On integrating the function f(x), we get - (x³/45) + (3x²) - (2x³) + C.
What is integration?An integral is a function, of which a given function is the derivative. Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects. Mathematically, we can write -[tex]$\int_a^b \! f(x) \, \mathrm{d}x.[/tex]
Given is the function, as follows -
f(x) = (x²/15 + 6x - 9x²/{3/2})
The given function is -
f(x) = (x²/15 + 6x - 9x²/{3/2})
∫f(x) = ∫(x²/15 + 6x - 9x²/{3/2}) dx
∫f(x) = ∫(x²/15)dx + ∫(6x)dx - ∫(6x²)dx
∫f(x) = (1/15)(x³/3) + C₁ + (6)(x²/2) + C₂ - (6)(x³/3) + C₃
∫f(x) = (x³/45) + (3x²) - (2x³) + {C₁ + C₂ + C₃}
∫f(x) = x³/45) + (3x²) - (2x³) + C (C = C₁ + C₂ + C₃)
Therefore, on integrating the function f(x), we get (x³/45) + (3x²) - (2x³) + C.
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Check for Reasonableness What is a good estimate for 380% of 60? Explain.
Martin climbs 3 meters in the first 10 minutes How many meters does Martin climb in 60 minutes? Hint: Either multiply 3 by 6 or set up this proportion and solve for x 3/10 = x/60
The distance Martin climbs in 60 minutes is 18 meters
Calculating Distance climbedFrom the question, we are to determine how many meters Martin can climb in 60 minutes
Let the distance he climbs in 60 minutes be x
From the given information,
Martin climbs 3 meters in the first 10 minutes
If Martin climbs 3 meters in 10 minutes
Then,
Martin will climb x meters in 60 minutes
Thus,
x × 10 = 3 × 60
Solve for x
10x = 180
x = 180/10
x = 18
Hence, the distance is 18 meters
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If
m
⌢
=
21
6
∘
m
UPE
⌢
=216
∘
and
m
⌢
=
5
8
∘
m
LS
⌢
=58
∘
, find
m
∠
L
B
S
m∠LBS.
Answer:
use the way I told u down
Step-by-step explanation:
Angle ABC is a straight angle.
Angles ABD and DBC are right angles.
Angles CBE and DBE are acute angles.
Angle ABE is an obtuse angle.
Angles
The sum of the three angles in any triangle is always 180°.
a + b + c = 180°
Knowing that the sum of the angles of triangle is 180° can help you to solve problems about triangles.
Angles
In this triangle, angle b is a right angle and angle c = 40°. What is the measure of angle a?
a + b + c = 180°
Since b is a right angle, b = 90°.
The problem states that c = 40°.
Therefore, a + 90° + 40° = 180°
a + 130° = 180°
a + 130° − 130° = 180° − 130°
a = 50°
Angle a measures 50°.
Angles
Click on the figure that matches this description.
An obtuse angle
Question 1 of 8
This is an acute angle. It measures less than 90°. Try again
This is a right angle. The square in the corner shows that it measures 90°. Try again
This is a straight angle. It measures 180°. Try again.
This angle is obtuse. It is greater than 90° and less than 180°.
One of these figures is an obtuse angle. Try again.
An obtuse angle is larger then a right angle and smaller then a straight angle.
Angles
Click on the figure that matches this description.
An acute angle
Question 2 of 8
This is an acute angle. It measures less than 90°.
This is a right angle. The square in the corner shows that it measures 90°. Try again
This is a straight angle. It measures 180°. Try again.
This angle is obtuse. It is greater than 90° and less than 180°. Try again.
One of these figures is an acute angle. Try again.
An acute angle is smaller then a right angle.
Angles
Click on the figure that matches this description.
A right angle
Question 3 of 8
This is an acute angle. It measures less than 90°. Try again
This is a straight angle. It measures 180°. Try again.
This angle is an obtuse angle. It measures more than 90° and less than 180°. Try again.
This is an acute angle. It measures less than 90°. Try again.
A right angle looks like a square corner and measures 90°.
A right angle measures 90°.
Angles
There are five question remaining. In each of these question, you will be asked to find the size of a missing angle.
Angles
Click on the correct answer.
Angle ABC is a right angle. If angle n is 40°, how large is angle m?
50°
140°
90°
60°
None of these
Question 4 of 8
90° − 40° = 50°
Angle m is 50°.
Angle ABC is 90° , and angle m is only part of this right angle. It is less than 90°. Try again.
Angle ABC is 90°, and angle m is only part of this right angle. Try again.
Angle m and n together from a 90° angle. Subtract 40° from 90° .Try again.
One of these is size of angle m. Try again.
Since angle ABC is a straight angle, angle m + angle n = 90°.
Consider the function below. (If an answer does not exist, enter DNE.)h(x) = 5x3 − 3x5(a) Find the interval of increase. (Enter your answer using interval notation.)(−1,0)∪(0,1)
The interval in which the function h(x) = 5x³ - 3x^5 is increasing is given as follows:
(−1,0)∪(0,1).
How to obtain the intervals in which the function is increasing?The function in this problem is defined as follows:
h(x) = 5x³ - 3x^5.
To obtain the intervals for increase of decrease, the critical points of the function need to be obtained, which are the values of x for which the derivative is of zero.
The derivative of the function in this problem is given as follows:
h'(x) = 15x² - 15x^4.
Hence the critical points of the function are given as follows:
15x² - 15x^4 = 0
15x²(1 - x²) = 0.
Hence:
15x² = 0 -> x = 0.1 - x² = 0 -> x² = 1 -> x = -1, x = 1.Then the signals of the derivative in each interval is given as follows:
x less than -1: negative, as (1 - x²) < 0.x between -1 and 0: positive, as (1 - x²) > 0.x between 0 and 1: positive, as (1 - x²) > 0.x greater than 1: negative, as (1 - x²) < 0.The function is increasing when the derivative is positive, hence the interval is given as follows:
(−1,0)∪(0,1).
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Calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1
The value of the double integral ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77
In this question we need to calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1
i.e., to find ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1]
First we integrate the function (8x)/(1 + xy) as a function of y, treating the variable x as a constant.
G(x) = ∫_[0, 8] ((8x)/(1 + xy) ) dy
G(x) = 8 ln(8x + 1)
Now we calculate the integral of the previous result as a function of x.
i.e., ∫_[0, 1] G(x) dx
= ∫_[0, 1] [8 ln(8x + 1)] dx
= 9 ln(9) - 8
= 11.77
Therefore, the solution to the double integral (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77
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Madion went out to eat and pent $13. Thi wa 3/5 of the amount that he received. How much money did he receive?
The total money received by madison was $ 21.6 from which she spent $13 when she went out.
We are given that -
Madison spent $13 in all when she went out.
Also, this was 3/5 of the amount that she had received.
Now let us find the total money she received as follows -
Money spent by madison = 3/5 of the total money received by madison
i.e. 13 = 3/5 x (total money received by madison)
or we can say that total money received by madison = (5/3) x 13
= 65/3
= 21.6
Hence, the total money received by madison was $ 21.6
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Find the value of x and show your work.
5x+10
7x-6
im gussing you mean 5x+10=7x-6
if so
5x+10=7x-6
-5x = -5x
10=2x-6
+6=+6
16=2x
/2=/2
8=x
The value of x = 8
here, 5x+10 is the 1st Equation
and 7x-6 is the 2nd Equation
We have to form an equation
5x+10=7x-6
To solve for x, we need to isolate it on one side of the equation. To do this, we need to use inverse operations.
put the variable term on one side and the numerical term on the other side of the equal to sign, and while doing this change the sign from
plus with minus and vice versa
multiply with divide and vice versa
5x+10=7x-6
5x-7x=10+6
2x=16
x=[tex]\frac{16}{2}[/tex]
x=8
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it took samantha 6 years to double the money in her account. what interest rate was samantha receiving on her account?
Samantha was receiving an interest rate of 12% on her account.
What is Present value ?Present value is the present value of future cash flows discounted at a certain rate. Present value is based on the concept of the time value of money, where a dollar today is worth more than a dollar in the future.
PV = FV /(1 + r )ⁿ
Information provided to us ,
time period , n = 6 years
let " $x " be the present value of Samantha's account money.
After 6 years it becomes double that is
future value, F = $2x
let "r" be rate of interest was Samantha receiving on her account.
plugging all known values in above formula,
$x = $2x /(1+r)⁶
=> (1+r)^6 = 2
=> 1 + r = (2)^1/6 = 1.122
=> r = 1.122 - 1 = 0.122
=> r = 12%
So, rate of interest is 12% .
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pls help me in this homework id really appreciate it <3
Solve for x. Round to the nearest tenth.
X= type your answer...
X
28
32
The value x is 28. By using Pythagorean theorem on the given triangle.
What is the meaning of the nearest tenth?
To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.
Given that,
DC = 28
BC = 32
Assume that, AB = a and AD = b
Applying Pythagorean theorem on △BCD:
BC² = DC² + DB²
Putting BC = 32 and DC = 28 in the above equation:
32² = 28² + DB²
DB² = 32² - 28²
DB² = 32² - 28²
DB² = 240
The length of AC is CD + DA = 28 + b.
Now applying Pythagorean theorem on △ABC:
BC² = AB² + AC²
32² = a² + (28 + b)²
a² = 32² - (28 + b)² .....(i)
Now applying Pythagorean theorem on △ABD:
AB² = AD² + BD²
a² = b² + 240 ....(ii)
Now comparing equation (i) and equation (ii)
32² - (28 + b)² = b² + 240
1024 - (28² + 56b + b²) = b² + 240
1024 - 784 - 56b - b² = b² + 240
b² + 240 - 1024 + 784 + 56b + b² = 0
2b² + 56b = 0
2b(b + 28) = 0
Either,
2b = 0, b + 28 =0
b = 0, b = -28
Since the value of b can't be negative. Thus b = 0.
The length of AC is CD + DA = 28 + b = 28.
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The catter plot how the number of people at a fair baed on the outide temperature. How many fewer people would be predicted to be at the fair on a 100 f day then on a 75 f
The difference between the two numbers is the number of fewer people that would be predicted to be at the fair on a 100°F day than on a 75°F day.The answer will depend on the specific data from the catter plot.
1. Look at the catter plot and identify the points that correspond to the temperatures of 75°F and 100°F.
2. Note the number of people at the fair for each temperature.
3. Subtract the number of people at the fair in the 75°F point from the number of people at the fair in the 100°F point.
The difference between the two numbers is the number of fewer people that would be predicted to be at the fair on a 100°F day than on a 75°F day.
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two planes flying at the same altitude are heading toward jwd airport. the paths of these planes form a right triangle. the jet is flying due east toward jwd at 450 mph. the turboprop is approaching jwd from the south at 275 mph. when each is 100 miles from the airport how fast is the distance between the planes changing?
The speed of the distance between the two planes is increasing at 325 mph as they approach JWD Airport.
The two planes form a right triangle, with the jet flying due east at 450 mph and the turboprop approaching from the south at 275 mph. The hypotenuse of the triangle is the distance between the planes, and the length of the hypotenuse is changing as the planes approach the airport. The rate of change of the length of the hypotenuse is equal to the sum of the rates of change of the two sides of the triangle, which are the speeds of the jet and the turboprop. As they are both 100 miles from the airport, the speed of the distance between the two planes is equal to the sum of the two speeds, or 450 mph + 275 mph = 325 mph. Therefore, the distance between the two planes is changing at a rate of 325 mph.
Rate of change of distance between the planes = Rate of change of jet + Rate of change of turboprop
= 450 mph + 275 mph
= 325 mph.
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part of a regression output is provided below. some of the information has been omitted. source of variation ss df ms f regression 3177.17 2 1588.6 residual 17 17.717 total 3478.36 19 the ss (residual) is a. 3177.17. b. 301.19. c. impossible to determine. d. 17.71.
The SS(residual) is - 301.19. Option (b) is the correct answer.
Given the table :
Source of Variation - - SS - - - df - - - MS - - - - F
Regression - - - - - -3177.17 - - -2 - - 1588.6
Residual - - - - - - - - ______ --17 - - -17.717
Total - - - - - - - - - - 3478.36 - - 19
Calculate the SSR, the Sum of the Square residual.
The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR), and Degree of Freedom RESIDUAL (DFR) are related by the formula :
MSR = SSR / DFR
Hence,
SSR = MSR × DFR
For the table ;
MSR = 17.717 ; DFR = 17
SSR = (17.717 × 17)
SSR = 301.19
So, the SS(residual) is - 301.19.
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Draw a line l, and take two point A and B on it. Through A and B, draw line L2 and L3 perpendicular to L1. On L2, mark a point C at a ditance 4cm from L1 and draw a line L4 parrallel to L1 through C. If L4 interect L3 at D , what type of quadrilateral i ABDC?
ABDC is a quadrilateral with two non-parallel sides. It has two pairs of opposite sides which are parallel. It is also known as a trapezoid.
ABDC is a four-sided figure with two pairs of opposite sides that are parallel. This type of quadrilateral is also known as a trapezoid. A trapezoid has two non-parallel sides, while the other two sides are parallel to each other. In this case, the two parallel lines are L1 and L4, while L2 and L3 are the two non-parallel sides. We can see that the point C on L2 is a distance of 4cm from L1, and L4 is a line that is parallel to L1 and passes through C. Finally, L4 intersects L3 at the point D, which completes the trapezoid ABDC.
The length of AB can be determined by using the Pythagorean Theorem. We know that the length of L1 is 8 cm, so the length of AB is 3 cm.
example
AB = √(8^2 - 4^2) = √64 - 16 = √48 = 6 cm
The length of BD can also be determined by using the Pythagorean Theorem. We know that the length of L2 is 4 cm, so the length of BD is 3 cm.
BD = √(4^2 - 4^2) = √16 - 16 = 0 cm
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Write an equation in the form of y= mx for the proportional relationhip that pae through the point (2, -5) and (6, -45)
y=-10x+15 is the equation passing through the point which is in the form of y=mx+b
The equation of a line y = mx+b is called a straight line.
Where:
m is the slope, and b is the y-intercept.
given points are (2,-5) and (6,-45) consider these points as (x1,y1) and (x2,y2)
we have to find m: the slope of the line...
[tex]m=\frac{y2-y1}{x2-x1}[/tex]------------(1)
Now, plug the values into the formula of equation(1):
[tex]m=\frac{-45-(-5)}{6-2} \\\\m=\frac{-40}{4}[/tex]
m=-10
y=mx+b will become y=-10x+b
To find the b values:
for point(2,-5) consider x as 2,y as -5 and substitute in y=mx+b-5=-10*2+b
b=15
for point(6,-45) consider x as 6,y as -45 and substitute in y=mx+b-45=-10*6+b
b=15
so the final equation is y=-10x+15
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Describe all the
positive integers that would make (32)x greater than 39. Explain your reasoning
The positive integers that will make (32)x greater than 39 must be greater than 39/32
How to find positive integers that will make (32)x greater than 39A whole number that is greater than zero is what is meant by the term "positive integer."
All counting numbers are included in the set of positive integers (that is, the natural numbers)
In the problem, the given expression is (32)x greater than 39 rewriting gives
(32)x > 39
solving for x
x > 39/32
the integer must be greater than 39/32
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The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x – h| is solid.
Use the slider to change the value of h. How does changing the value of h affect the vertex?
Positive values of h shift the graph
.
Negative values of h shift the graph
.
Answer:
Step-by-step explanation:
The graph of the parent function f(x) = |x|
transformed function g(x) = |x – h|
To Find : How does changing the value of h affect the vertex?
Positive values of h shift the graph
Negative values of h shift the graph
Solution:
f(x) = |x|
is f(x) = x for x ≥ 0
f(x) = -x for x < 0
g(x) = |x – h|
Positive values of h shift the graph to the right
f(x) = x - h for x ≥ 0
f(x) = h - x for x < h
As values of h increase graph keep shifting to right
Vertex is ( h , 0) Vertex keep shifting to right with increases value of h
g(x) = |x – h|
Negative value of h shift the graph to the left
f(x) = x - h for x ≥ 0
f(x) = h - x for x < h
Vertex is ( h , 0) Vertex keep shifting to left with increases magnitude of negative h
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The linear functions f(x) and g(x) are represented on the graph ...
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The linear functions f(x) and g(x) are represented on the graph ...
The cost C in dollars of manufacturing x bicycles at a production plant is given by the function shown below.
C(x) = 5x²-1500x + 125,000
a. Find the number of bicycles that must be manufactured to minimize the cost.
b. Find the minimum cost.
a. How many bicycles must be manufactured to minimize the cost?
bicycles
Given function:
C(x) = 5x² - 1500x + 125000It has a positive leading coefficient, hence the parabola opens up. It means it has the minimum point at vertex.
The x-coordinate of the vertex is:
x = - b/(2a) = - (-1500)/(2*5) = 150The minimum cost is:
C(150) = 5(150)² - 1500(150) + 125000 = 12500Answer:
a) The minimum number of bicycles is the x-coordinate of the vertex, 150,b) The minimum cost is the value of C when x is 150, this is $12500.Find the value of x for {(-2/5)^2}^x*(-5/2)^-1=-8/125
Answer: x=1
Step-by-step explanation:
[tex][(-\frac{2}{5})^2] ^x*(-\frac{5}{2}) ^{-1}=-\frac{8}{125} \\\\(-\frac{2}{5})^{2*x}*(-\frac{2}{5})^1 =-\frac{2^3}{5^3} \\\\(-\frac{2}{5} )^{2x+1}=(-\frac{2}{5})^3 \\\\Hence,\\\\2x+1=3\\\\2x+1-1=3-1\\\\2x=2[/tex]
Divide both parts of the equation by 2:
[tex]x=1[/tex]
i need help desperately please don’t ignore!! :(
LN= 5x-8
NM= 12
m
find the value of x
The value of the missing part which is x is; x = 8
How to find the missing part of a triangle?
From the given triangle, we are told that;
LN = 5x - 8
NM = 12
∠KNL = (13x - 14)°
Now, since KN is an altitude in ΔKLM, it means that KN is perpendicular to LM and as such ∠KNL is a right angle which is 90 degrees. Thus;
(13x - 14)° = 90
1x = 90 + 14
13x = 104
x = 104/13
x = 8
This is the value of the missing value
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Write the expression using exponents.
5.2 x y x y x y
The ( X ) stands for multiplication. So 5.2 times Y times Y times Y.
9/2 * -(8/3) pls answer fast!...step by step explanation plss
Answer:
9 * -8
____ =-72/6
2 * 3
Given: AB = CD
Prove: AC = BD
What reason can be used to justify statement 3 in the proof above?
the addition property the subtraction property the division property the substitution property
To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.
In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.
Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.
suppose that a box contains 6 cameras and that 5 of them are defective. a sample of 2 cameras is selected at random ( without replacement). define the random variable x as the number of defective cameras in the sample. write the probability distribution for x .write your answer in fraction form or round to 3 decimal places.
If x is the number of defective cameras in the 2-size sample, that means that:
P(x = 0) = 0 (since there are no 2 cameras that can be selected without replacement that are not defective)
P(x = 1) = 5/15 = 1/3 (since there are 15 total ways to select a distinct sample and only 5 of these would have the non-defective one in them)
P(x = 2) = 10/15 = 2/3 (since there are 15 total ways to select a distinct sample and 10 of these would NOT have the non-defective one in them)
Vivian and her friends are planning a superhero movie marathon. Vivian is in charge of the
popcorn, so she buys a 2-pound jar of unpopped kernels. The jar's label says that 1 ounce of
kernels will make 1 quart of popcorn. How many cups of popcorn will her jar make?
If the jar level says that 1 ounce of kernels will make 1 quart of popcorn then 128 cups of popcorns will her jar make the popcorns.
The term ounce is a unit of measurement used in the Imperial system. It is mostly used in the United States. Ounces can be used to measure either liquid or dried goods. There are 32 ounces in one quart using the Imperial System of measurement. There are 4 cups in one quart. 1 quart is same as 32 ounces. Vivian and her friends are planning a superhero movie marathon. if Vivian buys 2 pound jar of unpropped kernels. then it will make 128 cups of popcorn. we know that 1 pound is equal to the 16 ounces so Vivian will make 32 ounces in 2 pound. A quart represented is a measuring unit used in the Imperial system and United States to measure liquids and dried goods. As per the leveling of the jar it will make 32 ounces in 32 quartz. then in 32 quartz it will make 128 cups of popcorn.
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Simplify this expression
Distribute first in the box below
2 (3x − 6) (2x + 1)
Answer: [tex]12x^{2} -18x-12[/tex]
Step-by-step explanation:
(6x-12)(2x+1)
Foil method
6x*2x
6x*1
-12*2x
-12*1
add them up
[tex]12x^{2} -18x-12[/tex]
12. Juan is a programmer going to school at
night to earn a higher degree. He starts the
month with $500 in his savings account. His
income is $4750. Each month he currently
spends $750 on food; $400 on clothes; $530
on video games and movies. His classes cost
$500 each month. His essential expenses
(rent, medical costs, insurance, tax) total
$2800. How much does Juan have for his Net
Cash Flow and Ending Cash at the end of the
month?
[A]Net Cash Flow: -$230
Ending Cash: $730
[B] Net Cash Flow: $2,570
Ending Cash: $3,070
[C] Net Cash Flow: -$230
Ending Cash: $270
[D] Net Cash Flow:-$270
Ending Cash: $230
[E] Net Cash Flow: $270
Ending Cash: -$770
Juan's Net Cash Flow at the end of the month is -$230 and his Ending Cash is $270.
To calculate Juan's Net Cash Flow and Ending Cash, you need to subtract his expenses from his income.
Juan's income is $4750 per month. His essential expenses, including rent, medical costs, insurance, and tax, total $2800 per month. He also spends $750 on food, $400 on clothes, and $530 on video games and movies, for a total of $2680 in non-essential expenses.
Therefore, his total expenses are $2800 + $2680 = $5480.
His Net Cash Flow is his income minus his expenses, which is $4750 - $5480 = -$730.
His Ending Cash is his Net Cash Flow plus his starting balance of $500, which is -$730 + $500 = $270.
Therefore, the correct answer is option C: Net Cash Flow: -$230, Ending Cash: $270.
Mustafa walks 15 km east and then 10 km south. How far is Mustafa from the starting point? Is in which direction
Answer:
25 kilometres West direction
Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme out
There is no statistical support in the data for the claim that seeded clouds typically cover more than 300 acres per foot by average acrefeet.
Since the significance level is set at 0.10, the meteorologists can conclude that the data does not provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
This is because the calculated p-value is greater than the significance level. This means that there is not sufficient evidence to reject the null hypothesis, which states that the average acrefeet from seeded clouds is no greater than 300.
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A rectangular aquarium is 12 inches tall. The perimeter of the base is 80 inches. The length of the base is 4 times the width of the base. Enter the volume, in cubic inches, of the aquarium.
Answer:
Step-by-step explanation:
Okay so you have to multiple 12 x 80 which gives you 960, then you mulitply 960 x 4 to get your final answer which is 3840 cubic inches