Step-by-step explanation:
the derivative of an inverse function is
1/f'(f^-1(x))
f'(x) = -6x²
f^-1(7) is solving the original function equation for x under the knowledge that y = 7
7 = 5 - 2x³
2 = -2x³
-1 = x³
=>
x = -1
f'(-1) = -6×(-1)² = -6×1 = -6
so,
(f^-1)'(7) = -1/6
Do the ratios 7:14 and 3:6 form a proportion?
Answer:
Yes
Step-by-step explanation:
7:14=1:2
3:6=1:2
find the slope of the parabola y equals to e^(-4x) sin6x at the point P(2,4). write an equation for the tangent to the parabola at this point
The equation of the tangent line to the curve is:
[tex]y - 4 = 0.0024(x - 2)[/tex]
Which has a slope of 0.0024.
The tangent line of a curve [tex]f(x)[/tex] at a point [tex](x_0,y_0)[/tex] is given by:
[tex]y - y_0 = f^{\prime}(x_0)(x - x_0)[/tex]
In this problem, the curve is:
[tex]f(x) = e^{-4x}\sin{6x}[/tex]
The derivative is:
[tex]f^{\prime}(x) = -4e^{-4x}\sin{6x} + 6e^{-4x}\cos{6x}[/tex]
Point P(2,4), thus [tex]x_0 = 2, y_0 = 4[/tex].
The slope is:
[tex]f^{\prime}(2) = -4e^{-4(2)}\sin{6(2)} + 6e^{-4(2)}\cos{6(2)} = 0.0024[/tex]
Then, the equation of the line is:
[tex]y - y_0 = f^{\prime}(x_0)(x - x_0)[/tex]
[tex]y - 4 = 0.0024(x - 2)[/tex]
A similar problem is given at https://brainly.com/question/22426360
Which is the best definition of coefficient?
A letter that represents an unknown value.
O A number that itinultiplied by a variable.
Operations that "undo" each other.
O A fixed value that does not change.
Answer:
A number multiplied by a variable.
Step-by-step explanation:
For example, 4 is a coefficient.
[tex]4x[/tex]
4x-5y=6 for y
Solve the equation for the specified variable
Answer:
[tex]y = - \frac{4}{5} x + \frac{6}{5} [/tex]
Step-by-step explanation:
First subtract 4x on both sides in order to get -5y alone. Now you have -5y = 4x + 6 (since neither 6 nor 4x are like terms). Now divide -5 on both sides in order to get rid of it, so we can get y by its self. Now you have y = -4/5 x + 6/5
Hope this makes sense. Also please tell me if I'm wrong and I'll be happy to look at it again for ya :)
If x is semi-prime, how many prime factors does it have?
please, 20 points for this!!
Answer:
2 prime factors
Answer: 2 prime factors
Step-by-step explanation: A semiprime is a number n that has just 2 prime factors p and q so n = p × q. It is therefore "almost" a prime (which has only one prime factor, itself!) or a semiprime.
PLEASE HELP ITS MATH THANK YOUUUU
Answer:
5:1
Step-by-step explanation:
The ratio in this case is inches to yards so it would be 5 inches to 1 yard
simplify the expression shown
A:-xy+3y
B:xy+3y
C:-xy-3y
D:xy-3y
Answer:
C:-xy-3y is the answer your welcome
Simplify each radical 1-4
Answer:
1- H , 2- B , 3- A , 4- F
Step-by-step explanation:
Just simplify and you will get the answer.
Goodluck
Which of the following is equivalent to 10,000
30 points so please give right answers
Answer:
just count the zero A is the answer
Step-by-step explanation:
Algebra 2 Need help with b
Answer:
a. was incorrect a = -0.109569028 so...
y = -0.109569028(x + 7)² + 54
b. It's been the above vertex equation for a parabola then
set y = 40 equal to the parabolic equation, we get
40 = -0.109569028x² - 1.533966392x + 48.631117628
solve for x we get
x = -18.3036867393939 or ~ 18.3 feet
Step-by-step explanation:
y = a(x - h)² + k
(h, k) = vertex = (-7, 54)
x = h is the axis of symmetry -7
y = a(x -(-7))² + 54
y = a(x + 7)² + 54
solve for a by inputting the point (15.2, 0)
0 = a(15.2 + 7)² + 54
-54 = a(22.2)²
-54 = 492.84a
a = -54/492.84
a = -0.109569028
Freeman High School's drill team will be attending the national competition and needs to raise $1,600. To raise money for the trip, the girls are selling tickets to a luncheon. Tickets are $8 for students and $10 for adults. The equation 8x+10y=1600, where x represents the number of student tickets sold and y represents the number of adult tickets sold, can be used to represent this situation. The graph of this equation is shown below.
The equation that can be used to represent this situation is 8x + 10y = 1600
Let x represent the number of student tickets sold and y represents the number of adult tickets sold.
Since students ticket cost $8 and adult tickets cost $10, and the total ticket sold was $1600, hence this can be represented by the equation:
8x + 10y = 1600
Therefore the graph of the above equation is attached
Find out more at: https://brainly.com/question/24947711
15/2.25(step by step 100 points and mark brainliest)
Answer:
[tex]\sf\longmapsto \: 6.666[/tex]
Step-by-step explanation:
[tex]\sf\longmapsto \: \: \frac{15}{2.25} [/tex]
Or it can be written as 15÷2.25
Thus,the answer will be in decimal.
[tex]\sf\longmapsto \: 6.666[/tex]
Hello! I need help with coordinate planes in math. I don't need an explanation, because I do kind of understand it. If you don't know the answer, please don't answer it. If you have any questions about the question, please drop in a comment! Thank you!
Answer:
the first one
the third one
thats all I know but this should help I have some work to do soooo sorry big zozo ;(
Step-by-step explanation:
Write the expression using exponents. g⋅g⋅g⋅g⋅g
How much money will be in an account at the end of 6 years if $8000 is deposited at 7% interest compounded 2 times per year? Assume no deposits or withdrawals are made. HELPPPPPPPPPPPP
Answer:
$12,088.55
Step-by-step explanation:
$8000(1+(0.07/2))^(2*6)
$8000(1.035)^(2*6)
$8000(1.51106865)
$12088.5492 - exact
$12088.55 - real
Explain why every square is a quadrilateral. Choose the correct answer below.
A.Every square is a quadrilateral because it is a polygon in which opposite angles have the same measure.
B.Every square is a quadrilateral because it is a polygon with exactly one pair of parallel sides.
C.Every square is a quadrilateral because it is a four-sided polygon.
The following equation models a rock that is thrown upward from an elevation of 4.9 feet
at a speed of 63.2 feet per second. The variable h represents the height in feet, and
represents the time in seconds.
h= –1672 + 63.2t + 4.9
The rock reaches 50 feet on its way up, and again on its way down.
How long does it take the rock to reach 50 feet on its way down? Round your answer to 1
decimal places.
3.0 seconds
13.2 seconds
0.9 seconds
54.9 seconds
Answer:
3.0 seconds
Step-by-step explanation:
i took the test.
The time it takes the rock to reach 50 feet on its way down is 13.2 seconds and option B is the correct answer.
We have,
We are given the equation for the height of the rock as it travels upward and then downward:
h = -1672 + 63.2t - 4.9t²
We want to find the time it takes for the rock to reach a height of 50 feet on its way down.
This means we need to solve for t when h = 50:
50 = -1672 + 63.2t - 4.9t²
Rearrange the equation to isolate the quadratic term:
4.9t² - 63.2t + (1672 + 50) = 0
4.9t² - 63.2t + 1722 = 0
For an equation of the form "ax² + bx + c = 0", the solutions for "x" are given by:
x = (-b ± √(b² - 4ac)) / 2a
In your equation, the coefficients are:
a = 4.9
b = -63.2
c = 1722
Plugging these values into the quadratic formula:
t = (-(-63.2) ± √((-63.2)² - 4 * 4.9 * 1722)) / (2 * 4.9)
Now, let's calculate the discriminant (the value inside the square root):
Discriminant = (-63.2)² - 4 * 4.9 * 1722 ≈ 39884.96 - 33529.6 ≈ 6355.36
Since the discriminant is positive, there are two distinct real solutions for "t".
Now, plug the discriminant back into the quadratic formula and solve for "t":
t = (63.2 ± √6355.36) / 9.8
Now, calculate the square root of the discriminant:
√6355.36 ≈ 79.58
Now, plug in the values for "t":
t₁ = (63.2 + 79.58) / 9.8 ≈ 13.02
t₂ = (63.2 - 79.58) / 9.8 ≈ -1.69
So, the solutions for the equation 4.9t² - 63.2t + 1722 = 0 are approximately:
t₁ ≈ 14.61
t₂ ≈ -1.69 (rejected)
Thus,
The time it takes the rock to reach 50 feet on its way down is B. 13.2 seconds.
Learn more about equations here:
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What is the answer can you hello me
Answer:?
Step-by-step explanation:
?
write an addition equation or subtraction equation your choice to describe the diagram. I'll Mark brainest
Answer:
[tex]0+2-4=-2[/tex]
Step-by-step explanation:
We start at 0 and move 2 to the right to get to 2. Then, we move 4 to the left to get to -2.
So, our equation is [tex]0+2-4=-2[/tex], the 0 being our starting point, the +2 coming from moving to the right 2, the -4 coming from moving to the right 4, and the -2 being our end point.
Solve for w.
–1.01 = 1.4(w + 2) − 2.41
Answer:
w=-1
Step-by-step explanation:
Algebra.
Answer:
w = - 1Step-by-step explanation:
–1.01 = 1.4(w + 2) − 2.412.41 - 1.01 = 1.4(w + 2)1.4 = 1.4(w + 2)w + 2 = 1w = 1 - 2w = - 1Which of these is the smallest number?
A. 1 1/2 ( one and one over two)
B. 1/3
C. 1 1/10 (one and one over ten)
D. 1/4
E. 1/2
Answer:
B this is the smallest number
Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
x + y = 2
–5x - 5y = -10
Step-by-step explanation:
The usual thing to do is to try to get rid of one variable first. So to get rid of x, we multiply the first equation by 5.
5(x + y) = 2(5)
-5x - 5y = -10
---> 5x + 5y = 10
-5x - 5y = -10
---> 0 = 0
As you can see, everything cancels out. If the statement is true, then it is infinitely many solutions.
PLS SOLVE I WILL GIVE BRAINLIEST
Answer:0.8004
Step-by-step explanation:
Daniel was offered a job after college earning a salary of $60,000. He will get a raise of $4,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.
Answer: point o.
Step-by-step explanation:
The population P of a small town, measured in hundreds, is modeled by the inverse of the function P−1(t) = 10ln(50t − 1000), where t is measured in years. Find the equation to model the population and determine its initial value.
P = 5t +100 where P(0) = 100
P = 1/50 In(0.1t)+20
P = 1/500e^t + 20
P = 1/50e^0.1t + 20
Using the inverse function, it is found that the equation is:
[tex]P(t) = \frac{e^{0.1t}}{50} + 20[/tex]
It's initial value is 20.
---------------------------
We want to find the inverse of:
[tex]y = P^{-1}(t) = 10\ln{50t - 1000}[/tex]
To do this, we exchange y and t, and isolate y.
Then:
[tex]10\ln{50y - 1000} = t[/tex]
[tex]\ln{50y - 1000} = \frac{t}{10}[/tex]
[tex]e^{\ln{50y - 1000}} = e^{0.1t}[/tex]
[tex]50y - 1000 = e^{0.1t}[/tex]
[tex]50y = e^{0.1t} + 1000[/tex]
[tex]y = \frac{e^{0.1t} + 1000}{50}[/tex]
[tex]y = \frac{e^{0.1t}}{50} + \frac{1000}{50}[/tex]
[tex]P(t) = \frac{e^{0.1t}}{50} + 20[/tex]
It's initial value is:
[tex]P(0) = \frac{e^{0.1(0)}}{50} + 20 = 0.02 + 20 = 20.02[/tex]
Rounding, 20.
A similar problem is given at https://brainly.com/question/23950969
Answer:
P = 1/50e^0.1t + 20
Step-by-step explanation:
Joshua delivered 30 hives to the local fruit farm. If the farmer has paid to use 5% of the total number of Joshua’s hives, how many hives does Joshua have in all?
Answer:
600 hives
Step-by-step explanation:
If 30 is 5% of the total number of hives Joshua has, then 5%x20=100%
So, 30x20=100%
30x20=600
hope it helped :)
Find the missing factor A that makes the equality true
8x 3 =(−2x)(A)
Solve for t in 2^t²- t= 4
Answer:
t= -1/2 ,t=4
Step-by-step explanation:
2t^2- t -4 =0
2t^2 - 8t+t -4=0
(we have to find the factor here. I have used The Product Sum method of factorization)
2t( t-4) + 1( t-4)=0
(2t+1) (t-4)=0
t= -1/2 ,t=4
8/t + t^2; t=4 please help me
Answer:
8/t + t^2 = 18
Step-by-step explanation:
8/t + t^2
t = 4
8/4 + 4^2
2 + 16 = 18
8/t + t^2 = 18
Lori brought sunglasses and flip-flops at a half-off sale.If she spent a total of $21 on the two items, what was the original price of the sunglasses?
The sunglasses were originally priced at $ 21.
Given that Lori brought sunglasses and flip-flops at a half-off sale, to determine, if she spent a total of $ 21 on the two items, what was the original price of the sunglasses (taking into account that they both cost the same) will be you must perform the following calculation:
50 = 21 100 = X 100 x 21/50 = X 2100/50 = X 42 = X
Thus, the total price of both goods is $ 42, which, divided in half, results in $ 21 (42/2).
Therefore, the sunglasses were originally priced at $ 21.
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