Answer:
[tex] \displaystyle \frac{1}{12} \ln( |{4x}^{ 3} + 9|) + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following indefinite integral:
[tex] \displaystyle \int \frac{ {x}^{2} }{4 {x}^{3} + 9} dx[/tex]
in order to integrate it we can consider using u-substitution also known as the reverse chain rule and integration by substitution as well
we know that we can use u-substitution if the integral is in the following form
[tex] \displaystyle \int f(g(x))g'(x)dx[/tex]
since our Integral is very close to the form we can use it
let our u and du be 4x³+9 and 12x²dx so that we can transform the Integral
as we don't have 12x² we need a little bit rearrangement
multiply both Integral and integrand by 1/12 and 12:
[tex] \displaystyle \frac{1}{12} \int \frac{ 12{x}^{2} }{4 {x}^{3} + 9} dx[/tex]
apply substitution:
[tex] \displaystyle \frac{1}{12} \int \frac{ 1}{u} du[/tex]
recall Integration rule:
[tex] \displaystyle \frac{1}{12} \ln(|u|) [/tex]
back-substitute:
[tex] \displaystyle \frac{1}{12} \ln( |{4x}^{ 3} + 9|) [/tex]
finally we of course have to add constant of integration:
[tex] \displaystyle \frac{1}{12} \ln( |{4x}^{ 3} + 9|) + \rm C[/tex]
and we are done!
Maxis ordering a salad for lunch. He can choose one of chicken, tofu, hard-boiled eggs, or turkey to have on the salad. He can also pick one vegetable topping. The vegetable choices are sprouts, tomatoes, or olives. How many different combinations can Max create? Draw a tree diagram and the answer this question DON'T GIVE ME BULL JUST FOR POINTS
Edgar rolls two 6-sided number cubes What is the probability that he rolls a sum of 9? Use the diagram of the sample space to help you A. 2/36 , or 1/15 B. 1/11 C. 9/36, or 1/4 D. 1/36 or 1/9
The probability that he rolls a sum of 9 given the sample space is . 9/36, or 1/4.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that he rolls a sum of 9 = cubes that have a sum of 9 / total number of cubes
9/36 = 1/4
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Answer:
I believe it's A
Step-by-step explanation:
A. 2/36, or 1/15
Lee watches TV for 4 hours per day. During that time, the tv consumes 150 watts per hour. Electricity cost (12 cents)/(1 kilowatt-hour). How much does Lee's tv cost to operate for a month of 30 days?
Answer:
$2.16
Step-by-step explanation:
150 * 4 = 600watt-hours
600 = 0.6kilowatt-hours
0.6 * 30 = 18kilowatt-hours
18 * 0.12 = $2.16
A motorboat travels 204 kilometers in 6 hours going upstream. It travels 372 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
9514 1404 393
Answer:
boat: 48 km/hcurrent: 14 km/hStep-by-step explanation:
The upstream speed is ...
u = (204 km)/(6 h) = 34 km/h
The downstream speed is ...
d = (372 km)/(6 h) = 62 km/h
The speed of the boat in still water is the average of these values:
b = (34 kph +62 kph)/2 = 48 kph
The speed of the water is the difference between the boat's speed and the speed made good:
w = 48 -34 = 14 . . . km/h
The rate of the boat in still water is 48 km/h. The rate of the current is 14 km/h.
Yall wanna hear a joke
Answer:
Sure!
Step-by-step explanation:
Answer:
yeah sure...
....!!!!!!!!!!
Grass seed is going to be spread over a playing field. The number of
bags of seed needed depends on the size of the field. The rectangular
field is 90 yards long and 54 yards wide. What is the area of the field?
Answer:
4, 860 yards
Step-by-step explanation:
To find area multiply l*w. So, multiply 90 by 54 to get your answer:
90 yards × 54 yards = 4, 860 yards
if rectangular field is 90 yards long and 54 yards wide then the area of the field is 4860 square yards.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that Grass seed is going to be spread over a playing field.
The number of bags of seed needed depends on the size of the field.
The rectangular field is 90 yards long and 54 yards wide.
We need to find the area of the field.
Length of field = 90 yards
Width of field = 54 yards
Area of Field = Length×Width
=90×54
=4860 square yards.
Hence, if rectangular field is 90 yards long and 54 yards wide then the area of the field is 4860 square yards.
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Probability Event:
You ask 5 people what month their birthday is in. What is the probability that they will all be in the summer?
Label the probability event above as either
A
Independent
B
Dependent
Answer:
Dependent
Explanation:
All of the birthdays being in summer depends on the birthdays of each person.
Players of a game at the school carnival will be
allowed to draw a token for a prize. The prizes
include 8 yo-yos, 9 key chains, 12 stuffed
animals, 11 movie passes, 16 video rentals, and 14
flying disks. For each prize, there is one token
available to be drawn.
What is the probability that the first winner to
draw a token will win a stuffed animal?
Answer:
if what the person draw wot the stuffed animal there is a probability for the winner to win stuffed animal
2.66 x 10^-26
1.99x 10^-26
1.67 x 10^-27
2.33 x 10^-26
6.65 x 20^-26
5.14 x 10^-26
Convert into standard form!
Answer:
[tex]2.66 \times {10}^{ - 26} = 0.266 \times {10}^{ - 25} [/tex]
[tex]1.99 \times {10}^{ - 26} = 0.199 \times {10}^{ - 25} [/tex]
[tex]1.67 \times {10}^{ - 27} = 0.167 \times {10}^{ - 26} [/tex]
[tex]2.33 \times {10}^{ - 26} = 0.233 \times {10}^{ - 25} [/tex]
[tex]6.65 \times {10}^{ - 26} = 0.665 \times {10}^{ - 25} [/tex]
[tex]5.14 \times {10}^{ - 26} = 0.514 \times {10}^{ - 25} [/tex]
Step-by-step explanation:
good luck
the figure above, not drawn to scale, consists of a triangle resting on a square of side 5cm. the height of the triangle is 4cm. what is the total area of the figure?
Answer:
5x4x2
Step-by-step explanation:
The total area of the figure id 35 square cm.
What is area?The amount of space taken up by a two dimensional space is called area.
What is the formula for the area of triangle?The formula for the area of a triangle is
[tex]A = \frac{1}{2} (b)(h)[/tex]
Where,
A is the area of triangle.
b is the base of a triangle.
h is the height of the triangle.
What is the formula for the area of square?The formula for the area of square is
[tex]Area = a^{2}[/tex]
Where,
a is the side length of square.
According to the given question.
A triangle is resting on a square.
Side length of square, a = 5cm
So, the area of square = [tex]5^{2} = 25 square cm[/tex]
Also, a triangle with height 4cm.
Since, the triangle is resting on a square.
⇒ Base length of the triangle = 5cm
So, the area of triangle = [tex]\frac{1}{2} (5)(4)= 10 square cm[/tex]
Therefore,
The total area of the given figure = Area of square + Area of triangle
⇒ Total area of figure = (25 + 10) square cm
⇒ Total area of figure = 35 square cm
Hence, the total area of the figure id 35 square cm.
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A model predicts that the population of a certain town was 10,000 in 2001. The model also
predicts that each year for the next 5 years, the population p increased by 8% of the previous
year's population. Which equation best represents this model, where X is the number of years after
2001, for X < 5?
Answer:
The equation that best represents this model is [tex]P(x) = 10000(1.08)^x[/tex]
Step-by-step explanation:
Exponential equation for population growth:
The exponential equation for population growth, after x years, is given by:
[tex]P(x) = P(0)(1+r)^x[/tex]
In which P(0) is the initial population and r is the growth rate.
A model predicts that the population of a certain town was 10,000 in 2001.
This means that [tex]P(0) = 10000[/tex]
8% yearly increase.
This means that [tex]r = 0.08[/tex]. So
[tex]P(x) = P(0)(1+r)^x[/tex]
[tex]P(x) = 10000(1+0.08)^x[/tex]
[tex]P(x) = 10000(1.08)^x[/tex]
The equation that best represents this model is [tex]P(x) = 10000(1.08)^x[/tex]
Plz hurry in need help !!
In ΔQRS, r = 1.5 inches, ∠S=23° and ∠Q=22°. Find the length of s, to the nearest 10th of an inch.
Answer:
0.8 inches
Step-by-step explanation:
< R = 180-23-22 = 135°
the length of s = 1.5 × sin 23° / sin 135°
= 1.5 × 0.391 / 0.707 = 0.5865/0.707
= 0.8 inches
Me.red's science class , the ratio of boys to girls is 2.1 . If there are 9 total students in the class , how many boys are there ?
Answer:
6
Step-by-step explanation:
this is how I calculate:
2x + x = 9
3x=9
x=3 girls
2(3)=6
6 boys
Heres a math thingy because im slow and dk how to do it :)
Draw a line between each description and the transformation it describes.
1. Shift up, down, right and/or left (Rotation)
2. A flip over line (Reflection)
3. A turn about a point (Dilation)
4. A change in size (Translation)
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Types of shifting.
1.) Shift up, down, right and/or left - Translation
2.) A flip over line - Reflection
3.) A turn over a point - Rotation.
4.) A change in size - Dilation
Answer:
1.) Shift up, down, right and/or left - Translation
2.) A flip over line - Reflection
3.) A turn over a point - Rotation.
4.) A change in size - Dilation
Sam is getting ready for a big date when he realizes that he has no money. his roommate, Bill, also has no money, but he has a credit card. knowing that nobody will let Sam use Bill's credit card, Sam asks Bill to put out a cash advance for $120.00. Bill agrees under the condition that Sam is responsible for all interest that accrues on the cash advance which is 30% interest rate, compounded monthly. The $120 cash advance is repaid in monthly installments over 5 years. How much should Bill ask Sam to pay in interest for the cash advance?
Answer:
b 112.80
Step-by-step explanation:
took test on edge
The interest that accrues on the initial down payment at 30% interest rate is $408 .
What is interest?The term interest refers to money that accrues on a principal sum. It is commonly employed in the parlance of borrowing money.
Since it is a compound interest;
A = P(1 + r/n)^nt
Where;
A = amount
P = principal
r = rate
n = number of times compounded per year
t = total time taken
A = 120(1 + 0.025)^12 × 5
A = $528
A = P + I
I = A - P
I = $528 - $120
I = $408
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can you please answer this
Answer:
C is the correct answer
Step-by-step explanation:
jonathan walks to school on a sidewalk by going 8 blocks to the east and then 6 blocks south. how much distance (in blocks) would he save if he cut across the field to go to achool instead of walking along the sidewalk?
Answer:
Is there an image to visualize the field?
Step-by-step explanation:
I would love to help.
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ipt If M is the midpoint of AB, what is AB?
Answer:
43
Step-by-step explanation:
The midpoint means that it is in the middle. So 3x+8=5x-1. You need to find x to really fine the amount. Could be 8x+7, but if you want to find the amount without x you need to find x.
3x+8=5x-1
3x-3x+8=5x-3x-1
8=2x-1
8+1=2x-1+1
9=2x
9/2=4.5
if x is 4.5 then all you need to do is multiply 8 by 4.5 and then add 7. You will get 43.
Leahs family is going camping her parents bring a tent. Which is in the shape of a triangular prism. what is the surface area of the tent
Answer:
leah is going to diie due to a forest fire
Step-by-step explanation:
Math help! I need help!!
Answer:
D. angle 7 and angle 5.
Step-by-step explanation:
Angle 7 and angle 5 are vertical angles; vertical angles will always be congruent (equal).
Find P(15,6) The subject is permutations
Answer:
3603600
Step-by-step explanation:
I used my calculator
¿Cuál es el área de un solar rectangular cuyas dimensiones son 12m de largo y 11m de ancho?
Answer:
Es 46m. (opción B)
Step-by-step explanation:
12m. x 2 = 24m.
11m. x 2 = 22m.
22m. + 24m. = 46m.
Espero que te ayude
What's the perimeter of the trapezoid?
Answer:
Something about 39,40 or 41
Its mostly 40
A person invests 9500 dollars in a bank. The bank pays 6.25% interest
compounded daily. To the nearest tenth of a year, how long must the
person leave the money in the bank until it reaches 18700 dollars?
A = P(1 + -)nt
n
Answer:
10.8 years
Step-by-step explanation:
18700 = 9500(1 + 0.0625/365)^365t where t is the time in years.
(1 + 0.0625/365)^365t = 18700/9500
365t ln(1 + 0.0625/365) = ln 18700/9500
t = ln 18700/9500 / 365 ln(1 + 0.0625/365)
10.837
= 10.8 years.
sandwiches to milk cartons
A class has 6 boys and 15 girls. What is the ratio of boys to girls?
Answer:
6:15
Step-by-step explanation:
Boys : Girls
6 : 15
BRAINLIEST if correct
Answer:
A=38.88 or 38.9
Step-by-step explanation:
If both are similar then the 9 and the 7.2 are the same
9-7.2= 1.8
9x6=54
7.2-1.8=5.4
7.2x5.4=38.88 or 38.9
please help me on this question,...........
Estimate the line of best fit using two points on the line 100 90 80 70 (e, 80) 60 30 20 10 (2.20) 10 O A. y= 2x O B. y = 2x+10 C. y= 10x + 2 OD. y= 10x
Answer:
[tex]y = 10x[/tex]
Step-by-step explanation:
Given
The attached plot
Required
The line of the best fit using [tex](8,80)[/tex] and [tex](2,20)[/tex]
We have:
[tex](x_1,y_1) = (8,80)[/tex]
[tex](x_2,y_2) = (2,20)[/tex]
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{20 - 80}{2- 8}[/tex]
[tex]m = \frac{-60}{-6}[/tex]
[tex]m = 10[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 10(x - 8) + 80[/tex]
Expand
[tex]y = 10x - 80 + 80[/tex]
[tex]y = 10x[/tex]