Answer:
If the concavity of f changes at a point (c,f(c)), then f′ is changing from increasing to decreasing (or, decreasing to increasing) at x=c. That means that the sign of f″ is changing from positive to negative (or, negative to positive) at x=c. This leads to the following theorem
Step-by-step explanation:
The previous section showed how the first derivative of a function, f′ , can relay important information about f . We now apply the same technique to f′ itself, and learn what this tells us about f . The key to studying f′ is to consider its derivative, namely f′′ , which is the second derivative of f . When f′′>0 , f′ is increasing. When f′′<0 , f′ is decreasing. f′ has relative maxima and minima where f′′=0 or is undefined. This section explores how knowing information about f′′
Let f be differentiable on an interval I . The graph of f is concave up on I if f′ is increasing. The graph of f is concave down on I if f′ is decreasing. If f′ is constant then the graph of f is said to have no concavity.
Note: We often state that " f is concave up" instead of "the graph of f is concave up" for simplicity.
The graph of a function f is concave up when f′ is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure 3.4.1 , where a concave up graph is shown along with some tangent lines. Notice how the tangent line on the left is steep, downward, corresponding to a small value of f′ . On the right, the tangent line is steep, upward, corresponding to a large value of f′ .
.......plz answer it plz
Answer:
a: x=90 b: x=45 y=45 c: y=68 x=68
Simplify each numerical expression.
1) 6 + 2 x 8 - 12 + 9 - 3
Answer:
16
Step-by-step explanation:
using BODMAS rule
6 + 16 - 12 + 9 - 3............step 1
22 - 3 - 3....…...................step 2
16
describe the Y intercept an end behavior of the following graph
PLEASE HELP
ILL MARK BRAINIEST IF YOU DO THIS CORRECTLY!!!
Drag each tile to the correct box.
Order the expressions from least value to greatest value.
Answer:
I think thats the answer. Check it. (:
Step-by-step explanation:
-2.2x3.4= -74.8
42/-6= -7/10
-3 3/5-( 3 1/10)= -21/10
-2 3/4+(3 1/6)= -2
!I might be wrong!
Someone check this!
Thank you!
6. Alex and Brian park their bikes side-by-side. Alex leaves to visit friends, and Brian leaves 30 minutes later,
headed for the same destination. Alex pedals 5 miles per hour slower than Brian. After 1 hour, Brian passes Alex. At
what speed are they each pedaling?
Answer:
See below.
Step-by-step explanation:
When Brian passes Alex they both have travelled the same distance.
Call this distance d.
Let the speed that Brian passes = x miles/hour.
Distance = speed * time so:
For Alex:
d = (x - 5) * 1.5 ( Alex cycles for 1 + 30 minutes = 1.5 hours)
For Brian:
d = x * 1
So substituting d = x in Alex's equation:
x = 1.5(x - 5)
x = 1.5x - 7.5
7.5 = 0.5x
7/5 / 0.5 = x
15 = x.
ANSWER:
Brian's speed is 15 miles/hour.
Alex's speed is 15 - 5 = 10 miles/hour.
What are the x- and y-intercepts of g(x) = 4 - X2?
Answer:
g(x) = 4 - x^2
at x-intercept, y=0
0=4-x^2
x^2=4
x = ± 2
=> two x- intercepts, (-2,0) and (2,0)
at y-intercept, x = 0
g(x) = y = 4 - 0 = 4
y-intercept = (0,4)
The x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).
What is an intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.
This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
g(x) = 4 - x²
At x-intercept, y = 0
0=4-x²
x² = 4
x = ± 2
Two x- intercepts, (-2,0) and (2,0)
at y-intercept, x = 0
g(x) = y = 4 - 0 = 4
y-intercept = (0,4)
Therefore, the x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).
To know more about an intercept follow
https://brainly.com/question/1884491
#SPJ2
what is the value of |-403|×|-3|
Answer:
1209
Step-by-step explanation:
| - 403 | × | - 3 |
= | 403 | × | 3 |
= 403 × 3
= 1209
Use the diagram to complete the statements.
Angles 1 and 5 are
because they are
angles.
7
3
(2
Angles 4 and 6 are
because they are
4
5
angles.
7X6
8
a
S
Answer:
Can you show the options?
Step-by-step explanation:
Angle 1 and 4 are equal and angle 4 and 6 add up to 180
Answer:
congruent, corresponding, supplementary, same side interior
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
At the Scott wedding, 12 guests sat on the groom's side and 10 guests sat on the bride's side. At the Smith wedding, 13 guests sat on the bride's side and 18 guests sat on the groom's side. Which wedding had a lower ratio of guests of the groom to guests of the bride?
A. not enough information
B. the Smith wedding
C. neither, the ratios are equivalent
D. the Scott wedding
Answer:
D. The Scott Wedding
Step-by-step explanation:
Scott: 12 guests on the groom's side and 10 guests on the bride's side
Smith: 18 guests on the the groom's side and 13 guests on the bride's side
The inequality 1 ≤ 2x − 5 is true for all values of x in which of the following sets?
1. 0, 1, and 2
2. 1, 2, and 3
3. 2, 3, and 4
4. 3, 4, and 5
Answer:
4. 3, 4, and 5
Step-by-step explanation:
1 ≤ 2x − 5
Add 5 to each side
1+5 ≤ 2x − 5+5
6 ≤ 2x
Divide by 2
6/2 ≤ 2x/2
3 ≤ x
x must be greater than or equal to 3
Find all complex numbers z such that z^4 = -4.
Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.
Latisha drove around town running errands all afternoon. The path she took is shown on the map below.
A path is 17 inches long. The scale is 2 inches = 3 miles.
To the nearest mile, what is the total distance that she traveled?
17/2 to x/3
cross multiply
51 = 2x
x= 25.5 miles or 26
Geometry, please answer question ASAP
Answer:
C
Step-by-step explanation:
The 2 angles lie on a straight line and sum to 180° , then
5x + 19 + 8x = 180
23x + 19 = 180 ( subtract 19 from both sides )
23x = 161 ( divide both sides by 23 )
x = 7
Then
∠ OML = 15x + 19 = 15(7) + 19 = 105 + 19 = 124° → C
Help me with these questions plz
Answer:
Step-by-step explanation:
2) Cost Price = CP = $ 35
Tax = $ 3.29
Tax percent = [tex]\frac{tax}{CP}*100[/tex]
[tex]= \frac{3.29}{35}*100\\\\[/tex]
= 9.4 %
Total amount paid by Ian = CP + tax = 35 + 3.29
= $ 38.29
3) Price of the order = $ 56.50
Shipping cost % = 3 % = 0.03
Shipping cost = price of the order * shipping cost %
= 56.5 * 0.03
= 1.695
= $ 1.70
Total cost = Price of the order + Shipping cost
= 56.5 + 1.70
= $ 58.20
4) Bill amount = $ 26
Tip % = 18%
Tip amount = Tip % * bill amount
[tex]= \frac{18}{100}*26\\[/tex]
= $ 4.68
5) commission% = 3.5 %
Commission amount = commission% * Sales
[tex]= \frac{3.5}{100}*50000[/tex]
= $ 1750
Base salary for a week = $400
Base salary for two weeks = 400 * 2 = $ 800
Emmett's earning for this two weeks period = Base salary for two weeks + commission
= 800 + 1750
= $ 2550
6) Tax % = 10.25 %
Purchase amount = $ 310.50
Tax = Tax% * Purchase amount
[tex]= \frac{10.25}{100}*310.50[/tex]
= $ 31.83
Total = Purchase amount + Tax
= 310.50+ 31.83
= $ 342.33
Can someone help me on this please
3% of what number is 1.86
Answer:
62
Step-by-step explanation:
Of means multiply and is means equals
.03 * n = 1.86
Divide each side by .03
.03n/.03 = 1.86/.03
n =62
find the following ratios right triangle. PLS HURRY and disregard my answers.
Answer:
sinA= 5/13; cosB= 5/13
Step-by-step explanation:
sine is opposite over hypotenuse so 5/13. cosine is adjacent over hypotenuse so 5/13
which choices are equivalent to the exponential expression below? check all that apply. 5/3^3
Answers:
5^3/3^3
3 x (5/3)
25/9
15/9
5/3 x 5/3 x 5/3
125/27
Answer:
5/3 x 5/3 x 5/3
125/27
5^3/3^3
3 x (5/3)
Step-by-step explanation:
(5/3)^3 = 5×5×5/3×3×3 = 125/27.
Find the value of x.
Round to the nearest tenth.
Х
120°
10
x = [?]
Answer:
X is 11.8
Step-by-step explanation:
You already have the formula so just put in the values and rearrange to get the answer. c is what you are looking for so that is x. a can be 3 and b is 10. CosC is Cos(120) the rest work it out on calculator.
An airplane landed at a point 100 km east and 420 km south from where it took off. If the airplane flew in a straight line from where it took off to where it lands, how many kilometers did it fly? Enter only the number rounded to the nearest kilometer.
Answer:
[tex]\sqrt{100^2 + 420^2}[/tex]
[tex]\sqrt{100^2+420^2}=20\sqrt{466}\quad \left(\mathrm{Decimal:\quad }\:431.74066\dots \right)[/tex]
Step-by-step explanation:
Will Mark Brainlest Help Please ,,,,
[tex]\\ \sf\longmapsto 2x+y=2[/tex]
[tex]\\ \sf\longmapsto 2x=2-y[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}\dots(1)[/tex]
And
[tex]\\ \sf\longmapsto x+1=y+2[/tex]
[tex]\\ \sf\longmapsto x=y+2-1[/tex]
[tex]\\ \sf\longmapsto x=y+1[/tex]
Put the value[tex]\\ \sf\longmapsto \dfrac{2-y}{2}=y+1[/tex]
[tex]\\ \sf\longmapsto 2-y=2(y+1)[/tex]
[tex]\\ \sf\longmapsto 2-y=2y+2[/tex]
[tex]\\ \sf\longmapsto 2-2=2y+y[/tex]
[tex]\\ \sf\longmapsto 3y=0[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{0}{3}[/tex]
[tex]\\ \sf\longmapsto y=\infty[/tex]
Put in eq(1)[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2-\infty}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
Answer:
x=1 , y=0
Step-by-step explanation:
2x+y=2.......1
x+1=y+2
x-y=2-1
x-y=1...... 2
from equation 2 we get ,
x-y=1
x=1+y
putting the value of x in equation 1 we get,
2*(1+y) +y=2
2+2y+y=2
2+3y=2
3y=2-2
3y=0
y=0/3
y=0
putting the value of y in equation 2 we get,
x-0=1
x=1+0
x=1
hence x=1 , y=0
Phoebe took a survey of her classmates' favorite sport. The results are in the table below:
The relative frequency for football is the number of people who like football divided by total people:
4/28 = 0.14
Answer: 0.14
4.
A turtle crawls 567 mm in 27 minutes. How far (measured in cm) can the turtle
crawl in a minute?
Answer: 2.1 cm per minute
Step-by-step explanation:
567/27 =21 mm
convert mm to cm (1mm = 0.1c,)
21mm = 2.1cm
Answer:
2.1 cm or 21 mm
Step-by-step explanation:
567 ÷ 27 = 21
Therefore the turtle can crawl 21 mm in a minute.
To covert mm to cm, we simply divide by 10.
21 ÷ 10 = 2.1
For 4 hours Sam traveled at 40 miles per hour. Then he increased his speed to 60 miles per
hour and drove for another 3 hours. How far did he go in the 7 hours he traveled?
Resolve into factor :(a+b) ^3+1
Answer:
use the formula a^3+b^3= (a+b)-3ab(a+b)
in above question assume (a+b) as a and 1 as b
later in (a+b+1) take (a+b) as a and 1 as b
and use the formula (a+b)^2 = a^2+2ab+b^2
Pls help will give brainliest
Answer:
[tex] \frac{3}{2} + 2(x - 1) = 3 - 2x \\ \frac{3}{2} + 2x - 2 = 3 - 2x \\ 2x + 2x = 3 - \frac{3}{2} + 2 \\ 4x = 3 - \frac{3}{2} + 2 \\ 4x = \frac{6 - 3 + 4}{2} \\ 4x = \frac{7}{2} \\ x = \frac{7}{2} \div 4 \\ x = \frac{7}{8} [/tex]
Step-by-step explanation:
it was helpful to you ♫︎♫︎♫︎♫︎
For a positive integer n, if the difference between all neighbouring digits are all greater than 3 (e.g. 150),
it is defined as a “good number”. How many three-digit “good number(s)” is/are there?
Answer:
166 numbersStep-by-step explanation:
Let n = abc is the 3-digit number
b = 0 - 9, total 10 options
If b = 0, a= 4 to 9, c = 4 to 9, so 6 options each 6*6 = 36 good numbersIf b = 1, a= 5 to 9, c = 5 to 9, so 5 options each 5*5 = 25 good numbersIf b = 2, a= 6 to 9, c = 6 to 9, so 4 options each 4*4 = 16 good numbersIf b = 3, a= 7 to 9, c = 7 to 9, so 3 options each 3*3 = 9 good numbersIf b = 4, a = 8, 9, c = 0, 8, 9, so 2*3 = 6 good numbersIf b = 5, a = 1, 9, c = 0, 1, 9, so 2*3 = 6 good numbersIf b = 6, a = 1, 2, c = 0, 1, 2, so 2*3 = 6 good numbersIf b = 7, a = 1, 2, 3, c = 0, 1,2,3, so 3*4 = 12 good numbersIf b = 8, a = 1, 2, 3, 4, c = 0, 1, 2, 3, 4, so 4*5 = 20 good numbersIf b = 9, a = 1,2,3,4,5, c = 0, 1, 2, 3, 4, 5, so 5*6 = 30 good numbersTotal good 3-digit numbers:
36 + 25 + 16 + 9 + 6 + 6 + 6 + 12 + 20 + 30 = 166Please help asap! Will give brainly
=========================================================
Work Shown:
The notation f(4) means we want to find f(x) when x = 4.
If x = 4, then we go for the middle definition since 4 makes [tex]3 \le x \le 10[/tex] to be true (ie, 4 is between 3 and 10)
Therefore,
f(x) = x^2 - 7 when [tex]3 \le x \le 10[/tex]
f(4) = 4^2 - 7
f(4) = 16 - 7
f(4) = 9
Answer:
f(4) = 9
Step-by-step explanation:
4 is between 3 and 10 so we use the middle function
f(4) = x^2 -7
= 4^2 -7
= 16 -7
= 9
no calculator needed! been stuck for a while. how do I solve this style of question?
Answer:
- [tex]\sqrt{3}[/tex] and 0
Step-by-step explanation:
tan(2x)
= tan(2 × [tex]\frac{\pi }{3}[/tex] ) = tan([tex]\frac{2\pi }{3}[/tex] ) = - tan([tex]\frac{\pi }{3}[/tex] ) = - [tex]\sqrt{3}[/tex]
cos(3x) = cos(3 × [tex]\frac{\pi }{6}[/tex] ) = cos([tex]\frac{\pi }{2}[/tex] ) = 0
6y−3=57 what does y equal
Answer:
y = 10
Step-by-step explanation:
6y−3=57
6y = 60
y = 10
