Answers
Answer:
Take a look at the 'proof' below
Step-by-step explanation:
The questions asks us to determine the anti-derivative of the function f(x) = 4x^3 [tex]*[/tex] sec^2 [tex]*[/tex] x^4. Let's start by converting this function into integral form. That would be the following:
[tex]\mathrm{\int \:4x^3sec^2x^4dx}[/tex]
Now all we have to do is solve the integral. Let's substitute 'u = x^4' into the equation 'du/dx = 4x^3.' We will receive dx = 1/4x^3 [tex]*[/tex] du. If we simplify a bit further:
[tex]\mathrm{\int \:\:sec^2\left(u\right)du}[/tex]
Our hint tells us that d/dx [tex]*[/tex] tan(x) = sec^2(x). Similarly in this case our integral boils down to tan(u). If we undo the substitution, we will receive the expression tan(x^4). Therefore you are right, the first option is an anti-derivative of the function f(x) = 4x^3 [tex]*[/tex] sec^2 [tex]*[/tex] x^4.
Related Questions
Algebra 1A, I need help
Answers
Answer:
for the first question at the top, x=10
Step-by-step explanation:
x+3+9x=8x+23
(subtract 8x from both sides)
x+3+x=23
(combine the x terms)
2x+3=23
(subtract 3 from both sides)
2x=20
(divide by 2 from each side)
x=10
ILL GIVE YOU BRAINLIST !!!
Evaluate the expression given the replacement values.
Answers
Answer:
24
Step-by-step explanation:
[tex]a^{2}[/tex]= 49 because any number squared is positive.
Since b=2,
2(-4)= -8.
Then this is 49-8-17, which equals 24.
Answer:
24
Step-by-step explanation:
please help me with this problem
Answers
Answer:
A) sin 70 = x/10
Step-by-step explanation:
From the angle 70 degrees, 10 is the hypotenuse and x is the opposite and if we go by SOH-CAH-TOA I have an O and a H so its sin.
so we know it's sin so we need to figure out the equation. since we have a hypotenuse as a factor it is on top. and the other number is on the bottom.
so,
A) sin 70 = x/10
Israel started to solve a radical equation in this way:
square root of x plus 6 − 4 = x
square root of x plus 6 − 4 + 4 = x + 4
square root of x plus 6 = x + 4
(square root of x plus 6)2 = (x + 4)2
x + 6 = x2 + 8x + 16
x + 6 − 6 = x2 + 8x + 16 − 6
x = x2 + 8x + 10
x − x = x2 + 8x + 10 − x
0 = x2 + 7x + 10
0 = (x + 2)(x + 5)
x + 2 = 0 x + 5 = 0
x + 2 − 2 = 0 − 2 x + 5 − 5 = 0 − 5
x = −2 x = −5
Solutions = −2, −5
What error did Israel make?
He subtracted 6 before subtracting x.
He added 4 before squaring both sides.
He factored x2 + 7x + 10 incorrectly.
He did not check for extraneous solutions.
Answers
Answer:
He did not check for extraneous solutions.
Step-by-step explanation:
He solved the equation correctly and obtained solutions -2 and -5, but there is one final step he did not do.
Every time you square both sides of an equation to solve it, you must check for extraneous solutions. If he did, he would have eliminated x = -5.
Answer: He did not check for extraneous solutions.
Evaluate the integral by interpreting it in terms of areas. integral -3 to 0(1+(9-x^2)^1/2)dx
Answers
Answer:
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Step-by-step explanation:
We need to evaluate the following integral by interpreting it in terms of areas :
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx[/tex]
The first step is to separate the integral into two easier integrals
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=\int\limits^0_{-3} 1 \, dx+\int\limits^0_{-3}\sqrt{9-x^{2}}\, dx[/tex] (Integral of the sum)
Now we can calculate each integral by studying the area below each function.
For the first integral the function is [tex]f(x)=1[/tex]
(I will attach a file with the functions)
The area below this function is the area of a rectangle with sides 1 and 3 ⇒
[tex]\int\limits^0_{-3}1 \, dx=3[/tex]
For the second integral the function is
[tex]f(x)=y=\sqrt{9-x^{2}}[/tex]
If we study this function :
[tex]y=\sqrt{9-x^{2}}[/tex]
[tex]y^{2}=9-x^{2}[/tex] (I)
[tex]x^{2}+y^{2}=9[/tex]
Which is the equation of a circle centered at (0,0) with radius equal to 3
From the equation (I)
[tex]y^{2}=9-x^{2}[/tex]
[tex]|y|=\sqrt{9-x^{2} }[/tex]
The two possible solutions are :
[tex]y=\sqrt{9-x^{2}}[/tex] (II) and [tex]y=-\sqrt{9-x^{2}}[/tex]
We will use (II) to solve the integral (which is the upper part of the circle)
The area of a circle with radius equal to 3 is
[tex]\pi.3^{2}[/tex]
In the integral we only need a quarter of circle ⇒ We divide the total area by 4 ⇒ [tex]\frac{\pi.3^{2}}{4}[/tex] ⇒ [tex]\frac{9\pi }{4}[/tex]
Finally the integral is equal to
[tex]\int\limits^0_{-3}(1+\sqrt{9-x^{2}})\, dx=3+\frac{9\pi}{4}=10.068[/tex]
Please help 4+(-10)-(-9)
Answers
Answer:
-15
Step-by-step explanation:
-10+-9=-19+4=-15
Find an equation of the plane.
The plane through the point (1, -1, - 1 ) and parallel to the plane 5x - y - z = 6
Answers
Answer: equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
Step-by-step explanation:
Given data;
5x - y - z = 6
therefore vector of plane is n° = ( 5, -1, -1)
so equation will be
n°(x-x₀, y-y₀, z-z₀) = 0
( 5, -1, -1) (x-x₀, y-y₀, z-z₀) = 0
5(x- (1)) -1(y - (-1)) -1(z - (-1)) = 0
5x - 5 - y - 1 - z - 1 = 0
5x - y - z - 7 = 0
Therefore equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
the question can been seen in the picture
Answers
Answer:
(2)
Step-by-step explanation:
A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 6 meters per second. -Let t represent the number of seconds that have elapsed since the start gun was fired. 1) Write an expression in terms of t that represents the hare's distance from the starting line (in meters) 2) Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters) 3) Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.
Answers
Answer:
1. 8t
2. 510 + 6t
3. 510 - 2t
Step-by-step explanation:
1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t
2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t
3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.
d' = 510 + 6t - 8t
= 510 - 2t
A bakery wants to determine the best placement for day-old goods. What type of data collection source do you think the bakery should use? Choose the correct answer below. A. The bakery should conduct an experiment. B. The bakery should collect information from operational or transactional systems. C. The bakery should conduct an observational study. D. The bakery should obtain information that was distributed by an organization or individual. E. The bakery should conduct a survey
Answers
Answer: C. The bakery should conduct an observational study
Step-by-step explanation:
From the question, we are informed that a bakery wants to determine the best placement for day-old goods. The type of data collection source that the bakery should use is an observational study.
An observational study is a form of study whereby the individuals who are to be observed are being studied by the researcher and certain conclusions are derived about them. When the bakery conductd an observational study, the behavior of the customers regarding goods placement can be observed.
Help please if u can
Answers
Answer:
Negative infinity
Step-by-step explanation:
The line points down infinitely in the graph.
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to:________
a. manipulation; chance
b. manipulation; experimental error
c. sampling error; independent variable
d. independent variable; experimental error
Answers
Answer:
Option (A)
Step-by-step explanation:
There are 2 main branches of statistics. They are:
1. Descriptive Statistics
2. Inferential Statistics
Descriptive statistics describes the characteristics of observed subjects or items while Inferential statistics makes inferences, based on given or derived data.
Inferential Statistics allow you to decide whether a difference between the experimental group and control group is due to manipulation or chance.
The Experimental group is the group that an effect is tested on while the Control group is the group that is left untested or uninfluenced. Inferential statistics allow you to decide whether a difference between these 2 groups is due to
- manipulation or interference by any force (which may be the experimenter/researcher)
or
- probability which is chance.
Option a. manipulation; chance
Inferential statistics is a statistical method for estimating the characteristics of a larger population from a small but representative sample. In other words, it enables the researcher to make generalizations about a larger group based on a smaller subset of that group.
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to a. manipulation; chance
For more information:
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Write an equation in slope-intercept form (y = mx + b).
Perpendicular to 7x - 2y = 16 passing through (-7, 5).
Answers
Answer:
y = 2/7x + 7
Step-by-step explanation:
We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other. So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.
Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.
5 = -14/7 + b
5 = -2 + b
7 = b
Finally, plug the b value into your final equation and you will have your answer.
Veronica has been wanting to learn to ice skate for years!
When the Glacier Zone Ice Rink opened, Veronica bought 12
ice-skating lessons during their grand-opening sale. Veronica
paid $305.40 in all. How much did each lesson cost?
Answers
Answer:
25.45 per lesson
Step-by-step explanation:
divide $305.40 by 12
which of the following verifies that triangle YXZ is similar to triangle QPR?
Answers
Answer:
AA postulate
Step-by-step explanation:
Because both the angle are identical?
What is the difference between math content and math skills
Answers
The skill is knowing how to make it happen-- knowing how to find the LCD, multiplying the top and bottom by the same amount to find the equivalent fractions, knowing that you add the numerators but don't change the denominators, and knowing how to reduce the resulting answer.
Answer
B
Step-by-step explanation:
Took quiz
drag each statement to show it true,based on the graph.
Answers
Answer:
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
Step-by-step explanation:
x-values on the graph define the weight of cinnamon and y-values define the price.
Slope of the line drawn from the origin (0, 0) and (0.75, 5.25) will determine the per lb price of the cinnamon.
Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points on the given line re (0,0) and (0.75, 5.25),
Slope = [tex]\frac{5.25-0}{0.75-0}[/tex]
= 7
Therefore, two options are the correct options.
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
Solve for b: 15 - 2b = -9
pleasee help:(
Answers
Answer:
b = 12
Step-by-step explanation:
15 - 2b = -9
Minus 15 to both sides
-2b = -24
Divide both sides by -2
b = 12
Find an equation of a plane through the point (3, 0, 2) which is orthogonal to the linex=?2+3t,y=2+4t,z=?1?3tin which the coefficient of x is 3.
Answers
Answer: 3x + 4y - 3z - 3 = 0
Step-by-step explanation:
with the given point (3, 0, 2), the plane is orthogonal to this line so it
has directional ratios (3, 4, -3)
therefore the given equation can be written as;
(x+2)/3 = (y-2)/4 = (z+1)/-3
so equation of the plane passing through point x1, y1 and z1 in the one point form is given as;
a(x-x1) + b(y - y1) + c(z -z1) = 0
abc represent the direction ratio
so we substitute
3(x-3) + 4(y-0) + (-3(z-2)) = 0
3x - 9 + 4y - 0 - 3z + 6 = 0
3x + 4y - 3z - 3 = 0
therefore the equation of the plane through the point is 3x + 4y - 3z - 3 = 0
Six classes of 31,28,27,32,24 and 26 students are to travel on buses that each hold 36 students. How many buses are needed?
Answers
Answer:
5 buses
Step-by-step explanation:
You add all the students up to get 168, because that's the total number of students, and divide it by 36. The buses can only carry 36 people, so you will need 4.666 buses, but you can't have 0.666 of a bus, so you will need 5 buses to fit everyone.
Drag the fraction that is equivalent to each repeating decimal. Each fraction may be used only once.
Answers
Answer:
Step-by-step explanation:
The easiest way to do any of these is to put the fraction into your calculator and see what comes up.
So for 32/9 you get 3.5555555555 which is the same as 3.5 with a bar over it.
7/30 is the same as .23333333333 which is the same as 0.23 with a bar over the three.
5/3 = 1.6666666 which is 1.6 with a bar over the 6
4/9 is 0.4444444 which is the same as 0.4 with a bar over the 4.
HURRRRYYYYYYY PLEASE Write the equation of the line that passes through the points (-8,-1) and (5,−7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
Answer:
y + 8 = 2x + 2
Step-by-step explanation:
Use the points given to find the slope. Divide the difference in y-values by the difference in x-values.
(-1) - (-7) = 6
5 - (-8) = 3
6/3 = 2
The slope is 2.
Now, pick one of the points to put in point-slope form. It doesn't matter which. You will get the right answer either way. I will use (-1, -8).
y - y₁ = m(x - x₁)
y - (-8) = 2(x - (-1))
y + 8 = 2(x + 1)
y + 8 = 2x + 2
Which answer describes the type of numbers that are dense? whole numbers and integers whole numbers but not integers rational numbers and irrational numbers rational numbers but not irrational numbers
Answers
Answer:
rational numbers and irrational numbers
Step-by-step explanation:
what five parts make up a data table
Answers
Answer:
Step-by-step explanation:
Check boxes.
Sorting (on columns)
Icons that communicate alerts.
Pagination.
Headers Row.
what is 12.3 -(-9.6) =12.3 + 9.6 simplified?
Answers
Answer:
Step-by-step explanation:
12.3 + 9.6 = 21.9
The expression 12.3 - (-9.6) is equivalent to 21.9.
Given is an expression 12.3 -(-9.6) = 12.3 + 9.6, we need to simplify it,
To simplify the expression 12.3 - (-9.6), we can rewrite it as 12.3 + 9.6.
When subtracting a negative number, it is equivalent to adding the positive value of that number.
So, -(-9.6) becomes +9.6.
Therefore, 12.3 - (-9.6) simplifies to 12.3 + 9.6.
Adding 12.3 and 9.6 gives us 21.9.
So, 12.3 - (-9.6) = 21.9.
Learn more about expression click;
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The product of -4 and d
Answers
Answer:
-4d
Step-by-step explanation:
Thrice the product of two and "Y".
Answers
Answer:
6Y
Step-by-step explanation:
We need to solve the statement ' Thrice the product of two and "Y" '.
Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.
Let the result is R. It can be calculated as follows :
[tex]R=3\times 2\times Y[/tex]
We know that, 3×2 = 6
So,
[tex]R=6Y[/tex]
Hence, Thrice the product of two and "Y" is 6Y.
4(z – 2) + 3z
Need help
Answers
Answer:
5z-8
Step-by-step explanation:
(8z-8)+3z=
5z-8
Answer:
z-8
Step-by-step explanation:
4(z -2)+3z
4z -8 +3z
-3 -3
z -8
If John has drank three drinks per day how many will he have drank in 3 day's?
Answers
Answer:
9 drinks
Step-by-step explanation:
3+3+3=9
Or 3*3=9
Answer:
9
Step-by-step explanation:
-4.5 x (-2)???????????????????????
Answers
Answer:
9
Step-by-step explanation:
-4.5 x (-2) is equal to 9