Step-by-step explanation:
[tex]\sf x = \sqrt{a^{sin^{-1} \ t}}\\\\\\Derivative \ rule:\boxed{\dfrac{d(\sqrt{x})}{dx}=\dfrac{1}{2}*x^{\frac{-1}{2}}=\dfrac{1}{2\sqrt{x}}}[/tex]
[tex]\sf \dfrac{d(\sqrt{a^{sin^{-1} \ t}}}{dt}=\dfrac{1}{2\sqrt{a^{sin^{-1} \ t}}}*\dfrac{d(a^{sin^{-1} \ t})}{dt}\\\\\\Derivative \ rule: \boxed{\dfrac{d(a^{x})}{dx}=log \ a *a^{x}}[/tex]
[tex]\sf = \dfrac{1}{2\sqrt{a^{sin^{-1}} \ t}}*a^{sin^{-1} \ t}* log \ a *\dfrac{d(Sin^{-1} \ t)}{dt}\\\\[/tex]
[tex]Derivative \ rule:\boxed{\dfrac{d(sin^{-1} \ x}{dx}=\dfrac{1}{\sqrt{1-x^2}}}[/tex]
[tex]\sf = \dfrac{1}{2\sqrt{a^{sin^{-1} \ t}}}*a^{Sin^{-1} \ t}*log \ a*\dfrac{1}{\sqrt{1-x^2}}}}}\\\\ = \dfrac{a^{Sin^{-1} \ t}*log \ a}{2\sqrt{a^{sin^{-1} \ t}}*\sqrt{1-x^2}}[/tex]
[tex]\boxed{ \dfrac{a^{sin^{-1} \ t}}{\sqrt{a^{sin^{-1} \ t}}}=\dfrac{\sqrt{a^{sin^{-1} \ t}}*\sqrt{a^{sin^{-1} \ t}}}{\sqrt{a^{sin^{-1} \ t}}} = \sqrt{a^{sin^{-1} \ t}}}[/tex]
[tex]\sf = \dfrac{a^{sin^{-1} \ t}*log \ a}{2\sqrt{1-x^2}}[/tex]
[tex]\sf \dfrac{dy}{dt}=\dfrac{d(a^{cos^{-1} \ t})}{dt}[/tex]
[tex]= \dfrac{1}{2\sqrt{a^{cos^{-1} \ t}}}*a^{cos^{-1} \ t}*log \ a *\dfrac{-1}{\sqrt{1-x^2}}}\\\\\\=\dfrac{(-1)*a^{cos^{-1} \ t}*log \ a}{2*\sqrt{a^{cos^{-1} \ t}}*\sqrt{1-x^2}}[/tex]
[tex]\sf = \dfrac{(-1)*\sqrt{a^{Cos^{-1} \ t}}* log \ a }{2\sqrt{1-x^2}}\\\\[/tex]
[tex]\sf \bf \dfrac{dy}{dx}=\dfrac{dy}{dt} \div \dfrac{dx}{dt}\\[/tex]
[tex]\sf \bf = \dfrac{(-1)*\sqrt{a^{cos^{-1} \ t}}*log \ a}{2*\sqrt{1-x^2}} \ \div \dfrac{\sqrt{a^{sin^{-1} \ t}} *log \ a}{2*\sqrt{1-x^2}}\\\\\\=\dfrac{(-1)*\sqrt{a^{cos^{-1} \ t}}*log \ a}{2*\sqrt{1-x^2}} \ * \dfrac{2*\sqrt{1-x^2}}{\sqrt{a^{sin^{-1} \ t}} *log \ a}\\\\= \dfrac{(-1)* \sqrt{a^{cos^{-1} \ t}} }{\sqrt{a^{sin^{-1} \ t}}}\\\\= \dfrac{-y}{x}[/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: x = \sqrt{ {a}^{sin {}^{ - 1}t } } [/tex]
here, let's differentiate it with respect to t ~
[tex]\sf \dashrightarrow \: \dfrac{dx}{dt} = \dfrac{1}{2 \sqrt{a {}^{sin {}^{ - 1}t } } } \times a {}^{sin {}^{ - 1}t } \sdot ln(a) \times \dfrac{1}{ \sqrt{1 - {x}^{2} } }[/tex]
[tex]\sf \dashrightarrow \: \dfrac{dx}{dt} = \dfrac{ \sqrt{ {a}^{sin {}^{ - 1}t } } \sdot ln(a)}{2 \sqrt{1 - {x}^{2} } } [/tex]
[tex]\sf \dashrightarrow \: \cfrac{dt}{dx} = \dfrac{2 \sqrt{1 - {x}^{2} } }{ \sqrt{a {}^{sin {}^{ - 1} t} \sdot ln(a)} }[/tex]
Smililarly,
[tex]\sf \dashrightarrow \: \dfrac{dy}{dt} = \dfrac{1}{2 \sqrt{a {}^{cos{}^{ - 1}t } } } \times a {}^{cos {}^{ - 1}t } \sdot ln(a) \times \dfrac{ - 1}{ \sqrt{1 - {x}^{2} } }[/tex]
[tex]\sf \dashrightarrow \: \dfrac{dy}{dt} = - \dfrac{ \sqrt{ {a}^{cos {}^{ - 1}t } } \sdot ln(a)}{2 \sqrt{1 - {x}^{2} } }[/tex]
Now : Lets get Required result ~
[tex]\sf \dashrightarrow \: \dfrac{dy}{dx} = \dfrac{dy }{dt} \times \dfrac{dt}{dx} [/tex]
[tex]\sf \dashrightarrow \cfrac{dy}{dx} = - \dfrac{\sqrt{ {a}^{cos {}^{ - 1}t } \sdot \cancel{ ln(a)}}}{ \cancel{2 \sqrt{1 - {x}^{2}}}} \sdot \dfrac{ \cancel{2 \sqrt{1 - {x}^{2}} } }{ \sqrt{a {}^{sin {}^{ - 1} t} }\sdot \cancel{ln(a)}}[/tex]
[tex]\sf \dashrightarrow \cfrac{dy}{dx} = - \dfrac{\sqrt{ {a}^{cos {}^{ - 1}t } }}{ \sqrt{a {}^{sin {}^{ - 1} t} }}[/tex]
[tex]\sf \dashrightarrow \cfrac{dy}{dx} = - \dfrac{y}{x} [/tex]
[ since y = [tex]\sf{\sqrt{a^{cos^{-1}t}} } [/tex] and x = [tex]\sf{\sqrt{a^{sin^{-1}t}} } [/tex] ]
When finding an indefinite integral, your answer must include:.
Answer:
is the set of infinitely many primitives that a function can have. It is represented by ∫ f(x) dx. It reads: integral of x differential of x. ∫ is the integration sign.
Suppose that there are two types of tickets to a show advance and same day the combined cost of one advance ticket and one same-day ticket is $70 for one performance 20 advance tickets and 35 same day tickets were sold.The total amount paid for the tickets was $1850.what was the price of each kind of ticket
The price of the advance ticket is $40 and the price of the same day tickets is $30.
What are the linear equations that reperesent the question?a + b = $70 equation 1
20a + 35b = 1850 equation 2
Where:
a = cost of one advance ticket
b = cost of one same day ticket
What is the cost of one same day ticket?
Multiply equation 1 by 20
20a + 20b = 1400 equation 3
Subtract equation 3 from equation 2
15b = 450
Divide both sides by 15
b = $30
What is the cost advance ticket?
Subtract $30 from $70.
$70 - $30 = $40
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
what are the steps to solving 7(x+2)=91
X=11
Answer:
Below.
Step-by-step explanation:
7(x + 2) = 91
Distribute the 7 over the parentheses:
7x + 14 = 91
Subtract 14 from both sides of the equation:
7x = 91 - 14
7x = 77
x = 77/7 = 11.
Answer:
X=11
Step-by-step explanation:
[tex]7\left(x+2\right)=91[/tex]
Divide both sides by 7:
[tex]\frac{7\left(x+2\right)}{7}=\frac{91}{7}[/tex]
Simplify:
[tex]x+2=13[/tex]
Subtract 2 from both sides:
[tex]x+2-2=13-2[/tex]
Simplify:
X=11
Which polynomial matches the expression -x (x – 3)?
Answer:
=> -x² + 3x
Step-by-step explanation:
-x (x – 3)
=> -x² + 3x
Find the side ratio given
pls show work<3 :)
Answer:
5/2 See below
Step-by-step explanation:
L x W x H = 125/8
for a CUBE L W and H are the same
L^3 = 125/8
L = 5/2
Queetlon 10 or 15
People leaving the library were aaked how many books they checked out that
day The resulta are:
1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
Which histogram correctly ahows the data set?
Books Checked Out
0-5 6-11 12-1718-23
Number of booke
Books Checked Out
Answer:
[B]
Step-by-step explanation:
Given:
People leaving the library were asked how many books they checked out that day The result are: 1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
To Find:
Which histogram correctly shows the data set?
Solution:
Since it given from the histogram:
0-5, 6-11, 12 - 17,18-23
From the result :
1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
Thus,
1,2,3,5 = 0-5
8,9,10,11 = 6-11
12,13,14,15,16 = 12-17
18,20 = 18-23
From this we can see that:
for
0 - 5 = 4
6 - 11 = 4
12 - 17 = 5
18 - 23 = 2
Hence, the answer is [B]
Kavinsky
Which of the following numbers are greater than or equal to 1.75?
Choose all answers
A) 1 4/11
B) 1.6
C) 7/4
Answer:
Only C
Step-by-step explanation:
1 4/11 is 1+4/11 and 4/11 is less than 1/2 so it has to be less than 1.5, which is less than 1.75
1.6 is less than 1.75 because 1.75-1.6 is 0.15 which is a positive number
4/7 is 1 3/4 which is 1.75
Answer:
a and c
Step-by-step explanation:
they are over 1
My sister needs help again MATHHH
Answer:
31
Step-by-step explanation:
PEMDAS is Parentheses, Exponent, Multiplication, Addition, Subtraction
This is just the order you do the operations.
First, Parentheses.
Second, Exponents,
Third, Multiplication or Division
Last, Addition or Subtraction
So we have,
[6(20) + 3(15)] ÷ 5
We first look at Parentheses.
The first case is 6(20)
6(20) = 120
We have [120 + 3(15)]÷ 5
We solve 3(15) as its the next parentheses
3(15) = 45
We have [120 + 45] ÷ 5
Then we solve for [120 + 45] as it's in brackets.
[165] ÷ 5 = 31
The answer is 31.
In how many ways can she grab 3 Snickers, 2 Starbursts, and 2 Reese's?
(1) Basket (2) Hands (3) Cart. 3 ways i can think of
Which two terms in (3+14) +27 could you add to get a multiple of ten?
Answer:
3 and 27
Step-by-step explanation:
Step 1: Determine which two terms we can use
We have the following numbers to choose from: 3, 14, 27
Adding two numbers to get a multiple of ten means that the number that we come up with needs to be divisible by ten. For example: 20, 30, 50, 100 are all multiples of ten.
In this example the only one that would add up to create a multiple of ten is 27 and 3 which would give us 30 which is a multiple of 10.
Answer: 3 and 27
On Monday, Andrew ate some grapes. On Tuesday, he ate 2 more grapes than what he ate on Monday. On Wednesday, He ate 2 more grapes than what he ate on Tuesday. Each day of that week he ate 2 more grapes than what he ate the day before. By the end of Friday, He had eaten 30 grapes in total. How many grapes did Andrew eat on Monday?
Answer: I think It's 38
Step-by-step explanation:
you can multiply or add all of them together
Answer: Andrew ate 22 grapes on Monday.
Step-by-step explanation:
From Monday to Friday it is 4 days. since he ate 2 more grapes every day. You multiply 2 by 4. To get 8 and subtract 30 by 8 to get 28.
The cost, y, of red apples can be represented by the equation y = 2x, where x
is the number of pounds of red apples.
The graph shows the cost of green apples.
Which type of apple costs more per pound?
Cost of Green Apples
11
10
PLEASE HURRY I NEED IT IN 5 mins
Cost (5)
.
3
Weight (pounds)
A. Red apples
B. Red and green apples cost the same.
C. Green apples
Answer:
red apples
Step-by-step explanation:
1 lb of green apples is 1.5
1 lb of red apples is 2
If a1 = 7 and an = an-1 + 4 then find the value of a4.
Answer:
[tex]a_4=19[/tex]
Step-by-step explanation:
Given:
[tex]a_1=7[/tex][tex]a_n=a_{n-1}+4[/tex][tex]\implies a_2=a_{1}+4=7+4=11[/tex]
[tex]\implies a_3=a_{2}+4=11+4=15[/tex]
[tex]\implies a_4=a_{3}+4=15+4=19[/tex]
Put values get answer
a_n=a_(n-1)+4a_4=a_3+4a_4=a_2+4+4a_4=a_1+4+4+4a_4=7+12a_4=19For funcitons f(x)=2x+3 and g(x)=-3x-2, please find (f∘g)(-1)
Answer:
[tex]\displaystyle (f\circ g)(-1) = 5[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle f(x) = 2x + 3\text{ and } g(x) = -3x - 2[/tex]
And we want to find:
[tex]\displaystyle (f\circ g)(-1)[/tex]
Recall that this is equivalent to:
[tex]\displaystyle (f\circ g)(-1) = f(g(-1))[/tex]
Hence, find g(-1):
[tex]\displaystyle \begin{aligned} g(x) & = -3x - 2\\ \\ g(-1) & = -3(-1) - 2\\ \\ & = (3) - 2 \\ \\ & = 1 \end{aligned}[/tex]
Substitute:
[tex]\displaystyle f(g(-1)) = f(1)[/tex]
Find f(1):
[tex]\displaystyle \begin{aligned} f(x) & = 2x+ 3 \\ \\ f(1) & = 2(1) + 3 \\ \\ & = 5\end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (f\circ g)(-1) = 5[/tex]
Find the value of x
x =
Answer:
[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the value of x.}[/tex]
[tex]\textsf{The value of x is an angle for this triangle.}[/tex]
[tex]\textsf{Note that we are given 2 other angles, we can use what is given to us to solve for x.}[/tex]
[tex]\large\underline{\textsf{What is a Triangle?}}[/tex]
[tex]\textsf{A Triangle is a shape with 3 sides, and 3 angles. Sometimes these can be congruent,}[/tex]
[tex]\textsf{other times, and most of the time they're not. These are called Equilateral}[/tex]
[tex]\textsf{Triangles. Every Triangle consists of 3 angles that add up to 180}^{\circ}. \ \textsf{If the angles}[/tex]
[tex]\textsf{don't add up to 180}^{\circ}, \ \textsf{then the shape is not a triangle.}[/tex]
[tex]\textsf{Now that we know a Triangle has 3 angles that add up to 180}^{\circ}, \ \textsf{we can create an}[/tex]
[tex]\textsf{equation where x is the \underline{subject}.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{All 3 angles add up to 180}^{\circ}, \ \textsf{let's create an equation.}[/tex]
[tex]\tt 180^{\circ} = 37^{\circ} + 53^{\circ} + x^{\circ}[/tex]
[tex]\textsf{To make x the subject, move x to the other side of the equation by subtracting x.}[/tex]
[tex]\tt 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} + x^{\circ} - x^{\circ}[/tex]
[tex]\textsf{We should also move 180}^{\circ} \ \textsf{to the other side of the equation as well.}[/tex]
[tex]\tt 180^{\circ} - 180^{\circ} - x^{\circ}= 37^{\circ} + 53^{\circ} -180^{\circ}[/tex]
[tex]\underline{\textsf{We should have;}}[/tex]
[tex]\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}[/tex]
[tex]\textsf{We should remove the negative for x by dividing the whole equation by -1.}[/tex]
[tex]\frac{\tt- x^{\circ}= -180^{\circ} + 37^{\circ} + 53^{\circ}}{-1} \rightarrow \tt x^{\circ}= 180^{\circ} - 37^{\circ} - 53^{\circ}[/tex]
[tex]\underline{\textsf{Simplify the right side of the equation;}}[/tex]
[tex]\large\boxed{\tt x^{\circ}= 90^{\circ}}[/tex]
Answer 12 please thank you
Answer: 30%
Step-by-step explanation:
because my friend said so? <3
hope this helps!
If f(1) = 1 and f(n) = 5f(n-1) + 4 then find the value of f(5).
Answer:
[tex]f(5)=1249[/tex]
Step-by-step explanation:
Given:
[tex]f(1)=1[/tex][tex]f(n) = 5f(n-1)+4[/tex][tex]\implies f(2) = 5f(1)+4=5(1)+4=9[/tex]
[tex]\implies f(3) = 5f(2)+4=5(9)+4=49[/tex]
[tex]\implies f(4) = 5f(3)+4=5(49)+4=249[/tex]
[tex]\implies f(5) = 5f(4)+4=5(249)+4=1249[/tex]
Find the inverse function of y=7x.
Answer:
f^−1(x)=x7
Step-by-step explanation:
To find the inverse , inerchange the variable and slove for Y
pls help me solve this answer its urgent
Answer:The equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
Step-by-step explanation:Lines that are perpendicular to each other have slopes that are negative reciprocal of each other.
For example, if a line has a slope of 2, the slope of a line that is perpendicular to it would be, -1/2 (negative reciprocal of 2).
Determine the slope of the given line whose equation is, y + 2 = 3/2(x + 4). Rewrite the equation in slope-intercept form [y = mx + b]:
y + 2 = 3/2x + 6
y = 3/2x + 6 - 2
y = 3/2x + 4
The slope is therefore 3/2.
Negative reciprocal of 3/2 is -2/3.
Examine each of the equations given and see which equation has a slope of -2/3.
A. y = -3/2x +4, the slope is -3/2.
B. y = -2/3x + 4, the slope is -2/3. (perpendicular)
C. y = 2/3x +4, the slope is 2/3.
D. y = 3/2x +4, the slope is 3/2.
E. y+1=-4/6(x+5), rewrite in slope-intercept form
y+1=-4/6x + 20/6
y + 1 = -2/3x + 10/3
The slope is -2/3. (perpendicular)
F. y+ 1 = 3/2(x + 5), the slope is 3/2.
Therefore, the equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
Why is this a right triangle? A) Two angles are acute. B) One angle measures exactly 90°. C) All three angles are less than 90°. D) All three sides are of equal length.
Answer:
B)
Step-by-step explanation:
The main feature in a right triangle is that it has a right angle (90°)
Hope this helps
What is the radian equivalent for 180°? 2 pi radians pi radians startfraction pi over 2 endfraction radians
Answer:
180° = pi radians
Step-by-step explanation:
360° = 2pi radians
90° = pi/2 radians
see image
180° is pi radians.
pi radians is equivalent to 180 degrees, option B is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The radian equivalent of 180° is pi radians.
This is because a full circle is 360°, which is equivalent to 2 pi radians. Therefore, half of a circle or an angle of 180° is equivalent to half of 2 pi radians, which is pi radians.
Hence, pi radians is equivalent to 180 degrees, option B is correct.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ5
Which table represents a function?
X y
-4 6
0 8
4 12
X y
-4 3
-2 6
-2 9
X y
-3 7
-1 9
-3 -7
X y
1 2
1 6
2 10
Answer:
-2x+4>18.
Step-by-step explanation:
Solve and graph a one variable inequality. Solve the inequality and graph the solution on a number line.
Evaluate a+4a+4a, plus, 4 when a=7a=7a, equals, 7
Answer:
the answer is 11
Step-by-step explanation:
What is the measure of WV
(Value of x is 19)
A museum receives an average of 488 visitors per day. The museum 15 open every day. A. Estimate the number of visitors the museum receives during a month.
An estimate of the number of visitors that vist the museum during a month given the average number of visitors per day is 15,128.
What is multiplication?
Multiplication is an arthmetic operation that can be used to determine the product of a number. The sign used to denote multiplication is x.
How many visitors does the museum have in a month?
In order to determine this value, multiply the average daily visitors by the number of days in a month
488 x 30 = 15,128
To learn more about multiplication, please check: https://brainly.com/question/13814687
Which number is closest to
68?
9
64
8
34
Answer:
64
Step-by-step explanation:
Harper has a bag that contains apple chews, cherry chews, and lime chews. She
performs an experiment. Harper randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Harper performs the experiment 38 times.
The results are shown below:
An apple chew was selected 22 times.
A cherry chew was
selected 6 times.
A lime chew was selected 10 times.
Based on these results, express the probability that the next chew Harper removes
from the bag will be lime chew as a percent to the nearest whole number.
Please help me - geometry
Answer:
v≈4.7
w≈1.6
Step-by-step explanation:
sin71º＝v/5
v=5*sin71º≈4.7
cos71º＝w/5
w=5*cos71º≈1.6
Mr. Ramos's monthly mileage allowance for a company car is 750 miles. He drove 8 miles per day for 10 days, then went on a 3-day trip. The table shows the distance he drove on each day of the trip.
Trip Mileage
Day Miles Driven
Tuesday 156.1
Wednesday 240.8
Thursday 82.0
After the trip, how many miles remain in Mr. Ramos's monthly allowance? Record your answer in the box.
Answer:
558.9 miles total
Step-by-step explanation:
See attached spreadsheet.
Huan works at a pizza restaurant in the morning he made 23 pizzas to sell at noon he had five pizzas left how many pizzas did he sell
Answer:
18. Huan sold 18 pizza's. 23 - 5 = 18.
You can also start at 23, and count down to 5.
Step-by-step explanation: