Find the slope of the tangent to the curve [tex]y=3+4 x^{2}-2 x^{3}[/tex] at the point where [tex]x=a\text{.}[/tex]
Derivatives:The derivative of a function can be determined using different rules and formulations. One of the important rules here is the power rule. Power rule is used to differentiate functions in the form of [tex]f(x) = x^n[/tex].
[tex]\; \dfrac{d}{dx} (x^n) = nx^{n-1}[/tex]
Explanation:We are supposed to find the slope of the tangent to the curve [tex]y=3+4 x^{2}-2 x^{3}[/tex] at the point where [tex]x=a[/tex].
[tex]\implies \dfrac{d}{dx}(3+4x^2-2x^3)[/tex]
[tex]\implies \dfrac{d}{dx}(0+4(2x^{2-1})-2(3x^{3-1})[/tex]
[tex]\implies \dfrac{d}{dx}(0+4(2x)-2(3x^2)[/tex]
[tex]\implies \dfrac{d}{dx}(8x-6x^2[/tex]
Now plugging [tex]x=a[/tex] in the above equation, we obtain the following results:
[tex]\implies \boxed{8a -6a^2}[/tex]
Hence, this is our required solution for this question.
Which expression is equivalent to (-3m-2n³)²(4mn²p-4)?
Answer:
36
m
3
n
2
p
−
36
m
2
+
48
m
2
n
5
p
−
48
m
n
3
+
16
n
8
m
p
−
16
n
6
Step-by-step explanation:
2 in 4x = 2 in 8 What is the true solution to
Answer:
2In4x= 2In8 ln(16x^2) = ln64 Multiply e by both sides.
Step-by-step explanation:
how many cattle are there on the lazy circle double o bar four square ranch
The expression shown in the cattle on the lazy circle will be 22m + 42 and 17m + 3.
How to calculate the expression?
From the complete information, the first expression is given as:
= 7(2m + 6) + 8m
= 14m + 42 + 8m
= 22m + 42
The second expression is given as:
= 3(1 + 4m) + 5m
= 3 + 12m + 5m
= 17m + 3
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(08.06)The dot plot shows how many swimmers are in each line at a waterpark:
Dot plot titled Swimmers in Line and labeled Number of Swimmers shows a number line from 1 to 10. There is 1 dot over 1, no dots over 2, 3, 4, 5 and 6, 2 dots over 7, 4 dots over 8, 6 dots over 9, and 5 dots over 10.
Answer:
The answer is
A. Median, because the data are skewed and there is an outlier
Step-by-step explanation:
Answer:
The answer is median, because the data is skewed and there is an outlier.
Step-by-step explanation:
-15=8z + 7 slove for z
Answer:
-11/4
Step-by-step explanation:
Answer:
- 2.75 is the answer
Step-by-step explanation:
-8z = 7 + 15
- Z = 22 / 8
- Z = -2.75
Which of the following are square roots of
256
A-16
B. 2561/2
C. 2561/2
D. 8
E. 16
F. 128
Answer:
16
Step-by-step explanation:
16^2 = 256
E. the square root of 256 is 16
NEED HELP ASAP!!!!!!
Answer:
Vertex: (-2,-8)
Axis of Symmetry: x = -2
x intercept(s): x = 2,-6
Min/Max Value: Min; y= -8
y-intercept: -6
Step-by-step explanation:
Draw and write to solve. Explain
your reasoning.
1. Jean has 10 fish. She gets
4 more fish. How many fish
does she have now?
Answer:
14
Step-by-step explanation:
she has 10
she gets 4 more
10+4=14
is 24L greater than 240ml
Answer:
yes
Step-by-step explanation:
24L (litres) = 24000 ml
1L = 1000 ml
hope this helps!
Answer:
Yes
Step-by-step explanation:
We know that,
1 Litre = 1000 milliliters
Then,
24 L
= 24 * 1000
= 24000 mL
Also,
24000 mL > 240 mL
So,
Yes, 24L IS greater than 240ml.
[tex]\rule{150pt}{2pt}[/tex]
Which function has an inverse that is also a function?
O {(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)}
O ((-4, 6), (-2, 2), (-1, 6), (4, 2), (11, 2))
O {(-4, 5), (-2, 9), (-1, 8), (4, 8), (11, 4)}
O ((-4,4), (-2, -1), (-1, 0), (4, 1), (11, 1)
keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, well, in this case, all of them have no X-repeats, that means all of them are functions. However, only one-to-one functions have an inverse that is also a function.
A one-to-one function is one that has no X-repeats as well as no Y-repeats, so each pair in the set has no coordinate repeats, Check the picture below.
For an ordered pairs to represent has an inverse a that is function, It shouldn't show one-to-many relation in the pairs. The answer is {(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)} represents a function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The set of all potential values that the function would be return when the domain is provided as input is the definition of range.
The one-to-one function has inverse where the inverse is the function.
That is, should be unique output for each input values.
{(-4, 3), (-2, 7), (-1, 0), (4, -3), (11, -7)} in this option, There are no one-to-many relations. So, It is a function.
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What is the metric system based on
50 points
Please show work !!!
PLEASE ANSWER A AND B, GIVING BRAINLIEST!
Answer:
a) V = (8 -4/3π)r³
b) 2048(2 -π/3) cm³ ≈ 1951.34 cm³
Step-by-step explanation:
When a sphere is placed in a box the empty space volume is the difference between the box volume and the sphere volume. Here, the box is a cube with the same outside dimensions as the sphere.
__
a. (formula)The side length of the cube is 2r, where r is the radius of the sphere. So, the volume of the cube is ...
V = s³ = (2r)³ = 8r³
The volume of the sphere is given by the formula ...
V = 4/3πr³
The volume of the empty space is the difference of these:
V = (8r³) -(4/3πr³)
V = (8 -4/3π)r³ . . . . . . . formula for the empty volume
__
b. (empty space)For r=8 cm, the empty volume is ...
V = (8 -4/3π)(8 cm)³ = 4(2 -π/3)(512 cm³)
V = 2048(2 -π/3) cm³ ≈ 1951.34 cm³ . . . . empty volume
Write an equation of the line that passes through (2, -5) and has a slope of 4
Step-by-step explanation:
(y-(-5))/(x-2) = 4
(y+5)/(x-2) = 4
y+5 = 4x - 8
y = 4x - 13
Which number is rational?
Answer:
[tex]\sqrt{16}[/tex]
Step-by-step explanation:
16 has a perfect square, 4.
Answer:
the square root of 16
Step-by-step explanation:
16 is a perfect square so
the square root of 16 is 4
4*4 = 16
3500 people attend a show. The
next time the show is on the amount
of people has increased by 142%. Find
out how many people are at the
second show.
Answer:
8470 people are at the second show
1/10 (as a fraction) of the animal pictures on Amelia’s smartphone are of cats. Write and solve an equation to find what fraction of all her pictures have cats in them.
1/10 that mean that there are 10 animal pics and 1 cat pic. your equation could be 10-9=1 showing only one 1 cat image.
A deposit of $2,960 is placed into a scholarship fund at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually, and paid at the end of the six months. How much is in the account right after the last deposit? Select the correct answer below:
Answer:
where are the awnsers??
The value of the initial deposit is $2,960, so a1=2960. A total of 26 six-month deposits are made in the 13 years, so n=26. To find r, divide the annual interest rate by 2 to find the biannual interest rate and add 1 to represent the new biannual deposit.
r=1+0.072=1.035
Substitute a1=2960, n=26, and r=1.035 into the formula for the sum of the first n terms of a geometric series and simplify to find the value of the annuity.
S26=2960(1−1.03526)1−1.035≈122286.78
Therefore, the account has $122,286.78 after the last deposit is made.
A furniture store book shelf was priced at
$
345.00
The store was having a
60
%
off sale store wide. What is the sale price of the book shelf?
Answer:
$138.00
Step-by-step explanation:
The original price of the shelf is $345.00. The new sale price is the original price of 100% less the 60% of the original price. That means the sales price is 40% of the original price.
You can do this 2 ways:
1. $345 x 60% or .60 = $207
$345-207 = $138
or
2. $345 x 40% or .40 = $138
Answer:$138
Step-by-step explanation:
Since the store is on sale 60% out of a whole 100%
= 100% - 60% = 40%
40% is [tex]\frac{40}{100}[/tex] = 0.4
0.4 x 345 = $138
A cubical dice is thrown two times, find the probability that the outcomes is 5 in first throw and odd number in second throw.
All the numbers present in cubical dice = 6
( 1 , 2 , 3 , 4 , 5 ,6 ) Total Outcomes = 6Probability = Favorable outcomes / Total number of outcomes
Probability that 5 will come in first throw :-Favorable Outcomes = 1
Favorable Outcomes = 1 Probability = 1/6
Probability that an odd number will come in second throw :-Favorable Outcomes = 3
Probability = 3/6 ; 1/2
In a survey, 125 people were asked to choose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 1.
Answer: probably 4 cards each person
Step-by-step explanation:
Compare using >,<,or=.
2/3 and 9/12
Scott wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has 200 feet of fencing available. Find the dimensions that will enclose the
maximum area.
a
The fence parallel to the house is
the yard is
feet, the fence perpendicular to the house is
feet and the area of
square feet
Answer:
66 2/3 66 2/3 4 444.44 ft^2
Step-by-step explanation:
the largest area will be a square
200/3 = 66 2/3 feet side length
Find the volume of the solid.
3 cm
2 cm
6 cm
4 cm
4 cm
2 cm
7 cm
Answer:
8064cm.
Step-by-step explanation:
When trying to find volume,All you have to do is multiply all the numbers.
Answer:
3 x 2=6 x 6 = 36 x 4 = 144 x 4 = 576 x 2 = 1152 x 7 = 8064
Step-by-step explanation:
simplify 4 times the square root of 6 divided by the square root of 30 by rationalizing the denominator. show your work.
Answer:
4*[tex]\sqrt{5}[/tex]/5
Step-by-step explanation:
(4*[tex]\sqrt{6}[/tex])/[tex]\sqrt{30}[/tex]
This is my interpretation, although the question could also be interpreted as 4 * ([tex]\sqrt{6}/\sqrt{30}[/tex])
Multiply the nominator and denominator by sqrt 30
4* sqrt 6 * sqrt 30/ 30
4 * sqrt 6 * sqrt 6 * sqrt 5/30
24*sqrt 5 / 30
4*sqrt5/5
Please Solve |x+3| if x > 5
Answer:
x< -8 or x>2
Step-by-step explanation:
apply the absolute root
If lu| > a, a>0 then u< -a or u>a
it is equal to
x+3<-5 or x+3> 5
x<-8 or x>2
Please help on math.
Answer:
3
Step-by-step explanation:
First set up your data in order
0,0,0,0,1,1,1,2,2,2,2,3,3
Second subtract the lowest to the highest which is 3-0=3
Hope this helps!
*100 points* pls help on this edulastic, brainly community. Answer the questions in the pic.
Answer:
4. 48, 24, 12
21. A, B, B, C
Step-by-step explanation:
There are two different questions here. One where you get to make up an exponential function and write a table of values. The other is a statistics problem in which you compare 5-number summaries.
__
Exponential FunctionFor the function f(x) = a·b^x, the value of f(0) is 'a'. The given table shows a=96. The only requirement for choosing 'b' is that it not be 1. We can choose b=1/2, and our table will be ...
y = 96·(1/2)^x
[tex]\begin{array}{c|cccc}x&0&1&2&3\\y&96&\boxed{48}&\boxed{24}&\boxed{12}\end{array}[/tex]
For each increase of x by 1 unit, the value of y is cut in half.
__
StatisticsThe attachment shows you how to find the answers to the questions.
The median is the bar in the middle of the box. The values for the different teams are ...
A: 78B: 86C: 82Team A has the lowest median; Team B has the highest median.
The interquartile range (IQR) is the length of the box. For the different teams, the values are ...
A: 88-74 = 14B: 90-78 = 12C: 86-70 = 16Team B has the smallest IQR; Team C has the largest.
25-42 Differentiate the function.
25. [tex]f(x)=x^{5}+5^{x}[/tex]
Answer:
y'= 5x^4 + 5^x In(5)
Step-by-step explanation:
Differentiate with Respect to x
f(x)'=5x^4 + In(5^x)
f(x)'= 5x^4 + x In(5)
with respect to x, we have
y'= 5x^4 + y In(5)
y'= 5x^4 + 5^x In(5)
Use the scenario and elimination by multiplication to answer the question.
At lunch, Marc bought 2 quesadillas and 2 tacos for $10.16, and Jason paid $11.84 for 5 tacos and 1 quesadilla. What was the cost of each taco and quesadilla? Let the cost of a quesadilla be x and the cost of the taco be y.
A. The quesadillas cost $3.11 each, and the tacos cost $1.69 each.
B. The quesadillas cost $1.57 each, and the tacos cost $3.45 each.
C. The quesadillas cost $3.39 each, and the tacos cost $1.69 each.
D. The quesadillas cost $3.39 each, and the tacos cost $1.57 each.