Answer:
x^6 - (8/5)x^5 - 3x^3 + C.
Step-by-step explanation:
f(x) = 6x^5 - 8x^4 - 9x^2.
Using the general form antiderivative of Ax^m = Ax(m+1) / (m+1)+ C:
Antiderivative = 6 * x^(5+1) / 6 - 8 * x^(4+1) / 5 - 9 * x^(2+1) / 3 + C
= 6x^6/6 - 8x^5/5 - 9x^3/3 + C
= x^6 - (8/5)x^5 - 3x^3 + C.
Differentiating:
f'(x) = 6x^(6-1) - 8 x^(5-4) - 9x^(3-1) + 0
f'(x) = 6x^5 - 8x^4 - 9x^2.
The most general antiderivative of the given function f(x) = 6x5 − 8x4 − 9x2 is F(x) = x^6 - 8/5 * x^5 - 3x^3 + C, where C is the constant of the antiderivative.
Explanation:To find the most general antiderivative of the given function f(x) = 6x5 − 8x4 − 9x2, we need to perform the process of integration, which is the reverse of differentiation. The antiderivative F(x) will be found by integrating each term of the function separately.
The antiderivative of f(x) will then be:
F(x) = ∫6x5 dx - ∫8x4 dx - ∫9x2 dx,
Transitioning to the next step by applying the power rule for integration, we add 1 to the exponent and divide by the new exponent, we obtain
F(x) = 6/6 * x^(5+1) - 8/5 * x^(4+1) - 9/3 * x^(2+1) + C
Simplified, the antiderivative F(x) becomes:
F(x) = x^6 - 8/5 * x^5 - 3x^3 + C,
where C is the constant of the antiderivative.
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A cab company charges a $3 boarding rate in addition to its meter which is $2 for every mile. How much does it cost to ride this cab for 1 minute?
Answer:
try using this it might help out with the question
Step-by-step explanation:
Y=2x+3
A store offers 20% off all items. If x is the original purchase price, which expression represents the final price
with the discount? Select all that apply.
O
A 1.2x
B. 0.8x
X-0.2x
EX+0.2x
Answer:
0.2x
Step-by-step explanation:
Answer:
0.2x---------------------------------------------------------------------------------------
In triangle ABC, side AB measures 3 cm, side BC measures 5 cm, and side AC measures 7 cm. The measures of the angles are 21.8º, 38.2º, and 120º. What could the measure of angle A be? 21.8º 38.2º 120º answer is 38.2
Answer:
B
Step-by-step explanation:
I got it correct
Answer:
38.2º
hope you have a good day!
650grams= how many kg
Answer:
0.65 kilograms
Step-by-step explanation:
Answer:
0.65 kg
Step-by-step explanation:
[tex] \because \: 1 \: gram = \frac{1}{1000} kg \\ \\ \therefore \: 650 \: grams = \frac{650}{1000} \\ \\ \red{ \boxed{\bold {\therefore \: 650 \: grams =0.65 \: kg} }}[/tex]
Select the correct answer.
Sam's height is 15 centimeters less than 2 times Martha's height. If Sam Is 185 centimeters tall, and Martha's height is x, the relationship
between the heights can be represented by the equation 2x - 15 = 185. What Is Martha's height?
A 90
B. 95
°C 100
D. 105
Reset
Next
m.com/assessments delivery/ua/mt/launch/49072603/849589754/aHROCHM6Ly9m MSShCHAUZWRIZW50dW0uY29tL2xYXJEZXIvc2Vjb25kYXJ5L2xYXJuaW5ndGF0ac9pbmRleCBOOTA3MjYwMz9iYWNT
Answer:
C. 100 cm
Step-by-step explanation:
2x-15=185
+15 +15
2x=200
/2 /2
x=100
What is the following product?
Answer:
b
Step-by-step explanation:
The square root of b times the square root of b is simply b.
b^(1/2)*b^(1/2) = b^1 = b
The Students at Winwood elementary school collected 574 cans of food in 20 days for a food drive. What was average number of cans of food collected each day
Answer:
About 29
Step-by-step explanation:
575 cans of food / 20 days = About 28.75 cans a day, rounded to 29.
Answer:
28.7 cans
Step-by-step explanation:
We want to find the unit rate for cans per day
To find this, divide the number of cans by the number of days
cans/days
574/20
28.7
About 28.7 cans per day
Which of the following is the inverse of y = 3 Superscript x?
The one that is an the inverse of y = 3 Superscript x is y = 3x is f-1(x) = 1/3x.
What is the inverse about?The use of the idea of inverse function to look for the solution is given below:
Note that, y = 3x
Then let f(x) = y = 3x
One will need to Switch x and y and as such, x = 3y
Then one should express y in terms of x and as such, y = 1/3 x
Since f(x) = y ⇒ x = f-1(y)
Then f-1(y) = 1/3x
Therefore, the inverse of y = 3x is f-1(x) = 1/3x.
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A football selling for 35% off the original price the original price was 60 what is a sales price of the football
Answer:
Sales Price = $21.00
New Price = $39.00
Step-by-step explanation:
Convert 35% into a decimal and multiply that with the $60.00. After you get the product, which is $21.00, you then need to subtract $21.00 from $60.00 and that gets you $39.00.
Solve for r 4r + 8 = 7.2 + 5r
Answer: r=0.8
Step-by-step explanation:
4r + 8 = 7.2 + 5r
-4r -4r
8=7.2+r
8-7.2=r
0.8=r
Answer: [tex]r=0.8[/tex]
Step-by-step explanation:
-Solve:
[tex]4r+8=7.2+5r[/tex]
-Subtract [tex]5r[/tex] from both sides:
[tex]4r+8-5r=7.2[/tex]
Combine [tex]4r[/tex] and [tex]5r[/tex] to get [tex]-r[/tex]:
[tex]-r+8=7.2[/tex]
-Subtract [tex]8[/tex] from [tex]7.2[/tex] to get [tex]-0.8[/tex]:
[tex]-r=7.2-8[/tex]
[tex]-r=-0.8[/tex]
-Multiply both sides by [tex]-1[/tex]:
[tex]r=0.8[/tex]
-Result:
[tex]r=0.8[/tex]
Find the measure of an angle whose supplement is sixteen times its complement. Hint: Supplement and complement of an angle are (180-0) and (90-0) respectively.
Answer:
The angle is 84 degrees
Step-by-step explanation:
Let's call the angle by 'x'.
the supplement of x is equal to 180-x, and the complement of x is equal to 90-x.
If the supplement is sixteen times the complement, we can write the following equation:
(180 - x) = 16 * (90 - x)
180 - x = 1440 - 16x
16x - x = 1440 - 180
15x = 1260
x = 84
The angle is 84 degrees.
Answer:
84⁰
Step-by-step explanation:
Complement = 90 - x
Supplement = 180 - x
Given:
180 - x = 16(90 - x)
180 - x = 1440 - 16x
15x = 1260
x = 84
Somebody please help me with this
She invited 150 friends. But she only had 5 activities for her friends and her party only lasted 4 hours. How much time will each friend get on each activity
Answer:
19.20 seconds.
Step-by-step explanation:
Given:
She invited 150 friends.
But she only had 5 activities for her friends and her party only lasted 4 hours.
Question asked:
How much time will each friend get on each activity ?
Solution:
First of all convert 4 hours into seconds:-
1 hour = 3600 seconds
4 hours = 3600 [tex]\times[/tex] 4 = 14400 seconds
By unitary method:
150 friends get time in 5 activities = 14400
1 friend get time in 5 activities = 14400 [tex]\div[/tex] 150 = 96 seconds
That means each friend get 96 seconds in all 5 activities.
Each friend get time on each activity = ?
Each friend get time on 5 activities = 96
Each friend get time on 1 activity = 96 [tex]\div[/tex] 5 = 19.20 seconds
Thus, each friend will get 19.20 seconds on each activity.
There are 3 red, 1 blue and 2 yellow marbles in a bag. Once a marble is selected it is not replaced. Find
Plred then yellow).
a) 1/6
b) 1/5
c) 5/6
d) 2/5
Final answer:
The probability of selecting a red marble followed by a yellow marble from a bag, without replacement, is 1/5. Option B) 1/5 is correct.
Explanation:
The probability of selecting a red marble and then a yellow marble without replacement from a bag is determined by multiplying the probability of the first event by the probability of the second event, given the first has occurred.
First, calculate the probability of drawing a red marble (P(red)). With 3 red marbles out of 6 total marbles, that probability is 3/6 or 1/2.
Next, calculate the probability of drawing a yellow marble after a red one has been drawn (P(yellow | red)). Now there are only 5 marbles left in the bag, 2 of which are yellow, so that probability is 2/5.
Finally, multiply these two probabilities to find the probability of both events occurring in sequence: P(red then yellow) = P(red) × P(yellow | red) = (1/2) × (2/5) = 2/10 or 1/5.
The probability of selecting a red and then a yellow marble from a bag containing 3 red, 1 blue, and 2 yellow marbles, without replacement, is 1/5.
Calculate the probability of selecting a red marble first. There are 3 red marbles out of a total of 6 marbles, so the probability is 3/6 or 1/2.After removing a red marble, there are now 5 marbles left (2 of which are yellow). The probability of then selecting a yellow marble is 2/5.Multiply the probabilities of the two events to find the combined probability: (1/2) * (2/5) = 2/10 or 1/5.Therefore, the probability of selecting a red marble and then a yellow marble without replacement is 1/5, which corresponds to option b).
Shelly buys desk to sell in her furniture store. She marks up the price by 35% and sells the desk for $290.25. What price did Shelly pay for the desk.
Answer:
Shelly paid $215 for the desk
Step-by-step explanation:
In this question, we are asked to calculate the price a particular desk was bought given the price at which it was sold and the percentage of profit associated with the sales of the desk. In other words, we are calculating the cost price
Mathematically,
% profit = (selling price - cost price)/cost price * 100%
Our percentage profit here is 35% and our selling price is $290.25, we are left with calculating the selling price. let’s input these values into the equation;
Before that, let’s say the cost price is $x
35 = (290.25-x)/x * 100
100(290.25-x) = 35x
29025 -100x = 35x
135x = 29025
x = 29025/135
x = $215
Sis worked 14.4 hours and saved $271.30 for a new bike.The equation 14.4x=271.30 could be used to represent how much aid earned per hour. What is the hourly rate, x, Sid worked to pay for the new bike? Round to the nearest hundredths place.
Answer:
The hourly rate she worked to pay for the new bike is $18.84.
Step-by-step explanation:
Given:
Sis worked 14.4 hours and saved $271.30 for a new bike.
The equation 14.4x=271.30 could be used to represent how much she earned per hour.
Now, to find the hourly rate she worked to pay for the new bike.
The hourly rate = [tex]x[/tex].
Number of hours = 14.4.
Money she saved = $271.30.
According to the question, the equation used to represent she earned per hour is:
[tex]14.4x=271.30[/tex]
Now, to solve the equation to get the hourly rate:
[tex]14.4x=271.30[/tex]
Dividing both sides by 14.4 we get:
[tex]x=\$18.840.[/tex]
Thus, the hourly rate rounding to the nearest hundredths place is $18.84.
Hence, the hourly rate she worked to pay for the new bike is $18.84.
Which of the following statements are correct when deciding whether to use the z or the t distribution?A. Use z when we have a normal population and we know the standard deviation B. Use t when the population is normal and the population standard deviation is not known
Using normal distribution concepts, we can conclude that the correct statement is:
B. Use t when the population is normal and the population standard deviation is not known
-------------------------
Both the z and the t distributions are for normal variables.If the population standard deviation is known, the z-distribution is used.If the population standard deviation is now known, only the sample standard deviation, the t-distribution is used.Option A is wrong as the standard deviation is know in both cases, only in one case it is the sample(t-distribution) and the other is the population(z-distribution).Thus, option B is correct.A similar problem is given at https://brainly.com/question/21774082
Karen has already knit 15 centimeters of scarf, and can knit 1 centimeter each night. After
23 nights of knitting, how many centimeters of scarf will Karen have knit in total?
Answer:
I think it is 38 centimeters.
Step-by-step explanation:
A ball is thrown into the air with an initial upward velocity of 46 ft/s. Its height (h) in feet after t seconds is given by the function h equals negative 16 t squared plus 46 t plus 6. After how many seconds will the ball hit the ground? A. 3 B. 4 C. 5 D. 6
Answer:
t = 3 seconds
Step-by-step explanation:
This is a quadratic equation. First set it up and set it equal to 0 (the ground).
-16t² + 46t + 6 = 0
The quadratic formula is (-b ± √(b² - 4ac))/2a
a= -16
b = 46
c = 6
Plug those numbers into the equation and solve which will result in -.125 or 3.
The time of course can not be negative in this case. Therefore, t=3 seconds.
The ball will hit the ground after 3 seconds.
Explanation:The problem deals with the quadratic equation representing the motion of the ball. When the ball hits the ground, the height (h) is 0. So, we need to solve the equation -16t^2 + 46t + 6 = 0 for (t). The roots of this quadratic equation can be found using the quadratic formula, t = [-b ± sqrt(b^2 - 4ac)]/2a. Substituting a=-16, b=46, and c=6 into the formula, you will find the solutions are t = 3 seconds and t = -0.375 seconds. Therefore, the ball will hit the ground after 3 seconds. The correct choice is A. 3.
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A good rule of thumb is to design the horizontal stabilizer so that its area is about 1/6 to 1/8 of the area of the wing. If the area of the wing is 101.25 cm2, which of the following would be a good horizontal stabilizer design?
answer choices:
Stabilizer with area = 32 cm2.
Stabilizer with area = 20 cm2.
Stabilizer with area = 14 cm2.
Stabilizer with area = 11 cm2.
What is f(−2) for f(x) = 3x−5
Step-by-step explanation:
Given
f(x) = 3x - 5
f(-2) = 3 * (-2) - 5
= -6 -5
= - 11
Answer:
f(×)=
Step-by-step explanation:
[tex] f(- 2 )= 3( - 2) - 5 [/tex]
[tex] - 2 = - 6 - 5[/tex]
[tex] - 2 = - 11[/tex]
Josie is training for a race. The ratio of the number minutes she runs to the number of miles she runs is 24 to 3 She plans to run 10 miles. How many minutes will it take her?
Answer:
80 minutes
Step-by-step explanation
24/3=8
8mins/1 mile
8 minsx10 miles= 80 mins for 10 miles
The first artificial satellite to orbit Earth was Sputnik I, launched by the Soviet Union in 1957. The orbit was an ellipse with Earth's center as one focus. The orbit's highest point above Earth's surface was 583 miles, and its lowest point was 132 miles.a) find an equation of the orbit.b) how far from Earth is the other focus?c) What is the length of the major axis?
Answer:
A) (x²/127806.25) + (y²/76956) = 1
B) 451 miles
C) 715 miles
Step-by-step explanation:
Center is at (0,0) and focus is at (c,0) while vertex is at (a,0)
Thus, a - c = 132 miles
and a + c=583 miles
Adding both equations together, we have;
2a= 715 miles
Thus, a = 715/2
a = 357.5 miles
Since a+c=583
Thus, c = 583-357.5 = 225.5 miles
Now, for an ellipse it is defined by; a² = b² + c²
a² = 357.5² = 127806.25
c² = 225.5² = 50850.25
So, b² = 127806.25 - 50850.25
b² = 76956
b = √76956
b = 277.409
A) Equation of tangent to ellipse which is equation of orbit would be;
(x²/a²) + (y²/b²) = 1
Thus,
(x²/127806.25) + (y²/76956) = 1
B) distance between the earth and the other focus is = 2c = 2 x 225.5 = 451 miles
C) Length of other major axis = 2a = 2 x 357.5 = 715 miles
a) The equation of the orbit is \(\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\). b) The distance from the center to the other focus is calculated using the formula \(c = \sqrt{(583+3963)^2 - 132^2}\). c) The length of the major axis is \(2(583+3963)\).
Explanation:a) To find an equation of the orbit, we can use the standard form equation for an ellipse:
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\] where \((h,k)\) represents the center of the ellipse, \(a\) represents the distance from the center to the vertices along the major axis, and \(b\) represents the distance from the center to the co-vertices along the minor axis. In this case, the center of the ellipse is the Earth's center, which is at the origin \((0,0)\). The highest point of the orbit is 583 miles above the Earth's surface, so the distance from the center to the vertices along the major axis is 583 miles + the radius of the Earth. The radius of the Earth is approximately 3963 miles. The lowest point of the orbit is 132 miles above the Earth's surface, so the distance from the center to the co-vertices along the minor axis is 132 miles. Substituting the values into the equation:
\[\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\]
b) The distance from the center to the other focus can be found using the relationship \(c = \sqrt{a^2 - b^2}\), where \(c\) represents the distance from the center to the foci. Substituting the values into the equation:
\[c = \sqrt{(583+3963)^2 - 132^2}\]
c) The length of the major axis can be found using the formula \(2a\), where \(a\) represents the distance from the center to the vertices along the major axis. Substituting the values into the equation:
\[2a = 2(583+3963)\]
there were 816 people at a concert when a band starting playing
Answer: 408/x
Step-by-step explanation:
Total number of people = 816
after 1 song = 816/2 people remained
after 2 songs = 816/4 people remained
after 3 songs = 816/8 people remained
after x songs = 816/x*2 people remained
People that remained = 816/2x
where x is the number of songs
Simplified = 408/x
Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis. Region R is rotated about the line y=-2. Find the volume of Region R after being rotated.
The volume of rotation of region R is [tex]192\pi[/tex] cubic units.
Given information:
Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis.
Region R is rotated about the line y=-2.
So, the region R is a rectangle with length 6 units (x=0 to x=6), and the height of the rectangle is 4 units (y=0 to y=4).
After rotating this rectangle about y=-2, we will get a hollow cylinder.
The outer radius of the cylinder will be,
[tex]R=4-(-2)=6[/tex]
The inner radius of the cylinder will be,
[tex]r=0-(-2)=2[/tex]
And the length of the cylinder is 6 units.
So, the volume of the solid formed after the rotation will be,
[tex]V=\pi R^2L-\pi r^2L\\V=\pi L(R^2-r^2)\\V=\pi \times 6(6^2-2^2)\\V=\pi\times 6 \times 32\\V=192\pi[/tex]
Therefore, the volume of rotation of region R is [tex]192\pi[/tex] cubic units.
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To find the volume of the solid formed by rotating region R about the line y=-2, we use the washer method which results in a volume of 216π cubic units.
Explanation:The problem involves calculating the volume of a solid of revolution, which is formed when a two-dimensional region is rotated around a line that does not intersect the region.
Region R is defined as the area bounded by y=4, x=6, the y-axis, and the x-axis. The volume of the solid formed by rotating this region around the line y=-2 can be calculated using the washer method, which involves integrating over the area of concentric washers.
The general formula for the volume V of a washer is given by V = π∫[R2(x) - r2(x)]dx , where R(x) and r(x) are the outer and inner radii of the washers, respectively. In this case, the outer radius is R(x) = 4 - (-2) = 6 and the inner radius is r(x) = -2 - (-2) = 0.
Therefore, the volume V is:
V = π∫06[62 - 02 ]dx = π∫0636dx = 36π∫06dx = 36π[6] = 216π cubic units.
Find the approximate value of each trigonometric function.
Given that sin0 = 0.312 where - <0
Since 0 lies in Quadrant II, where cos0 <0, cos is approximately
Answer:
-0.95
Step-by-step explanation:
cos(theta) = sqrt(1 - sin²(theta))
= sqrt(1 - 0.312²)
= sqrt(0.902656)
= +/- 0.9500821017
Since cos is negative in quadrant 2,
cos(theta) = -0.95
To approximate the value of cos0, we can use the given value of sin0 and the Pythagorean identity. The approximate value of cos0 is -0.95022.
Explanation:Since the given angle 0 lies in Quadrant II where cos0 is negative, we can approximate the value of cos0 using the given value of sin0.
Using the Pythagorean identity sin^2(0) + cos^2(0) = 1, we can find cos0.
sin^2(0) + cos^2(0) = 1
0.312^2 + cos^2(0) = 1
0.097344 + cos^2(0) = 1
cos^2(0) = 1 - 0.097344
cos^2(0) = 0.902656
cos0 = √0.902656
cos0 ≈ -0.95022
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Alexis uses toy blocks to build a model of a building each toy block is 1 cubic inch The first three floors of the model are Made up of six rows of four blocks floors four through eight are made up of 4 rows of 4 blocks what is the volume of the model
Answer: The volume is 40 cubic inches
Step-by-step explanation: Each toy block is 1 cubic inch, which means each toy block is a cube with all sides (Length, width and height) measuring 1 inch. That makes the volume of each cube or block to be derived as;
Volume = L x W x H
Volume = 1 x 1 x 1
Volume = 1 cubic inch
The first 3 floors are made up of six rows of four blocks. This means, the first 3 floors has six by four blocks, that is, six times four blocks and that gives us 24 blocks.
The fourth to eighth floors are made up of four rows of four blocks. This also means four by four blocks, that is, four times four blocks and that gives us 16 blocks.
Having determined the amount of blocks used in the total model building as
1st - 3rd = 24 blocks
4th - 8th = 16 blocks
The total number of blocks used is 24 plus 16 which equals 40. Having been told that each block has a volume of 1 cubic inch, the volume of the model building equals 40 cubic inches.
A television station broadcast a court trial in its entirety. During a news program, viewers were asked to go to the TV station’s website and state whether they thought the defendant was guilty or not guilty. Of the 1,840 viewers who gave their opinion, 1,521 felt that the defendant was not guilty. The viewers who registered their opinions constitute what type of sample?
Answer:
Voluntary response sample
Step-by-step explanation:
They constitute voluntary response sample. Voluntary response sample is a sample that is made up of volunteers.
Apart from voluntary response sample, it can also be called or known as self-selected sample.
A good example of this sample is the typical phone in polls u can witness on radio or tv stations where people call to air their views or make their stands known.
The voluntary response sample is most times chosen or selected by the people that will respond rather than the administrator of the survey.
One of the standout advantages or benefit of the voluntary response sampling is the convenience and probably the ethical considerations as well. The demerit is that this self-selected samples are sometimes subject to bias.
In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of _______.
2a is used in the equation because the _______ is a point on the hyperbola and it is the difference in the distances from this point to the foci.
This can be shown algebraically if we let a be the distance from the ______ to the vertex. Then, the difference of the distances is (c + a) – _______.
Answer:
1. 2a
2. Vertex
3. Center
4. (c-a)
Step-by-step explanation:
The missing black in the paragraph will be 2a, vertex, center, and (c – a).
What is a hyperbola?The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of 2a.
2a is used in the equation because the Vertex is a point on the hyperbola, and it is the difference in the distances from this point to the foci.
This can be shown algebraically if we let a be the distance from the Center to the vertex. Then, the difference of the distances is (c + a) – (c – a).
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Ten less than a number is three more than six times the number.
Write it as an equation:
X - 10 = 6x + 3
Now solve for x:
Subtract 3 from both sides:
x-13 = 6x
Subtract 1 x from both sides:
-13 = 5x
Divide both sides by 5:
x = -13/5
Answer:
x = -2.6.
Step-by-step explanation:
Let the number be x, then:
x - 10 = 6x + 3
x - 6x = 3 + 10
-5x = 13
x = -13/5
= -2.6.