Answer:
X = -24
Step-by-step explanation:
Using the inverse:
26 + 6 = 32
x = 32 / (-4/3) = -24
Let f and g be the functions defined by f(t) = 2t2 and g(t) = t3 + 4t.
1) Determine f'(t) and g′(t).
2) Let p(t) = 2t2 (t3 + 4t) and observe that p(t) = f(t) ⋅ g(t). Re-write the formula for p by distributing the 2t2 term. Then, compute p′(t) using the sum and constant multiple rules.
3) p′(t) = f′(t) ⋅ g′(t).
A. True
B. False
4) Let q(t) = t3 + 4t2/2t2 and observe that q(t) = g(t)/f(t). Rewrite the formula for q by dividing each term in the numerator by the denominator and simplify to write q as a sum of constant multiples of powers of t. Then, compute q′(t) using the sum and constant multiple rules.
5) q′(t) = g′(t)/f'(t).
A. True
B. False
Answer:
1) [tex]f'(t)=4t,\ g'(t)=3t^2+4[/tex]
2) [tex]p(t) =2t^5+8t^3[/tex]
[tex]p'(t)=10t^4+24t^2[/tex]
3) False
4)[tex]q(t) =\dfrac{1}{2}t+2t^{-1}[/tex]
[tex]q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
5) False
Step-by-step explanation:
Given that:
[tex]f(t) = 2t^2[/tex] and [tex]g(t) = t^3 + 4t[/tex]
Formula:
[tex]1. \dfrac{d}{dx}x^n=nx^{n-1}[/tex]
[tex]2. \dfrac{d}{dx}C.f(x)=C.f'(x)\ \{\text{C is a constant}\}[/tex]
1) Using above formula:
[tex]f'(t)=2\times 2 t^{2-1}=4t[/tex]
[tex]g'(t)=3t^{3-1}+4\times 1 t^{1-1}=3t^2+4[/tex]
2) [tex]p(t) =2t^2(t^3+4t)[/tex]
Rewriting the formula by distributing the [tex]2t^2[/tex] term:
[tex]p(t) =2t^2.t^3+2t^2.4t=2t^5+8t^3[/tex]
[tex]p'(t) = 10t^4+24t^2[/tex]
3) By using answers of part (1):
[tex]f'(t).g'(t)=12t^3+16t[/tex]
[tex]p'(t) = 10t^4+24t^2[/tex]
Therefore it is False that [tex]p'(t) = f'(t).g'(t)[/tex]
4) [tex]q(t)=\dfrac{t^3+4t}{2t^2}[/tex]
Writing by distributing:
[tex]q(t)=\dfrac{t^3}{2t^2}+\dfrac{4t}{2t^2}\\\Rightarrow q(t) =\dfrac{t}{2}+\dfrac{2}{t}\\\Rightarrow q(t) =\dfrac{1}{2}t+2t^{-1}[/tex]
Using the formula:
[tex]q'(t)=\dfrac{1}{2}t^{1-1}+2\dfrac{-1}{t^2}\\\Rightarrow q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
(5)By using answers in part (1):
[tex]\dfrac{g'(t)}{f'(t)}=\dfrac{3t^2+4}{4t}=\dfrac{3}{4}t+\dfrac{1}t[/tex]
[tex]q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
Therefore, it is False that:
[tex]q'(t)=\dfrac{g'(t)}{f'(t)}[/tex]
Is it -56/65????????????????
Answer:
[tex] \cos (u + v) = -\dfrac{56}{65} [/tex]
Good job!
Step-by-step explanation:
[tex] \cos (u + v) = \cos u \cos v - \sin u \sin v [/tex]
[tex] \sin u = -\dfrac{3}{5} [/tex]; u is in QIII.
That makes [tex] \cos u = -\dfrac{4}{5} [/tex]
[tex] \sin v = -\dfrac{12}{13} [/tex]; v is in QIV.
That makes [tex] \cos v = \dfrac{5}{13} [/tex]
[tex] \cos (u + v) = (-\dfrac{4}{5})(\dfrac{5}{13}) - (-\dfrac{3}{5})(-\dfrac{12}{13}) [/tex]
[tex] \cos (u + v) = -\dfrac{20}{65} - \dfrac{36}{65} [/tex]
[tex] \cos (u + v) = -\dfrac{56}{65} [/tex]
You are correct.
Answer:
Step-by-step explanation:
-0.8615
Need help rn will give brainlyest if correct answer with explaining
unit ratio
Answer: The cost per bag is $27
Step-by-step explanation:
Divide 135 by 5 = 27
Unit ratio means that if you know the rate per unit, you can calculate the cost by multiplying the constant rate by the number of units. In this question, the rate is $27 and the unit is the bag.
The ratio looks like
1:27 as 2:54 as 3:81 as 4:108 as 5:135
They are all equivalent to 1/27
y = 27x is another way of writing an equation for this ratio.
If possible, express each of the following as the sum of a perfect square and a prime number. Give all possible answers and explain how you found them. . 21 28. 52. 68 . 13 . 20
Answer:
4^2 + 5 = 21, 5^2 + 3 = 28, 7^2 + 3 = 52, 3^2 + 43 = 52, 7^2 + 19 = 68, 3^2 + 11 = 20, 1^2+19 = 20. I can't find a prime number and a perfect square that sums to 13.
Explanation:
these are primarily derived by finding the closest perfect square to a number and finding the difference to make the sum work, or finding the simplest prime number that will reduce the number which is a multiple of a perfect square.
prime factorization of 60 error
Answer:
2*2*3*5
Step-by-step explanation:
Which situation can be represented by this inequality?
3 + 2.0 > 8x
Select one:
The cost of 2 candy bars plus a $3 bag of chips is greater than 8 candy bars.
The cost of 2 candy bars with a discount of $3 is greater than 8 candy bars.
o The cost of a $3 bag of chips plus 2 candy bars is at least as much as 8 candy bars.
The cost of a $3 bag of chips plus 2 candy bars is less than 8 candy bars.
Answer: D
Step-by-step explanation:
f(X)=3x+7, find f(10)
Answer:
37
Step-by-step explanation:
Sorry if this is wong I haven't done these in awhile, but this is how I got it.
f(X)=3x+7
f(10)=3(10) +7
f(10)=30 +7
f(10)=37
Answer:
f(10)=37
Step-by-step explanation:
f(x)=3x+7
(for f(10) we sub 10 for x)
f(10)=3×10+7
=30+7
=37
Given f(x) = -x + 7, find x when f(x)= -4
Answer:
x = 11
Step-by-step explanation:
f(x) = -x + 7
f(x) = -4
Using substitution, -x + 7 = -4
Then you can solve from there
-x + 7 = -4
-x = -11
x = 11
Hope this helps!
(I apologize if I'm incorrect)
Let xy=6 and x2 + y2 = 23 what is the value of (x+y)??
Answer:
I'll assume that x2 = x^2 and y2 = y^2 and the answer is sqrt{35}.
Step-by-step explanation:
This problem invovles completing the square, so if I square (x+y), I get
x^2+2xy+y^2, and since xy = 6, 2xy = 12, 23+12 = 35, and your answer is sqrt{35}.
What is the smallest value that x^(2)+6 can have?
Answer:
-56.9034
Step-by-step explanation:
2,9,23,51,107
Determine the next terms of sequence
Answer:
answer is 142
Step-by-step explanation:
Three partners are investing a total of $700,000 to open a garden and landscaping store. The first partner wns 30% of the business, and the second partner owns 25% of the business. What percent does the third partner own? Just input the numerals for your answer -do not add a percent sign. hip
Answer: 45
Step-by-step explanation: The 3rd partner has 45% of the store. Which is also $315,000.
Answer: the third partner owns 45% or $315,000 of the business.
Step-by-step explanation:
30 percent of 700,000=210,00
25 percent of 700,000=175,000
175,000+210,000=385,000
700,000-385,000= 315,000
the third partner owns 315,000 and 315,000=45%
salome tiene 4 veces la edad de esmeralda.si ambas edades suman 75 años¿que edad tiene cada una?
Round 17.68694 to the nearest tenth
Answer:
17.7
Step-by-step explanation:
The tenths place is the very first value after the decimal. The number 17.68694 rounds up to 17.7, because .68 is closer to .7 than it is to .6.
Write the equation of each line described in slope-intercept form (y = mx + b) with a slope of -6 and x-intercept of 4. (4,0)
Answer:
ill give u the answer if u do 73 divided by 2628
Step-by-step explanation:
Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions.
x1 +hx2 = 3
5x1 + 15x2 = k
a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
A. The system has no solutions only when k nothing and h is any real number.
B. The system has no solutions only when h nothing and k nothing.
C. The system has no solutions only when h nothing and k is any real number.
D. The system has no solutions only when h nothing and k nothing.
E. The system has no solutions only when h nothing and k nothing.
F. The system has no solutions only when k nothing and h is any real number.
G. The system has no solutions only when h nothing and k nothing.
H. The system has no solutions only when h nothing and k is any real number.
b. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)
A. The system has a unique solution only when h and k
B. The system has a unique solution only when h =-and k is any real number.
C. The system has a unique solution only when k | and h is any real number.
D. The system has a unique solution only when h-U and k = 1
Answer:
a) C) The system has no solutions only when h=3 and k is any real number.
b) D) The system has a unique solution when [tex]h=(-\infty,3)U(3,\infty)[/tex] and k is any real number.
c) The system has may solutions when h=3 and k=15
Step-by-step explanation:
a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:
[tex]x_{1}+hx_{2}=3[/tex]
so
[tex]x_{1}=3-hx_{2}[/tex]
Next we can substitute this into the second equation so we get:
[tex]5(3-hx_{2})+15x_{2}=k[/tex]
We distribute the 5 into the first parenthesis so we get:
[tex]15-5hx_{2}+15x_{2}=k[/tex]
and group like terms:
[tex]-5hx_{2}+15x_{2}=k-15[/tex]
we factor x2 so we get:
[tex]x_{2}(-5h+15)=k-15[/tex]
and solve for x2:
[tex]x_{2}=\frac{k-15}{-5h+15}[/tex]
this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:
[tex]-5h+15= 0[/tex]
and solve for h:
[tex]-5h= -15[/tex]
[tex]h=\frac{-15}{-5}[/tex]
[tex]h= 3[/tex]
so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.
b)
For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.
So we take the second equation and factor it:
[tex]5x_{1}+15x_{2}=k[/tex]
we start by factoring a 5 from the left side of the equation so we get:
[tex]5(x_{1}+3x_{2})=k[/tex]
Next, we divide both sides of the equation into 5 so we get:
[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]
we now compare it to the first equation:
[tex]x_{1}+hx_{2}=3[/tex]
[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]
In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and [tex]\frac{k}{5}=3[/tex]
when taking the second condition and solving for k we get that:
[tex]k=3(5)[/tex]
so
k=15
Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:
D) The system has a unique solution when and k is any real number.
c)
We have already solved part c on the previous part of the problem, so the answer is:
The system has many solutions when h=3 and k=15
What is the pattern in the numbers 1,8,27,64
Answer:
3
Step-by-step explanation:
he pattern is continued by adding 3 to the last number each time, like this: 1, 8, 27, 64, 125, 216, 343, 512, 729
Steve drew line segments CDEF, GHI, ADH, and BEH as shown in the
diagram below. Scalene ADEH is formed.
If segment CDEF is parallel to segment GHI, which statement is true? *
Answer:
BEF=IHEStep-by-step explanation:
ADE=DHG
FEH=IHE
ADE=DHE
ADC=EHI
BEF=IHE <This would be the correct answer if segment CDEF is parallel to segment GHI.
sharon drops a rubber ball from a height of 160 feet every bounce sends the ball half as high as it was before what is the total vertical (up and down ) distance the ball has traveled from the mament it is dropped to the moment it hits the floor for the fourth time
Answer:
10 feet.
Step-by-step explanation:
First time: 160/2=80.
Second time: 80/2=40.
Third time: 40/2=20.
Fourth time: 20/2=10.
Boom.
Four times a number, added to 8, is 32
Answer: 6
Step 1: Subtract 8.
32 - 8 = 24
Step 2: Divide by 4, since the question is asking for 4 times the number.
24 ÷ 4 = 6
Answer = 6
Part b at the airport to walk from the car to the waiting area by the gate was
Answer:
24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
There are 24 marbles in a jar. 3 marbles are added to the jar when the class is good. How many times can the class be rewarded to get 100 marbles
Look at the incomplete multiplication problem below.
638 times 56 = 3828. 3828 + question mark = blank
What value is missing?
31,500
31,900
35,280
35,728
Answer:
B
Step-by-step explanation:
ayuda nose ayudaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
486 inches 162 inches 4 1/2 yards ?
Answer:
486 inches is 13.5 yards and 162 inches is 4.5 yards please mark brainlist thank you
Translate the sentence into an equation.
Twice the difference of a number and 2 equals 6.
Use the variable b for the unknown number.
Answer:
b + 2 = 6
Step-by-step explanation:
This may not be the right answer, but its what I think it is.
why does the graph of a proportional relationship must pass through the origin (0,0)
Answer:
Directly proportional relationships always pass through the origin (0,0). There are other linear relationships that do not pass through the origin.
The graph of a proportional relationship must pass through the origin (0,0). Because of the value of k, the ordered pair (0, 0) satisfies this equation.
What is a graph?
The relation between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and connecting lines. It doesn't matter how long the lines are or where the points are located. A node is specified for each element in a graph.
A ray is used to describe any proportional relationship using an equation of the form y = kx. The ordered pair (0, 0) satisfies this equation regardless of the value of k, hence the ray or line must traverse the origin.
Thus, the graph of a proportional relationship must pass through the origin (0,0). Because of the value of k, the ordered pair (0, 0) satisfies this equation.
Learn more about the graph here,
https://brainly.com/question/17267403
#SPJ2
Which factor can cause secondary succession?
A. clear cutting
B. glacial melting
C. competition
D. predation
(Which one from these answers?)
Answer:
a
Step-by-step explanation:
2x + 3x = 60 for x = 12
True or false
Answer:
true
Step-by-step explanation:
Trust me
Answer:
True
Step-by-step explanation:
2(12)+3(12)=60
24+36=60
Evaluate : (r - 3)³ + r² if r = -3 and s = -4. Show all the steps of working for this question.
I have a math test please give me the right answer!!
Answer:
-207
Step-by-step explanation:
Using r= -3, we can substitute r in the whole equation as (-3) which gives you: ((-3)-3)^3 +(-3)^2. Now you can calculate these values in a step by step manner. (-6)^3 +9 then to -216 +9 which brings you to the answer of -207.
Answer:
225
Step-by-step explanation:
(r - 3)³ + r² if r = -3 and s = -4
(-3 - 3)^3 + (-3)^2
(-6)^3 + (9)
(-6 x -6 x -6) + 9
-216 + 9
-207