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Determine whether the following statement is true or false, and explain why.
If a function is concave upward on an interval, it must be increasing on the interval.
Is the statement true or false?
A. The statement is true. Functions that are concave upward are always increasing.
B. The statement is false. Functions that are concave upward are always decreasing.
C. The statement is false. Functions that are concave upward are constant and do not increase or decrease.
D. The statement is false. Functions that are concave upward can be either increasing or decreasing.
11
Answers
The statement is true. Functions that are concave upward are always increasing.
What is Concave Upward Function?
Where the derivative f′ is growing, a function f is concave up (or upwards). This is equivalent to the derivative of f′, which is represented by the notation f′′f, start superscript, prime, end superscript, positive.
Explanation:
If a function is concave upward on an interval, it must be increasing on the interval. Given statement is true. Functions that are concave upward are always increasing.
A function is said to be concave upward on an interval if f″(x) > 0 at each point in the interval and concave downward on an interval if f″(x) < 0 at each point in the interval.
At interval if function is increasing then functions that are concave upward are always increasing.
Hence, The statement is true. Functions that are concave upward are always increasing.
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Related Questions
Determine whether the graph represents a linear or nonlinear function. Explain.The graph represents a
function, because the graph
is or is not a line
Answers
Answer:
The graph represents a nonlinear function, because the graph isn't a line.
Reason: A linear function is a graph with a straight line, in this case the graph isn't straight, so it is nonlinear function.
Rena, a pharmacy technician, is looking to make a 45%
solution. She has the alligation pictured below.
A.
20
45
Which solution can be used to fill in location A?
O 35
O 40
O45
O 55
Answers
The solution that can be used to fill in location A is 45%.
In this case, Rena is trying to make a 45% solution. The alligation diagram shows two solutions with concentrations of 20% and 45%. The concentration at location A represents the concentration of the final mixture.
To determine the concentration at location A, we can visually observe the positioning of the concentrations on the diagram. The closer a concentration is to location A, the more it contributes to the final mixture.
In this case, the concentration of 45% is closer to location A than the concentration of 20%.
This means that more of the 45% solution should be used in the mixture to achieve a 45% concentration.
Therefore, the solution that can be used to fill in location A is 45%.
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The position of a particle moving along a coordinate line is s=√24+6t , with s in meters and t in seconds. Find the particle's velocity and acceleration at t=2 sec.
Answers
The correct value of particle's acceleration at t = 2 seconds is -1/12 m/s^2.
To find the particle's velocity, we need to take the derivative of the position function with respect to time (t).
Given the position function:
s = √24 + 6t
To find the velocity, we differentiate the position function with respect to time:
v = ds/dt
Applying the power rule and chain rule for differentiation, we get:
v = (1/2) * (24 + 6t)^(-1/2) * 6
Simplifying further:
v = 3 / √(24 + 6t)
To find the velocity at t = 2 seconds, we substitute t = 2 into the velocity equation:
v = 3 / √(24 + 6(2))
v = 3 / √(24 + 12)
v = 3 / √36
v = 3 / 6
v = 1/2 m/s
So, the particle's velocity at t = 2 seconds is 1/2 m/s.
Now, let's find the particle's acceleration. Acceleration is the derivative of velocity with respect to time.
a = dv/dt
To find the acceleration, we differentiate the velocity function with respect to time:
a = d(3 / √(24 + 6t)) / dt
Applying the quotient rule and chain rule, we get:
a = -3 * (24 + 6t)^(-3/2) * 6
Simplifying further:
a = -18 / (24 + 6t)^(3/2)
To find the acceleration at t = 2 seconds, we substitute t = 2 into the acceleration equation:
a = -18 / (24 + 6(2))^(3/2)
a = -18 / (24 + 12)^(3/2)
a = -18 / 36^(3/2)
a = -18 / 36^(3/2)
a = -18 / 216
a = -1/12 m/s^2
So, the particle's acceleration at t = 2 seconds is -1/12 m/s^2.
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What is the total price for the zoo? What is the total price for the carnival?: 3
People went to the zoo and tickets cost $15 each in comparison to: 3 people go
to the carnival, where tickets cost $15 each and parking costs $10.*
FOR BRAINLOST!!!
Answers
Answer:
45:55
75:85
Step-by-step explanation:
a:b
a = zoo
b = carnival
total amount:
15 x 3 = 45
15 x 3 = 45 + 10 = 55
45:55
5 people:
15 x 5 = 75
15 x 3 = 75 + 10 = 85
75:85
Question 3 on math!
Please help me 15 points
Answers
Answer:
2nd one
Step-by-step explanation:
if you were to look on a grid the slope would point up
Triangle with exactly
2 equal sides
Answers
Hey there!
ALL triangles has 3 sides. (Top and the two corners)
The only try that has the sides that are equal to each other is, the isosceles triangle ; the isosceles triangle is equal to 180°
Answer: ISOSCELES TRIANGLE ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Here’s an example SIDE A is EQUIVALENT (EQUAL) to SIDE B
Find all complex solutions of 3x^2+4x+5=0 please guide!
Answers
Answer:
Step-by-step explanation:
A 2 cm x 2 cm x 2 cm cube holds 468 grains of rice. How many grains of rice would fit in a box with
dimensions 6 cm x 2 cm x 12 cm?
Answers
V1 = 2 * 2 * 2
= 8 cm*3
Let the Volume of the second cube be V2
V2 = 6 * 2 * 12
= 144 cm*3
Now, cube1 with volume of 8 cm*3 holds 468 grains of rice.
Thus, 1 cm*3 volume can hold 58.5 grains of rice ( 468 / 8 = 58.5)
Cube2 has volume of 144 cm*3.
Hence, it can hold 8424 grains of rice ( 144 * 58.5 = 8424)
The number of grains of rice that would fit in a box with dimensions of 6 cm x 2 cm x 12 cm will be 8424 grains.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A 2 cm x 2 cm x 2 cm cube holds 468 grains of rice.
Then the number of grains of rice would fit in a box with dimensions of 6 cm x 2 cm x 12 cm will be
⇒ [(6 x 2 x 12) / (2 x 2 x 2)] x 468
⇒ (144 / 8) x 468
⇒ 18 x 468
⇒ 8424 grains
The number of grains of rice that would fit in a box with dimensions of 6 cm x 2 cm x 12 cm will be 8424 grains.
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Jake has $120 to spend for a party. Juice costs $8. Pizza costs $12. Write the standard equ.
how much juice and pizza Jake can buy?
Answers
Answer:
$8x + $12y = $120
Step-by-step explanation:
x = amount of juice
y = amount of pizza
$120 = his total money
Find the dot product of u and v.
u = (−4, 1)
v = (5,-4)
UxV =
Answers
Answer: -24
13. Mark and his brother signed up for the Catch Up
phone plan. They share the minutes every month
equally. How many minutes can Mark use each
day without going over his share of minutes?
Answers
Answer: 12 minutes
Let us suppose the number of minutes per month is 720. ( i have assumed this data from myself, you use any data you want, remember the procedure)
Now, Mark and his brother share the minutes every month equally.
So, clearly, Mark and his brother would get 360 minutes each every month.
Now, Mark has 360 minutes each month
therefore, Mark has 360/30 minutes per day
= 12 minutes each day.
Step-by-step explanation:
A circle has a radius of 4 ft.
What is the area of the sector formed by a central angle measuring 270 degrees
Use 3.14 for pi and round the decimal to the nearest tenth.
42.8 ft
37.7 ft
12 ft
9.4 ft
Answers
The area of the sector is 37.7 ft.
What is sector:
A sector is a region of a circle that is bounded by two radii and the arc of the circle that lies between the endpoints of those radii.
The formula for the area of a sector is given by
A = (θ/360)πr²Where θ is the central angle in degrees, and r is the radius of the circle
Here we have
A circle has a radius of 4 ft.
The central angle of sector formed = 270°
Using the formula, Area of sector = (θ/360°) × π r²
Area of the given sector = [ 270/360] × 3.14 × (4)²
= [0.75 ] × [50.24]
= 37.68 ft
= 37.7 ft
Therefore,
The area of the sector is 37.7 ft.
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For the following right triangle, find the side length x.
15
Answers
Step-by-step explanation:
Pythagorean Theorem
a^2+b^2=c^2
8^2+15^2=c^2
64+225=c^2
289=c^2
Now square both sides
x=17
Answer:
x = 17
Step-by-step explanation:
\(c^{2} = a^{2} + b^{2}\)
\(c^{2} = 8^{2} + 15^{2}\)
\(c^{2} = 64 + 225\)
\(c^{2} = 289\)
\(\sqrt{c^2} = \sqrt{289}\)
\(c = 17\)
Suppose x and y are sets such that XuB=(-8,-4,-2,0,2,4,6,8), XnY =(-2,0,2) and X/Y =(-8,8) on this basis which of the following is not true
Answers
Answer:
I need points
Step-by-step explanation:
solve for z 3=(z+1) write your answers as integers or as proper or improper fractions
Answers
Answer:
z=2
Step-by-step explanation:
Just solve
1 + z = 3 (minus 1 on both sides)
z = 2
Plug in
3=(2+1)
3 = 3
Given z, find |z|.
z=-2-6i
Answers
\( \Large{\boxed{\sf | \sf z| = \sf \sqrt{40} = 2\sqrt{10} }} \)
\( \\ \)
Explanation:We are given a complex number in algebraic form, and we would like to find its modulus, |z|.
\( \\ \\ \)
Modulus of a complex number\( \\ \\ \)
Let's recall that a complex number in algebraic form is written as \( \sf z = a + ib \) , where a is its real part and b is its imaginary part.
\( \\ \)
The modulus of said complex number is calculated as follows:
\( \sf | \sf z| = \sqrt{a^2 + b^2} \)
\( \\ \)
\( \hrulefill \)
\( \\ \)
Let's identify our values:
\( \sf z = -2 - 6i \Longleftrightarrow z = \underbrace{\sf -2}_{\sf a} + (\underbrace{\sf -6}_{\sf b})i \)
\( \\ \)
Now, substitute these values into our formula:
\( \sf | \sf z | = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \boxed{\sf \sqrt{40}} \)
\( \\ \)
While this may be optional, the result can be simplified by using the following property:
\(\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Product \: rule \: of \: square \: roots\text{:}}}} \\ \\ \sf{ \diamond \: \sqrt{ab} = \sqrt{a} \times \sqrt{b} } \\ \end{array}}\\\end{gathered} \end{gathered}}\)
\( \\ \)
\( \sf \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = \boxed{\boxed{\sf 2\sqrt{10}}} \)
\( \\ \)
\( \hrulefill \)
\( \\ \)
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In an experiment, the one factor that the scientist changes is called what?
Answers
Answer:
independent
Step-by-step explanation:
Answer:
Independent Variable
Step-by-step explanation:
In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answers
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
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Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
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yo whats i lowkey cant think rn 3/4 times 2 ??
Answers
Answer:
1.5 in a decimal
Step-by-step explanation:
i hope it helps
Help help please please
Answers
9514 1404 393
Answer:
b = √32
Step-by-step explanation:
The Pythagorean theorem tells you the relation between the side lengths is ...
2² + b² = 6²
b² = 36 -4 = 32
b = √32
_____
Additional comment
This radical can be simplified by removing a square from under the radical.
\(b = \sqrt{32}=\sqrt{16\cdot2}=\sqrt{16}\cdot\sqrt{2}=4\sqrt{2}\)
The figure below shows three small circles, each
with a diameter of 6 centimeters, inside a larger
circle.
Answers
Solve. Write out your answer (i.e. x is greater than 2)
6x−2<22
Answers
Answer:
x<4
Step-by-step explanation:
4*6-2=22
Arthur, Yusuf, and Bill had some stamps in the ratio 3: 5: 6. When Yusuf gave some stamps to Arthur and Bill gave Arthur 42 stamps more than what Yusuf gave Arthur, they all had the same number of stamps each. How many stamps did Yusuf have at first?
Answers
Answer:
210 stamps
Step-by-step explanation:
Given:
Arthur ⇒ a = 3 kYusuf ⇒ y = 5kBill ⇒ b = 6kYusuf gave x stamps to Arthur, then:
y = 5k -xa = 3k + xBill gave Arthur 42 stamps more than Yusuf gave to Arthur, then:
b = 6k - (x+42)a = 3k + x + x + 42Now all 3 have same amount of stamps:
5k -x = 6k - x - 42 = 3k + 2x + 42From the first part of the equation we get:
6k - 5k = 42 + x - xk = 42How many stamps did Yusuf have at first?
y = 5k y =5*42 y = 210 stampsYusuf had 210 stamps at first
The dashed triangle is the image of the solid triangle for a dilation centered at the origin. What is the scale factor?
Answers
Option(c) is the correct answer i.e. the scale factor of the given triangle is 4/9.
What is Scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.
Let's take the measurement of one side of the original triangle and dashed triangle.
The side of Original triangle is 18 units and,
The side of dashed(new) triangle is 8 units
We know that,
Scale factor = dimension of new figure ÷ dimension of original figure
= 8 units / 18 units
= 4/9.
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On August 20, 1989, in Cologne, West Germany, Said Aouita of Morocco also established a world record when he ran the 3000. m run in 7 minutes, 29.45 seconds. What was his average speed (in m/s) for the race? Remember to include your data, equation, and work when solving problem
PLS HURRY I HAVE TO TURN THUS IN!!!!!
Answers
Answer:
Average speed of Aouita = 6.68 meter per second.
Step-by-step explanation:
To create a world record Aouita ran a distance = 3000 m
He took the time to cover this distance = 7 minutes 29.45 seconds
= (7×60) + 29.45 seconds
= 449.45 seconds
Since, formula for the average speed is given by,
Average speed = \(\frac{\text{Total distance covered}}{\text{Total time taken}}\)
Therefor, average speed of Aouita = \(\frac{3000}{449.45}\)
= 6.675
≈ 6.68 meter per second
Average speed of Aouita was 6.68 meter per second.
Answer:
6.67 m/s
Step-by-step explanation:
7 * 60 = 420
420 + 29.45 = 449.45
V = 3000. / 449.45= 6.67 m/s
A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6 days. Its average brightness is 3.5 and the brightness changes by /-0.25. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days: B(t)=4.2 +0.45sin(2pit/4.4)
A) Find the rate of change of the brightness after t days.
B) Find the rate of increase after one day.
Answers
Answer:
a) The rate of change of the brightness after t days is \(B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}\)
b) The rate of increase after one day is of 0.0915.
Step-by-step explanation:
The brightness after t days is given by:
\(B(t) = 4.2 + 0.45\sin{(\frac{2\pi t}{4.4})} = 4.2 + 0.45\sin{(0.4545\pi t)}\)
A) Find the rate of change of the brightness after t days.
This is \(B^{\prime}(t)\)
The derivative of a constant is 0, the derivative of \(\sin{at}\) is \(a\cos{at}\)
So, in this case, we have that:
\(B^{\prime}(t) = 0.45*0.4545\pi\cos{(0.4545\pi t)} = 0.204525\pi\cos{(0.4545\pi t)}\)
The rate of change of the brightness after t days is \(B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}\)
B) Find the rate of increase after one day.
This is \(B^{\prime}(1)\). So
\(B^{\prime}(1) = 0.204525\pi\cos{(0.4545\pi)} = 0.0915\)
The rate of increase after one day is of 0.0915.
I forgot how to do this, can someone help
Answers
Answer:
B, no need to use calculator, a negative number minus a positive number is a negative number
Step-by-step explanation:
Which is the smallest tow rope needed to pull an 8000 N pallet across a warehouse floor? Click the image to find the answer
10000 n
4000 n
24000 n
2700 n
Answers
Answer: force F = uN, u 0.34 and N = 8000 N also F = 2720 N, thus 4000 N is enough
It
Step-by-step explanation:
Answer:
10,000 i think....i hope this helps
Step-by-step explanation:
Divide the following complex numbers:
\((2 + i) \div (1 - 4i)\)
Answers
Answer:
\(-\dfrac{2}{17} + \dfrac{9}{17}i\)
Step-by-step explanation:
\( (2 + i) \div (1 - 4i) = \)
\( = \dfrac{2 + i}{1 - 4i} \)
\( = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} \)
\( = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} \)
\( = \dfrac{2 + 8i + i + 4i^2}{1 + 16} \)
\( = \dfrac{2 + 9i - 4}{17} \)
\( = \dfrac{-2 + 9i}{17} \)
\(= -\dfrac{2}{17} + \dfrac{9}{17}i\)
14 less then 3 times a number is 31 written out and solved
Answers
Answer:
3x-14=31 ,= 15
Step-by-step explanation:
3x= 45
x= 45/3
x= 15
hope it helps