The derivative of the natural log function y = e^(-1/x^2) is
2x^(-3)e^(-1/x^2)How to solve for the derivativeThe given function is
y = e^(-1/x^2)
The given function is rearranged as
y = e^(-1/x^2) = e^u such that u = (-1/x^2)
Applying chain rule
y = e^u
y' with respect to u = e^u
u = (-1/x^2) = -x^(-2)
u' with respect to x = 2x^(-3)
(y' with respect to u) * (u' with respect to x)
= e^u * 2x^(-3)
plugging in the value of u
= e^(-1/x^2) * 2x^(-3)
= 2x^(-3)e^(-1/x^2)
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One number exceeds another by 7. The sum of the numbers is 27. What are the numbers?
The numbers are
(Use a comma to separate answers.)
K
Answer:
10, 17
Step-by-step explanation:
let the number be n then the other number is n + 7 and
n + n + 7 = 27
2n + 7 = 27 ( subtract 7 from both sides )
2n = 20 ( divide both sides by 2 )
n = 10
n + 7 = 10 + 7 = 17
the numbers are 10, 17
When we add any two multiples of 5 and 10 we sometimes,always or never get a number ending in 2.
Sometimes
Never
Always
Answer:
Never
Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45
Answer:
Step-by-step explanation:
never
what is the momentum of an automobile with a mass of 1200 kilograms moving at 6 meters per second
The momentum of the automobile is 7200 kgm/s
What is momentum?
Momentum can be described as the product of the velocity and mass of an object.
It is a vector quantity which is defined as a quantity having both magnitude and direction.
The formula for calculating momentum is expressed as;
p = mv
Where;
p is the momentum of the objectm is the mass of the objectv is the velocity of the objectNow, let's substitute the values
p = 1200(6)
expand the bracket
p = 1200 × 6
Multiply the values
p = 7200 kgm/s
Hence, the value is 7200 kgm/s
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Given that 150 students were interviewed, 85 signed for mathematics, 70 signed for English, and 50 signed for both. Draw a venn diagram to show.
How many signed for only mathematics
Answer: 35
Step-by-step explanation:
If 85 students signed up for mathematics but 50 of those students also signed up for both then you need to subtract 85 from 50 to get 35.
dont know how to do this either if u could feel free to help me
The graph that beast describes the slope of -2/3 passing through points (-1, 0) is in option c
How to determine the graph that matches the slope and the pointsInformation given in the question include
a linear function graph
The data is plotted as a linear function
What is linear function ?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m = -2/3
negative slopes slants from top left to bottom right as in a and c
from the graph, option c has points (-1, 0) and (0, -2/3)
m = (-2/3 - 0) / (0 - -1)
m = (-2/3) / (0 + 1)
m = -2/3
This matches with option C
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A company's policy is to spend no more than $350,000 a year for salaries. The president's salary is $110,000. The salaries of the eight other employees are equal. How much can be spent on each salary?
To go to the theater you would pay $8.00 for each ticket you purchase. Which answer choice correctly represents the algebraic expression for the cost of t tickets?
A. 8t
B. 8 + t
C. 8 – t
D.
The algebraic expression that correctly represents the cost of t tickets is 8t , the correct option is (a) .
In the question ,
it is given that
the cost of 1 ticket for the theater is = $8.00
let the number of ticket be = t
so , the cost for t tickets = (cost of 1 ticket ) × ( number of tickets )
Substituting the values of number of tickets and cost of 1 ticket ,
we get ,
cost for t tickets = 8 × t
= 8t
Therefore , The algebraic expression that correctly represents the cost of t tickets is 8t .
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Question 1 (Multiple Choice Worth 5 points) (Graphing Proportional Relationships MC) The table shows a proportional relationship between x and y. x 4.3 9.2 3.4 y 17.2 36.8 13.6 Which of the following correctly describes the graph of the relationship? a.A line that goes through (0, 0) and (17.2, 4.3). b.A line that goes through (4.3, 17.2) and (36.8, 9.2). c.A line that goes through (17.2, 4.3) and (9.2, 36.8). d.A line that goes through (0, 0) and (4.3, 17.2).
The statement that correctly describes the graph of the relationship is (d) A line that goes through (0, 0) and (4.3, 17.2).
How to describe the graph?The table of values is given as
x 4.3 9.2 3.4
y 17.2 36.8 13.6
The table shows a proportional relationship
This means that the line of the graph must pass through the origin i.e. (0, 0)
From the table of values, we have the following point
(4.3, 17.2)
This means that the line of the graph goes through (0, 0) and (4.3, 17.2).
Hence, the true statement is (d)
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Answer:
No, it is not proportional because 9.2 over 18.4 does not equal 17.6 over 52.8.
Step-by-step explanation:
The data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975. Judge whether a t-interval could be constructed using the data in the sample.
It could be said that the normal probability plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
If the data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975., on analysing
The normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
Therefore, It could be said that the normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.
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HELP, ASAP PLEASE. 15 POINTS! ( Only 1 picture is attached)
The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million
How to find the input values of functions?
We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;
A(h) = -0.06h² + 2h + 4
where h is the time in number of hours after which the concentration is recorded.
Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;
A(4) = -0.06(4²) + 2(4) + 4
A(4) = -0.96 + 12
A(4) = 11.04 parts per million
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Mike has some t-shirts. 1/4 of the
t-shirts are pink, 1/2 of the
remaining tshirts are white and the rest are
purple. What fraction is purple?
Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8
Mike has some t-shirts
The fraction of pink t-shirts = 1/4
The remaining t-shirts = 1 - (1/4)
= 3/4
1/2 of the remaining t-shirts are white
Then the fraction of white t-shirt = 3/4 × 1/2
= 3/8
The fraction of purple t-shirt = 1 - (1/4 + 3/8)
= 3/8
Hence, Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8
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Do you think the blue dot represents the y-intercept of this line? Why or why not?
Answer:
No, the point is on the x-axis, it is not a y-intercept.
parallel lines, traversal, and algebra
need help!
The values of the variables, x and y in the angles formed by the parallel lines that have a common transversal are;
x = 4°, y = 10°
11. x = 9°, y = 12°
12. x = 14°, y = 5°
13. x = 8°, y = 11°
14. x = 16°, y = 23°
15. x = 9°, y = 13°
What are parallel lines?Parallel lines are lines that maintain the same distance from each other along their lengths.
From the figure, we get;
(29·x - 3) and (15·x + 7) are linear pair angles, therefore;
(29·x - 3) + (15·x + 7) = 180°
44·x + 4 = 180
x = (180 - 4)/44 = 4
x = 4°
(15·x + 7) and (13·y - 17) are same side exterior angles between parallel lines, therefore;
(15·x + 7) + (13·y - 17) = 180°
(15×4 + 7) + (13·y - 17) = 180°
67 + 13·y - 17 = 180°
50 + 13·y = 180
13·y = 180 - 50 = 130
y = 130 ÷ 13 = 10
y = 10°
11. (18·x - 44)° and (8·x - 10)° are same side exterior angles, therefore;
(18·x - 44)° + (8·x - 10)° = 180°
26·x - 54 = 180
x = (180 + 54)/26 = 9
x = 9°
(8·x - 10)° and (13·y - 38)° are linear pair angles, therefore;
(8·x - 10)° + (13·y - 38)° = 180°
(8 × 9 - 10)° + (13·y - 38)° = 180°
62 - 38 + 13·y = 180
13·y = 180 - (62 - 38) = 156
y = 156 ÷ 13 = 12
y = 12°
12. (9·x - 2)° and (5·x + 54)° are corresponding angles, therefore;
(9·x - 2)° = (5·x + 54)°
(9·x - 2)° = (5·x + 54)°
9·x - 5·x = 54 + 2 = 56°
4·x = 56°
x = 56° ÷ 4 = 14°
x = 14°
(9·x - 2)° and (10·y + 6)° are linear pair angles, therefore;
(9·x - 2)° + (10·y + 6)° = 180°
(9 × 14 - 2)° + (10·y + 6)° = 180°
124 + 6 + 10·y = 180
10·y = 180 - 130 = 50
y = 50 ÷ 10 = 5
y = 5°
13. The angle to which the angle (8·x - 1)° is an alternate interior angle is a corresponding angle to the angle (11·x - 25)°, therefore;
(8·x - 1)° is congruent to angle (11·x - 25)°
(8·x - 1)° = (11·x - 25)°
11·x - 8·x = 25 - 1 = 24
3·x = 24
x = 24 ÷ 4 = 8
x = 8°
Angles (15·y - 48)° and (8·x - 1)° are linear pair angles, therefore;
(15·y - 48)° + (8·x - 1)° = 180°
(15·y - 48)° + (8 × 8 - 1)° = 180°
(15·y - 48)° + 63° = 180°
15·y + 15° = 180°
15·y = 180° - 15° = 165°
y = 165° ÷ 15 = 11°
y = 11°
14· The angle (4·x + 4)° and (7·x - 44)° are alternate exterior angles, therefore;
(4·x + 4)° = (7·x - 44)°
7·x - 4·x = 44° + 4° = 48°
3·x = 48°
x = 48° ÷ 3 = 16°
x = 16°
The vertical angle to angle 39° is a linear pair angle to the angle (8·y - 43)°
Therefore;
39 + 8·y - 43 = 180°
8·y = 180 + 43 - 39 = 184
y = 184 ÷ 8 = 23
y = 23°
15. The diagram indicates that the angles (15·x - 26)° and (12·x + 1)° are congruent, therefore;
(15·x - 26) = (12·x + 1)
(15·x - 12·x) = (26 + 1)
3·x = 27
x = 27 ÷ 3 = 9
x = 9°
The vertical angle to (2·x + 1) is therefore;
12·x + 1 = 12 × 9 + 1 = 109
The angle sum property indicates that we have;
28° + 109° + (4·y - 9)° = 180°
(4·y - 9)° = 180° - (28° + 109°) = 43°
(4·y - 9)° = 43°
(4·y)° = 43° + 9° = 52°
y = 52°/4 = 13°
y = 13°
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7v-7-4v-10=v+7-4v help now pleas
Answer:
v = 4
Step-by-step explanation:
[tex]collect \: like \: terms \: \\ 7v - 4v - v + 4v = 7 + 7 + 10\\ 3v - v + 4v = 14 + 10\\ \\ 2v + 4v = 24 \\ 6v = 24 \\ v = 4[/tex]
Find all zeros of f(x) = x³ - 4x² - 5x + 14. Enter the zeros separated by commas. Enter exact values,
using radicals and/or fractions if necessary, not decimal approximations.
Question Help: Message instructor
Check Answer
Jump to Answer
Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
f(x) = x³ - 4x² - 5x + 14
-2 | 1 -4 -5 14
-2 12 -14
1 -6 7 0
x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)
x²-6x+7=0
x²-6x+9-2=0
(x²-6x+9)-2=0
x²-6x+9=2
x²-3x-3x+9=2
x(x-3)-3(x-3)=2
(x-3)²=2
x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]
x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
our first "suspicion" for a factoring is an integer factor of the constant term : 14.
14 = 2 × 7 or -2 × -7
I started to try 2 or -2 and found that -2 is indeed a zero solution.
so, the first factors are
f(x) = (x + 2)(x² + ...)
let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.
x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7
- x³ + 2x²
--------------
0 -6x² - 5x
- -6x² - 12x
----------------
0 7x + 14
- 7x + 14
------------
0 0
f(x) = (x + 2)(x² - 6x + 7)
the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation
ax² + bx + c = 0
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =
= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =
= 3 ± sqrt(8/4) = 3 ± sqrt(2)
x1 = 3 + sqrt(2)
x2 = 3 - sqrt(2)
so, the zeros are
-2, 3 - sqrt(2), 3 + sqrt(2)
a) Find the circumference of a circle whose radius is 4 inches. Round to the nearest tenth.
b) Find the length of if mACB = 60º and the radius of the circle is 4 inches. Round to the nearest tenth.
Complete your work in the space provided.
The circumference of the circle is 25.1 inches.
The length of the arc ACB is 4.2 inches.
How to find circumference of a circle?The circumference of a circle is the perimeter of the circle.
Therefore,
circumference of a circle = 2πr
where
r = radiusHence,
circumference of a circle = 2 × 3.14 × 4
circumference of a circle = 8 × 3.14
circumference of a circle = 25.1 inches
The length of the arc ACB can be found as follows:
length of arc = ∅/ 360 × 2πr
length of the arc = 60 / 360 × 2 × 3.14 × 4
length of the arc = 60 / 360 × 25.12
length of the arc = 1507.2 / 360
length of the arc = 4.18666666667
length of the arc = 4.2 inches
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Luis bought a $2,100 TV and had to make a 20% down payment at the time of purchase. What was his down payment price?
Answer:
Luis had to make a $420 down payment
Step-by-step explanation:
10%: $2,100 / 10 = $210
20%: $210 x 2 = $420
The diagram shows a triangle. Complete parts a and b below. (4 points)
53⁰
8p+10°
2p+17°
A- write an equation and solve for p. Show all work.
B-List the measures of the three angles.
The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.
Given that,
In the picture there is a triangle with angles 53°, 8p+10°, 2p+17°.
We have to find the p value and each of the angles also.
What is angles in triangles?While the exterior angles of a triangle are equal to the sum of the two interior angles that are not adjacent to it, the interior angles of a triangle always add up to 180°. By deducting the angle of the target vertex from 180°, one can also determine a triangle's exterior angle.
Take the angles ,
180 degrees is the sum of the angles in an triangle.
53°+ 8p+10°+ 2p+17°=180°
10p+80°=180°
10p=180°-80°
10p=100°
p=100/10
p=10°
The value of p=10.
The angles of the triangles are:
53°
8p+10=8(10)+10=80+10=90°
2p+17=2(10)+17=20+17=37°
Therefore, The value of p is 10 and the angles of the triangles are 53°, 90°, 37°.
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Consider a particle moving along the x-axis where
x(t)
is the position of the particle at time t,
x ′(t)
is its velocity, and
x ″(t)
is its acceleration
Regarding the velocity and acceleration functions, it is found that:
b) The particle is moving to right on these following intervals: (0,1) U (3,10).
c) The velocity when the acceleration is of zero is: -1 m/s.
When a particle is moving to right?A particle is moving to right when it's velocity is positive.
In this problem, the velocity function is presented as follows:
v(t) = 3t² - 12t + 9.
The velocity function is a concave up quadratic function, which is positive to left of the smaller root and to the right of the larger root.
The roots of the function are given as follows:
v(t) = 3(t² - 4t + 3)
Then:
3(t² - 4t + 3) = 0
t² - 4t + 3 = 0
(t - 1)(t - 3) = 0.
t - 1 = 0 -> t = 1.t - 3 = 0 -> t = 3.Considering the domain of the function, the intervals in which the car is moving right are:
(0,1) U (3,10).
What is the velocity when the acceleration is of zero?The acceleration is given by the following equation:
a(t) = 6t - 12.
It is of zero when:
6t - 12 = 0
6t = 12
t = 12/6
t = 2.
The velocity at this instant is of:
v(2) = 2² - 4(2) + 3 = -1 m/s.
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A rectangular fish tank has a base that is 4 inches by 9 inches. How much water will it take to fill the tank to a depth of 3 inches? A 150 cubic inches B 685 cubic inches C 108 cubic inches 16 cubic inches
Answer:
C: 108 cubic inches
Step-by-step explanation:
This problem is simply asking us to calculate volume, and in a rectangular shape can be calculate as: length * width * height
Since we know that the base is 4 inches by 9 inches, we already have the length and width.
We're also given that the depth, which in this case is our height, as 3 inches.
So we multiply these three numbers: [tex]4 \text{ in} * 9 \text{ in} * 3\text{ in} = 108\text{ in}^3[/tex]
So our answer is 108 cubic inches
Scott must choose a number between 55 and 101 that is a multiple of 2,4, and 5. Write all the numbers that he could choose.
Answer:
60, 80, 100
Step-by-step explanation:
All 3 of these numbers are between 55 and 101, and can be divided by all 3 numbers provided.
10 = 6/5 W
Solve the missing variable, W
[tex]\framebox{w=$\dfrac{25}{3}$}[/tex]
Flip the equation:
[tex]\frac{6}{5} w=10[/tex]
Multiply both sides by [tex]\frac{5}{6}[/tex]:
[tex](\frac{5}{6} )\times(\frac{6}{5} w)=(\frac{5}{6} )\times(10)[/tex]
[tex]w=\frac{25}{3}[/tex]
Graph the solution of this inequality: 2x - 7 > 3 or 4 -x < -4
The solution for the given inequality has been graphed in detail.
What is linear inequality?A linear inequality can be gives the values for a variable in an interval of numbers.
Given inequalities are as below,
2x - 7 > 3 and 4 - x < -4
They can be simplified as,
2x - 7 > 3
=> 2x > 10
=> x > 5
And,
4 - x < -4
=> x - 4 > 4
=> x > 8
The solution of the given inequality is the intersection of two solutions x > 5 and x > 8, which is x > 8.
This is graphed as follows,
Hence, the given inequality has solution x > 8 which has been graphed.
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Helppp meee !!
It’s due today !!
Answer:
-8
Step-by-step explanation:
i think
Answer:
Your answer is -8
Step-by-step explanation:
Please helppppppppppp
Answer:
1
2
[
x
2
2
−
x
3
3
]
2
0
=
1
2
[
(
4
2
−
8
3
)
−
(
0
)
]
=
1
2
(
−
2
3
)
=
−
1
3
Step-by-step explanation:
Question Solve the equation. −2 1/4=r−4/5 r=
Answer:
[tex]r=\frac{21}{20}[/tex]
Step-by-step explanation:
Given the following question:
[tex]\frac{1}{4} =r-\frac{4}{5}[/tex]
Add 4/5s on both sides:
[tex]-\frac{4}{5} +\frac{4}{5} =0[/tex]
[tex]\frac{1}{4} +\frac{4}{5}[/tex]
Find the LCM:
[tex]\frac{5}{20}+\frac{16}{20}[/tex]
[tex]\frac{5+16}{20}[/tex]
[tex]\frac{21}{20}[/tex]
[tex]r=\frac{21}{20}[/tex]
Hope this helps.
let's firstly convert the mixed fraction to improper fraction, now keeping in mind that the LCD of the denominators 4 and 5 is 20, let's use that LCD to do away with the denominators.
[tex]\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{9}{4}=r-\cfrac{4}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( -\cfrac{9}{4} \right)=20\left( r-\cfrac{4}{5} \right)}\implies -45=20r-16 \\\\\\ -29=20r\implies -\cfrac{29}{20}=r\implies -1\frac{9}{20}=r[/tex]
If 8 g of a radioactive substance are present initially and 3 yr later only 4 g remain, how much of the substance will be present after 7 yrs?
Anyone can help on this one ?
Answer:
model a is more benfit the other one b/c of by hard working effort from b
Juan is playing a game in which he can win $100 with probability 0.2, $300 with probability 0.3, and $500 with probability 0.5. What is the expected value of Juan's winnings?
Juan's winnings has an expected value of $360
How to determine the expected value of Juan's winnings?The given parameters in the question are:
$100 with probability 0.2,
$300 with probability 0.3,
$500 with probability 0.5.
The expected value is then calculated as
E(x) = Sum of (amount * probability)
Substitute the known values in the above equation, so, we have the following representation
E(x) = 100 * 0.2 + 300 * 0.3 + 500 * 0.5
Evaluate
E(x) = 360
Hence, the expected value is $360
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What is the value of X? x(x² - 3x - 40) = 0
please show me how u solve it
Answer: x = 0, 8, -5
Step-by-step explanation:
We are trying to solve what value we substitute x into to get the value of 0. We have x outside of (x² - 3x - 40), and we can set that equal to 0. That will be one value of x because we are still left with (x² - 3x - 40). To solve this, we can factor it out into (x-8)(x+5). Set each equal to 0, (x-8) = 0 which leaves us with x = 8, and (x+5) =0, which leaves us with x = -5.