥ 18x + 57000≥ 1000 cyclistsStep-by-step explanation:
We want ...
revenue ≥ cost + desired profit
60x +15000 ≥ 18x + 57000 . . . . . . an inequalty
42x ≥ 42000 . . . . . . . . . . . . . . . . subtract 18x+15000
x ≥ 1000 . . . . . . . . . . . . . . . . . . divide by 42
The group needs at least 1000 cyclists to raise at least $57,000.