Answer:
The instantaneous rate of change of [tex]y[/tex] with respect to [tex]x[/tex] at the value [tex]x = 3[/tex] is 18.
Step-by-step explanation:
a) Geometrically speaking, the average rate of change of [tex]y[/tex] with respect to [tex]x[/tex] over the interval by definition of secant line:
[tex]r = \frac{y(b) -y(a)}{b-a}[/tex] (1)
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds of the interval.
[tex]y(a)[/tex], [tex]y(b)[/tex] - Function exaluated at lower and upper bounds of the interval.
If we know that [tex]y = 3\cdot x^{2}[/tex], [tex]a = 3[/tex] and [tex]b = 6[/tex], then the average rate of change of [tex]y[/tex] with respect to [tex]x[/tex] over the interval is:
[tex]r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}[/tex]
[tex]r = 27[/tex]
The average rate of change of [tex]y[/tex] with respect to [tex]x[/tex] over the interval [tex][3,6][/tex] is 27.
b) The instantaneous rate of change can be determined by the following definition:
[tex]y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}[/tex] (2)
Where:
[tex]h[/tex] - Change rate.
[tex]y(x)[/tex], [tex]y(x+h)[/tex] - Function evaluated at [tex]x[/tex] and [tex]x+h[/tex].
If we know that [tex]x = 3[/tex] and [tex]y = 3\cdot x^{2}[/tex], then the instantaneous rate of change of [tex]y[/tex] with respect to [tex]x[/tex] is:
[tex]y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}[/tex]
[tex]y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}[/tex]
[tex]y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}[/tex]
[tex]y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h[/tex]
[tex]y' = 6\cdot x[/tex]
[tex]y' = 6\cdot (3)[/tex]
[tex]y' = 18[/tex]
The instantaneous rate of change of [tex]y[/tex] with respect to [tex]x[/tex] at the value [tex]x = 3[/tex] is 18.
Mrs. Walters drove 360 miles on 25 gallons of gas. Mr. Walters drove 480 miles on 32 gallons of gas.
b. Find the mileage per gallon for Mr. Walters's car.
Please explain how you got this answer
Answer:
Mr.Walters car can go 15 miles on one gallon of gas.
Step-by-step explanation:
To find this, you first want to put it into a ratio.
480:32
Next, you want to divide.
480/32
After you divide, you get 15. That tells you that you get 15 miles off of one gallon of gas.
Answer:
15 miles
Step-by-step explanation:
A store sells comic books. Each comic book costs the same amount. During a sale, the store reduces the price of each comic book by $1.45. Miguel
spends $12.88 on 2 comic books at the sale price
Answer:
the original price is $7.89
the price on sale is $6.44
i hope this helps
Step-by-step explanation:
divide $12.88 by 2 to get the price of one of those comic books on sale which gives you $6.44
if you want the original price you just add $1.45 to $6.44 and then thats the price before the sale.
52. Cole worked part-time at an amusement park. The amount of money Cole earned for each of six weeks is shown. $ 45, $ 85, $ 43, $ 45, $ 37, $ 70. Calcule the meant absolutely deviation to the nearest tenth
Which of these numbers is a prime number?
A. -3
B. 0
C. 17
D. 33
Answer:
c: 17
Step-by-step explanation:
Answer:17
Step-by-step explanation:did the practice and got it right
5(x+6)12 how do i solve this
Answer:
60x + 360
Step-by-step explanation:
5 • (x+6) • 12
(5x+30) • 12
60x +360
are these triangle obtuse or acute using the pythagorean theorem?
Answer:
they are acute triangles and right triangles
Step-by-step explanation:
factorise 2x^2 +3x -20=0. 25 points!! plsss could someone help :)
Answer:
(2x - 5) (x + 4)
Step-by-step explanation:
b - 1 > -17 what does b equal?
Answer:
b > -16
Step-by-step explanation:
The inequality is given as:
b - 1 > -17
To solve this problem, add +1 to both sides of the expression:
b - 1 + 1 > -17 + 1
Now;
b > -16
So, all values for which b is more than -16 satisfy the solution for this problem.
2-2|2x+1|=0 what is the answer for this please
Answer:
x=0
hope it's helpful ❤❤❤
THANK YOU.
Tia is making lemonade for a baseball tournament. The recipe calls for 2/3 cup of strawberries for each gallon of lemonade. She has 6 cups of strawberries. How many gallons of lemonade can she make?
Given:
The recipe calls for [tex]\dfrac{2}{3}[/tex] cup of strawberries for each gallon of lemonade.
Tia has 6 cups of strawberries.
To find:
The number of gallons of lemonade she can make.
Solution:
We have,
[tex]\dfrac{2}{3}[/tex] cup of strawberries for = 1 gallon of lemonade
[tex]1[/tex] cup of strawberries for = [tex]\dfrac{1}{\frac{2}{3}}[/tex] gallons of lemonade
= [tex]1\times \dfrac{3}{2}[/tex] gallons of lemonade
= [tex]\dfrac{3}{2}[/tex] gallons of lemonade
[tex]6[/tex] cup of strawberries for = [tex]6\times \dfrac{3}{2}[/tex] gallons of lemonade
= [tex]\dfrac{18}{2}[/tex] gallons of lemonade
= [tex]9[/tex] gallons of lemonade
Therefore, 9 gallons of lemonade she can make by using 6 cups of strawberries.
A biology class has a total of 25 students. The number of females is 15 less than the number of males. How many males and how many females are in the
class?
Answer:
10 males
Step-by-step explanation:
because 15 + 10 is 25 so the answer is 10 males and 15 females
What is the surface area??
Answer:
X-32
Step-by-step explanation:
We don’t know the value of s so therefore x-32
Please help. Due in 30 minutes, whoever answers 1st I'll mark them brainlist
Answer:
the E is the same as the circles
Step-by-step explanation:
What is 0.8 with an line on top written as a fraction?write you answer in the box.
Answer:
i think 8/1000
Step-by-step explanation:
The fraction is 8/9.
What is Rational Number?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number.
We have the decimal is 0.8(bar).
let x= 0.888888.... (1)
Now, multiply above equation by 10
10x = 8.8888..... (2)
Subtraction equation (1) and (2), we get
10x - x = 8.8888.... - 0.88888...
9x = 8
x = 8/9
Thus, the fraction is 8/9.
Learn more about Rational Number here:
https://brainly.com/question/24540810
#SPJ2
please help, would be greatful :)
Answer:
h is approximately equal to 13.4
Step-by-step explanation:
We can use the sine rule to solve this. We're told that the hypotenuse is 18 cm and we know that it's opposite a corner of 90 degrees. We also know that the corner opposite the side of length h has an angle of 48 degrees.
With that we can use the sine rule to solve for h:
[tex]\frac{h}{sin(48)} = \frac{18}{sin(90)}\\\frac{h}{sin(48)} = \frac{18}{1}\\h = 18 sin(48)\\h \approx 13.4[/tex]
Please help! Find the value of a.
I’ll give Brainliest!
help me polssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
2560
Step-by-step explanation:
10%/100% = 256/x
100/10=10
256x10 = 2560
bobux man will come to your house tonight
Answer:
whoses that
Step-by-step explanation:
Answer:
oh no
Step-by-step explanation:
what do I do to stop him
Help please will give Brainlist
Answer:
D) No solution
4 yd
8.5 yd
What is are of the given shape
Answer: Knock Knock!
Step-by-step explanation: (Who's there?)
HURRY!! BRAINLIEST IF RIGHT!!
Need help HMI 10th Geometry
Find two positive numbers that satisfy the given requirements. The sum of the first number squared and the second number is 54 and the product is a maximum.
Answer:
36
Step-by-step explanation:
Calculation to Find two positive numbers
First step
Let the first positive number be a
Let the second positive number be b
Second step is to create the Equation
a^2+b= 54....... Equation (1)
b = 54-a^2........ Equation (2)
Third step is to find the product
Product= a(54-a)^2 = 54a-a^3
Fourth step is to differentiate
dP/dx = 54-3a^2
dP/dx = 0
Fifth step is to solve for 54-3a^2 = 0
Hence,
3a^2=54
a^2 = 18
Last step
a= √(18)
b= 54-(√(18))^2
b=54-18
b = 36
Therefore the two positive numbers are 36
Hello students answer this for branliest and 10 points
4+1=
Answer:
5
Step-by-step explanation:
ty, have a good day!
What is the value of y=6−4x when x=2?
Answer:
y = -2
Step-by-step explanation:
You substitute 2 as x, y = 6 - 4 * 2, which is y = 6 - 8 = -2.
what is the answer to this sqrt{243}
Answer:
It is 9√3 and in decimal form it's 15.58845726
Step-by-step explanation:
I need help with this
Answer:
The mixed number is still 4 1/4. It wont change.
Step-by-step explanation:
Answer:
17/4
Step-by-step explanation:
first, you convert the expression, 4x4+1/4
next, you multiply, 16+1/4
and lastly, you calculate 16+1 and get 17. (The denimonator always stay the same) hope this helped!!
Please help due ASAP
Show workings
Answer:
7
Step-by-step explanation:
BW is 1/3 of the way of JB
like the other question we set up an equation
2x+1=10x+1 but because BW is only one third of the way we have to multiply its side by 3 and the new equation is
9x+3=10x+1
step 1: subtract each side by 9x
3=x+1
step 2; subtract each side by 1
2=x
Next we plug in 2 to x in 3x+1 and get a final answer of
BW = 7
What is the value of x 2(3x-1) ≥ 4x-6
Helpppp
Answer:
if you put it backward you get the answer
Step-by-step explanation:
Answer: the answer is -1
Step-by-step explanation:
Hopes this helps !!!
The side of a cube measures \large 2.2\times10^{-6} cm. What is the volume of the cube in cubic centimeters? Write your answer in scientific notation.
Answer:
The volume is [tex]10.648 \times10^{-18}[/tex] cm³
The scientific notation [tex]1.0648 \times10^{-17}[/tex] cm³.
Step-by-step explanation:
Consider the provided information.
The side of a cube measures [tex]2.2\times10^{-6}[/tex] cm.
The volume of cube = [tex]s^3[/tex]
Where, s is the side.
The volume of cube: [tex]V=(2.2\times10^{-6})^3[/tex] .
[tex]V=(2.2)^3 \times(10^{-6})^3[/tex]
[tex]V=10.648 \times10^{-18}[/tex]
Hence, the volume is [tex]10.648 \times10^{-18}[/tex] cm³
The scientific notation [tex]1.0648 \times10^{-17}[/tex] cm³.