Calculus - need work shown
Easy evaluation!
[tex]5( ln( |4x - 15| ) + c[/tex]
Step-by-step explanation:
Feel free to ask if you're left with any doubts.
Answer:
[tex]\large \text{$ 5 \ln|4x-15|+C $}[/tex]
Step-by-step explanation:
[tex]\large \displaystyle\begin{aligned}\textsf{let }\:u & =4x-15\\\implies \dfrac{du}{dx} & =4\\\implies dx & =\dfrac{1}{4}\: du\\\end{aligned}[/tex]
[tex]\large\displaystyle\begin{aligned}\int \dfrac{20}{4x-5}\:dx &=\int \dfrac{20}{u}\cdot \dfrac{1}{4}\:du\\\\&=\int \dfrac{20}{4u}\:du\\\\&=\int \dfrac{5}{u}\:du\\\\&=5 \ln |u| +C\\\\&=5 \ln |4x-15| + C\end{aligned}[/tex]
Sean has a plastic container in the shape of a cube with side lengths of 4 in. can he close the lid on the container with a 6 in. marker inside it?
Seen can close the lid on the cube container with a 6 in. marker inside it which has the side length of 4 inches.
What is a cube shape?The cube shape is the three-dimensional solid which has 6 equal side. The diagonal of a cube can be calculated with the following formula;
d=6∛a
Here, (a) is the length of the side of the cube.
Sean has a plastic container which is in the shape of a cube. The side lengths of the cube container is 4 in. Thus, the diagonal of the cube is,
d=6∛a
d=6∛(4)
d=6 x 1.587
d=9.522 inches.
The diagonal of the cube container is 9.522 inches, which is more than the length of the marker.
9.522 in >6 in
Hence, Seen can close the lid on the cube container with a 6 in. marker inside it, which has the side length of 4 inches.
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7. Use the compound-interest formula to find the account balance A with the given conditions, where P=principal, r=interest rate, n=number of compounding periods per year, t=time, in years, and A=account balance.
Answer:
$173,954.01
Step-by-step explanation:
Finding compound interest :
A = (150,000)(1 + 0.025)⁶A = (150,000)(1.025)⁶A = (150,000)(1.15969342)A = $173,954.01Use the product rule to simplify a ^7 x a ^11
Answer:
The answer to the question a∧18
Answer:
[tex]a^{18}[/tex]
Step-by-step explanation:
Use the product rule to simplify a ^7 x a ^11
[tex]a^{7}[/tex] × [tex]a^{11}[/tex] =
(add the exponents)
7 + 11 = 18
[tex]a^{18}[/tex]
PLEASE HELP I NEED THE CORRECT ANSWER AS I ONLY HAVE ONE TRY AND I NEED TO SUBMIT IT IN 10 MINUTES
Answer:
A, B, D
Step-by-step explanation:
A 6x3 =18
B 9x2=18
D 9x2=18
can anybody help me...
Answer: The 3 angles shown need to equal 180 degrees
x = 180 - 75 - 65
x = 40 degrees
Step-by-step explanation:
I had someone help out with this one...hope this helps u out have a good rest of ur day!!!!!
Which expression represents the volume of the cone that is startfraction pi over 4 endfraction times the volume of the pyramid that it fits inside? startfraction pi over 4 endfraction(2r2h) startfraction pi over 4 endfraction(4r2h) startfraction pi over 4 endfraction(startfraction r squared h over 3 endfraction) startfraction pi over 4 endfraction(startfraction 4 r squared h over 3 endfraction)
The expression of the volume of the cone that is π/4 of the volume of the pyramid, is expressed as: [tex]\mathbf{\frac{\pi}{4} (\frac{4r^2h}{3} )}[/tex].
What is the Volume of a Pyramid?Volume of a pyramid = 1/3(length)(width)(height)
Find the volume of the pyramid in the image given:
Volume of the pyramid = 1/3(2r)(2r)(h)
Volume of the pyramid = 4r²h/3
We are given that the volume of the cone is π/4 of the volume of the pyramid.
Therefore, the expression that represents the volume of the cone would be: [tex]\mathbf{\frac{\pi}{4} (\frac{4r^2h}{3} )}[/tex]
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Answer:
D:
Step-by-step explanation
Find the exact value of the given angle. Simply all radicals and rationalize all denominators.
Answer:
4√33/33
Step-by-step explanation:
Solution,
Here,
sinθ=4/7
p/h=4/7
b=?
Now using Pythagoras theorem,
[tex]\hookrightarrow h^{2} =p^{2} +b^{2} \\\\\hookrightarrow (7)^{2} =(4)^{2} +b^{2}\\\\\hookrightarrow 49-16=b^{2} \\\\\hookrightarrow b=\sqrt{33}[/tex]
Again,
tanθ=p/b
[tex]tan\theta=\frac{4}{\sqrt{33} } \\\\tan\theta=\frac{4}{\sqrt{33} } \times \frac{\sqrt{33} }{\sqrt{33} } \\\\tan\theta=\frac{4\sqrt{33} }{33}[/tex]
According to the question ,
Sin θ = 4/7
We know that , Sin θ = Perpendicular/Hypotenuse
So , by Pythagoras theorem
Perpendicular = 4 unitsHypotenuse = 7 units Base = let it be xHypotenuse² = Perpendicular ² + Base ²
7² = 4² + x²
49-16 = x²
√33 = x
5.7 = x
So , the base is 5.7 units (approx)
Tan θ = Perpendicular/base
Tan θ = 4/5.7
PLEASE HELPP PLEASEE SHOW WORK AND EXPLAIN
Step-by-step explanation:
I hope you will understand
ricky bobby wants to buy a new automobile for $23000 in 4 years. How much money must ricky’s original investment be if he makes a single deposit into an account monthly compounding and annual interest rate of 3.70% in order to reach his goal ?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$23000\\ P=\textit{original amount deposited}\\ r=rate\to 3.70\%\to \frac{3.70}{100}\dotfill &0.037\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]23000=P\left(1+\frac{0.037}{12}\right)^{12\cdot 4}\implies 23000=P\left( \frac{12037}{12000} \right)^{48}\implies \cfrac{23000}{~~ \left( \frac{12037}{12000} \right)^{48}~~}=P \\\\\\ \cfrac{23000}{~~ \frac{12037^{48}}{12000^{48}}~~}=P\implies \cfrac{23000\cdot 12000^{48}}{12037^{48}}=P\implies 19840.43\approx P[/tex]
It has rained two out of the past nine days.
Based on this data, what is the probability
that it will not rain for the next four days?
Answer:
There is only a 25% of the probability
Find the value of X round to the nearest degree
Answer:
50
Step-by-step explanation:
to find the value of x use "sinerule"
sinx/13= Sin90/17
sinx = sin90×13/17
sinx= 14/17
sinx= 0.764705882
X= SIN^-1(0.764705882)
X = 49.888
X= 50
HELP ILL GIVE BRAINLIEST
Answer:
B) 8/9
Step-by-step explanation:
0.3 + 0.5 = 0.8Change to repeating decimal (0.888888...)The decimal converts to 8/9Answer:
B
Step-by-step explanation:
0.3333 + 0.5555 = 0.8888
as a fraction it's 8/9
10 TSW #8 (Volume)
A rectangular prism has volume of 126 cm
Its length is to W ks w dkh 57cm Whit
the prism's height"
Answer:
h=6cm
Step-by-step explanation:
V=lwh
126=3×7×h
h=6cm
50 POINTS AND BRAINLIEST!!!!!!!
This table represents a proportional relationship between x and y.
x 1.3 1.6 1.9 2.2
y 1.82 2.24 2.66 3.08
What is the constant of proportionality?
Enter your answer as a decimal in the box.
Reason:
Pick any column and divide y over x
column one: y/x = (1.82)/(1.3) = 1.4column two: y/x = (2.24)/(1.6) = 1.4column three: y/x = (2.66)/(1.9) = 1.4column four: y/x = (3.08)/(2.2) = 1.4You only need to pick one column when it comes to showing your work.
The constant of proportionality is 1.4
This leads to the equation being y = 1.4x
5
Find the missing angle.
94
23°
?
Answer:
degrees
Answer:
63 degrees as 94 +23 =117
180-117=63
Write an algebraic expression for each of the statements below.
Answer:
i) 3x + 7
ii) x/3 = 9
iii) y = 2x +4
iv) y = 6x
Please help with this limit, I have tried everything but this won't work.
You're lucky that I was able to do this :)
The answer is [tex]\huge\boxed{\frac{1}{4}} [/tex]
George wants to buy a new game the original price is $54.99 but it is on sale for 25% off what is the sale price of the game?
Answer:
41.24
Step-by-step explanation:
54.99 * .25 = 13.7475
54.99 - 13.7475 =
41.2425
Answer:
$41.24
Step-by-step explanation:
54.99 x 0.25 = 13.7475
54.99 - 13.7475 = 41.2425
41.2425 ≈ 41.24
hope this helps
have a good day
please asap correct answer gets brainliest
Answer: 36 square units
Step-by-step explanation:
Divide the figure into 2 shapes: a rectangle and a triangle. Count the squares to find the dimensions of each figure. The rectangle has a width of 4 units and a length of 6 units. The triangle has a base of 6 units and a height of 4 units.
The formula for the area of a rectangle is length * width. The area of the rectangle is 4*6 = 24 square units.
The formula for the area of a triangle is (base * height)/2. The area of the triangle is (4*6)/2 = 24/2 = 12 square units.
Add the areas of both the rectangle and triangle. 24+12 = 36 square units.
The area of a
triangle is 21 in
The base is 7cm.
What is the
height?
Answer:
7 inches
Step-by-step explanation:
1. Covert 7cm into inches: approximatly 3 inches.
2. 21/3: 7
3. 7 inches
Y-intercept of x- 2y = -10
Please help
Answer:
y = [tex]\frac{1}{2} x\\[/tex]+5
Step-by-step explanation:
Y-intercept 5
Answer:
y- intercept = 5
Step-by-step explanation:
to find the y- intercept let x = 0 in the equation and solve for y
this relies on the fact that when the line crosses the y- axis the x- coordinate is zero, then
0 - 2y = - 10 , that is
- 2y = - 10 ( divide both sides by - 2 )
y = 5
then y- intercept = 5
3. Triangle JKL is shown below. Which of the following is not a true statement about
the angles in the triangle?
J 7X+2
A. The sum of 2J + ZK + ZL = 180°
B. The measure of ZJ is 65
L
4x + 7
C. The measure of ZK is 89
D. The measure of ZL is 43°
8x
Option A is true because the sum of angles in a triangle is 180, so we can rule that one out immediately.
We can solve for x for the other 3 options by setting up this equation:
7x+2 + 4x+7 + 8x = 180 | Simplify
19x + 9 = 180 | Subtract 9
19x = 171 | Divide by 19
x=9
Now we can substitute x into all the values:
<J = 7x+2 = 65
<L = 4x+7 = 43
<K = 8x = 72
Looking at the options again, we can see that A, B, and D are true, leaving C to be false.
What is the measure of
Answer:
can i have life orientation project memo for term 2
Find the surface area of the pyramid. The side lengths of the base are equal.
the radius of a sphere is r=17
what is the volume
Answer:20579.53
Step-by-step explanation:round it to its hundreth or tenth based on the question or full
In triangle ABC, what is the measure of b if a = 51, c = 38, and B = 11°?
Round the answer to the nearest hundredth.
Answer:
see photo attached for your reference.
Step-by-step explanation:
15.50 (to the nearest hundredth)
Answer:
The area of a triangle is the region enclosed between the sides of the triangle. Area of ΔABC = 1/2 × Base × Height. Let us know the basics of the area of a triangle. If ABC is an equilateral triangle, Area of ΔABC = (√3/4)a2 where a is the length of a side of the equilateral triangle.
It's seventh grade social studies the question is written "how did the issue of slavery cause the Civil War?"
Answer:
The civil war started because the south wanted to keep the country enslaved while the north wanted a free slave country. This divison between the north and the south created the civil war
Answer:
It divided the nation.
Step-by-step explanation:
North wanted to banned slavery, while the south didn't. At that time states from the north and the south were in the union. The south succeeded from the union, because of some slavery issues which lead to the Civil War.
HELP PLSSSSS!!!! ASAP!!! Insert operation signs (+,-,*,/) and parentheses as needed to make the equation true.
4 3/4 _ 7 1/2 _ 1 1/6 _ 1 1/3 = 1
Or in other words:
4.75 _ 7.5 _ 1.16666... _ 1.33333... = 1
TY PLSS HURRY!!!!
Answer:
This cannot be explained properly by me, but the answer is 4 3/4*1 1/3 divided by (7 1/2-1 1/6). I just did a lot of trial and error
Step-by-step explanation:
The mathematical operations used [tex](4.75/7.50) * 1.17 * 1.34[/tex].
What are mathematical operations?
An operation exists as a mathematical action. Addition, subtraction, multiplication, division, and calculating the root exist all instances of a mathematical operation.
Given: 4 3/4 _ 7 1/2 _ 1 1/6 _ 1 1/3 = 1 or
4 3/4 _ 7 1/2 _ 1 1/6 _ 1 1/3 = 1
Convert mixed fraction into a proper fraction we have
[tex](19/4) * (15/2) * (7/6) * (4/3) = 1[/tex]
Now convert the proper form of the fraction into a decimal
[tex]$4.75 * 7.50 * 1.16 * 1.34[/tex]
Inserting operation signs, then we get
[tex]= (4.75/7.50) * 1.17 * 1.34[/tex]
= 0.99294
= 1 (approximately)
Therefore, the correct answer is [tex](4.75/7.50) * 1.17 * 1.34[/tex].
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What do I need to know for these and how to do it and answer