differentiate with respect to x:y= sinh^-1(x^2+1)
Answer:
The first derivative of [tex]y = \sinh^{-1} (x^{2}+1)[/tex] is [tex]y' = \frac{2\cdot x}{\sqrt{x^{2}+2\cdot x +2}}[/tex].
Step-by-step explanation:
We proceed to find the first derivative of [tex]y = \sinh^{-1} (x^{2}+1)[/tex] by explicit differentiation and rule of chain:
[tex]y = \sinh^{-1} (x^{2}+1)[/tex]
[tex]y' = \frac{2\cdot x}{\sqrt{(x^{2}+1)^{2}+1}}[/tex]
[tex]y' = \frac{2\cdot x}{\sqrt{x^{2}+2\cdot x +2}}[/tex]
The first derivative of [tex]y = \sinh^{-1} (x^{2}+1)[/tex] is [tex]y' = \frac{2\cdot x}{\sqrt{x^{2}+2\cdot x +2}}[/tex].
For the following right triangle, find the side length x. Round your answer to the nearest hundredth
12
9
Answer:
7.94
Step-by-step explanation:
[tex]a^{2} + 9^{2} =12^{2} \\a^{2} +81 = 144\\a^{2} = 63\\a = \sqrt{63} \\a= 7.93725[/tex]
4. Samara's monthly taxable income was $3276.54. If she paid $757.24 in taxes, what
percentage of her taxable income did she pay?
Answer:
23.1%
Step-by-step explanation:
Given data
monthly taxable income was $3276.54
Tax= $757.24
Percentage of tax paid= tax paid/monthly income* 100
Percentage of tax paid=757.24/3276.54* 100
Percentage of tax paid=0.231* 100
Percentage of tax paid=23.1%
Kate is building with blocks. She needs to build a rectangular prism that is 4 meters long by 3 meters wide by 112 meters high. She is building with cubes that have side lengths of 12 meter. What is the volume of the box she needs to build in cubic meters?
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Answer:
1344 cubic meters
Step-by-step explanation:
The volume is the product of the dimensions for a rectangular prism:
V = LWH
V = (4 m)(3 m)(112 m) = 1344 m³
Kate needs a volume of 1344 cubic meters.
please help A video game box is shaped like a rectangular prism with the following dimensions Length = 20 in • Width = 8.25 in. • Height = 4.5 in. What is the volume of the box in cubic inches?
Answer:
V= 742.4 in³
Step-by-step explanation:
V= L x W x H = (20)(8.25)(4.5) = 742.4 in³
Joey is buying a new flat screen TV for $359.99. Sales tax in Jeoy's state is 8.25%. Calculate the amount of sales tax that Jeoy will pay for the purchase
Answer: 389.69
Step-by-step explanation:
Answer: $29.70
Step-by-step explanation:
total x tax rate= 359.99 x 8.25 = 2969.92
divide by 100% = $29.70
sales tax total: $29.70
product is to multiplications as quotient is to
ANSWER AND STEPS PLEASE
A container that holds wheat is shaped like a cone. The diameter of the base of the container is 21 and 3/4 feet, and the height of the container is 10.3 feet.
Which measurement is closest to the volume of the container in cubic feet?
Answer choices:
A. 15,307.55 ft3
B. 1,275.63 ft3
C. 5,102.52 ft3
D. 3,826.89 ft3
Answer:
answer is b.
Step-by-step explanation: use formula
V=1/3(hπr²)
so using this formula gives us 1275.62897 but rounded off gives us 1,275.63 ft3
Element X is a radioactive isotope such that every 11 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 60 grams, how much of the element would remain after 25 years, to the nearest whole number?
Answer:
Ending Amount = beginning amount / 2^n where "n" is the number of half-lives or elapsed time / half-life
For this problem "n" = 25 / 11 = 2.2727272727
Ending Amount = 60 grams / 2^2.2727272
Ending Amount = 60 / 4.832357534
Ending Amount = 12.4162998242 grams
Source: www.1728.org/halflife.htm
Step-by-step explanation:
A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. The element would remain after 25 years, to the nearest whole number is 2 grams.
What is a radioactive isotope?A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. This surplus energy can be discharged as gamma radiation from the nucleus, transferred to one of its electrons and released as a conversion electron, or used to generate and produce a new particle from the nucleus.
Given the life of radioactive material is stated by the formula,
[tex]N_t = N_o e^{-\lambda t}[/tex]
Now, given the half-life of the comes in 11 years, therefore, the rate of decay will be,
[tex]N_t = N_o e^{-\lambda t}\\\\\dfrac{N_t}{ N_o }=e^{-\lambda t}\\\\0.5 = e^{-\lambda \times 11}\\\\\dfrac{ln(0.5)}{11}=\lambda[/tex]
λ = 0.14631
Given the initial mass is 60 grams, therefore, the amount that will be remaining after 25 years will be,
[tex]N_{25} = 60 \times e^{(-0.14631\times 25)}\\\\N = 1.5474\rm\ grams \approx 2\ grams[/tex]
Hence, the element would remain after 25 years, to the nearest whole number is 2 grams.
Learn more about Radioactive Isotopes:
https://brainly.com/question/1907960
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i need help now, The rectangle and the trapezoid have the same area. What is the length l of the rectangle?
Answer:
The I is 12.
Step-by-step explanation:
You dont count the slang when you are finding the area, im not good at explaining but its basically just 12x9. 12x9=x. X is the area- aka 108. Divide 108 by the 9 in the rectangle. IM BAD AT EXPLAINING SORRY
Answer:
36
Step-by-step explanation:
(figure out length of triangle)24-12=12
(find full length of base which is equal to L of rectangle)24+12=36
The local grocery store is having a sale on watermelons. Mr. Jackson purchases 10 watermelons for a school picnic. He pays $39.90 for the watermelons. What is the price of each watermelon?
Answer:
$3.99 per watermelon
Step-by-step explanation:
$39.90 total paid divided by 10 watermelons is $3.99
Colin slices a cake into 8 equal-sized slices. He and his friends eat 5 slices of the cake.
What fractional part of the cake do Colin and his friends eat?
Answer:
5/8
Step-by-step explanation:
there are 8 slices.
if he and his friends eat 5 pieces, they ate 5 out of 8 pieces.
in maths, we write 5 out of 8 like 5/8
hope this helped, any questions - just ask
good luck,
-cheesetoasty
plz help solve,
velocity units are ft/min
Answer:
t = 11 min
and
t = 18 min
Step-by-step explanation:
When we have unidimensional motion, the sign of the velocity defines the direction.
So we could say that a positive velocity like:
v = 4ft/min
Means that you are moving to the right with a speed of 4 feet per minute.
And a negative velocity like:
v = -3 ft/min
means that you are moving to the left with a speed of 3 feet per minute.
Then the bug changes direction when the velocity changes of sign.
In the graph, we can see that the velocity changes of sing in two points, these points are:
t = 11 min
and
t = 18 min
3. Figure ABCD Shown below is
made up of a semlore and a
rectangle. O is the contre of the
line DC
(Use
- )
10 cm
Calculate the area of
anglo AOB
Answer:
In a rectangle ABCD of 3 mx 4 m, starting from A and D, along the sides AB and DC after every 30 cm, a square shape of 10 cm is taken out as shown below. What will be the perimeter (in cm)
Step-by-step explanation:
12 CM And 300 CM is the answer
The fourth grade classes are painting designs on tile
squares to make a mural. Mrs. Kirk's class painted 3/10
of the mural. Mr. Becker's class painted 21/100 of the
mural. What part of the mural is painted?
You know how to add fractions with parts that are the
same size. You can use equivalent fractions to add
fractions with parts that are not the same size.
Example 1 Find o + 700
STEP I Write to and 200 as a pair of fractions STEP 2 Add
with a common denominator.
Think: Write using fractions with a common
Think: 100 multiple of 10 ose 100
denominator
the common denominator
30 21
Thinkt already
3 3 x
has 100 in the
100 100 100
10
100 denominator
+
Do
10x
Math
Talk
So
of the mural is painted.
100
MATHEMATICAL PRACTICES
Draw Conclusions When adding
tenths and hundredths, can you
100common
Answer:
51/100
Step-by-step explanation:
Solve the quadratic equation by using either a numeric or a graphic approach. x^2-14x-49=0
A. X= -11.1 or x=-12
B. X=12.3 or x=-10.82
C. X=16.9 or x=-2.9
D.X=1 or x=-3
Answer:
The answer to this question is A
Step-by-step explanation:
What is the area of a triangle that has a base of 15 yards and a height of 11 yards?
O 165 yd 2
41.25 yd 2
O 330 yd 2
O 82.5 yd 2
Please asap
Answer:
The shape is a triangle, not a quadrilateral.
Step-by-step explanation:
A= hbb/2 = 11·15/2 = 82.5
The area of the triangle is 82.5 yd².
Resale Value Garland Mills purchased a certain piece of machinery 2 years ago for $500,000. Its present resale value is $420,000. Assuming that the machine's resale value decreases exponentially, what will it be (in dollars) 4 years from now? (Round your answer to the nearest dollar.)
Answer:
260,000
Step-by-step explanation:
The value decreases by 40,000 per year (500000-42000/2 years) the value will decrease by 240000 in six (4 years plus 2 years already passed) years. 6 x 40,000 =240000
So, the value should be 260,000 (500000-240000)
Or
year 1 500000-40000=460000
year 2 460000-40000=420000
year 3 420000-40000=380000
year 4 380000-40000=340000
year 5 340000-40000=300000
year 6 300000-40000=260000
The machine's resale value Garland Mills purchased in 4 years from now will be; $353,049
What is the future value amount?
We are told that the machines present resale value is $420000. Now formula for future value is;
Future value = present value * exp(cx)
Thus;
$420,000 = $500,000 * exp(2c)
420000/500000 = exp(4c)
2c = In(420000/500000)
c = -0.087
Future value = present value * exp(cx)
Future value = $500,000 * exp(-0.087 * 4)
Future value = $353,049
Therefore, the machine's resale value in 4 years from now will be $353,049
Read more about future value amount at; https://brainly.com/question/13961729
plsss help with this question pls with whole procedure pls help
i hope this helps.......
For the function y = -1+6 cos (39(x-5) (x-5), what is the minimum value?
m = 0 , b = - 1+6cos (39)...
What is the volume of the fish tank if the base is 4 feet, the width is 2 feet, and
the height is 3 feet? Be sure to label your units.
Answer:
24 ft³
Step-by-step explanation:
The volume formula for a rectangular prism is ...
V = LWH
V = (4 ft)(2 ft)(3 ft) = 24 ft³
The volume of the fish tank is 24 cubic feet.
Find the midpoint of the segment below and enter its coordinates as an
ordered pair. If necessary, express.coordinates as fractions, using the slas
mark ( / ) for the fraction bar.
(-4,3) (-4,-3)
During a certain epidemic, the number of people that are
infected at any time increases at a rate proportional to the
number of people that are infected at that time. If 1,000 people
are infected when the epidemic is first discovered, and 1,200
are infected 7 days later, how many people are infected 12 days
after the epidemic is first discovered?
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Answer:
1367 people
Step-by-step explanation:
The wording "a rate proportional to the number" indicates the function is exponential. The growth factor is 1200/1000 = 1.2 in 7 days, so the exponential function can be written ...
i(t) = 1000(1.2^(t/7))
After 12 days, the number infected is modeled as ...
i(12) = 1000(1.2^(12/7)) ≈ 1367
About 1367 people are infected 12 days after discovery.
First answer gets brainest. 8th grade math root question
Answer:
9
Step-by-step explanation:
Answer: 9
Step-by-step explanation:
Square Rooting is basically going down to the origins of the number, trying to figure out what times (x) would give you your current number. In order it get 81, you would need to do 9*9, therefore making the square root 9
Plzzzz answer fast......
Answer: (d)
Step-by-step explanation:
Given
XYZA is a rhombus and side XY is 8 units
We know, In a rhombus
All sides are equalsDiagonals bisect each other perpendicularlyUsing the above property, we can write
[tex]XY=ZA=8\ \text{units}[/tex]
Thus, option (d) is correct.
A magician is filling his underwater escape tank with water. It is being filled by two water hoses. Hose 1 can fill the tank in 4 hours, while both hoses together can fill the tank in 2 hours. How long does it take to fill the underwater escape tank tank using only hose 2? type just the number no words
Answer:
4 hours
Step-by-step explanation:
Mr. Taylor arranges some chairs in rows. He puts the same number of chairs in each of the 7 rows and puts 7 chairs in the last row. He sets up 70 chairs. How many chairs does he pt in each of the 7 equal rows?
Choose the equation that can be used to solve the problem.
(7xc) +7=70
(70/7) +7=C
(7xc)-7=70
Answer:
The first one
Step-by-step explanation:
We need to find out how much chairs there are in each of the 7 rows, so we put it as 7c. The last row has 7 chairs, so we use an addition sign to include that. Since there are 70 chairs in total, the sum is 70.
Hope this helps!
Find the distance between the points (-4,-5) and (3, -1).
✓17
37
65
Answer:
3.16
Step-by-step explanation:
Given data
points (-4,-5) and (3, -1)
x1=-4
y1=-5
x2=3
y2=-2
The expression for the distance between two points is
d=√((x_2-x_1)²+(y_2-y_1)²)
substitute
d=√((3-4)²+(-2-(-5))²)
d=√((-1)²+(-2+5)²)
d=√1+(3)²
d=√1+9
d=√10
d=3.16
Hence the distance is 3.16
The following table shows the values of y for different values of x:
x y
0 0
1 0
2 4
Which statement best explains whether the table represents a linear function or a non-linear function?
It represents a linear function because its points are on a straight line.
It represents a linear function because its points are not on a straight line.
It represents a nonlinear function because its points are on a straight line.
It represents a nonlinear function because its points are not on a straight line.
Answer:
I believe it is D
Step-by-step explanation:
Not 100% dont trust double check
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic/cc-6th-volume-with-fractions/e/volume_with_fractions?modal=1
???? Do we go to that website to answer the question? I’m lost