THIS IS THE COMPLETE QUESTION BELOW
The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.
Answer
$168.27
Step by step Explanation
Given p=90000/400+3x
With the limits of 40 to 50
Then we need the integral in the form below to find the average price
1/(g-d)∫ⁿₐf(x)dx
Where n= 40 and a= 50, then if we substitute p and the limits then we integrate
1/(50-40)∫⁵⁰₄₀(90000/400+3x)
1/10∫⁵⁰₄₀(90000/400+3x)
If we perform some factorization we have
90000/(10)(3)∫3dx/(400+3x)
3000[ln400+3x]₄₀⁵⁰
Then let substitute the upper and lower limits we have
3000[ln400+3(50)]-ln[400+3(40]
30000[ln550-ln520]
3000[6.3099×6.254]
3000[0.056]
=168.27
the average price p on the interval 40 ≤ x ≤ 50 is
=$168.27
Simplify -12w + 7w - 3 - 6
Answer: Hi!
We can simplify this by combining like terms:
-12w + 7w - 3 - 6
-12w + 7w = -5w
-3 - 6 = -9
Out equation now looks like this:
-5w - 9
There's nothing left to simplify, so we're done!
Hope this helps!
What is the answer, what are the steps to solve this, and what do the parts of the equation represent?
Answer:
[tex]\sum_{a=1}^{7}(500-a)=3472[/tex]
Step-by-step explanation:
[tex]\sum_{a=1}^{7}(500-a)[/tex] will form a sequence as,
499, 498, 497.......7 terms
Since there is a common difference between successive and previous term,
d = 498 - 499 = -1
This sequence is an arithmetic sequence.
Sum of n terms of an arithmetic sequence is,
[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]
where a = first term of the sequence
n = number of term
d = common difference
For the given given sequence,
[tex]S_{7}=\frac{7}{2}[2(499)+(7-1)(-1)][/tex]
= [tex]\frac{7}{2}[998-6][/tex]
= [tex]\frac{7}{2}(992)[/tex]
= 3472
Therefore, sum of seven terms of the given sequence will be 3472.
3.24 (4 being repeated) to a fraction
Answer:
146/45
Step-by-step explanation:
Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.
[tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]
__
Comment on procedure
The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.
Which parent functions have an intercept at (0,0)Choose all that are correct.
Linear
Quadratic
Radical
Absolute Value
Rational
Exponential
Logarithmic (Log)
Cubic
Cube Root
Answer:
Linear, Quadratic, Radical, Absolute Value, Cubic, Cube Root
Step-by-step explanation:
To find:
Which functions have an intercept at (0, 0).
That means, when we put a value [tex]x=0[/tex] in the [tex]y =f(x)[/tex], value of [tex]y=0[/tex].
Let us discuss each parent function one by one:
1. Linear:
[tex]y = x[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
2. Quadratic:
[tex]y = x^2[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
3. Radical:
[tex]y = \sqrt x[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
4. Absolute Value:
[tex]y = |x|[/tex]
When we put x = 0, y = 0
Therefore, it has intercept at (0, 0).
5. Rational:
[tex]y = \dfrac{1}{x}[/tex]
When we put [tex]x = 0\Rightarrow y \rightarrow \infty[/tex]
Therefore, it does not have intercept at (0, 0).
6. Exponential:
[tex]y = b^x[/tex]
b is any base
When we put [tex]x = 0\Rightarrow y =1[/tex]
Therefore, it does not have intercept at (0, 0).
7. Logarithmic:
[tex]y = logx[/tex]
When we put [tex]x = 0 \Rightarrow y\rightarrow[/tex] Not defined
Therefore, it does not have intercept at (0, 0).
8. Cubic:
[tex]y = x^3[/tex]
When we put [tex]x = 0\Rightarrow y =0[/tex]
Therefore, it has intercept at (0, 0).
9. Cube Root:
[tex]y = \sqrt[3]x[/tex]
When we put [tex]x = 0\Rightarrow y =0[/tex]
Therefore, it has intercept at (0, 0).
What is the approximate diameter of a sphere whose surface area is 83.96 square inches? Use π = 3.14.
Answer:
5.17
Step-by-step explanation:
The surface area of a sphere is 4[tex]\pi[/tex]r².
83.96=4[tex]\pi[/tex]r²
Divide by 4
20.99=3.14r²
divide by 3.14
6.6847=r²
take the square root
2.585=r
mulitply by 2 (diameter is twice the radius)
5.17
The diameter of the sphere is 5.17 inches.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any object is called as the surface area.
The surface area of a sphere is 4πr².
83.96=4πr²
Divide by 4
20.99=3.14r²
Divide by 3.14
6.6847=r²
Take the square root.
2.585=r
Multiply by 2 (diameter is twice the radius).
r= 2 x 2.585
r = 5.17 inches
Therefore, the diameter of the sphere is 5.17 inches.
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Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?
Answer:
135.06 feet
Step-by-step explanation:
Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.
opposite side = x
adjacent side = 150 feet
angle = 42°
tan(42°) = x/150 feet
150 feet * tan(42°) = x
x = 135.06 feet
Stock prices used to be quoted using eighths of a dollar. Find the total price of the transaction. 400 shares of national semi at 135 1/2
Answer:
The value is [tex]T = \$54200[/tex]
Step-by-step explanation:
From the question we are told that
The number of shares is n = 400
The rate of each share is [tex]k = 135\frac{1}{2} = 135.5[/tex]
Generally the total price is mathematically represented as
[tex]T = 400 * 135.5[/tex]
[tex]T = \$54200[/tex]
rate = 45 mph time=4 hours distance =
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▹ Answer
180 miles
▹ Step-by-Step Explanation
Distance = mph * hours
Distance = 45 mph * 4 hrs
Distance = 180 miles
Hope this helps!
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Classify the expression: 5x + 3x^2 − 7x^3 + 2
A. Linear Expression
B. Quadratic Expression C. Cubic Expression
D. Quartic Expression
Answer:
C. Cubic expression.
Step-by-step explanation:
The highest exponent is 3 ( in the term 7x^3) so it is cubic.
Answer:
C. Cubic Expression.
Step-by-step explanation:
5x + 3x^2 - 7x^3 + 2
= 3x^2 - 7x^3 + 5x + 2
= -7x^3 + 3x^2 + 5x + 2
The highest value of exponent in the equation is 3.
For a linear expression, the highest exponent is 1.
For a quadratic expression, the highest exponent is 2.
For a cubic expression, the highest exponent is 3.
For a quartic expression, the highest exponent is 4.
So, this is C. Cubic Expression.
Hope this helps!
WILLL GIVE 5 STARS BRAINIEST AND THANKS AND 20 POINTS EACH ANSWER In Minot, North Dakota, the temperature was 15 degrees Fahrenheit at 4:00 P.M. By 11:00 P.M. the temperature had fallen 17 degrees. What was the temperature at 11:00 P.M.?
Answer:
-2 degrees
Step-by-step explanation:
Our original temperature is 15. We're asked to find the temperature at 11:00 P.M., which is 17 less than 15. We can set up the equation 15 - 17 to get -2. This is your answer.
Answer:
The temperature was -2 degrees Fahrenheit
Step-by-step explanation:
The starting temperature was 15 degrees
It fell 17 degrees
15 -17 = -2
The temperature was -2 degrees Fahrenheit
Which statements about the sum of the interior angle measures of a triangle in Euclidean and non-Euclidean geometries are true? A. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees. B. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees. C. In Euclidian geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees. D. In Euclidian geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees. E. In Euclidian geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
Answer:
its b and e
Step-by-step explanation:
The statements given in options B and E are true so options B and E are right options.
Given some statements we have to determine that which of the following statements are true
The given statements are as follows
A. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is less than 180 degrees.
B. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in elliptical or spherical geometry the sum is greater than 180 degrees.
C. In Euclidean geometry the sum of the interior angle measures of a triangle is less than 180 degrees, but in hyperbolic geometry the sum is equal to 180 degrees.
D. In Euclidean geometry the sum of the interior angle measures of a triangle is greater than 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
E. In Euclidean geometry the sum of the interior angle measures of a triangle is 180 degrees, but in hyperbolic geometry the sum is less than 180 degrees.
We know some facts about each type of geometry
In Euclidean geometry plane is used to plot the points and line.
In spherical geometry uses the sphere to plot the points and circles
Elliptical geometry is such a geometry where no parallel lines exists.
The sum of interior angles of a triangle is dependent on the type of geometry we are dealing with and they can be written down in the following points
In Euclidean geometry the sum of interior angles of a triangle is 180° In spherical or elliptical geometry the sum of interior angles of a triangle is more than 180° In hyperbolic geometry the sum of interior angles of a triangle is less than 180°So from the above observations we can conclude that statements given in options B and E are true so options B and E are right options.
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Two trains are moving towards each other on the same railroad track. From this track there's an offshoot piece of railroad − the length of which is shorter than the length of the train but longer than the length of one train car. How can the trains pass each other?
Answer:
one car at a time
Step-by-step explanation:
For each car in the shorter train* (A) ...
train A leaves one of its cars on the offshootboth trains move until train B can move the car from the offshoot to the portion of track away from train Atrain B moves to allow the cycle to repeatWhen there are no more train A cars in front of train B, both trains can continue on their journey.
We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.
_____
* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.
Solve the following equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week: x = 0.7x + 24 How many total items were stocked for that week? 14 56 80 10
Answer:
80
Step-by-step explanation:
The total of 80 items were stocked for that week.
What is a system of equations?
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Solve equation for x to find the total number of sale items stocked on the shelves of a toy store for a certain week:
x = 0.7x + 24
We need to find How many total items were stocked for that week
Solving;
x = 0.7x + 24
x - 0.7x = 24
0.3x = 24
x = 80
Therefore, the total of 80 items were stocked for that week.
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According to the U.S. Energy Information Administration the average number of televisions per household in the United States was 2.3. A college student claims the average number of TV’s per household in the United States is different. He obtains a random sample of 73 households and finds the mean number of TV’s to be 2.1 with a standard deviation of 0.84. Test the student’s claim at the 0.01 significance level.
Let [tex]\mu[/tex] be the average number of televisions per household in the United States .
As per given ,
[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]
Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.
For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]
T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]
Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]
This means we cannot reject null hypothesis.
We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.
A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆ y = 3 − 5 x y^=3-5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way:
1.) When amount of schooling increases by one year, the number of pregnancies decreases by 4.
2.) When amount of schooling increases by one year, the number of pregnancies increases by 4.
3.) When amount of schooling increases by one year, the number of pregnancies increases by 5.
4.) When amount of schooling increases by one year, the number of pregnancies decreases by 5.
Answer:
1. When amount of schooling increases by one year, the number of pregnancies will decrease by 4.
Step-by-step explanation:
Regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, there is regression equation given. X and Y are considered as dependent variables. When number of schooling increases by 1 year then number of pregnancies will decrease by 4
Simplify to create an equivalent expression.
\qquad{7n-(4n-3)}7n−(4n−3)
Answer:
[tex]3n + 3[/tex]
[tex]3(n+1)[/tex]
Step-by-step explanation:
Given
[tex]7n - (4n - 3)[/tex]
Required
Simplify
To simplify the given expression, you start by opening the bracket
[tex]7n - (4n - 3)[/tex]
[tex]7n - 4n + 3[/tex]
Next, you perform arithmetic operations on like terms
[tex]3n + 3[/tex]
The answer can be further simplified;
Factorize [tex]3n + 3[/tex]
[tex]3(n+1)[/tex]
Hence;
[tex]7n - (4n - 3)[/tex] when simplified is equivalent to [tex]3n + 3[/tex] or [tex]3(n+1)[/tex]
Answer:
3n+n
Step-by-step explanation:
Help please!!! Thank you
Answer:
Option (G)
Step-by-step explanation:
Let the length of the race = a miles
Since, Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
Time taken to cover 'a' miles with the speed = 12 mph,
Time taken '[tex]t_1[/tex]' = [tex]\frac{a}{12}[/tex]
Time taken to cover 'a' miles with the speed = 11 mph,
Time taken '[tex]t_2[/tex]' = [tex]\frac{a}{11}[/tex]
Since the time taken by David to cover 'a' miles was 10 minutes Or [tex]\frac{1}{6}[/tex] hours more than the time he expected.
So, [tex]t_2=t_1+\frac{1}{6}[/tex]
[tex]\frac{a}{11}=\frac{a}{12}+\frac{1}{6}[/tex]
[tex]\frac{a}{11}-\frac{a}{12}=\frac{1}{6}[/tex]
[tex]\frac{12a-11a}{132}=\frac{1}{6}[/tex]
a = 22 mi
Therefore, distance of the race = 22 mi
Option (G) is the correct option.
Write an equation for a line perpendicular to y = − 5 x + 5 and passing through the point (5,5)
Answer:
The answer is
[tex]y = \frac{1}{5} x + 4[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the line perpendicular to
y = -5x + 5 we must first find the slope of
Comparing with the general equation above
Slope = - 5
The slope of the perpendicular line is the negative inverse of the slope of the original line
Slope of perpendicular line = 1/5
Equation of the line using point (5,5) and slope 1/5 is
[tex]y - 5 = \frac{1}{5} (x - 5)[/tex][tex]y - 5 = \frac{1}{5} x - 1[/tex][tex]y = \frac{1}{5} x - 1 + 5[/tex]We have the final answer as
[tex]y = \frac{1}{5} x + 4[/tex]Hope this helps you
Answer:
y=0.2x+4 or y=1/5 x+4.
Step-by-step explanation:
When one line is perpendicular to another, you have to find the opposite reciprocal for the slope of the given equation.
For instance, if you have the number 5, the reciprocal of 5 is 1/5 or 0.2. The opposite of positive is negative. Therefore, it is -0.2.
Therefore, if the slope of the first equation is -5, the slope for the next equation is 1/5. Reciprocal of -5 is -1/5. The opposite of -1/5 is positive 1/5. Or, the opposite of negative is positive. Therefore, it would be 1/5x.
However, we are not done.
Since we are given that the line passes through the point (5,5), we need to find the y-intercept of this equation.
The formula for slope-intercept is y=mx+b.
M is your slope
B is your y-intercept.
We can find the y-intercept by actually plugging in the point (5,5) into the new equation.
5=0.2(5)+b.
5 is x and 5 is also y.
(x,y).
Simplify the equation by multiplying 0.2 times 5. That is equal to 1.
We now have 5=1+b.
Isolate for the letter "b" by subtracting 1 from both sides.
1-1 is 0.
5-1 is 4.
Therefore, b=4.
Finally, we can plug in the y-intercept into the new equation.
y=0.2 or 1/5x+4.
I hope this helps! I also hope you have a great rest of your day!
Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression below.
Answer:
The resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].
Step-by-step explanation:
The distributive property of multiplication is:
[tex]a\times (b+c)=(a\times b)+(a\times c)[/tex]
The two polynomials provided are:
[tex](2x+3)\\(x^{2}+x-2)[/tex]
Determine the final expression by multiplying the two polynomials as follows:
[tex](2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)][/tex]
[tex]=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6[/tex]
Thus, the resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].
Please tell me the answer ASAP Lynette's average score on five tests is 18. If she scores 24 points on her sixth test, what is her average score on all six tests? Show Your Work
Answer:
The average score of 6 tests is 19.
Step-by-step explanation:
Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :
[tex]let \: x = total \: no. \: of \: scores[/tex]
[tex] \frac{x}{5} = 18[/tex]
[tex]x = 18 \times 5[/tex]
[tex]x = 90[/tex]
We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :
[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]
Given:Average score in 5 tests = 18He scored 24 points in 6th pointTo FinD:Find the average score in all six tests?How to find?We need to know how to find the average
☄ For this case, We are gonna find average score...!
[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]
So, Let's proceed further towards solution....
Solution:We have,
Avg. score = 18No. of tests = 5Finding total score in 5 tests,
⇛ Total score = Avg. score × No. of tests
⇛ Total score = 18 × 5
⇛ Total score = 90
According to question,
He scored 24 marks in 6th test⇛ Total score now = 90 + 24 = 114
No. of tests = 6Finding the average score of 6 tests,
⇛ Avg. score = 114 / 6
⇛ Avg. score = 19 points
☄ Avg. score of lynette in 6 tests = 19
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What is numbers 1-30 added all together
Answer:
465
Step-by-step explanation:
The sum of consecutive numbers has a formula, and it's
[tex]\frac{n(n+1)}{2}[/tex].
Where n is the amount of numbers.
From 1-30, it's 30 numbers, so:
[tex]\frac{30(30+1)}{2} \\\\\frac{30(31)}{2} \\\\\frac{930)}{2} \\\\\\465[/tex]
Hope this helped!
Someone help me understand
Answer:
f¯¹(x) = 23/ (6x + 3)
Step-by-step explanation:
f(x) = (23 – 3x)/6x
The inverse, f¯¹, for the above function can be obtained as follow:
f(x) = (23 – 3x)/6x
Let y be equal to f(x)
Therefore, f(x) = (23 – 3x)/6x will be written as:
y = (23 – 3x)/6x
Next, interchange x and y.
This is illustrated below:
y = (23 – 3x)/6x
x = (23 – 3y)/6y
Next, make y the subject of the above expression. This is illustrated below:
x = (23 – 3y)/6y
Cross multiply
6xy = 23 – 3y
Collect like terms
6xy + 3y = 23
Factorise
y(6x + 3) = 23
Divide both side by (6x + 3)
y = 23/ (6x + 3)
Finally, replace y with f¯¹(x)
y = 23/ (6x + 3)
f¯¹(x) = 23/ (6x + 3)
Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is
f¯¹(x) = 23/ (6x + 3)
PLEASE HELP !! (4/5) -50 POINTS-
Answer:
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Step-by-step explanation:
An augmented matrix is the coefficients of the variables and then the solution in rows
Rewriting the equations
2x -7y +6x = 7
x +3y -4z = 5
x +6y -15z = -6
The matrix is
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Claire has to go to the movie theater the movie starts at 4:15 pm it is a 25min walk to the theater from her home what time dose the have to leave the house to get there on time
Answer:
3:50 pm
Step-by-step explanation:
Count backwards with the 25 min.
4:15 - 15 min >
25 - 15 = 10 >
4:00 - 10 = 3:50
Answer:
3:50 pm
Step-by-step explanation:
Starting Time + Time Interval = Ending Time
=> Ending Time - Time Interval = Starting Time
Ending Time = 4:15 pm
Time Interval = 25 minutes
Starting Time = x
=> 4:15 - 25 = x
=> 4:15 - 15 - 10 = x
=> (4:15 - 15) - 10 = x
=> 4:00 - 10 = x
=> 3:50 pm = x
So, she needs to leave the house at 3:50 pm to get to the movie theater on time.
rational number between 2 and 3 ?
Answer:
2:3
Step-by-step explanation:
It’s easy
Answer:
2.5
Step-by-step explanation:
i think
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t
The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.
Answer:
s = 17 units
Step-by-step explanation:
Given f(t) = t³ - 8t² + 27t
Differentiating f(t), we have
f'(t) = 3t² - 16 t + 27
At t = 0
f'(t) = 27
This is the required obtainaible distance, s.
Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity
We have
[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]
(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)
Recall for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]
Describe all numbers x that are at a distance of 2 from the number 8. Express this using absolute value notation.
Answer:
The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:
|x - 8| = 2
Step-by-step explanation:
The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:
|x - 8| = 2
The equation is written in the notation of absolute value as required.
Write as an equation: The sum of a number and 12 is 78.
Answer:
x+12=78
Step-by-step explanation:
like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.
Answer:
n + 12 = 78
Step-by-step explanation:
Let n = number.
n + 12 = 78
Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have? Assume that the planes cutting the prism do not intersect anywhere in or on the prism. EXPLAIN PLS
Answer:
36
Step-by-step explanation:
Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.
The new figure has 12+24 = 36 edges.
