Use the following graph to estimate the rate of change of the function at x=0.6 using the points (0,0) and (1,−0.5)
Answers
Answer:
The rate of change of the function at x = 0.6 is approximately -0.72
Step-by-step explanation:
The given information from the graph are;
Points (0, 0) and (1, -0.5)
We have that the graph is that of a cubic function, therefore;
f(x) = ax³ + bx² + cx + d
At f'(x) at (0, 0) and (1, -0.5) = 0 gives;
3ax² + 2bx + c = 0
∴ c = 0
Also
ax³ + bx² + cx + d = 0
d = 0
We have
3a(1)² + 2b(1) + 0 = 0
3·a + 2·b = 0..............(1)
a(1)³ + b(1)² + c(1) + d = -0.5
a + b + 0×(1) + 0 = -0.5
a + b = -0.5..........(2)
Multiplying equation (2) by 2 and subtracting it from equation (1) gives;
2 × (a + b = -0.5) = 2·a + 2·b = -1
3·a + 2·b - (2·a + 2·b) = 0 - (-1) = 0 + 1 = 1
a = 1
From
a + b = -0.5, we have;
1 + b = -0.5 = 0
b = -0.5 - 1 = -1.5
The equation becomes
f(x) = x³ - 1.5·x²
The rate of change of the function at x = 0.6 is therefore given as follows;
f'(x) = 3 × x² - 2 × (1.5)·x = 3·x² - 3·x
At x = 0.6, we have;
f'(0.6) = 3·(0.6)² - 3·(0.6)
f'(0.6) = 3×0.6² - 3×0.6 = -0.72
The rate of change of the function at x = 0.6 ≈ -0.72
Related Questions
Find a general term a, for the sequence whose first four terms are given.
1 /1,1/4,1/9,1/16
Answers
Answer:
an = 1/n^2
Step-by-step explanation:
We notice that the denominators are the squares of successive integers. The general term will be ...
[tex]\boxed{a_n=\dfrac{1}{n^2}}[/tex]
X3-6x-16=0 solve by factoring
Answers
Answer:
X = 3 √ 2 ( 3 x + 8 )
Step-by-step explanation:
Lynn and Max are divers. Lynn's depth gauge says she is 43.6 feet deep. Max's depth gauge says that he is 54.2 feet deep. Who is closer to the surface? Write two statements of inequality to describe the situation.
Answers
Answer: Lynn is closer to the surface.
Step-by-step explanation:
Lynn is 43.6 deep meaning -46.3. Max is 54.2 feet meaning that he is -54.2 feet below sea level. so the smaller the number the close it is to 0 (which in this case is the surface) hope this helped
You have taken up gardening for relaxation and have decided to fence in your new
rectangular shaped masterpiece. The length of the garden is 4 meters and 34 meters
of fencing is required to completely enclose it. What is the width of the garden?
Answers
Answer:
13 meters
Step-by-step explanation:
Adjacent sides form half the perimeter, so the sum of the unknown side and the given side is 34/2 = 17 meters.
4 meters + width = 17 meters
width = 13 meters . . . . . subtract 4 meters
Steve had 48 chocolates but decided to give 8 chocolates to each of his f coworkers. How many chocolates does Steve have left?
Answers
So if Steve divided 48 chocolates by how many he would give to each co worker he would have 6 workers and 0 chocolates left.
Hope this helped!! :))
Answer: 40 chocolates
Step-by-step explanation:
Please help please help
Answers
2. 1/3
3. 1/14
4. 4/45
5. 7/12
6. 14/55
7. 5/12
8. 2/9
9. 1/16
10. 7/6
11. 5/12
12. 4/5
13. 6/7
14. 7/12
15. 1
16. 3/2
17. 15/8
18. 4/7
If she does not make any deposits or withdrawals, what will be the balance in her
account after 2 days?
Answers
Answer:
the same as its been for 2 days
Step-by-step explanation:
Evaluate the following expression. cos315°
Answers
Answer:
[tex]\sqrt{2}/2[/tex]
Step-by-step explanation:
Making a unit circle will be very helpful if you don't already have one. You will use it for years to come.
Your school band is selling T-shirts. The group purchased the tees wholesale for $3.00 each. If the team has a 310% markup, what price are they selling the t-shirts for?
Answers
Answer:
$9.10
Step-by-step explanation:
hope this helps buddy
HELP PLS THIS IS IMMEDIATE
Answers
Find the product -1(-15) . Oh and also -1(-24) pls help
Answers
Answer:
15 and 24
Step-by-step explanation:
distribute the -1 to the -15 amd it will cancel out same for the other
helphelphelphelphelp
Answers
Answer:
Point A
Step-by-step explanation:
which point is the center of a circle
Answers
Answer:
isnt it called the focus thats what i think
Step-by-step explanation:
Alfred and his 4 friends bought 13 1/4 pounds of gummy bears at $1.20 pound . If the cost is divided between alfred and his four friends what would each person pay
Answers
to find the total cost, just multiply 13.25 by $1.20 to get $15.90. to find the cost per person, just divide $15.90 by 5, which results in each person paying $3.18
At the fair, Terrell has 47 ride tickets. Each ride on the Ferris wheel costs 6 tickets. After
riding the Ferris wheel as many times as possible, how many tickets will Terrell have left?
Answers
Answer:
Terrell has 5 tickets left.
Step-by-step explanation:
What
is
the
solution
to
the
equation?
5x – 4 = 3x + 10
Answers
Answer:
x = 7
Step-by-step explanation:
5x - 4 = 3x + 10
Combine Like Terms
2x = 14
Divide
x = 7
What is f(-2) of the function given below? *
f(x) = 3x2 - 4x + 1
Answers
Answer:
f(-2) = 21
Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 4x + 1
f(-2) is x = -2
Step 2: Substitute and Evaluate
f(-2) = 3(-2)² - 4(-2) + 1
f(-2) = 3(4) + 8 + 1
f(-2) = 12 + 9
f(-2) = 21
Point B has 3 lines extending from it. One line extends to point A, another to C, and another to D. Angle A B D is a right angle. Which information do you know is true from the diagram? Check all that apply. ∠ABD is a right angle. Ray B C bisects angle ∠ABD. m∠ABC = 45° m∠CBD = 45° m∠ABD = 90°
Answers
Answer:
A) ∠ABD is a right angle.
E) m∠ABD = 90°
Step-by-step explanation:
just took the test
∠ABD is a right angle and ∠ABD = 90° will be correct for the given angles.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
The angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given that,
Angle A B D is a right angle.
The right angle is a 90-degree angle.
So,
m∠ABD = 90°
Hence "∠ABD is a right angle and ∠ABD = 90° will be correct for the given angles".
For more about the angle,
brainly.com/question/13954458
#SPJ2
Which of the following is an equation of the line with slope 2 that passes through the point (-1,-4)
Show complete working format
Answers
Answer:
y = 2x - 2
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Define
Slope m = 2
Random point (-1, -4)
y = 2x + b
Step 2: Find b
-4 = 2(-1) + b
-4 = -2 + b
-2 = b
Step 3: Rewrite linear equation
y = 2x - 2
a rectangular piece of metal is 15in longer then it is wide. squares with sides 3in long are cut from the four corners and the flaps are folded upward to form an open box. if the volume of the box is 1092in cubed what were the original dimensions of the piece of metal?
Answers
Step-by-step explanation:
Let x equal the width of the box and x + 15 equal the length of the box. Subtract 6 (the amount cut out) from both of the these to get the following terms: (x+9) and (x-6). These are the length and width of the box respectively. We also know that the height of the box is 3. Plugging these into the formula for the volume of a box gives you:
3(x+9)(x-6)=1092
Expanding this out gives:
3x^2+9x-162=1092
Subtract 1092 from both sides to make the quadratic equation equal zero. Plug the a, b and c coefficients into the quadratic formula (or factor) to find x.
3x^2 +9x-1254 = 0
a = 3 b = 9 c = -1254
I hope this helps :)
Simplify the expression 8+10p-4-7p
Answers
- Find the coordinates of A if B(0,5.5) is the midpoint of AC and C has coordinates
(-3,6).
Answers
Given:
Coordinates of point C are (-3,6).
Point B(0,5.5) is the midpoint of AC.
To find:
The coordinates of A.
Solution:
Let the coordinates of point A are (a,b).
Formula for midpoint:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Using the above formula, the midpoint of A(a,b) and C(-3,6) is
[tex]B=\left(\dfrac{a+(-3)}{2},\dfrac{b+6}{2}\right)[/tex]
[tex](0,5.5)=\left(\dfrac{a-3}{2},\dfrac{b+6}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{a-3}{2}=0[/tex]
[tex]a-3=0[/tex]
[tex]a=3[/tex]
and,
[tex]\dfrac{b+6}{2}=5.5[/tex]
[tex]b+6=11[/tex]
[tex]b=11-6[/tex]
[tex]b=5[/tex]
Therefore, the coordinates of point A are (3,5).
Cans of peas are 3 for $1.29. How much would one can of peas and a bag of chips priced at $2.19 cost all together?
Answers
Answer:
It would be 2.62
Step-by-step explanation:
Describe the 6 ways to transform a function.
Answers
You want to buy a new hat that costs $9.20 on the price tag. How much
will you pay at the register if there is an 8.5% tax? Round to the nearest
cent. *
Answers
Answer:
$9.98 :)
Step-by-step explanation:
just multiply the tax (0.085) by the price ($9.20) then add the initial price ($9.20) to that.
Evaluate the expression for p = –4.
3p2 − 18(–2 − p) =
Answers
Answer:
12
Step-by-step explanation:
p = -4
3p² - 18(-2 - p)
plug in p
3(-4)² - 18(-2 - (-4))
solve the exponent
3(16) - 18(-2 - (-4))
solve within the parentheses
3(16) - 18(-2 + 4)
3(16) - 18(2)
multiply each expression
48 - 36
subtract
12
Beach Bicycles sells two-seater bicycles. Its markup rate is 68%. Which equation represents the new price for a bicycle, y, given an original price, x?
Answers
Answer:
y = 1.68x
Step-by-step explanation:
The markup rate of a product or service refers to how higher the selling price is than the total production cost. In this case, this company doesn't produce the bikes, instead it purchases them from a wholesaler, distributor or even the factory, and then resells them in order to make a profit.
E.g. Beach Bicycles purchases two-seater bikes at $200 each, and then it will resell them to their customers at 1.68 x $200 = $336. The total markup in this example is $136, which represents $136/$200 = 68% of the purchase price.
6x+2y=12 ( solve for y )
How do I show my work on a piece of paper would help a lot :)
Answers
Answer:
y=6-3x
Step-by-step explanation:
factor out common terms 2(3x+y)=12divide both sides by 2
3x+y=[tex]\frac{12}{2}[/tex] simplify 3x+y=6 subtract 3 from both sides
y=6-3x
D
Question 1
(02.03)
Read the following statement: Line segment CD is congruent to line segment XY.
Which of the following is an equivalent statement? (4 points)
Answers
4. A recipe for pasta dough says, "Use 150 grams of four per large egg."
a. How much flour is needed if 6 large eggs are used?
b. How many eggs are needed if 450 grams of flour are used?
Answers
Answer:
900 grams of flour 150x6=900
3 eggs 450/150=3