Answer:
[tex]\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}[/tex]
Step-by-step explanation:
We want to find the equation of the line tangent to the graph of:
[tex]\displaystyle y=\sin^{-1}\left(\frac{x}{5}\right)\text{ at } x=\frac{5}{2}[/tex]
So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:
[tex]\displaystyle y^\prime=\frac{1}{\sqrt{1-\left(\dfrac{x}{5}\right)^2}}\cdot\frac{1}{5}[/tex]
Simplify:
[tex]\displaystyle y^\prime=\frac{1}{5\sqrt{1-\dfrac{x^2}{25}}}[/tex]
We can factor out the denominator within the square root:
[tex]\displaystyle y^\prime =\frac{1}{5\sqrt{\dfrac{1}{25}\big(25-x^2)}}[/tex]
Simplify:
[tex]\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}[/tex]
So, we can find the slope of the tangent line at x = 5/2. By substitution:
[tex]\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}[/tex]
Evaluate:
[tex]\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\dfrac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}[/tex]
We will also need the point at x = 5/2. Using our original equation, we acquire that:
[tex]\displaystyle y=\sin^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}[/tex]
So, the point is (5/2, π/6).
Finally, by using the point-slope form, we can write:
[tex]\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}\left(x-\frac{5}{2}\right)[/tex]
Distribute:
[tex]\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}[/tex]
Isolate. Hence, our equation is:
[tex]\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}[/tex]
Approximately 24% of the calls to an airline reservation phone line result in a reservation being made. (a) Suppose that an operator handles 15 calls. What is the probability that none of the 15 calls result in a reservation
-
First, rewrite
13 9
and
30 20
so that they have a common denominator.
13 9
Then, use <, =, or > to order and
30 20
13
9
<
D>
30
20
Х
?
13
9
30
20
Answer:
18/14=64+7%×r try it out
The values shows 13/30 < 9/20.
What is fraction?Fractions are the components of a collection or whole. Two parts make up a fraction. The numerator is the number at the top of the line. It indicates the number of equal portions taken from the collection or whole. The term "denominator" refers to the number below the line. It indicates the total number of identical parts that make up a collection or the total number of parts that make up the whole.
The number of parts we take is a fraction when the whole is divided into equal parts.
Given 13/30 and 9/20
to make the common denominator,
multiply by 20 in numerator and denominator of 13/30
(13 x 20)/(20 x 30) = 260/600
multiply by 30 in numerator and denominator of 9/20
(9 x 30)/(20 x 30) = 270/600
the terms with same denominator are
260/600 and 270/600
as we can see that 270/600 > 260/600
so 13/30 < 9/20.
Hence 13/30 is less than 9/20.
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[2] + [-13]=
please help me!!!
[tex]Answer:[/tex]
[tex]-11[/tex]
[tex]Step-by-step~explanation:[/tex]
[tex]2+-13[/tex]
[tex]= -11[/tex]
So your answer is -11 :)
Reduce fractions to lowest terms
3/8 + 1/3
The requried reduced fraction of the given fraction is given as 17/24.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given fraction,
= 3 / 8 + 1 / 3
= [3 × 3 + 1 ×8] / 8×3
= 9 + 8 / 24
= 17/24
Thus, the requried reduced fraction of the given fraction is given as 17/24.
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Ratio of 200m and 1km.
Answer:
the ratio of this one is 0.2\1
Answer:
To calculate the ratio, we should have both quantities in same units, so we can convert the kilometer into meters, knowing that 1 kilometerr are 1000m.
1 * 1000 = 1000m
We know we need to calculate the ratio 200:1000.
We can know divide both quantities by 200 and get...
200/200:1000/200 = 1:5
And now,, we know this ratio is 1:5..
g According to government data, 25% of employed women have never been married. If 10 employed women are selected at random, what is the probability that two or fewer of them have never been married
Answer:
The probability is 0.5263
Step-by-step explanation:
Probability of employed women being unmarried = 25% = 0.25 ( let this be p)
Probability of employed women ever being married = 1-0.25 = 0.75 (let this be q)
Now, we want to calculate the probability that two or less have never been married
We can use the Bernoulli approximation of the Binomial distribution here;
In this case, we have three cases
We have cases of;
Exactly two + Exactly one + None
For exactly two;
10 C 2 0.25^2 0.75^8 = 0.282
For exactly one
10 C 1 0.25^1 0.75^9 = 0.188
For none
10C 0 0.25^0 0.75^10 = 0.0563
Adding these 3 to get the probability of two or fewer, we have;
0.0563 + 0.188 + 0.282 = 0.5263
Let g(x)=4x and h(x)=x^2-3. Find (g o h)(0)
Answer:
-12
Step-by-step explanation:
g(x) = 4x
h(x) = x^2 - 3
(g o h)(x) = g(h(x)) = g(x^2 - 3) = 4(x^2 - 3) = 4x^2 - 12
(g o h)(0) = 4(0)^2 - 12 = 0 - 12 = -12
Write the product in its simplest form:
7x^6 y^3 • (-7y^2)
Please explain this to me when you answer it
Step-by-step explanation:
7x6y².y.(-7y²)
7y²[x6y-1]
Answer:
-49x^6y^5
Step-by-step explanation:
multiply the like terms (7y^3 and -7y^2)
7*-7 = -49
y^3+2 = y^5
combine the terms
-49x^6y^5
The lengths of a professor's classes has a continuous uniform distribution between 60.0 min and 90.0 minutes. If one such class is randomly selected, find the probability that the class length is less than 76 min.
Answer:
0.533
Step-by-step explanation:
Given that :
Class length has a Continuous uniform distribution between 60 - 90 min
Lower limit (L1) = 60
Upper limit (L2) = 90
Probability that class length is less than 76 min
P(x < 76):
(x - L1) / (L2 - L1)
(76 - 60) / (90 - 60)
16 / 30
= 0.533
P(x < 76) = 0.533
Translate the phrase into a variable expression. Use the letter e to name the variable. If necessary, use the asterisk ( * ) for multiplication and the slash ( / ) for division.
... The number of seats in boxer stadium minus 15 ...
The mathematical expression of the phrase is e - 5
How to translate the phrase?The phrase is given as:
The number of seats in boxer stadium minus 15
The variable is represented with the letter e.
So, we have:
e minus 15
Express minus with the symbol -
e - 5
Hence, the mathematical expression of the phrase is e - 5
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Answer:
s-15............... m
A company that makes hair-care products had 9,000 people try new shampoo Of the 9,00 people, 27 had an mild allergic reaction what percent of the people had a mild allergic reaction
An ostrich that is it so many inches tall is 12 in taller than three times the height of a kiwi. What is the height of a kiwi in inches?
Answer:
the height should be 4.
Step-by-step explanation:
because 12 divided by 3 is 4
50 POINTS I NEED THIS IM CONFUSED
The distance between two points is 6√5. One endpoint is (4,−3). It is known that the y-coordinate of the other endpoint is 7. What is the x-coordinate of this endpoint?
what polynomial should be subtracted from 3x^2+4x-1 to get the difference equal to 0
Answer:
[tex] {x}^{2} + \frac{4}{3} x - \frac{1}{3} [/tex]
can be subtracted
A pizza chef begins to spin a constant volume of dough to make a pie by spinning and tossing the dough into the air, such that the dough takes on a cylindrical shape. The dough's radius increases while the height decreases, but the dough remains a cylinder. At time t = tı, the height of the dough is 1/2 inch, the radius of the dough is 16 inches, and the radius of the dough is increasing at a rate of 2 inches per minute.
Required:
a. At time tı, at what rate is the area of the "top" of the pizza (the part with the toppings) increasing with respect to time? Show the computations that lead to your answer, and indicate units of measure.
b. At time tı, at what rate is the height of the dough decreasing with respect to time?
Answer:
a ) dAt/dt = 50,24 in/min
dh/dt = - 0,125 in/min
Step-by-step explanation:
The area of the top is At :
At = π*r²
a) Tacking derivatives with respect to time:
dAt/dt = 2* π*r * dr/dt
At t = t₁ r = 16 in and dr/dt = 0,5
Then
dAt/dt = 2*3,14*16*0,5 in/min
a ) dAt/dt = 50,24 in/min
b) The volume of the cylinder is:
Vc = π*r²*h ( where h is the heigh of the cylinder )
Tacking derivatives with respect to time
dVc/dt = 2* π*r*h*dr/dt + π*r²*dh/dt
But dVc/dt = 0 since the volume remains constant, then:
π*r²*dh/dt = - 2* π*r*h*dr/dt
r*dh/dt = - 2*h*dr/dt
dh/dt = - 2*0,5*2/16 in/min
dh/dt = - 0,125 in/min
There are 12 basketball players on the team. In order to complete the main composition of the team for the
game, the coach can choose any 5 players from the team. How many different combinations of the main
compositions the coach can complete?
I get 792 but why is the answer 7.92. Kinda don't understand.
Step-by-step explanation:
We have been given that a basketball team has 12 players and the coach wants to pick which 5 players will start today's game.
We will use combinations formula to solve our given problem. , where,
n = Number of total items,
r = Number of items being chosen at a time.
Upon substituting our given values in combinations formula we will get,
Therefore, the coach can choose from 792 combinations
Jessica has one piece of ribbon that is 6 2/3 yards long and one piece that is 5 1/3 yards long. What is the total length, in feet, of the two pieces of ribbon?
The Positive Z-Equal Line, the Negative Z-Equal Line, and the Regression Line all pass through the same point. What are the standardized coordinates of this point
Answer:
The standard coordinates of the point are ; ( 0,0 )
Step-by-step explanation:
The standard coordinates of the point are ; ( 0,0 ) also the standard values of the means will also be ( 0, 0 )
This is because for the Positive Z-equal line, Negative Z-Equal line and Regression line to all pass through the same point indicates dependent and independent variables of the Z-score and regression lines respectively
PLS help. will give brainliest to first answer 6(7)/3
Answer:
14
Step-by-step explanation:
Answer:
It has to be 14
Step-by-step explanation:
42/3 is 14
Choose the correct answer.
Distance between Train 1 and Train 2 =95 miles.
Average speed of Train 1 = 45 mph.
Average speed of Train 2 60 mph.
If both trains leave at the same time and travel toward each other but on parallel tracks, in how much time will their
engines be opposite each other? (Hint: When the engines are opposite each other, together the trains will have traveled
95 miles. Their relative speed of travel is the sum of their respective speeds, or 105 mph.)
Travel time = Mhours
Step-by-step explanation:
Distance between Train 1 and Train 2=95 miles
Avg speed Train 1 = 45mph, avg speed Train 2=60mph
If both trains leave at the same time and travel toward each other but on parallel tracks, in how much time will their engines be opposite each other?
:
Let t = travel time (in hrs) until they are opposite each other
:
Like the hint said, when this happens the total distance traveled by both trains will be 95 mi.
:
write a distance equation from this fact: Dist = speed * time
;
Train 1 dist + train 2 dist = 95 mi
45t + 60t = 95
:
105t = 95
t = 95%2F105
t = .90476 hrs
or
.90476 * 60 = 54.3 min
:
:
Check solution by finding the total of the distances the two train travel
45(.90476) + 60(.90476) =
40.7 + 54.3 = 95 mi
Find the domain of the function h(t)=4-t^2\2-t
Step-by-step explanation:
(4-t)(4-t)/2-t
t^2-8t+16/2-t
the domain is all real number without 2
Please determine x.
Answer:
x=22.8 inches
I think T__T
Step-by-step explanation:
YES... SOMETHING I KNOW!
Use Pythagorean theroy
say 42.7=a
48.4=b
x=c
the formula is: a^2+c^2=b^2
so: 42.7^2+x^2=48.4^2
if we simplify:=1823.29+x^2=2342.56
then:519.27=x^2
It says, round to the nearest TENTH
x=22.787497
so then x would be
22.80
Integrate V-1 divided by 1+2V+V^2
Answer:
[tex]\int\limits {\frac{V-1}{1+2V+V^{2} } } \, dv[/tex] [tex]= log V + (\frac{2 }{1+v} )+C[/tex]
Step-by-step explanation:
Step(i):-
Given
[tex]\int\limits {\frac{V-1}{1+2V+V^{2} } } \, dv[/tex]
= [tex]\int\limits {\frac{V-2+1}{1+2V+V^{2} } } \, dv[/tex]
[tex]= \int\limits {\frac{V+1}{(1+V)^{2} } } \, dv+\int\limits {\frac{-2}{(1+V)^{2} } } \, dv[/tex]
= [tex]= \int\limits {\frac{1}{(1+V) } } \, dv+\int\limits {\frac{-2}{(1+V)^{2} } } \, dv[/tex]
Step(ii):-
By using integration formula
[tex]\int\limits {\frac{1}{x} } \, dx =logx +C[/tex]
[tex]\int\limits {x^{n} } \, dx = \frac{x^{n+1} }{n+1} +C[/tex]
[tex]= \int\limits {\frac{1}{(1+V) } } \, dv+\int\limits {\frac{-2}{(1+V)^{2} } } \, dv\\= log V + (\frac{-2(1+v)^{-2+1} }{-2+1} )+C[/tex]
[tex]= log V + (\frac{-2(1+v)^{-1} }{-1} )+C[/tex]
[tex]= log V + (\frac{2 }{1+v} )+C[/tex]
Complete the statement pls due in 20 minutes
Answer:
For the second one: NO congruent to MO.
For the third one: angle N congruent to angle O.
:)
Use the Distributive Property on the
equation below.
3(4y + 3) = [ ? ]y +[ ]
Answer:
12y+9
Step-by-step explanation:
4n+2 (n+1) >n+52 Please solve this inequality fast.
Answer:
n>10.2 or n>51/5
Step-by-step explanation:
4n+2(n+1)>n+52 distribute 2 to everything in the parentheses
4n+2n+1>n+52 combine like terms
6n+1>n+52 subtract 1 from both sides
6n>n+51 subtract n from both sides
5n>51 divide both sides by 5
n>10.2
Answer:
n>10.2
Step-by-step explanation:
Grant paid $12 for 4 baseball card packs. How many baseball card packs can he purchase for $21? Group of answer choices
Answer:
Grant can purchase 7 baseball card packs for $21. 12/4=3 and 21/3=7.
Answer: 7
Step-by-step explanation:
Answer:
7 packs
Step-by-step explanation:
12/4 = $3 ea.
21/3 = 7 packs
Matthew purchased a desk that was on sale for 45% off the orginal price of $480.If the sales tax was 8% (of the sale price), how much did mattew spend on the desk
Answer:
285.12
Step-by-step explanation:
discount amount = 45/100 x 480= 45x48/10
=216.0
price after discount= 480-216=264
sales tax= 8/100 x 264=21.12
total money spent = 264+21.12=285.12
45% of 480
= 45/100 x 480
= 0.45x480
=216
=480-216
=264
8% of 264
= 8/100 x 264
= 0.08 x 264
= 21.12
= 264 + 21.12
=285.12
Therefore, he paid $285 and 12 cents
apply the distributive property to factor out the greatest common factor
18d + 12=
Graph 2x+3y=-12
This is overdue lol
Answer:
5 1/3
Step-by-step explanation:
Answer:
Step-by-step explanation: Change the format of the equation. Make it 3y=-2x-12. Substitute different values for x and see what y is for each of those x values. For example, if you substitute x=3, you will get y=-6. I am going to put in a picture of the plotted line. I hope this helps!