Given the expression :
\(8\times\frac{1}{4}\)so, the answer will be as following :
\(8\times\frac{1}{4}=\frac{8}{4}=2\)so, the answe is 2
Workout to the simplest:
\( \int \: {x}^{2} ln( {x}^{3} ) dx\)
Answer:
\(\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} + \rm C\)
Step-by-step explanation:
we would like to integrate the following integration
\( \displaystyle \int {x}^{2} \ln( {x}^{3} ) dx\)
before doing so we can use logarithm exponent rule in order to get rid of the exponent of ln(x³)
\( \displaystyle \int 3 {x}^{2} \ln( {x}^{} ) dx\)
now notice that the integrand is in the mutilation of two different functions thus we can use integration by parts given by
\( \rm\displaystyle \int u \cdot \: vdx = u \int vdx - \int u' \bigg( \int vdx \bigg)dx\)
where u' can be defined by the differentiation of u
first we need to choose our u and v in that case we'll choose u which comes first in the guideline ILATE which full from is Inverse trig, Logarithm, Algebraic expression, Trigonometry, Exponent.
since Logarithms come first our
\( \displaystyle u = \ln(x) \quad \text{and} \quad v = {3x}^{2} \)
and u' is \(\frac{1}{x}\)
altogether substitute:
\( \rm \displaystyle \ln(x) \int 3{x}^{2} dx - \int \frac{1}{x} \left( \int 3 {x}^{2} dx \right)dx\)
use exponent integration rule to integrate exponent:
\( \rm \displaystyle \ln(x) \int 3{x}^{2} dx - \int \frac{1}{x} \left( 3\frac{ {x}^{3} }{3} \right)dx\)
once again exponent integration rule:
\( \rm \displaystyle \ln(x) 3\frac{ {x}^{3} }{3} - \int \frac{1}{x} \left( 3\frac{ {x}^{3} }{3} \right)dx\)
simplify integrand:
\( \rm \displaystyle \ln(x) 3\frac{ {x}^{3} }{3} - \int \frac{ 3{x}^{3} }{3x} dx\)
use law of exponent to simplify exponent:
\( \rm \displaystyle \ln(x) \frac{ 3{x}^{3} }{3} - \int \frac{ 3\cancel{ {x}^{3}} }{3 \cancel{x}} dx\)
\( \rm \displaystyle \ln(x) \frac{ 3{x}^{3} }{3} - \int \frac{ 3{x}^{3} }{3} dx\)
use constant integration rule to get rid of constant:
\(\rm \displaystyle \ln(x) \frac{3 {x}^{3} }{3} - 1 \int {x}^{2}dx\)
use exponent integration rule:
\(\rm \displaystyle \ln(x) \frac{3 {x}^{3} }{3} - \frac{ {x}^{3} }{3} \)
\(\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} \)
and finally we of course have to add the constant of integration:
\(\rm \displaystyle \ln(x) { {x}^{3} } - \frac{ {x}^{3} }{3} + \rm C\)
and we are done!
x-5y=16 , 4x-2y=-8 solve using elimination method
Answer:
x = -4
y = -4
Step-by-step explanation:
L1 x - 5y = 16
L2 4x - 2y = -8
4*L1 - L2
4x - 20y = 64
-4x + 2y = 8
-----------------------
-18y = 72
y = 72 / -18
y = -4
x - 5y = 16
x = 16 + 5y
x = 16 + 5(-4)
x = 16 - 20
x = -4
How to find the area of a 5in and 11in triangle
Answer:
27.5
Step-by-step explanation:
5 times 11 = 55
55 divided by 2 =27.5
You ask 40 students which of three items from the cafeteria they like the best. You record the results on the piece of paper shown. Result of a survey on a paper. Pizza: 30 percent. . Pasta: 18 students. . Salad: 10 students. What percent of students answered pasta?
Answer:
45%
Step-by-step explanation:
There are 45% percent of the students who answered pasta.
What is percentage?Percentage is a measurement to find value of a given number out of a hundred.
Given that,
Total number of students at cafeteria = 40
Percentage of students answered for pizza = 30%
Therefore, number of students answered for pizza = 40x30/100 = 12
Also given that,
18 students answered for pasta and 10 students answered for salad,
The percentage of students who answered for pasta
= (18/40)x100
= 45
45% of students answered for pasta.
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¿Cuál es la tangente de la siguiente derivada:
f’(x) = 6x^2 - 6x - 12
Esta es la pendiente de la recta tangente a la curva f(x) en el punto x = a.
Que es derivado?La tangente de una derivada no es una operación matemática bien definida. Supongo que lo que se quiere encontrar es la pendiente de la recta tangente a la curva representada por la función f(x) cuya derivada es f'(x) = 6x^2 - 6x - 12 en algún punto x = a.
La pendiente de la recta tangente a la curva f(x) en el punto x = a está dada por la derivada de f(x) evaluada en ese punto, es decir:
m = f'(a)
Entonces, para encontrar la pendiente de la recta tangente a la curva de la función f(x) en el punto x = a, tenemos que evaluar f'(x) en x = a:
m = f'(a) = 6a^2 - 6a - 12
donde f(a) es el valor de la función en el punto x = a.
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A = \(\frac{1}{2}\)h(B + b) Solve for B.
(area of a trapezoid)
A = 1/2h(B+b)
Multiply both sides by 2:
2A = h(B+b)
Divide both sides by h:
2A/h = (B+b)
Subtract b from both sides:
2A/h - b = B
Switch the equation so B is on the left side:
B = 2A/h - b
Step-by-step explanation:
\(a = \frac{1}{2} h( \beta + b) \\ 2a = h( \beta + b) \\ \frac{2a}{h} = \beta + b \\ \frac{2a}{h} - b = \beta \\ thank \: you\)
A 2,100-square-foot home in Cheyenne, WY , costs $110 per square foot. How much does this home cost? (Do not enter anything but numbers for the answer or it will count it wrong. Follow directions please because I am not coming back to grade if you mess up)
$231,000.
Step-by-step explanation:We have been given that a 2,100 square foot home in Cheyenne Wyoming costs $110 per square feet.
To find the total cost of home we will multiply the total area of home by the cost of per square feet area.
The total cost of home:2,100 × 110 = 231,000$
Solve the Exponential Equation:
\(5 { }^{66} = {3}^{42} \)
Select the correct answer from each drop-down menu.
The given composite shape has an area of (72,78,66,84) cm2 and a perimeter of (42,47,40,33) cm.
Answer:
78 cm²
42 cm
Step-by-step explanation:
To obtain the area of the shape given :
The figure is divide into three different rectanglular parts :
Recall, area of a rectangle = Length x width :
Rectangle 1 : 9* 6 = 54 cm²
Rectangle 2 = 6 * 2 = 12 cm²
Rectangle 3 = 4 * 3 = 12 cm²
Total area = (54 + 12 + 12). = 78 cm²
Perimeter = sun of the exterior sides of the shape
Perimeter = (9 + 8 + 3 + 4 + 3 + 6 + 3 + 6) = 42 cm
Each week Sanji gives a prize to one employee based on rolling an 8-sided solid with faces numbered 1 through 8. Select all of the true statements. Group of answer choices p(factor of 24) = 6/8 p(odd number) = 1/2 p(number less than 8) = 1 p(multiple of 3) = 1/4 p(even number) = 1/8 P(the number 9) = 0
The true statements are:
p(factor of 24) = 6/8p(odd number) = 1/2p(multiple of 3) = 1/4P(the number 9) = 0How to get the true statementsp(factor of 24) = 6/8: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Among these, the numbers 1, 2, 3, 4, 6, and 8 are on the 8-sided die. So, there are 6 favorable outcomes out of 8 possible outcomes. This statement is true.
p(odd number) = 1/2: There are 4 odd numbers (1, 3, 5, 7) on the 8-sided die, so the probability of rolling an odd number is 4/8 = 1/2. This statement is true.
p(number less than 8) = 1: All numbers on the 8-sided die are less than or equal to 8, but not all are less than 8. There are 7 numbers less than 8 (1, 2, 3, 4, 5, 6, 7), so the probability is 7/8, not 1. This statement is false.
p(multiple of 3) = 1/4: There are 2 multiples of 3 on the 8-sided die (3 and 6), so the probability of rolling a multiple of 3 is 2/8 = 1/4. This statement is true.
p(even number) = 1/8: There are 4 even numbers (2, 4, 6, 8) on the 8-sided die, so the probability of rolling an even number is 4/8 = 1/2, not 1/8. This statement is false.
P(the number 9) = 0: The 8-sided die only has numbers 1 through 8, so it is impossible to roll a 9. The probability of rolling a 9 is indeed 0. This statement is true.
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Courtney sold 48 cantaloupes at the farmers' market and had 23 left. Which equation could be used to find x, the number of cantaloupes Courtney had originally?
Hi there!
48-x=23
23+x=48
those would be the equatipns to find x....
Answer:
uwu
Step-by-step explanation:
uwu
What is the value of the expression 1/4 (16 + g)-h when g=4 and h = 2?
a.) 16/3
b.) 4/5
c.) 3
d.) 5
20 points to who answers!
Answer:
option 3 is a correct answer
Answer: C
Step-by-step explanation:
Where g appears in the expression, substitute 4 and where h appears, substitute 2, remember to follow PEMDAS
1/4(16+g)-h
= 1/4(16+4)-2
= 1/4(20)-2 --> 1/4 * 20 = 1/4 * 20/1 = 20/4 = 5
= 5 - 2
= 3
2x2x2x2.5 divided 1.2+120
Find the simple interest charged for a loan of:
a $2000 for 3 months at 1.1% per month
Answer:
$5.50
Step-by-step explanation:
I = Prt
P = $2,000r = 1.1% = 0.011t = 3 months = 0.25 yearsSolving :
I = (2,000)(0.011)(0.25)I = (500)(0.011)I = $5.50What is the value of 5/6 divided by 3/4 in a fraction form
Answer:
5/6 ÷ 3/4 = 20/18 as simplified as 10/9 in fraction form. 5/6 ÷ 3/4 = 1.1111 in decimal form.
Step-by-step explanation:
The value of 5/6 divided by 3/4 is 10/9.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
5/6 divided by 3/4
as, fraction does not perform proper division
So, 5/6 ÷ 3/4
= 5/6 x 4/3
= 20 / 18
= 10 / 9
Hence, the resultant value is 10/9
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Aron rides his bike 12 miles in 3 hours. if he rides at a constant speed, select the answers below that are equivalent ratios to the speed he rides. Select all ratios that are equivalent.
1) 4 miles in 1 hour.
2) 16 miles in 4 hours.
3) 8 miles in 3 hours.
4) 20 miles in 6 hours.
Answer:
A
Step-by-step explanation:
he is riding at a rate of 4 in one and the others do not match 4 in 1
Hope this helps
Answer:
1) 4 miles in 1 hour
2) 16 miles in 4 hours
Step-by-step explanation:
The simplest form of this ratio is 4:1
16:4 and 12:3 both reduce to 4:1
The graph of the equation y=-2 is a line
1 parallel to the x-axis
2 parallel to the y axis
3 passing through the origin
4 passing through the point(-2,0)
Solve
The commutative property does not work for which operations?check all that applys.
Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.
Step-by-step explanation:
Hope this is right!!!!
Due today!! Pls helppp
if we that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:
100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.
What do you mean by spending?If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.
So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:
On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.
However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.
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There are 125 balloons. 40% of them are green. How many are green?
Answer:
50 of the balloons are green
Step-by-step explanation:
50/125 =40%
40/100 = 50/125
Answer:
50 green balloons
Step-by-step explanation:
Step 1:
x/125 = 40/100 Equation
Step 2:
100x = 5000 Multipy
Step 3:
x = 5000 ÷ 100 Divide
Answwer:
x = 50
Hope This Helps :)
can some one talk with me
Answer:
hi ...huyfcthnvd5yijhg7
What would need to be used to show the triangles are congruent by AAS?
A: Nothing as the triangles can not be proved congruent by AAS.
B: Angles are congruent by vertical
angles.
C: Sides are congruent by the
reflexive property.
D: Angles are congruent by the
reflexive property.
Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given two triangles, Where the base of these triangles are same
And also given that the two angles are the same.
Since,
Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).
Thus, the third angle is also equal
From AAS:
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,
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The sun of the 2 digits of a certain number is 5. If 9 is added to the original number, the new number will have the original digits reversed. Find the number
Answer:
23
Step-by-step explanation:
Assume the digits are
1, 4 or 2,3
The number can be 14, 41, 23, 32
Test each one:
14 + 9 = 23 does not work
41 + 9 = 50 does not work
23 + 9 = 32 works
32 + 9 = 41 does not work
In △ABC, AB=5, BC=4, and AC=3. The triangle is translated left 2 units and up 6 units to △A′B′C′. What is the length of segment A′C′?
A′C′=6
cap A prime cap c prime is equal to 6
A′C′=3
cap A prime cap c prime is equal to 3
A′C′=4
cap A prime cap c prime is equal to 4
A′C′=2
Answer:
3
Step-by-step explanation:
The entire triangle shifts 2 to the left and up 6, the lengths of the sides remain the same, therefore:
AC = A'C' = 3
A person is shopping for cereal, oranges, and eggs at a grocery store.
part a
Which of the following is an input in this scenario?
part b
Which of the following is an output in this scenario?
Answer:
Input- the number of cereal boxes purchased
output- the price for cereal boxes
Step-by-step explanation:
i am honestly not too sure about this answer but hopefully you get it right :)
Answer
Part A:
The number of cereal boxes purchased
Part B:
The amount paid for oranges.
I did the test and got the answer right.
if you double a number and then add 36, you get 4 over 11 (4/11) of the original number,
what is the original number?
Answer:
The original number is -22
Step-by-step explanation:
We'll label our mystery number x.
2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22
Plug in to confirm
-44 + 36 = -88/11S
8 = 8
What is the product?
(-2a² + s) (5a^2 - 6s)
Answer:
10a²+17a²s-6s²
Step-by-step explanation:
(-2a²+s)(5a²-6s)
= -10a²+12a²s+5a²s-6s²
= -10a²+17a²s-6s²
Answer:
b
Step-by-step explanation:
Use the properties of logarithms to prove log81000= log210.
Answer:
Step-by-step explanation:
Given the expression \(log_81000 = log_210\), to prove this expression is true using the properties of logarithm, we will follow the following steps.
Starting from the Left Hand Side:
\(log_81000\\\)= log₈ 10³= log_ 2^3 (10³)= log₂10Find the volume of the solid whose base is the semicircle y= squareroot( 16-x^2), where -4< x< 4 and whose cross section perpendicular axis are squares
The volume of the solid whose base is the semicircle y = √(16 - x²), where -4 < x < 4 and whose cross section perpendicular axis are squares is 256/3 unit³
To obtain the volume of a 3D shape, the cross-section area is discovered and then integrated across a predetermined limit. This technique is known as the cross-sectional method of volume fining. The area of the square base is determined in the given problem, and it is then integrated to determine the overall volume.
To find the volume we will first find the cross-sectional area and then integrate it with respect to x from -4 to 4.
Thus the volume is given as follows:
y = √(16 - x²)
V = ₋₄∫⁴ (√(16 - x²))² dx
V = ₋₄∫⁴ (16 - x²) dx
V = [16x - x³/3]₋₄⁴
V = (64 - 64/3 + 64 -64/3)
V = 256/3 unit³
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A triangle has two sides of length 2 and 6. What is the largest possible whole-number length for the third side?
Answer:
7
Step-by-step explanation:
The sum of two sides of a triangle is always greater than the third side.
2 + 6 > 7