Step-by-step explanation:
f'(x)=-2sin(x)+2cos(2x)=0
as cos(2x)=2sin(x)cos(x),
-2sin(x)+4cos(x)sin(x)=0
sin(x)-2cos(x)sin(x)=0
(sin(x))(1-2cos(x))=0
-> x = 0, pi/3
testing these values along with the end points of the interval,
f(0)=2
f(pi/3)=1+(0.5sqrt(3))
f(pi/2)=0
so the min is 0 and the max is 2.
Find a polynomial f (x) of degree 5 that has the following zeros.
9, 6, -8, 7, 0
Leave your answer in factored form.
Answer:
[tex]f(x)=x(x-9)(x-6)(x+8)(x-7)[/tex]
Step-by-step explanation:
If [tex]9=x[/tex] then [tex]x-9=0[/tex]
If [tex]6=x[/tex] then [tex]x-6=0[/tex]
etc.
So [tex]f(x)=x(x-9)(x-6)(x+8)(x-7)[/tex]
If logb3=1.10, then logb27 = ____.
Step-by-step explanation:
27 = 3×3×3
logb(m×n) = logb(m) + logb(n)
logb(27) = logb(3×3×3) = logb(3)+logb(3)+logb(3) =
= 3×logb(3) = 3×1.10 = 3.30
PLEASE HELP I'LL GIVE BRAINLY AND POINTS
Simplify the expression
1/5 (-15w - 20) + 1/2 (3 - 4w)
Answer:
-5w - 5/2
Step-by-step explanation:
hope it helps
The 5th grade classes at Brookfield School used 5 identical buses to go on a field trip.
There were a total of 40 seats on each bus.
All of the seats on 4 buses were filled.
The fifth bus had 4/5 of the seats filled.
1/8 of all the passengers on the buses were adults.
How many adults went on the field trip with the 5th grade classes?
1/8 x 5 = 5/8
5/8 of the passengers were adults :)
solve for v. 29 = -6 + 5v
Which of the following is an example of a rational number?
Evaluate piecewise functions
Answer:
Step-by-step explanation:
f(t)=t²-5t , t≤-10
f(-10)=(-10)²-5(-10)=100+50=150
why is it important to convert your equation from standard form to slope intercept? How can this help you graph your equation?
Answer:
The slope intercept form is used to find the y-intercept and the slope of a straight line. If you look closely, it is a linear function too; meaning the function can tell you its domain and range.
Four movie tickets cost $34.00. How much do seven movie tickets cost?
Answer:
7 movie tickets 59.5
Step-by-step explanation:
divide 34 by 4 and then you get 8.5 then multiply that by 7
How can you find the perimeter of the rectangle by only knowing its area
Answer:
It's not possible to determine the perimeter of a rectangle given only the area. The area of a rectangle depends on two unknowns, the length and the width, so you must be given at least one side of the rectangle along with the area to determine the other side and, thus, the perimeter
Step-by-step explanation:
Answer:
It is not possible to determine the perimeter of a figure given its area.
Please help for this question what is the function and thanks
Answer:
b) local minimum at [tex]x=\frac{1}{e}[/tex]
c) Graph of the function is convex
Step-by-step explanation:
We are told that [tex]f'(\frac{1}{e})=0[/tex], which implies there is a turning/stationary point at [tex]x=\frac{1}{e}[/tex].
Substituting [tex]x=\frac{1}{e}[/tex] into [tex]f''(x)[/tex] will tell us if the turning point is a minimum or a maximum:
[tex]f''(\frac{1}{e})=\frac{1}{\frac{1}{e} } =e>0 \implies \textsf{local minimum}[/tex]
Therefore, statement a) is false and statement b) is true.
If the function has a minimum turning point, then this implies that the curve is convex. Therefore, statement c) is true.
Extremum = local min and max points.
We have already established that there is a local minimum at [tex]x=\frac{1}{e}[/tex], therefore statement d) is false.
I know this is not needed for this question, but here are the workings to detemine the equation of the function (I've also attached a graph). This supports the answers above.
[tex]\textsf{if} \ f''(x)=\frac{1}{x}\\\\\implies f'(x)=\int f''(x) \ dx \\\\\implies f'(x)=ln|x|+C\\[/tex]
[tex]\textsf{if} \ f'(\frac{1}{e})=0\\\\\implies ln|\frac{1}{e}|+C=0\\\\\implies -1+C=0\\\\\implies C=1\\\\[/tex]
[tex]\implies f'(x)=ln|x|+1\\[/tex]
[tex]\textsf{if} \ f'(x)=ln|x|+1\\\\\implies f(x)=\int f'(x) \ dx\\\\\implies f(x)=xln(x)-x+x+C\\\\\implies f(x)=xln(x)+C[/tex]
The perimeter of a rectangle is 52 cm. If its width is 2 cm more than one-third of its length, find the dimensions of rectangle.
(A) 12 cm x 4 cm (B) 18 cm x 8 cm (C) 15 cm x 9 cm
Answer:
(B) 18 cm × 8 cmStep-by-step explanation:
Perimeter of a rectangle = 52 cm
2(length + width) = 52 ==> l + w = 26
Let x be the length
width = (x/3) + 2
x + (x/3) + 2 = 26
[(3x + x)/3] + 2 = 26
4x / 3 = 24
4x = 24 (3)
x = 6(3) ==> 18 cm
Width = (18/3) + 2
= 6 + 2 = 8 cm
So, the required dimension is 18 cm x 8 cm.
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Thank You!
Answered by: ms115
Answer:
B. 18 * 8.Step-by-step explanation:
Let the perimeter be:
52 cm.Find the numbers for the perimeter:
For A:
(12 cm + 4 cm) * 2 = 32.That means A is incorrect.
For B:
(18 + 8) * 2 = 52 cm.That means B is correct.
For C:
(15 + 9) * 2 = 48 cm.That means C is incorrect.
Correct choice is B.
Jordan has 3.2 liters of paint left after painting the scenery for the school play. How can she convert this number to find how many milliliters of paint she has left?
A. Multiply by 100
B. Multiply by 1,000
C. Divide by 100
D. Divide by 1,000
Three pens cost $1.80. How many pens can you buy for $6?
Answer: 10
Step-by-step explanation:
3 = $1.80
1 = $0.60
$6 = 10 pens
Select the expressions that are equivalent to -6c - 2c.
A. -7c + c -2c
B. c • -8
C . -c - 6c
B. -9c
Answer:
A and B both equal -6c - 2c
Solve for m
bm + h = 9x
࿐αɴѕωєя࿐
m = 93 - h / b
Step-by-step explanation:
bm + h = 93
bm = 93 - h
m = 93 - h / b
Hope it helps ⚜
12. Suppose n is an integer. Select all statements below that are true: (3 points)
n?+n is always an even integer
nun is always an even integer when n is even
n+n is always an even integer when n is odd
n +n is never an even integer when nis odd
n2+ n is is never an even integer
n2 +n is sometimes an even integer
Find the value of a in the parallelogram. (a, AB, BC, CD, AD). Pls show work
Step-by-step explanation:
Hope it will helps you..
Your photo is so unclear ..but i try my best to understand...
Please help me and please dont say something thats not related to my post.
Answer:
The answer is 6 pounds Which is C
Step-by-step explanation:
At a hockey game, a vender sold a combined total of 217 sodas and hot dogs. The number of sodas sold was 59 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold
Answer:
sodas sold = 138
hot dogs sold = 79
Step-by-step explanation:
let s = number of sodas sold
let h = number of hot dogs sold
equation 1: h + s = 217
equation 2: h + 59 = s
Substitute equation 2 into equation 1 and solve for h:
⇒ h + (h + 59) = 217
⇒ 2h + 59= 217
⇒ 2h =158
⇒ h = 79
Substitute found value of h into equation 2 and solve for s:
⇒ 79 + 59 = s
⇒ s = 138
answer:
number of hot dogs is 79
number of sodas is 138
explanation:
let the number of hot dogs sold be xthen number of sodas is x + 59solve:
Therefore:
x + x + 59 = 217
2x = 158
x = 79
79 hot dogs
now find [ x + 59 ], number of soda's79 + 59
138 sodas
You take out a car loan for $7,300 at an interest rate of 4.2% for a duration of 5 years
compounded quarterly. What is the total amount that you will pay back to the bank?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7300\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=7300\left(1+\frac{0.042}{4}\right)^{4\cdot 5}\implies A=7300(1.0105)^{20}\implies A\approx 8996[/tex]
Your dinner bill was $58.00. If you leave a 20% tip, how much will the tip be?
Answer:
Ask yourself what a percentage means. It means out of a hundred.
20 percent is basicallly 20/100
20/100 is 0.2
So 20 percent of 58 is asking-
0.2*58 = ?
Solve and you’ll get
$11.60
Sarah is planning to take
aerobics classes at a gym.
Non-members pay $8 per
class, while members pay $4
per class and a $20
membership fee. If Sarah
plans to take 6 aerobics
classes, should she become a
member of the gym? Explain
why or why not?
Answer:
Yes
Step-by-step explanation:
Non members - 8*6 = $48
Members - 20+(4*6) = $46
She should become a member of the gym because she will pay $2 less overall.
Answer:
Sarah should become a member. She would be paying a lot less money and be able to take more classes for cheaper
Step-by-step explanation:
Non member amount for 6 classes- $8*6= $48
Member amount for 6 classes- $4*6= 24 ($20 fee) = $44
As you can see above, the cost for 6 classes with a membership is cheaper than without a membership
What is the slope of the line that passes through the points
(
−
5
,
8
)
(−5,8) and
(
−
5
,
4
)
(−5,4)? Write your answer in simplest form.
Step-by-step explanation:
Slope formula:
[tex] \frac{y2}{x2} - \frac{y1}{x1} = m[/tex]
Substitute the points into the formula format:
[tex] \frac{4}{ - 5} - \frac{8}{ - 5} = m[/tex]
Solve:
[tex] \frac{ - 4}{0} = m[/tex]
When a slope has a run (x) of 0, the slope is undefined.
Answer:
-4 / 0
Step-by-step explanation:
Given the following question:
(-5, 8), (-5, 4)
In order to find the answer to this question we will use rise over run, substitute the values, and then solve.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
(-5, 8), (x1, y1)
(-5, 4), (x2, y2)
4 - 8 = -4
-5 - -5 = 0
m = -4 / 0
Hope this helps.
Please help ! I do not understand the question and do not know the answer
Consider the arithmetic sequence presented in the table below.
n 3, 64
an 126 3,725
Hint: an = a1 + (n - 1), where a is the first term and d is the common difference.
Part A: What is the first term, a1, of the sequence? (2 points)
Part B: What is the general term equation, an, for this sequence? (1 point)
Part C: What is the value of the 13th term of this sequence? (1 point)
Answer:
3; 5; 35
Step-by-step explanation:
Sorry can’t help
What is an equation of the line that passes through the points (-7, -7) and (-7, 4)?
just answer
Since you requested for only the answer, here you go:
the slope is 0
The y int is none
the equation is
x=-7
please helppppppppppppppppppppppp
solve
[tex] {x}^{2} + \frac{9x}{2} = \frac{5}{2} [/tex]
pls I. need it Thx
Answer:
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Exact Form:
x=1/2,−5
Decimal Form:
x=0.5,−5
Step-by-step explanation:
branliest
What is 12/5 turned into a mixed number
Answer: 2 2/5
Step-by-step explanation:
Denominator stays the same, divide 12 and 5, remainder at the top