if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2? if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2?
To find d^2y/dx^2 when t = 1, we need to first express y in terms of x. Then, differentiate y with respect to x to find dy/dx. Finally, differentiate dy/dx to find d^2y/dx^2 and substitute t = 1.
Explanation:Given the equations x = t^2 - 1 and y = t^4 - 2t^3, we can find d^2y/dx^2 when t = 1.
First, we need to express y in terms of x. From the equation x = t^2 - 1, we can solve for t as t = sqrt(x + 1). Substituting this into the equation y = t^4 - 2t^3, we get y = (sqrt(x + 1))^4 - 2(sqrt(x + 1))^3.
Next, we need to find the first derivative of y with respect to x: dy/dx. Then, we can find the second derivative d^2y/dx^2 by differentiating dy/dx. Finally, substitute t = 1 into d^2y/dx^2 to find the value.
the smaller of two containers has a capacity of 150 gallons. When it is 4/5 full, its contents are emptied into a larger container, filling exactly 2/3 of it. What is the capacity, in gallons, of the larger container?
What is the expression in simplest radical form?
√384
find g'(4) given that f(4)=3 and f'(4) = -5. g(x) = f(x)/x
What is the gcf for 36, 54 and 135?
What is the value of ∑n=13(17n−15)?
the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.
To find the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex], we need to compute the sum of the expression 17n - 15 for n ranging from 1 to 13.
Using the formula for the sum of an arithmetic series, we can express this sum as:
[tex]\[ \sum_{n=1}^{13} (17n - 15) = \sum_{n=1}^{13} 17n - \sum_{n=1}^{13} 15 \][/tex]
We know that the sum of the first \(n\) natural numbers can be expressed as [tex]\( \sum_{n=1}^{N} n = \frac{N(N+1)}{2} \).[/tex]
So, the sum of [tex]\(17n\) from \(n=1\) to \(n=13\)[/tex] is:
[tex]\[ \sum_{n=1}^{13} 17n = 17 \sum_{n=1}^{13} n = 17 \cdot \frac{13 \cdot (13 + 1)}{2} \][/tex]
[tex]\[ = 17 \cdot \frac{13 \cdot 14}{2} = 17 \cdot 91 = 1547 \][/tex]
And the sum of 15, 13 times (since there are 13 terms) is[tex]\(15 \cdot 13 = 195\).[/tex]
Now, we can find the value of the given expression:
[tex]\[ \sum_{n=1}^{13} (17n - 15) = 1547 - 195 = 1352 \][/tex]
So, the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.
Given the two points (2,4) and (-3,2), what is the slope of the line that goes through both of these points?
what is 4/12 simplest form
Divide. Express your answer in lowest terms
=15/16 + (-3/4)
please tell me how you got your answer after
math plzz I got turn it in Monday she just barely sent me it
A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
Which of the following statements best compares the height of the bars of the histogram?
There are twice as many participants in the 60–79 age group than in the 0–19 age group.
There are 3 times as many participants in the 40–59 age group than in the 0–19 age group.
There are more participants in the 40–59 age group than in the 0–19 and 60–79 groups combined.
There are more participants in the 60–79 age group than in the 0–19 and 20–39 groups combined.
Answer:
Option: B
There are three times as many participants in the 40-59 age group than in the 0-19 age group.
Step-by-step explanation:
From the histogram we have following observations:
Number of people in the age group 0-19= 20
Number of people in the age group 20-39=40
Number of people in the age group 40-59=60
Number of people in the age group 60-79=50
Hence, from the data we could say that there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).
Hence, option B is correct.
What is 6 1/2 as a decimal?
What is the 8th term in the sequence?
Note: Use the explicit rule.
an=25−3n
Enter your answer in the box.
a8=
You are playing a game of Scrabble and have the 5 A tiles, 3 E tiles, 1 Z tile, 2 M tiles, 3 L tiles, and 1 Y tile to choose from. What is the probability that you choose E or Y on your next draw
Answer:
4/15
Step-by-step explanation:
To find the probability we use the mutually exclusive probability formula P(A) + P(B). The probability of picking a E tile is
1
5
and the probability of picking a Y tile is
1
15
. The sum is
4
15
.
Will give brainlyiest answer if explained.
In the figure below, lines g and h are parallel and are cut by transversal j to form the angles shown. If the measure of <8 is 82, what is the measure of <1?
A. 180.
B. 98.
C. 82.
D. 8.
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
a 45° rotation clockwise about the origin
a translation 6 units to the left and 8 units up
a reflection across the x-axis
a translation 3 units to the left and 6 units up
Two translation rigid transformations are required to transform shape 1 to shape 2
The rigid transformation that can be performed on shape 2 to show that shape 2 is congruent to shape 1 is the option
A transformation of 6 units to the left and 8Reasons:
The coordinates of the three points on shape 1 are; (2, 12), (4, 14), (6, 14)
The coordinates of the three points shape 2 are; (8, 4), (10, 6), (12, 6)
The difference in the coordinates are;
Difference in x-coordinate are;
Point 1 = 8 - 2 = 6
Point 2 = 10 - 6 = 6
Point 3 = 12 - 6 = 6
Therefore;
To get the x-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of -6 units or 6 units left
Difference in y-coordinate are;
Point 1 = 4 - 12 = -8
Point 2 = 6 - 14 = -8
Point 3 = 6 - 14 = -8
Therefore;
To get the y-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of 8 units or 8 units up
The composite transformation is therefore;
A transformation of 6 units to the left and 8 units upLearn more here:
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Lucia bought a table and some chairs at a furniture store. The equation that models this situation is y = 40x + 55, where y is the amount of money she spent and x is the number of chairs she bought. What does the y-intercept mean in this situation?
A. She paid $40 for each chair.
B. She paid $55 for the table.
C. She paid $40 for the table.
D. She paid $55 for each chair.
Answer: C. She paid $40 for each chair.
Step-by-step explanation:
You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain.
Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.
Your friend is correct because applying the permutations rule in this setting would be inappropriate.
Neither method is correct. The combinations rule should be applied in this setting.
Your method is correct because you are applying the permutations rule in the appropriate setting.
Answer:
Option A
Step-by-step explanation:
Whenever we want to arrange a number of objects or letters or numbers n then we must check whether
i) repitition is allowed
If repitition is allowed then total number of ways = n!
ii) repitition not allowed.
In this case again we have to check whether order matters or not.
If order matters then no of ways nPn.
Here n =5
We find that nPn = 5!
Thus both are correct.
Hence option A
On the cube in the figure above, each of the following points is the same distance from
P as it is from Q
EXCEPT
(A) A (B) B (C) C (D) D (E) E
A parabola has the equation –5x^2 + 30x – y – 34 = 0. Which equation is that of the parabola in vertex form? ...?
K-X=V-W solve for the letter x
To solve for 'x' in the equation 'K - X = V - W', we rearrange the equation to isolate 'x', resulting in 'X = K - V + W'.
Explanation:To solve the equation for the letter x, you need to isolate x on one side of the equation. It's a simple process of rearranging the equation.
Here we start with the original equation:
K - X = V - W
First, to separate your desired variable, or in this case 'x', we add 'X' to both sides to cancel 'X' from the left hand side:
K = X + V - W
Finally, to isolate 'x', we just need to subtract 'V' and add 'W' to both sides
X = K - V + W
So, the solution to the equation when solved for the letter 'x' is X = K - V + W.
Learn more about Solving for a variable here:
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What are the x and y intercept of c = 0.75m + 2.25?
Find the discriminant of the following equation.
4x2 + 12x + 9 = 0
Are 8:5 and 4:19 equivalent
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
a. 7 < h < 9
b. 7 > h > 9
c. h < 7 or h > 9
d. h > 7 or h < 9
car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next
10 years.
The salesman has observed that many students are looking for cars that cost less
than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
The mean will shift to the right.
The mean and the median will be the same.
The median will shift to the right.
The mean will shift to the left.
I think it's B
Answer:
The mean will shift to the left.
Step-by-step explanation:
What is the inverse of the conditional statement " If a number is divisible by 6, then it is divisible by 3"?
A) If a number is divisible by 3, then it is divisible by 6.
B)If a number is not divisible by 6, then it is not divisible by 3.
C)If a number is not divisible by 3, then it is not divisible by 6.
D)If a number is not divisible by 6, then it is divisible by 3.
...?
Answer: I think its A.
Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.
0
1
2
7
Answer:
C) 2
Step-by-step explanation:
I took the quiz and got a 100%.
When working with the square root of a number, when would you have only a positive answer and when would you have both a positive and negative answer?
can -2/5 be simplified