Find h(t) if h"(t) = 2 - 6t, h'(0) = 4, and h(0) = 1. Be sure to clearly state h' (t) and h(t).
Answers
In summary h'(t) = 2t - 3t²2 + 4 and h(t) = t²2 - t²3 + 4t + 1. To solve this problem, we will integrate the given second derivative of h(t) twice to find h(t).
Given: h"(t) = 2 - 6t
Integrating once with respect to t gives us:
h'(t) = ∫ (2 - 6t) dt
h'(t) = 2t - 3t²2 + C1
where C1 is the constant of integration.
Given: h'(0) = 4
Substituting t = 0 and h'(t) = 4 into the above equation, we get:
4 = 2(0) - 3(0)²2 + C1
C1 = 4
Substituting C1 = 4 back into h'(t), we get:
h'(t) = 2t - 3t²2 + 4
Integrating h'(t) once with respect to t gives us:
h(t) = ∫ (2t - 3t²2 + 4) dt
h(t) = t²2 - t²3 + 4t + C2
where C2 is the constant of integration.
Given: h(0) = 1
Substituting t = 0 and h(t) = 1 into the above equation, we get:
1 = 0²2 - 0²3 + 4(0) + C2
C2 = 1
Substituting C2 = 1 back into h(t), we get:
h(t) = t²2 - t²3 + 4t + 1
Therefore, h'(t) = 2t - 3t²2 + 4 and h(t) = t²2 - t²3 + 4t + 1.
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Related Questions
Please help me with this homework show me how you get it and the answer
Answers
Answer:
226.08
Step-by-step explanation:
V=pir^2h
=3^2 x pi x8
=226.08
You want to make a half-circle shaped marquee selection. You would do this by pressing __________ while using the Elliptical Marquee tool to draw a circle. Then with the Rectangular Marquee tool, hold down ____________ and draw a rectangle over half of the circle.
Answers
You would press and hold the Shift key while using the Elliptical Marquee tool to draw a circle. Then, with the Rectangular Marquee tool, hold down the Shift key and draw a rectangle over half of the circle.
To make a half-circle shaped marquee selection, you would do the following steps:
1. **Press and hold the Shift key** while using the Elliptical Marquee tool to draw a circle. This will constrain the shape to a perfect circle.
2. Then, with the Rectangular Marquee tool selected, hold down the Alt key** (Windows) or the Option key (Mac) and draw a rectangle over half of the circle. The Alt/Option key allows you to subtract from the existing selection, creating a half-circle shape.
By following these steps, you can create a half-circle shaped marquee selection by combining the use of the Elliptical Marquee tool and the Rectangular Marquee tool with the appropriate keyboard shortcuts.
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A line passes through the points (–1, –5) and (4, 5). the point (a, 1) is also on the line. a coordinate plane. what is the value of a? –2 –1 1 2
Answers
The value of a is 2
We can use the slope-intercept form of a line, y = MX + b, to find the equation of the line.
The slope (m) of the line can be found using the following formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
So, m = (5 - (-5)) / (4 - (-1)) = 10/5 = 2
Now, we can use the point-slope form of a line, y-y1 = m(x-x1)
where (x1,y1) is any point on the line and m is the slope of the line.
In this case, we will use the point (x1, y1) = (–1, –5)
so, y-y1 = m(x-x1) = -5 - 2(-1-x) = -5-2+2x
Now we know that the point (a,1) is also on the line, we can substitute the value of x and y in the equation
so, 1 - (-5) = 2(a - (-1))
1 +5 = 2a+2
6 = 2a+2
4 = 2a
a = 2
Therefore, the value of a is 2.
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If the geometric mean between two number is 8 and one of the numbers is 2, what is the value of the other number?
Answers
Answer: 14
Step-by-step explanation: To find the mean you have to add the two numbers and divide by the amount of numbers (which is 2). 14 plus 2 is equal to 16. and 16 divided by two is equal to eight
Point C is located at (1, 2) and point D is located at (−4, −2). Find the x value for the point that is 1 over 4 the distance from point C to point D. (5 points)
Answers
Check the picture below.
\(\textit{internal division of a segment using a fraction}\\\\ C(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad D(\stackrel{x_2}{-4}~,~\stackrel{y_2}{-2})~\hspace{8em} \frac{1}{4}\textit{ of the way from }C\to D \\\\[-0.35em] ~\dotfill\\\\ \stackrel{~\hfill \textit{component form of segment CD}}{ (\stackrel{x_2}{-4}-\stackrel{x_1}{1}, \stackrel{y_2}{-2}-\stackrel{y_1}{2})\qquad \implies \qquad (-5~~,~~-4)} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{~\hfill \textit{values to be added to Point C coordinates}} {\cfrac{1}{4}(-5~~,~~-4)\implies \cfrac{1}{4}(-5)~,~\cfrac{1}{4}(-4)\qquad \implies \qquad \left(-\frac{5}{4}~~,~~-1\right)} \\\\\\ \stackrel{\textit{addition of Point C coordinates and values}~\hfill } {\left(-\frac{5}{4}~~,~~-1\right)+\left( 1~~,~~2\right) \implies \left(-\frac{5}{4}+1~~,~~-1+2 \right)}\implies \underset{\stackrel{\uparrow }{x}\qquad }{\left(-\frac{1}{4}~~,~~1 \right)}\)
read it carefully bc ive tried every answer
Answers
Answer:
25/7 inches or 3.57 inches
Step-by-step explanation:
12 1/2 * 2/7
-->25/7 inches
Use the digits 1, 2, 4, 6, 7, 8, and 9 once in each number. Write five 7-digit numbers between 8 000 000 and 9 000 000. Order the numbers from
\
Answers
Answer:
8,976,421
8,974,621
8,974,612
8,976,124
8,976,214
Step-by-step explanation:
Express your answer in scientific notation.
7.9x10^7 +6.5x10^6
Answers
Answer:
8.55 × 10^7
Step-by-step explanation:
7.9 × 10^7 + 6.5 + 10^6 =
= 7.9 × 10^7 + 0.65 × 10^7
= 8.55 × 10^7
Which of the following statements about group decision making is true? If enough time is available, groups usually make higher-quality decisions than most individuals. If enough time is available, most individuals usually make higher-quality decisions than a group. There are far more disadvantages than advantages to group decision making. Individual decisions are generally more difficult to reach than group decisions. Group decisions should rarely be used to address significant business problems.
Answers
The statement "If enough time is available, groups usually make higher-quality decisions than most individuals" is true.
Group decision-making has both advantages and disadvantages, but when enough time is available, groups tend to make higher-quality decisions compared to most individuals. This is due to several reasons. First, groups offer diverse perspectives and expertise, allowing for a broader range of ideas and insights.
Different individuals bring unique knowledge and experiences to the table, leading to a more comprehensive examination of the problem. Second, group decision-making involves collective scrutiny and evaluation of options, which helps in identifying potential flaws or biases in individual opinions.
Group discussions allow for critical analysis, debate, and challenging of assumptions, leading to a more thorough decision-making process. However, it is important to note that time constraints can impact the effectiveness of group decision-making. When time is limited, individual decision-making may be more efficient.
Additionally, the success of group decision-making also depends on factors such as group dynamics, effective communication, and skilled facilitation. Therefore, while groups have the potential for making higher-quality decisions, it is essential to consider the specific context and constraints when determining the most appropriate approach to decision making.
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find the exact value of cos-1 (sqrt 3/2)
Answers
The exact value of cos^-1( √3/2) = 30°
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°
sin30 = 1/2
cos 30 = √3/2
tan 30 = 1/√3
cos 60 = 1/2
sin 60 = √3/2
tan 60 = √3
Therefore, if cos^-1( √3/2) = x
cos x = √3/2
cos 30 = √3/2
cos x = cos 30
therefore x = 30
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PLEASE HELP! 10 points!
Answers
Step-by-step explanation:
It easy isn't it my friend
what is the meaning of divisor
Answers
Answer:
Were a number is divided by another.
Answer:
look it up but I learned this. A divisor - I forgot but here, the Web told me:
divisor
[dəˈvīzər]
NOUN
mathematics
a number by which another number is to be divided.
a number that divides into another without a remainder.
"the greatest common divisor"
HOPE I HELPED!
Let A and B be two disjoint events such that P(A) = 0.24 and P(B) = 0.46. What is P(A or B)?
Answers
The probability of A or B occurring is 0.7.
How we find the probability of A or B?If A and B are disjoint events, it means they cannot occur at the same time. Therefore, the probability of A or B occurring can be found by adding the probabilities of A and B:
P(A or B) = P(A) + P(B)
However, we need to be careful when adding probabilities of events. If events are not disjoint, we may need to subtract the probability of their intersection to avoid double-counting. But in this case, since A and B are disjoint, their intersection is empty, so we don't need to subtract anything.
Substituting the given values, we have:
P(A or B) = P(A) + P(B) = 0.24 + 0.46 = 0.7
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When 288 seventh graders sit 8 to a table, there are 8 learners left without a place to sit. How many tables are there?
Answers
Answer:The answer is 28
Answer:
35
Step-by-step explanation:
Using N(1152, 84), the Normal model for weights of Angus steers , what percent of steers weigh a) over 1250 pounds? b) under 1200 pounds? c) between 1000 and 1100 pounds?
Answers
A) approximately 87.9% of steers weigh over 1250 pounds, b) approximately 71.2% of steers weigh under 1200 pounds, c) approximately 22.5% of steers weigh between 1000 and 1100 pounds. Total of 150 words.
a) Over 1250 poundsTo find the percentage of steers that weigh over 1250 pounds, you need to calculate the z-score first. The z-score formula is: `z = (x - μ) / σ`, where `x` is the weight in pounds, `μ` is the mean weight of the steers, and `σ` is the standard deviation of the weights.
Substituting in the values given, we get: `z = (1250 - 1152) / 84 = 1.17`.Using a standard normal distribution table, the area to the right of `z = 1.17` is 0.879, or 87.9%. Therefore, approximately 87.9% of steers weigh over 1250 pounds.b) Under 1200 pounds
To find the percentage of steers that weigh under 1200 pounds, you need to calculate the z-score again. `z = (1200 - 1152) / 84 = 0.57`.Using the same standard normal distribution table, the area to the left of `z = 0.57` is 0.712, or 71.2%.
Therefore, approximately 71.2% of steers weigh under 1200 pounds.c) Between 1000 and 1100 poundsTo find the percentage of steers that weigh between 1000 and 1100 pounds, you
need to find the area to the left of `z = (1100 - 1152) / 84 = -0.62` and the area to the left of `z = (1000 - 1152) / 84 = -1.71`.Using the standard normal distribution table, the area to the left of `z = -0.62` is 0.269, and the area to the left of `z = -1.71` is 0.044.
Therefore, the area between these two z-scores is 0.269 - 0.044 = 0.225, or 22.5%. Therefore, approximately 22.5% of steers weigh between 1000 and 1100 pounds.
Answer: a) approximately 87.9% of steers weigh over 1250 pounds, b) approximately 71.2% of steers weigh under 1200 pounds, c) approximately 22.5% of steers weigh between 1000 and 1100 pounds. Total of 150 words.
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b) Add the following equation:
x/3+4x/3
Answers
Answer:
5x/3
Step-by-step explanation:
is y = 7/8x proportional or non-proportional??
Answers
Answer:
It is proportional
Step-by-step explanation:
May have brainllest I only need 39 more to get to genius
Question 6 (5 points) Find the derivative of the following function and give your answer in an unsimplified form (note: further simplification beyond the initial calculation without work may result in no credit!) f(x) = |-x + 4|
Answers
The derivative of the function f(x) = |-x + 4| is: f'(x) = 1, for x < , f'(x) = -1, for x > 4
The derivative of the function f(x) = |-x + 4| can be found using the chain rule of differentiation. The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).
In this case, let g(x) = -x + 4, and let f(x) = |x|. Then f(g(x)) = |-x + 4|. We can now apply the chain rule:
f'(x) = f'(g(x)) * g'(x)
f'(x) = d/dx |x| * d/dx (-x+4)
The derivative of |x| is not defined at x=0, but it is equal to -1 for x < 0 and 1 for x > 0. Therefore, we need to consider two cases:
Case 1: x < 4
Here, g(x) = -x + 4 is negative, so f(x) = |-x + 4| = -(g(x)) = x - 4. Therefore,
f'(x) = d/dx (-x+4) * -1
f'(x) = -(-1) = 1
Case 2: x > 4
Here, g(x) = -x + 4 is positive, so f(x) = |-x + 4| = g(x) = -x + 4. Therefore,
f'(x) = d/dx (-x+4) * 1
f'(x) = -1
So the derivative of the function f(x) = |-x + 4| is:
f'(x) = 1, for x < 4
f'(x) = -1, for x > 4
Note that we cannot simplify this further without losing credit, so the answer is left in unsimplified form.
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Can you find the slope and type the correct code? Please remember to type in ALL CAPS with no spaces.
Answers
Yes, I can find the slope of a line and type the correct code. The SLOPE function will return the slope of the linear regression line that best fits the data.
The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. The formula for finding the slope of a line is (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.
The slope is a measure of how steep the line is. It can be positive, negative, zero, or undefined. The code for finding the slope of a line in ALL CAPS with no spaces is SLOPE.
To use this function in Excel, you need to provide the range of x-values and the range of y-values.
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one segment measures 161 cm. Calculate its multiple according to the number 3 and its submultiple according to the number 7
Answers
By using multiplication and division, it can be calculated that-
The multiple according to the number 3 = 162
The submultiple according to the number 7 = 7
What is multiplication and division?
Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.
Division is the process in which a value of single unit can be calculated from the value of multiple unit.
The number to be divided is called dividend. The number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.
This is a problem of multiplication and division.
One segment measures 161 cm
So, to find the multiple according to the number 3, we have to divide 161 by 3
161 \(\div\) 3 = 53.67
Nearest integer of 53.67 is 54
The multiple according to the number 3 = 54 \(\times\) 3 = 162
To find the submultiple according to the number 7, we have to divide 161 by 7
161 \(\div\) 7 = 23
Nearest integer of 23 is 23
The submultiple according to the number 7 = 161 \(\div\) 23 = 7
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Find 0 in degrees.
?] degrees
Round to the nearest hundredth
![Find 0 in degrees.?] degreesRound to the nearest hundredth](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/x2wqd6xb912omvBa9qnMA3NdK3GLpFbB.png)
Answers
Answer:
θ = 28.07°
Step-by-step explanation:
opposite/hypotenuse =sinθ
sinθ = 8/17
θ = \(sin^{-1}\)(8/17) = 28.07°
Answer:
28.07°
Step-by-step explanation:
For Θ, 8 is the opposite leg.
17 is the hypotenuse.
sin Θ = opp/hyp
sin Θ = 8/17
Θ = sin^-1 8/17
Θ = 28.07°
2x+34=6-5x pls help show work I’ll mark as brainliest!!
Answers
Answer:
x = -4
Step-by-step explanation:
2x + 34 = 6 - 5x
Subtract 34 from both sides.
2x = -28 - 5x
Add 5x to both sides.
7x = -28
Divide both sides by 7.
x = -4
Proof:
2x + 34 = 6 - 5x
Substitute variable.
2(-4) + 34 = 6 - 5(-4)
Multiply.
-8 + 34 = 6 + 20
Add.
26 = 26
Answer:
x = -4
Step-by-step explanation:
2x+34=6-5x
+5x +34 = 6+5x
------------------------
7x +34 = 6
7x -34 = -34
-----------------
7x = -28
--- ------
7 7
x = -4
Find f (-8) when...
f(x) = x2 - 3
f(-8) =
Answers
Answer:
The answer is 61.
Step-by-step explanation:
You have to substitute x = -8 into the function :
\(f(x) = {x}^{2} - 3\)
\(let \: x = - 8\)
\(f( - 8) = {( - 8)}^{2} - 3\)
\(f( - 8) = 64 - 3\)
\(f( - 8) = 61\)
Can someone help me with this please!!
Answers
Answer:
What are we meant to do its sideways
Step-by-step explanation:
What temperature is 9 degrees less than 0 degrees Celsius?
Answers
Temperature less than 0° C is -9° C.
What is subtraction?To subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.
Given a temperature 9 less than 0,
0° C - 9 = -9° C
Hence, Temperature less than 0° C is -9° C.
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Emma wants to give someone 5.2m every day she can donate 10k how long will it take her to donate 5.2m?
Answers
Answer:
520 days
Step-by-step explanation:
--------------------------------------
5.2 million = 5,200,000
10 thousand = 10,000
5,200,000 ÷ 10,000 =
= 520 days
---------------
Hope this helps.
Answer:
520 days
Step-by-step explanation:
thanks for the pts
✌️❤️✌️
F(x,y) = x^2 + y^2 - 2x, D is the closed triangular region with vertices (0,0), (0,2), and (0,-2). Find the absolute maximum and minimum values of f on the set D. I know the maximum and minimum are f(0,+-2) = 4, minimum f(1,0) = -1. I need a step by step process on how to get to this answer
Answers
The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.
The given function is F(x,y) = \(x^{2}\) + \(y^{2}\) - \(2x\) → 1
D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).
Differentiate 1 partially with respect to x:
df/dx = \(x^{2}\) + \(y^{2}\) - \(2x\)
\(f^{'}\)(x) = 2x - 2
Differentiate 1 partially with respect to y:
df/dy = \(x^{2}\) + \(y^{2}\) - \(2x\)
\(f^{'}\)(y) = 2y
Consider \(f^{'}\)(x) = 0 and \(f^{'}\)(y) = 0 to find the critical points.
\(f^{'}\)(x) ⇒ 2x -2 =0
x = 1
\(f^{'}\)(y) ⇒ 2y
y = 0
Thus, the critical point is (x,y) = (1,0).
Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).
At (x,y) = (0,0)
f(0,0) ⇒ 0 + 0 - 0 = 0
At (x,y) = (0,2)
f(0,2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (0,-2)
f(0,-2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (1,0)
f(1,0) ⇒ 1 + 0 - 2 = -1
Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.
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What is the empirical formula of a compound that is 15.65% Carbon, 2.16% Hydrogen, 18.26% Nitrogen, and 63.10% Oxygen?
Answers
Answer:
\(\mathbf{ CH_2NO_3}\)
Step-by-step explanation:
Element %by \((C)\) \((H)\) \((N)\) \((O)\)
composition 15.56 2.16 18.26 63.16
mole ratio
\(\dfrac{\% \ by \ mass}{atomic \ number }\) \(\dfrac{15.56}{12}\) \(\dfrac{2.16}{1}\) \(\dfrac{18.26}{14}\) \(\dfrac{63.16}{16}\)
\(= 1.297\) \(2.16\) \(1.304\) \(3.948\)
Divide by the
smallest value \(= \dfrac{1.297}{1.297}\) \(= \dfrac{2.16 } {1.297}\) \(= \dfrac{1.304} {1.297}\) \(= \dfrac{3.948} {1.297}\)
ratio \(1\) : \(2\) : 1 : 3
The empirical formula is = \(\mathbf{ CH_2NO_3}\)
7p-5=6p+8 what is the answer to that
Answers
Answer:
p=13
Step-by-step explanation:
P=13
Explanation:
First you move one of the p to combine with the other p. I choose the 6p to be the moving. Since 6p is a positive number, you subtract it when you move it. 7p-6p= 1p
Next you move the constants which are -5 and 8. Since we already move the ps to the left side, we should move the constants to the right side. Since -5 is a negative number, we need to add it when we move it. 5 + 8 =13
So p equals to 13
can anyone help me on this?
Answers
Answer:
Step-by-step explanation:
(1,3)
Answer:
I think the slope is 3/1
Step-by-step explanation:
3 rise ,1 run
(1,3)