![DEvaluatearcsin(6)]at X = 4.dx](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/KPfnpqMjjZ1ml4cuKvhak0cXNH2HyCAn.png)
Answers
Answer:
[tex]\frac{1}{2\sqrt{5} }[/tex]
Step-by-step explanation:
Let, [tex]\text{sin}^{-1}(\frac{x}{6})[/tex] = y
sin(y) = [tex]\frac{x}{6}[/tex]
[tex]\frac{d}{dx}\text{sin(y)}=\frac{d}{dx}(\frac{x}{6})[/tex]
[tex]\frac{d}{dx}\text{sin(y)}=\frac{1}{6}[/tex]
[tex]\frac{d}{dx}\text{sin(y)}=\text{cos}(y)\frac{dy}{dx}[/tex] ---------(1)
[tex]\frac{1}{6}=\text{cos}(y)\frac{dy}{dx}[/tex]
[tex]\frac{dy}{dx}=\frac{1}{6\text{cos(y)}}[/tex]
cos(y) = [tex]\sqrt{1-\text{sin}^{2}(y) }[/tex]
= [tex]\sqrt{1-(\frac{x}{6})^2}[/tex]
= [tex]\sqrt{1-(\frac{x^2}{36})}[/tex]
Therefore, from equation (1),
[tex]\frac{dy}{dx}=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}[/tex]
Or [tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{x}{6})]=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}[/tex]
At x = 4,
[tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{4}{6})]=\frac{1}{6\sqrt{1-\frac{4^2}{36}}}[/tex]
[tex]\frac{d}{dx}[\text{sin}^{-1}(\frac{2}{3})]=\frac{1}{6\sqrt{1-\frac{16}{36}}}[/tex]
[tex]=\frac{1}{6\sqrt{\frac{36-16}{36}}}[/tex]
[tex]=\frac{1}{6\sqrt{\frac{20}{36} }}[/tex]
[tex]=\frac{1}{\sqrt{20}}[/tex]
[tex]=\frac{1}{2\sqrt{5}}[/tex]
Related Questions
Solve for b in the equation 4(b + 2) = 16
Answers
Answer:
b=2
Step-by-step explanation:
One report said that it rained 3 inches in two days. It actually rained 1.05 inches and 1.8 inches. How far off was the report? Explain your answer.
Answers
Answer:
Step-by-step explanation:
1.80 + 1.05 = 2.85
3.00 - 2.85 = .15 inches
Tash conducted a survey of the students in her school.
From the results, Tash calculated that 60% of the
students go to school by bus.
Lian knows that 450 students go to school by bus.
How can she use the information to find the number of
students in the school?
Answers
Answer:
The total number of students in the school is 750. You can use algebraic equation to calculate the number of the students. Let x be the total number of students in the school. Hope this helps.
A cake was sliced into 8 parts. If each of these kids gets a slice of cake, what part of the cake will be left? Will the remaining cake be enough if there will be 5 more kids coming?
Answers
Step-by-step explanation:
Hello can you please give the amount of kids first?
If bricks are each 3 inches × 4 inches × 8 inches, how many bricks can be fit into a space which is 1 foot × 4 feet × 8 feet?
A 1 to 250
B 251 to 500
C 501 to 750
D 751 to 1000
E >1000
Answers
Answer:
The correct option is B.
Step-by-step explanation:
Consider the provided information.
The dimensions of bricks are in inches so convert foot into inches.
1 foot = 12 in
4 feet = 48 in
8 feet = 96 in
To calculate the number of bricks that fit into space we divide the space's volume by the volume of 1 brick.
[tex]\text{Number of bricks in space}=\dfrac{12\times 48 \times96}{3\times 4 \times8}[/tex]
[tex]\text{Number of bricks in space}=576[/tex]
Hence, 576 bricks can be fit into a space.
Therefore the correct option is B.
is a hotdog a taco or a sandwitch?
Answers
Answer:
Step-by-step explanation:
None of them
HELPPP
Ali and Jake went on a cross-country
trip. They took a train part of the way,
and took a bus the rest of the way. They
traveled a total of 1100 kilometers,
riding on the train 350 more kilometers
than on the bus.
Let x = kilometers traveled by bus. Let
y = kilometers traveled by train.
Answers
Answer:
so what are we trying to figure out?
Step-by-step explanation:
What is the equation of the line whose y-intercept is 3 and slope is 1?
O y=x-3
O y=x+3
O y= 3x+1
Answers
Answer:
y = x + 3
Step-by-step explanation:
y = mx + b
m is the slope
b is the y intercept
if m = 1 and b = 3 then
y = x + 3
Thirty-two of 50 marbles are blue. What percent of the marbles are blue?
Answers
Answer:
64%
Step-by-step explanation:
Thirty-two of 50 marbles = 32/50[tex]\frac{32}{50} = \frac{64}{100}[/tex] 64/100 = 64%I hope this helps!
Couch and coffee table cost a total of $996. The cost of the couch is two times the cost of the coffee table find the cost of each item.
Answers
Answer:500
Step-by-step explanation:
A shoe salesperson sold 20 pairs of shoes for $640. A brown pair of shoes sells for $30 and a black pair for $35. How many brown pairs were sold? A. 12 B. 14 C. 15 D. 8
Answers
Answer:
12 pairs
Step-by-step explanation:
Represent Brown with B and Black with A
So:
[tex]A + B = 20[/tex] --- Pairs sold
[tex]30B + 35A = 640[/tex] --- Amount
Required
Solve for B (the brown pairs)
Make A the subject in the first equation
[tex]A = 20 - B[/tex]
Substitute 20 - B for A in the second
[tex]30B + 35(20-B) = 640[/tex]
Open bracket
[tex]30B + 700 - 35B = 640[/tex]
Collect Like Terms
[tex]30B - 35B = 640 -700[/tex]
[tex]-5B = -60[/tex]
Divide both sides by -5
[tex]B = \frac{-60}{-5}[/tex]
[tex]B =12[/tex]
What are the x- and y-intercepts of the following Standard Form Equation:
- 2x + 5y = 0
Answers
Answer:
X-Intercept: [tex]x=-\frac{5}{2}y[/tex]
Y-Intercept: [tex]y=-\frac{2}{5}x[/tex]
Step-by-step explanation:
X-Intercept-
2x+5y=0 - Move the variable to the right-hand side and change its sign
2x=-5y - Divide both side of the equation by 2
x=-5/27 - Write the solution x in parametric form
x=-5/2y, y∈R
Y-Intercept-
2x+5y=0 - Move the variable to the right hand side and change its sign
5y=-2x Divide both sides of the equation by 5
y=-2/5x Write the solution y in parametric form
y=-2/5x, x∈R
find what x=______
show work pleae
Answers
Answer:
Use pythogoras theorem
a^2+b^2=c^2
x^2=c^2-a^2
x^2=15^2-12^2
x^2=81
x= square root of 81
x=9
Step-by-step explanation:
Y varies with x. When y=39, x=3. Find the value of y when x=2
Answers
Answer:
[tex] \frac{39}{y} = \frac{3}{2} \\ y = \frac{39 \times 2}{3} \\ \boxed{y = 26}[/tex]
26 is the right answer.What is the equation of the line that passes through the point (5,−2) and has a slope of -2/5
Answers
Answer:
y= -(2/5)x
Step-by-step explanation:
When you graph this line you can see it clearly passes through the point (5,-2)
Answer:
y + 2 = -2/5 (x - 5)
OR
y = (-2/5)x
Step-by-step explanation:
There are many ways you can find the equation.
There are two main ones, one called point-slope form, and the other called slope intercept form.
Point-slope form is easy. All you need a a point on the line, and the slope! Since they give you that in the question, all you need to do is plug things in.
Point slope form is y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
x and y are any points. [tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the points that the problem gives you. m is the slope.
The equation would be y + 2 = -2/5 (x - 5).
Slope intercept form is a bit harder. You need a point and the y-intercept.
Since you already have the slope, all you need to find is the y-intercept.
Slope intercept form is y = mx + b
x and y are the given points. m is the slope, and b is the y-intercept.
The y intercept is when the x value of a point is 0.
To find b, you can plug in the information you have, which is the point and the slope.
y = mx + b
-2 = (-2/5)(5) +b
-2 = -2 +b
b = 0
Since b is 0, the equation would just be y = (-2/5)x.
How do I solve this? PLEASE HELP TIME LIMIT
Answers
im not sure how to explain it, but i know its b
In the seating for a concert, the first row has 10 chairs. Every row after that has 2 more chairs. 7. What is the explicit formula that models this situation? 8. How many chairs are in row 20?
Answers
9514 1404 393
Answer:
7. c(n) = 10 +2(n -1)
8. c(20) = 48
Step-by-step explanation:
7. Your arithmetic sequence has first term a1=10 and constant difference d=2. The explicit formula for terms of an arithmetic sequence is ...
an = a1 +d(n -1)
If we use c(n) as the function name for the function giving the number of chairs in row n, then we can fill in the numbers we know to get ...
c(n) = 10 + 2(n -1)
__
8. Evaluating the function when n=20, we find ...
c(20) = 10 +2(10-1) = 10 +2·19 = 10 +38
c(20) = 48
There are 48 chairs in row 20.
In a standard deck of cards, what is the probability of drawing a face card?
Answer (round) to the hundredth place value.
Answers
Reasoning:
There are 12 face cards since there are 3 face cards in any suit, and 4 suits. So 3*4 = 12.
There are 52 cards total.
Dividing the values leads to 12/52 = 0.230769 which rounds to 0.23
use the number line to find the absolue value of 7 (A -7, (B 0, (C 7, (D 14
Answers
Answer:
Can you put a number line in the picture?
Step-by-step explanation:
That would really help
Answer:
I think its C but without the number line a cant tell.
Step-by-step explanation:
Decimal or fraction form round all the way!
Answers
Answer:
The answer to the question provided is
[tex] \frac{1}{4} [/tex]
An airplane ascended into the sky to a steady altitude of 35000 feet. The same plane descended to a steady altitude of 32000 feet. How many feet did the airplane descend
Answers
Answer:
3000 feets
Step-by-step explanation:
Given that :
Initial Ascent to steady altitude = 35,000 feets
Descent to steady altitude = 32,000 feets
Number of feets the plane descend :
(Initial ascent to steady altitude - descent to steady altitude)
(35000 - 32000) feets = 3,000 feets
pls help. i have to write it in exponential form
Answers
X × X - X × X × X × X × X + 17= X × X × X + 2
Simply please will give brainlist to first correct answer
Answers
plplpl solve the answer
Answers
Given:
The expression is:
[tex]\sqrt[3]{\dfrac{-512}{729}}[/tex]
To find:
The value of the given expression.
Solution:
We have,
[tex]\sqrt[3]{\dfrac{-512}{729}}[/tex]
It can be rewritten as
[tex]=\sqrt[3]{\dfrac{(-8)\times (-8) \times (-8)}{9\times 9\times 9}}[/tex]
[tex]=\sqrt[3]{\dfrac{(-8)^3}{9^3}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]=\sqrt[3]{\left(\dfrac{-8}{9}\right)^3}[/tex] [tex][\because \dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m][/tex]
[tex]=\dfrac{-8}{9}[/tex] [tex][\because \sqrt[n]{x^n}=x][/tex]
The value of given expression is [tex]\dfrac{-8}{9}[/tex].
Therefore, the correct option is b.
Please help I’ll give you brainlist or something
Answers
Answer:
1 slope of f is 5
slop of g is 2
2. connor
initial value is 200
rate of change is -10
Pilar
initial value is 242
rate of change is -8
3.
y intercept of f is -3
y intercept of g is -1
Step-by-step explanation:
Answer:
.
Step-by-step explanation:
.
OMG HELP OMG HELP OMG HELP
Answers
Answer:
a
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
3 bouquets of 3$ is 3*3 = 3^2
4 bouquets of 2$ = 2 * 4
Howie works at a petting zoo. He fed a piglet 1/5 of a bottle of milk then gave 3/4 of what was left to the calf. How much of the bottle of milk did the calf drink
Answers
Answer:
[tex]\frac{3}{5}[/tex]th part of the bottle will be drunk by the calf.
Step-by-step explanation:
Part of the bottle fed by the piglet = [tex]\frac{1}{5}[/tex]
Milk left in the bottle = 1 - [tex]\frac{1}{5}[/tex]
= [tex]\frac{5-1}{5}[/tex]
= [tex]\frac{4}{5}[/tex]
Milk drunk by the calf = [tex]\frac{3}{4}[/tex]th of the left part
= [tex]\frac{3}{4}\times \frac{4}{5}[/tex]
= [tex]\frac{3}{5}[/tex]th part of the bottle
Therefore, [tex]\frac{3}{5}[/tex]th part of the bottle will be drunk by the calf.
Tommy earned $5 mowing the lawn on Saturday. He earned more money on Sunday. Write an equation that shows the amount of money Tom has earned
Answers
Answer:
f(x)=2x+5
Step-by-step explanation:
If you think about it, 5 is the y intercept, meaning the money he earn that day. While Sunday, he earned more which is the Slope of 2x because its 2 times the number. And you add them together, and there you go.
Pls pls pls help me
Answers
Step-by-step explanation:
I hope its clear.
try finding help from others...
mine could be wrong
30 points! RIGHT ANSWER GETS BRAINLIEST!
Use 3 for pi. Area= (blank) circumference= (blank) meters
Answers
Answer:
Step-by-step explanation:
pi x 7 squared = 153.938040026