Answer:
The instantaneous rate of change as x approaches 3 is 18.
Step-by-step explanation:
From Differential Calculus and Geometry we remember that instantaneous rate of change of the function is represented by a tangent line, whose slope is determined by the first derivative of the curve. Let [tex]f(x) = 3\cdot x^{2}[/tex], the instantaneous rate of change of the function when x approaches 3 is deducted from the definition of derivative:
[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex] (1)
[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}[/tex]
[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot (x^{2}+2\cdot x\cdot h +h^{2})-3\cdot x^{2}}{h}[/tex]
[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot x^{2}+6\cdot x\cdot h+3\cdot h^{2}-3\cdot x^{2}}{h}[/tex]
[tex]f'(x) = \lim_{h\to 0} \frac{6\cdot x\cdot h +3\cdot h^{2}}{h}[/tex]
[tex]f'(x) = \lim _{h\to 0} (6\cdot x+3\cdot h)[/tex]
[tex]f'(x) = 6\cdot x \cdot \lim_{h\to 0} 1 + 3\cdot \lim_{h\to 0} h[/tex]
[tex]f'(x) = 6\cdot x[/tex] (2)
If we know that [tex]x = 3[/tex], then the instantaneous rate of change as x approaches 3 is:
[tex]f'(3) = 6\cdot (3)[/tex]
[tex]f'(3) = 18[/tex]
The instantaneous rate of change as x approaches 3 is 18.
I Think the answer Is C
Answer:
mee two
Step-by-step explanation:
Which city experiences a larger absolute change between the high temperature and low temperature, Nuuk in January or Isla Hoste in August?
Answer:
I believe it is Isla Hoste in August
Answer: it is Isla Hoste in August
Step-by-step explanation:
i am sure pls give me brainliest
Solve x-5= 2.
a. X = 3
b. X = -7
c. X= 7
d. x = -3
Answer: C.
Explanation: X= -7
what is the value of |-6.33|
Answer: the absolute value is 6.33
Written expression for (9x5)+(24-9)
35
- 34
3+10 121
105
los
a bag contain blue black balls and 5 Yellow baz two
balls are taton at random me ather the other without
replacement fond
both boro Probability That
a They ar both black
Yellow
. The forse is yellow and the second is black
a one is yecrow and the others black
they are of the same colour
5
Answer:
? ??
Step-by-step explanation:
You need to try and structure that question? or whatever that is better
Roxanna has a collection of silver spoons from all over the world.
- If the spoons are arranged in sets of 7, there are 5 left over.
- If the spoons are arranged in sets of 8, there is 1 left over.
- If the spoons are arranged in sets of 15, there are 14 left over.
If she has at least 50 spoons, what is the smallest possible number of spoons in her collection?
You build a model of Laurel Park using the scale 1.5 inches:10 feet. If the model 94.5
inches wide, what is the width of the school campus?
Answer:
The width of the school campus is:
[tex] \boxed{ \underline{ \rm{630 \: feet}}}[/tex]
Step-by-step explanation:
Scale = 1.5 inches : 10 feet
That means, 1.5 inches is equals to 10 feet in real.
Then for 1 inch:
⇛ 10 / 1.5 feet
⇛ 10/3 feet
We need to find for 94.5 inches,
⇛ 94.5 inches = 94.5 × 2/3 feet
⇛ 94.5 inches = 63 feet
Thus, the width of the school campus is 63 feet.
Solve for x: -2x + 14 = 20
Answer:
x = -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define equation
-2x + 14 = 20
Step 2: Solve for x
Subtract 14 on both sides: -2x = 6Divide -2 on both sides: x = -3Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: -2(-3) + 14 = 20Multiply: 6 + 14 = 20Add: 20 = 20Here we see that 20 does indeed equal 20.
∴ x = -3 is a solution of the equation.
I neeed help for 4,5, and 6
I have 15 more points left
plssss
Khan Academy
Factor using polynomial division
The polynomial p(x) = x3 + 7x2 – 36 has a known factor of (x + 3).
Rewrite p(x) as a product of linear factors.
p(2) =
Answer:
Rewriting p(x) as a product of linear factors: [tex]\mathbf{f(x)=(x+3)(x-2)(x+6)}[/tex]
Step-by-step explanation:
The polynomial [tex]p(x) = x^3 + 7x^2 - 36[/tex] has a known factor of [tex](x + 3)[/tex]
We need to find other factors.
First we find quotient of [tex]p(x) = x^3 + 7x^2 - 36[/tex] divided by [tex](x + 3)[/tex]
The division is shown in image attached.
The quotient is: [tex]x^2+4x-12[/tex]
Now, factoring the quotient [tex]x^2+4x-12[/tex]
[tex]x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)[/tex]
The other two factors are (x-2)(x+6)
So, Rewriting p(x) as a product of linear factors: [tex]f(x)=(x+3)(x-2)(x+6)[/tex]
need help on this one please
pls help :( plssss plsss pls
Answer:
you can alwayd use desmos for graphing
which of these is positive values and which have negative values
7-(-4)
-3+(-2)
5-8
-10+12
Answer:
Positive: 7-(-4) and -10+12
Negative -3+(-2) and 5-8
Step-by-step explanation:
Addition and subtraction rules
What is the value for ƒ(x) = 9 3 15 6
Answer:
8 9 16 7 hope this helps
Step-by-step explanation:
I'm not to good with math lol
Answer:
9
Step-by-step explanation:
I believe this is missing part of the equation. But if you are looking for the value of f(x)=3^2x+1 when x=1/2, this is the answer you are looking for.
You will have to substitute the given value into the function and evaluate.
For each boat he sells, Mick earns $149 in addition to 2% of the purchase price of the boat
as commission. How much will Mick earn for a boat that was purchased at $65,000?
Answer:
c = 149 + 0.02p
Step-by-step explanation:
Hurry I don’t know the answer
Answer:
I cant tell wich graph as all the options arnt present but I hope the picture will help you tell wich graph
Multiply and simplify the product.
(3 – 5i)(–2 + 4i)
Select the product.
14+ 2i
14 + 22i
15 + 22i
26+2i
Answer:
B
Step-by-step explanation:
We have the expression:
[tex](3-5i)(-2+4i)[/tex]
Distributive Property:
[tex]=(3-5i)(-2)+(3-5i)(4i)[/tex]
Distribute:
[tex]=(-6+10i)+(12i-20i^2)[/tex]
Simplify:
[tex]=(-6+10i)+(12i-20(-1))[/tex]
Simplify:
[tex]=-6+10i+12i+20[/tex]
Combine like terms:
[tex]=(-6+20)+(10i+12i)[/tex]
Simplify:
[tex]=14+22i[/tex]
Hence, our answer is B.
Answer:
14+22i
Step-by-step explanation:
A sample was taken of the metabolic rates of men participating in a study regarding diets. If each score is multiplied by 25 points , then the standard deviation of the new scores would:_______
Answer:
multiply by 25 also.
Step-by-step explanation:
If the scores are multiplied by 25, that means that the mean will also multiply by 25. Since the mean and the scores all increased by 25 times, the standard deviation will increase by 25 times.
If instead, you added 25 (or any other number) to each score, then the standard deviation would not change. The mean and each score will increase by 25, bu the difference between them will not change.
Tomas is a commercial real estate agent who earns a yearly salary of $82,500 and a 2.5% commission on his total sales. If Tomas sold properties that totaled $3.75 million in sales during one year, what are Tomas’s earnings for that year?
Answer:
$176,250
Step-by-step explanation:
Multiply $3.75 million by Tomas commission on his total sales. Since you can't multiply a percentage you have to turn the commission into a decimal by moving it two spaces to the left. (Note: If it doesn't have a decimal add one at the end of the number then move it two spaces to the left)
$3,750,000 x .025 or 0.025 = $93,750
Add $93,750 to Tomas yearly salary
$93,750 + $82,500 = $176,250
So
If Tomas sold properties that totaled $3.75 million in sales during one year, his earnings for that year would be $176,250
5
A bag of marbles had 16 red marbles and the rest were white. For a game, of the 16 red marbles were chosen, and 15 of the white marbles were also
chosen.
Use this information to answer the questions below.
If not enough information is given to answer a question, click on "Not enough information."
need help with question 2 and 3
Answer:
2. 122
3. 90 degrees
Step-by-step explanation:
Answer all of the following questions above. I will give brainliest to the correct answer!
Answer:
40
112
2n^2 + 2n C
Step-by-step explanation:
a)The correct formula is 2n^2 + 2n
So for n =4, the answer is
2*4^2 + 2*4
2*16 + 8
32 + 8
40
b) For the seventh answer you get
2 * 7^2 + 2*7
2*49 + 14
98 + 14
112
c) The correct formula to use is
2n^2 + 2n See diagrams for the number of matchsticks to be used.
n 2n^2 + 2n
1 2*1^2 + 2*1
1 2 + 2
1 4
2 2*2^2 + 2*2
2 2* 4 + 4
2 8 + 4
2 12
3 2*3^2 + 2*3
3 18 + 6
3 24
What an extremely interesting sequence. I'll bet not one person in 100 could get this without the match stick diagrams. I'm sorry I didn't read the question more carefully.
A store pays $1.50 for a bag of candy. If the store wants to mark-up the price 60%,
for how much will the store sell the bag of candy?
Answer:
Selling price = $2.4
Step-by-step explanation:
Given:
Purchase price = $1.50
Increase in price = 60%
Find:
Selling price
Computation:
Selling price = Purchase price + (Purchase price)(Increase in price)
Selling price = $1.5 + (1.5)(60%)
Selling price = $1.5 + 0.9
Selling price = $2.4
A library contains only paperback and hardback books. If the ratio of paperback books to the total number of books is 3 to 5, which statement must be true? The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 3 to 2. The ratio of paperback books to hardback books is 3 to 2. There are exactly 2 paperback books in the library. There are exactly 2 paperback books in the library. There are exactly 8 hardback books in the library. There are exactly 8 hardback books in the library.
Answer:
A library contains only paperback and hardback books. If the ratio of paperback books to the total number of books is 3 to 5, the true statement is:
The ratio of paperback books to hardback books is 3 to 2.
Step-by-step explanation:
The number of books in the library = 5
The number of paperback books in the library = 3
Therefore, the number of hardback books in the library = 2 (5 - 3)
Then, the relationship between the paperback books and the hardback books in the library can be expressed as a ratio of 3:2. This still gives the sum of the ratios as 5, which is the total number of books in the library, including paperback and hardback books.
Answer this right and i will mark you brainliest hellllllpppp meeee ❤️
Answer:
y represents the money raised for charity
Step-by-step explanation:
don't be putting random stuff and that's on period
Answer:
126 divided by 6 which is 27
Step-by-step explanation:
The answer is C
Answer is C!
Sawarasenaikimiwa⛓shoujonano?~
✨BöKùWâÿARiçHiñBįCChīńOoŠuDàYO!~~
Which graph correctly represents the information from the table?
Time (s) Speed (m/s)
0 0
2 4
3 6
4 8
6 12
Answer:
A.
Step-by-step explanation:
A and C are the only graphs it could be because they are the only graphs starting with (0, 0)
Graph C does not have (2, 4) on it but Graph A does meaning that the only possible answer is Graph A
Answer:
Yes, ( A )would be the correct answer
Step-by-step explanation:
Took the test.
Coordinate plane with triangle EFG with E at 0 comma 5, F at 1 comma 1, and G at negative 2 comma 1. Point H at 1 comma 1 is on segment GF, and points E and H are connected with a segment.
Triangle EFG is dilated by a scale factor of 2 centered at (0, 2) to create triangle E'F'G'. Which statement is true about the dilation?
segment EG ≅ segment E prime G prime.
The slope of segment EF is the same as the slope of segment E prime H prime.
segment H prime F prime will overlap segment HF.
segment EH and segment E prime H prime both pass through the center of dilation.
Answer:
The answer is A
Step-by-step explanation:
I'm taking the test
Answer:
Either way, dilations wont cause congruency, the triangles will be similar (Invalidates A)
Step-by-step explanation:
what is the answer to the question
Answer: The area of the triangle is 25 units^2.
Step-by-step explanation: The formula to find the area of the triangle is (base * height)/2. In this case, the base is 10 units long (on the x axis, it's the overall horizontal length of the triangle) and the height is 5 units long (the height can be calculated by finding the y axis length from the highest point of the triangle to the lowest). So (10*5)/2 = 50/2 which equals 25. And keep in mind, because this is the area, the unit will be units squared.