Answer:
A). slope = -1/12 y-intercept = 3/2
Step-by-step explanation:
y = -1/12x + b
2 = -1/12(-6) + b
2 = 1/2 + b
3/2 = b
y = -1/12x + 3/2
Find the integral of x(4x² + 1) from 0 to 2. a. 18 c. 22 b. 16 d. 20
Answer:
a. 18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsCalculus
Integrals
Definite IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^2_0 {x(4x^2 + 1)} \, dx[/tex]
Step 2: Integrate
[Integrand] Distribute x [Distributive Property]: [tex]\displaystyle \int\limits^2_0 {(4x^3 + x)} \, dx[/tex]Rewrite Integral [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^2_0 {4x^3} \, dx + \int\limits^2_0 {x} \, dx[/tex]Rewrite 1st Integral [Integration Property - Multiplied Constant]: [tex]\displaystyle 4\int\limits^2_0 {x^3} \, dx + \int\limits^2_0 {x} \, dx[/tex][Integrals] Reverse Power Rule: [tex]\displaystyle 4(\frac{x^4}{4}) \bigg| \limits^2_0 + (\frac{x^2}{2}) \bigg| \limits^2_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle 4(4) + 2[/tex]Evaluate: [tex]\displaystyle 18[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
a reflection over the x-axis, then a dilation by a scale factor of 3
a reflection over the x-axis, then a dilation by a scale factor of One-third
a 180° rotation about the origin, then a dilation by a scale factor of 3
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Answer:
A 180° rotation of then a dilation by a scale factor of one-third
Step-by-step explanation:
The coordinates of the vertices of ΔABC are;
A(-9, 3), B(-9, 6), and C(0, 3)
The coordinates of the vertices of ΔA'B'C' are;
A'(3, -1), B'(3, -2), and C'(0, -1)
We note that for a 180° rotation transformation about the origin, we get;
Coordinates of preimage = (x, y)
Coordinates of image after 180° rotation about the origin = (-x, -y)
Therefore, a 180° rotation of ΔABC about the origin, would give ΔA''B''C'' as follows;
A(-9, 3), B(-9, 6), and C(0, 3) = A''(9, -3), B''(9, -6), and C''(0, -3)
The formula for a dilation of a point about the origin is given as follows;
[tex]D_{O, \, k} (x, \, y) = (k\cdot x, \, k\cdot y)[/tex]
Where;
k =The scale factor = 1/3, (one-third) we have;
A dilation of ΔA''B''C'', by a scale factor of 1/3, we get ΔA'B'C' as follows;
[tex]D_{O, \, \frac{1}{3} } A''(9, \, -3) = A'(\frac{1}{3} \times 9, \, \frac{1}{3} \times -3) = A'(3, -1)[/tex]
[tex]D_{O, \, \frac{1}{3} } B''(9, \, -6) = B'(\frac{1}{3} \times 9, \, \frac{1}{3} \times -6) = A'(3, -2)[/tex]
[tex]D_{O, \, \frac{1}{3} } C''(0, \, -3) = C'(\frac{1}{3} \times 0, \, \frac{1}{3} \times -3) = C'(0, -1)[/tex]
The coordinates of the vertices of ΔA'B'C' are A'(3, -1), B'(3, -2), and C'(0, -1), which is the same as the required coordinates of the image;
Therefore, the transformation that can be performed to show that ΔABC and ΔA'B'C' are similar are rotating ΔABC by 180° then a dilating the image derived after rotation by a scale factor of one-third (1/3) we get ΔA'B'C'.
Answer:
D
Step-by-step explanation:
The tables below show the values of y corresponding to different values of x: Table A x 3 3 2 y 1 0 0 Table B x 3 5 5 y −2 2 −2 Which statement is true for the tables? (1 point) Both Table A and Table B represent functions. Both Table A and Table B do not represent functions. Table A does not represent a function, but Table B represents a function. Table A represents a function, but Table B does not represent a function.
Answer:
is it possable you can show the graph
Step-by-step explanation:
Answer:
2nd option ,that is, Both tables do not represent a function.
Step-by-step explanation:
For a table to represent a function it's input value must correspond to exactly one output value.
As in Table A the input value of 3 corresponds to 2 different outputs, where
as in table B the input value of 5 corresponds to 2 different outputs.
x is taken as the input and y is taken as output for both the tables.Therefore, Both tables dobnot represent a function.
Quadrilateral ABCD is a rectangle. FindBD ifAO = 6x - 22 and OC = 2x + 6.
40 units
20 units
7 units
10 units
determine which statement or statements are true. If none write “none”.
By accident I circled D for question 1 and C for question 2 I’m not sure if they are correct. But if anybody can help me with 1-3 that will be a life saver!!!
THANK UUUUUU
Answer:
number 1 is C number 2 is A and number 3 is D
Step-by-step explanation:
Answer:
yeah
Step-by-step explanation:
In 2005, there were 1000 rabbits on an island. The population grows 8% per year. AT this rate, how many
rabbits will there be on the island by 2020?
Answer: 3172
Step-by-step explanation:
[tex]solve : - \\ \\ (10 {}^{2} - 6 {}^{2} ) = {?}[/tex]
[tex]\longrightarrow{\blue{64}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] = (10 {}^{2} - 6 {}^{2} ) [/tex]
[tex] = [(10 \times 10) - (6 \times 6)][/tex]
[tex] = (10 0- 36)[/tex]
[tex] = 64[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
Which of the following has the same ratio as sin A?
I dont understand what to do?
Answer:
a) 122°
b) 37°
Step-by-step explanation:
a) supplement angle of 58° = 180° - 58° =122°
b) complement angle of 53° = 90° - 53° = 37°
It would be great if someone could help me with this problem
prove that . 1+cot2 theta = cosec2theta
Answer:
see explanation
Step-by-step explanation:
Using the Pythagorean identity
sin²θ + cos²θ = 1 ( divide terms by sin²θ )
[tex]\frac{sin^20}{sin^20}[/tex] + [tex]\frac{cos^20}{sin^20}[/tex] = [tex]\frac{1}{sin^20}[/tex] , that is
1 + cot²θ = cosec²θ ← as required
What is the value of d?
A.100 B.84 C.50 D.80
Answer:
A. 100
Step-by-step explanation:
84
Step-by-step explanation:
c + 100 =180
c=180-100
c=80
100+96+d+c=360
100+96+d+80=360
276+d=360
d=360-276
d=84
How to find the frequency in a histogram
Answer:Para preparar la tabla de frecuencia para un histograma, es necesario primero establecer el número de intervalos que se desea tener.
Luego, se debe determinar el ancho común de los intervalos (interval width). Para esto, se calcula la diferencia del dato mayor y el dato menor, y se divide entre el número de intervalos deseados. Este resultado se redondea al entero mayor más cercano.
Por ejemplo, si se desea tener 10 intervalos y encontramos que el dato mayor es 35 y el menor es 12,
Step-by-step explanation:
Can someone help me with this math homework please!
Answer:
option 3. (4, -2)
Step-by-step explanation:
For a relation to be a function there should be exactly one output value for a given input.
In the given relation :-
4 has 2 outputs, -2 and 2, so if we remove the pair (4, -2) 4 will have only one output value ,i. e., 2. And hence the relation will be a function.
So the answer is option 3. (4, -2)
أريد أن أجد طريقة لإيجاد ارتفاع المخروط عن طريق معرفة قطره ومساحته . بليز أرجو الرد .
Answer:
سأعطي فقط مثالاً مقدمًا أدناه آمل أن يساعد
Step-by-step explanation:
الارتفاع = 24 سم
نصف القطر = 14 ÷ 2 = 7 سم
ارتفاع مائل = L =؟
L2 = R2 + H2
م 2 = 72 +242
م 2 = 49 + 576
م 2 = 625
L = 25
الحجم = 1 ÷ 3 × 22 ÷ 7 × 7 × 24
الحجم = 1232 سم
مساحة السطح المنحني = 22 × 7 × 7 × 25
مساحة السطح المنحني = 550
إجمالي مساحة السطح = 22 × 7 × 7 × 25 + 7
مساحة السطح الكلية = 704 سم
يرجى وضع علامة لي على أنه أذكى
whats the function for y=-4x+3
Answer:
the function for y=-4x+3
= soln,
y=mx+b"
A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s. How many possible sequences of rolls could there have been? (For example, $3,2,3,1,3,2$ is one possible sequence.)
Answer:
Step-by-step explanation:
Answer:
Sequence = 120
Step-by-step explanation:
Given
6 rolls of a die;
Required
Determine the possible sequence of rolls
From the question, we understand that there were three possible outcomes when the die was rolled;
The outcomes are either of the following faces: 1, 2 and 3
Total Number of rolls = 6
Possible number of outcomes = 3
The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;
Sequence = \frac{6!}{3!}
Sequence = \frac{6 * 5 * 4* 3!}{3!}
Sequence = 6 * 5 * 4
Sequence = 120
Hence, there are 120 possible sequence.
Step-by-step explanation:
Hope this helps
How many 20 can lengths of a pipe can be cut from a pipe 8.7 m long?
Answer:
(8.7×100)cm=870cm
870cm/20cm=43.5
so 43 20cm can be cut
Find the length of PL
A. 23
B. 19
C. 30
D. 46
Harvey has a 5- gallon container of gasoline to fill all of his small engne tanks. He uses 1/2 gallon of the gasoline to fill each small engine tank he owns. How many small engine tanks does Harvey own? (give a reason) who ever helps me thank you
Answer:
10
Step-by-step explanation:
the small engine tanks that Harvey have = 5 ÷ ½ = 10
Using the figure below, find the value of x. Enter your answer as a simplified radical or improper fraction (if necessary) into the equation box below.
Hello,
M=middle[AB]
The triangle ABC is equilateral :
x= 15/2
Question 2 of 10
The graph of g(x), shown below, resembles the graph of f(x) = x - x2, but it
has been changed somewhat. Which of the following could be the equation
of g(x)?
Answer:
option C is correct
x^4 - x^2 - 2.5
If we add any constant c in the function then it gets shifted upward by the c unit. Then the function g(x) is above the function f(x) by 2.5 units.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable.
Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The functions are g(x) and f(x) are given below.
f(x) = x⁴-x²
g(x) = x⁴-x²+2.5
We know that if we add any constant c in the function then it gets shifted upward by the c unit.
The graph is shown.
More about the function link is given below.
brainly.com/question/5245372
#SPJ7
What is 6 1/3 divied by 1/6
Answer:
38
Step-by-step explanation:
6⅓÷⅙
change 6⅓ to improper fraction
19/3÷1/6
keep the first fraction, change the division sign to multiplication and reciprocate/flip the second fraction
19/3× 6/1
the denominator 3 and numerator 6 will simplify/cancel each other
the new fraction is now: 19/1 × 2/1
there is no need to multiply the denominators because it will still be equal to 1 so we just need to multiply the numerators by each other
19×2=38 OR 38/1 (both answers are the same)
In the given figure, ∠QPR = ?
Answer:
QPR=PRS(Being alternative Angel)
HELP ME PLSSSSSSS!!!!!!!!!
Domain of the function
[-3,5)What is the first step in solving the following systrm of equations?
3x + y = 23 and 8x + 2y = 23
A. Substitute the value of y from one equation into the other equation
B. Solve the first equation for y
C. Subtract the second equation from the first equation
D. Substitute the value of x from one equation into the other equation
Hello!
{3x + y = 23 _ {y = 23 - 3x
{8x + 2y = 23 {8x + 2(23 - 3x)
The answer is A.
Good luck! :)
Pls answer 13 b ill mark u brainlist
Answer:
7 students
Step-by-step explanation:
1+2+4=7students
Is the line that passes through the points A(0,1) and B(2,5) parallel to the line that passes through the points C(0,7) and D(4,15)?
Find the slope at AB
Answer:
Slope of AB = 2
Slope of CD = 2
equal slopes means the lines are parallel
Step-by-step explanation:
Use slope formula
m = [tex]\frac{(y_{2} -y_{1} )}{(x_{2} -x_{1} )}[/tex]
line AB = [tex]\frac{(5-1)}{(2-0)}[/tex] = [tex]\frac{4}{2}[/tex] = 2
line CD - [tex]\frac{(15-7)}{(4-0)}[/tex] = [tex]\frac{8}{4}[/tex] = 2
Express the following the number indecimal
form - 25
36
Answer:
0.6944
Step-by-step explanation:
25/36 is 0.6944 in division
find the slope of the line 3x-5y =0
Answer:
slope= ⅗
Step-by-step explanation:
Rewrite the equation into the slope-intercept form, y=mx +c, where m is the gradient and c is the y-intercept.
3x- 5y= 0
+5y on both sides of the equation:
5y= 3x
Divide both sides by 5:
y= ⅗x
From the coefficient of x, the slope of the line is ⅗.
