What function is represented below? graph begins in the first quadrant and decreases quickly while crossing the ordered pair 2, 1. Then the graph begins to decrease slowly as it approaches the x axis. f(x) = one fourth to the power of x plus 2 f(x) = one fourth to the power of x + 2 f(x) = one fourth to the power of x minus 2 f(x) = one fourth to the power of x − 2
Answers
It is a decreasing function that when x= 2, (1/4) is raised to the zero power which is 1, which is what the point (2,1) asks for.
Answer:
The represented function is :
[tex]f(x)=(\frac{1}{4})^{x-2}[/tex]
Step-by-step explanation:
[tex]1.\thinspace f(x)=(\frac{1}{4})^x +2[/tex]
And the equation must pass through (2,1) as given,
But, f(2) = 2.0625 ≠ 1 so this is not the required function.
[tex]2.\thinspace f(x)=(\frac{1}{4})^{x+2}[/tex]
And the equation must pass through (2,1) as given,
But, f(2) = 0.0039 ≠ 1 so this is not the required function.
[tex]3.\thinspace f(x)=(\frac{1}{4})^x -2[/tex]
And the equation must pass through (2,1) as given,
But, f(2) = -1.94 ≠ 1 so this is not the required function.
[tex]4.\thinspace f(x)=(\frac{1}{4})^{x-2}[/tex]
And the equation must pass through (2,1) as given,
We see, f(2) = 1 so this is the required function and the corresponding graph of the function is attached below :
Hence, The correct option is (4)
Related Questions
Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(t) = at2 + bt + c, where a, b, and c are to be determined.
Answers
[tex]x=at^2+bt+c[/tex]
[tex]x'=2at+b[/tex]
[tex](2at+b)+2(at^2+bt+c)=t^2+4t+7[/tex]
[tex]2at^2+(2a+2b)t+(b+2c)=t^2+4t+7[/tex]
[tex]\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4[/tex]
Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:
[tex]x'+2x=0\implies r+2=0\implies r=-2[/tex]
so that [tex]x_c=Ce^{-2t}[/tex] is a characteristic solution to the ODE, and the general solution would be
[tex]x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4[/tex]
To find a, b, c for the solution:
Let's start by writing down the expression for the function x(t) and its derivative:
We have:
x(t) = at² + bt + c
and
x'(t) = 2at + b
Using x' and x into the differential equation x′ + 2x = t² + 4t + 7 gives us:
2at + b + 2*(at² + bt + c) = t² + 4t + 7
Expanding this gives:
2at² + 2bt + b + 4at + 2c = t² + 4t + 7
By equating the coefficients of equivalent powers of t on both sides, we get three equations:
For t² :
2a = 1
So, a = 1/2
For t:
2b + 4a = 4
Substitute a = 1/2 into the equation gives b = 1 - 2 = -1
For the constant term:
b + 2c = 7
Substituting b = -1 gives c = 4.
So the solution is a = 1/2, b = -1, c = 4.
So the specific solution of this differential equation is given by x(t) = (1/2)t² - t + 4.
$185 DVD player 6% markup
Answers
i think.....
if it is right dont forget to give me brainliest
605 mi in 11 hours at the same rate how many miles would he drive in 13 hours
Answers
605/ 11= 55
55*13=715
In 13 hours, 715 miles will be traveled
What is the answer to the problem below?
Solve the system of equations graphically.
x=3
y=4
Answers
They already give us the answer, which is (3,4). So all we have to do is graph it on the graph. 3 is for x and 4 is for y.
Check the picture below.
(3,4)
You could solve this graphically by graphing the vertical line x = 3 and the horiz. line y = 4. A visual check would show that these two lines intersect at (3,4).
15 children voted for their favorite color. The votes for red and blue together we're double the votes for green and yellow together. How did the children vote?
Answers
and 5 voted gor green and yellow
How do you figure out what 1/10 of 1,7000.000 km squared is?
Answers
This would get you 28,900,000.
The five-number summary for scores on a statistics test is 11, 35, 61, 70, 79. in all, 380 students took the test. about how many scored between 35 and 61
Answers
Answer: There are 95 students who scored between 35 and 61.
Step-by-step explanation:
Since we have given that
The following data : 11,35,61,70,79.
So, the median of this data would be = 61
First two data belongs to "First Quartile " i.e. Q₁
and the second quartile is the median i.e. 61.
The last two quartile belongs to "Third Quartile" i.e. Q₃
And we know that each quartile is the 25th percentile.
And we need "Number of students who scored between 35 and 61."
So, between 35 and 61 is 25% of total number of students.
So, Number of students who scored between 35 and 61 is given by
[tex]\dfrac{25}{100}\times 380\\\\=\dfrac{1}{4}\times 380\\\\=95[/tex]
Hence, There are 95 students who scored between 35 and 61.
The number of students who scored between 35 and 61 is 95
The 5 number summary is the value of the ;
Minimum Lower quartile Median Upper quartile and Maximum values of a distribution.The total Number of students = 380
The lower quartile (Lower 25%) = 35
The median (50%) = 61
The Number of students who scored between 35 and 61 : 50% - 25% = 25%This means that 25% of the total students scored between 35 and 61.
25% of 380 = 0.25 × 380 = 95Hence, 95 students scored between 35 and 61.
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What is the unit rate for 822.6 km in 18 hours? Enter your answer, as a decimal, in the box. Please Help
Answers
answer
unit rate = 45.7 km per hour
822.6 km
-------------- = 45.7 km/hr
18 hrs
Note: this is approx 45.7 km/hr 0.625 mile
--------------- * ----------------- = 28.6 mph
1 1 km
What can be used as a reason in a two-column proof?
Select each correct answer.
conjecture
postulate
definition
premise
Answers
Therefore, what can be used as a reason in a two-column proof are:
Postulates
Definitions
Answer:
Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. The reason column will typically include "given", vocabulary definitions, and theorems.
Therefore, what can be used as a reason in a two-column proof are:
Postulates
Definitions
D is the midpoint of CE.E has coordinates (-3,-2), and D has coordinates (2 1/2, 1). Find the coordinate of C.
Answers
(-3,-2)....x1 = -3 and y1 = -2
(x,y)......x2 = x and y2 = y
now we sub
(-3 + x) / 2, (-2 + y) / 2
(-3 + x) / 2 = 2 1/2
-3 + x = 5/2 * 2
-3 + x = 5
x = 5 + 3
x = 8
(-2 + y) / 2 = 1
-2 + y = 1 * 2
-2 + y = 2
y = 2 + 2
y = 4
so the coordinates of point C are : (8,4)
The coordinate of point C on line CE will be (8, 4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
D is the midpoint of CE.
E has coordinates (-3,-2), and D has coordinates (2 1/2, 1).
Now, By the definition of midpoint;
Let the coordinate of point C = (x, y)
Then,
((x + (-3))/2 , (y + (-2))/2) = (2 1/2, 1)
By comparison we get;
x + (-3) / 2= 2 1/2
x - 3 = 2 (5/2)
x - 3 = 5
x = 3 + 5
x = 8
And, (y + (-2))/2 = 1
y - 2 = 2
y = 2 + 2
y = 4
Thus, The coordinate of point C = (x, y) = (8, 4)
So, The coordinate of point C on line CE will be (8, 4).
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Mrs. Milleman looked at another hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent.
Answers
[tex]2075-1195=880[/tex]
Now we can set up a proportion and solve for x:
[tex] \frac{1195}{100} = \frac{880}{x} [/tex]
[tex]x= \frac{(880)(100)}{1195} [/tex]
[tex]x= 73.64 [/tex] which rounded to the nearest integer is 74%
We now can conclude that the price increased in 74%
write a fraction less than 1 with a denominator of 6 that is greater than 3/4
Answers
Hope this helps!
Answer:= 5/6
Step-by-step explanation:hope this helps
If the radius of a circle measures 2 inches, what is the measure of its diameter?
Answers
~~Alexis
Given sina=6/7 and cosb=-1/6, where a is in quadrant ii and b is in quadrant iii , find sin(a+b) , cos(a-b) and tan(a+b)
Answers
now, keep in mind that, the hypotenuse is just a radius unit, and thus is never negative, so if a fraction with it is negative, is the other unit. A good example of that is the second fraction here, -1/6, where the hypotenuse is 6, therefore the adjacent side is -1. Anyhow, let's find the opposite side to get the sin(b).
[tex]\bf cos(b)=\cfrac{\stackrel{adjacent}{-1}}{\stackrel{hypotenuse}{6}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a \\\\\\ \textit{now, angle "b" is in the III quadrant, where the opposite is negative} \\\\\\ -\sqrt{35}=b\qquad \qquad \boxed{sin(b)=\cfrac{-\sqrt{35}}{6}}[/tex]
now
[tex]\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ [/tex]
[tex]\bf tan({{ \alpha}} + {{ \beta}}) = \cfrac{tan({{ \alpha}})+ tan({{ \beta}})}{1- tan({{ \alpha}})tan({{ \beta}})}\qquad tan({{ \alpha}} - {{ \beta}}) = \cfrac{tan({{ \alpha}})- tan({{ \beta}})}{1+ tan({{ \alpha}})tan({{ \beta}})}[/tex]
[tex]\bf sin(a+b)=\cfrac{6}{7}\cdot \cfrac{-1}{6}+\cfrac{-\sqrt{13}}{7}\cdot \cfrac{-\sqrt{35}}{6}\implies \cfrac{-1}{7}+\cfrac{\sqrt{455}}{42} \\\\\\ \cfrac{-6+\sqrt{455}}{42}\\\\ -------------------------------\\\\ cos(a-b)=\cfrac{-\sqrt{13}}{7}\cdot \cfrac{-1}{6}+\cfrac{6}{7}\cdot \cfrac{-\sqrt{35}}{6}\implies \cfrac{\sqrt{13}}{42}-\cfrac{\sqrt{35}}{7} \\\\\\ \cfrac{\sqrt{13}-6\sqrt{35}}{42}[/tex]
[tex]\bf -------------------------------\\\\ tan(a)=\cfrac{\frac{6}{7}}{-\frac{\sqrt{13}}{7}}\implies -\cfrac{6}{\sqrt{13}}\implies -\cfrac{6\sqrt{13}}{13} \\\\\\ tan(b)=\cfrac{\frac{-\sqrt{35}}{6}}{\frac{-1}{6}}\implies -\sqrt{35}\\\\ -------------------------------\\\\[/tex]
[tex]\bf tan(a+b)=\cfrac{-\frac{6}{\sqrt{13}}-\sqrt{35}}{1-\left( -\frac{6}{\sqrt{13}} \right)\left( -\sqrt{35} \right)}\implies \cfrac{\frac{-6-\sqrt{455}}{\sqrt{13}}}{1-\frac{6\sqrt{35}}{\sqrt{13}}} \\\\\\ \cfrac{\frac{-6-\sqrt{455}}{\sqrt{13}}}{\frac{\sqrt{13}-6\sqrt{35}}{\sqrt{13}}}\implies \cfrac{-6-\sqrt{455}}{\sqrt{13}-6\sqrt{35}}[/tex]
and now, let's rationalize the denominator of that one, hmmm let's see
[tex]\bf \cfrac{-6-\sqrt{455}}{\sqrt{13}-6\sqrt{35}}\cdot \cfrac{\sqrt{13}+6\sqrt{35}}{\sqrt{13}+6\sqrt{35}} \\\\\\ \cfrac{-6\sqrt{13}-36\sqrt{35}-\sqrt{5915}-6\sqrt{15925}}{({\sqrt{13}-6\sqrt{35}})({\sqrt{13}+6\sqrt{35}})} \\\\\\ \cfrac{-6\sqrt{13}-36\sqrt{35}-13\sqrt{35}-210\sqrt{13}}{(\sqrt{13})^2-(6\sqrt{35})^2} \\\\\\ \cfrac{-216\sqrt{13}-49\sqrt{35}}{13-210}\implies \cfrac{-216\sqrt{13}-49\sqrt{35}}{-197} \\\\\\ \cfrac{216\sqrt{13}+49\sqrt{35}}{197}[/tex]
sin(a+b) = -1/7 +√455/42 = 0.8721804464845457
cos(a-b) = √13/42 - √35/7 = -0.7761476987942811
tan(a+b )= (6√13/13 + √35) / (1 - 6√455/13) = -0.525
Given sin(a) = 6/7 and cos(b) = -1/6, with a in quadrant II and b in quadrant III, we need to utilize trigonometric identities to find sin(a+b), cos(a-b), and tan(a+b).
Firstly, since a is in quadrant II, cos(a) is negative. We use the identity sin²(a) + cos²(a)=1 to find cos(a):
cos(a) = -√(1 - sin²(a)) = -√(1 - (6/7)²) = -√(1 - 36/49) = -√(13/49) = -√13/7Similarly, since b is in quadrant III, sin(b) is also negative. We use the identity sin²(b) + cos²(b)=1 to find sin(b):
sin(b) = -√(1 - cos²(b)) = -√(1 - (-1/6)²) = -√(1 - 1/36) = -√(35/36) = -√35/6Now we can use the angle addition and subtraction formulas:
1. sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin(a + b) = (6/7)(-1/6) + (-√13/7)(-√35/6) = -1/7 + √(13×35)/(7×6) = -1/7 + √455/42 = -1/7 +√455/422. cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
cos(a - b) = (-√13/7)(-1/6) + (6/7)(-√35/6) = √13/(7×6) - (6√35)/(7×6) = √13/42 - √35/73. tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
Using tan(a) = -sin(a)/cos(a) = -(6/7)/(-√13/7) = 6/√13 and tan(b) = sin(b)/cos(b) = (-√35/6)/(-1/6) = √35:tan(a + b) = (6/√13 + √35) / (1 - (6/√13)(√35)) = (6√13/13 + √35) / (1 - 6√455/13)what 5x(4+gy) if x= 1 g= 20 Y=14
please show work
Answers
[tex]5x(4+gy)[/tex]
[tex]5(1)(4+(20)(14))=5(4+280)=5(284)=1420[/tex]
Round 5836197 to the nearest hundred
Answers
Answer:
5836200.
Step-by-step explanation:
Given : 5836197 .
To find : Round 5836197 to the nearest hundred.
Solution : We have given 5836197
Step 1 : First, we look for the rounding place which is the hundreds place.
Step 2 : Rounding place is 97.
Step 3 : 97 is greater than 50 then it would be rounded up mean next number to 97 would be increase to 1 and 97 become 00.
Step 4 : 5836200.
Therefore, 5836200.
Jonathan pays $1.90 per pound for potatoes. He buys 8.3 pounds of potatoes. He determines that he will pay $15.77, before tax, for the potatoes. Which best describes the reasonableness of Jonathan’s solution?
Answers
The correct answer is C.
Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77.
Hope this helps.
how can I adjust a quotient to solve a division problem
Answers
Suppose you have two credit cards. The first has a balance of $415 and a credit limit of $1,000. The second has a balance of $215 and a credit limit of $750. What is your overall credit utilization?
Answers
Compute for the total balance:
total balance = $415 + $215 = $630
Then we compute for the total credit limit:
total credit limit = $1,000 + $750 = $1,750
The credit utilization would simply be the percentage ratio of total balance over total credit limit. That is:
credit utilization = ($630 / $1,750) * 100%
credit utilization = 36%
The perpendicular bisector of side AB of ∆ABC intersects side BC at point D. Find AB if the perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
Answers
Answer:
Hence, AB=12.
Step-by-step explanation:
We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.
this means that side AE=BE.
Also we could clear;ly observe that
ΔBED≅ΔAED
( since AE=BE, side ED common, ∠BED=∠AED
so by SAS congruency the two triangles are congruent)
Now we are given that:
the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.
i.e. AB+AC+BC=AC+AD+CD+12
AB+BC=AD+CD+12
as AD=BD
this means that AD+CD=BD+CD=BC
AB+BC=BC+12
AB=12
Hence AB=12
Answer:
The required length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
Step-by-step explanation:
Given: The perpendicular bisector of side [tex]AB[/tex] of [tex]\bigtriangleup{ABC}[/tex] intersects side [tex]BC[/tex] at point [tex]D[/tex] and the perimeter of [tex]\bigtriangleup{ACD}[/tex].
From the figure,
[tex]AE=BE[/tex] .......(1) (as [tex]DE[/tex] is perpendicular bisector of side [tex]AB[/tex])
Now, In [tex]\bigtriangleup{BED}[/tex] and [tex]\bigtriangleup{AED}[/tex]
[tex]AE=BE[/tex] ( from equation 1 )
[tex]\angle {BED} =\angle {AED}[/tex] ( Both [tex]90^\circ[/tex] )
[tex]ED=ED[/tex] ( Common side)
[tex]\bigtriangleup{BED}\cong\bigtriangleup{AED}[/tex] ( by SAS congruence rule)
[tex]BD=AD[/tex] .........(2) (by CPCT)
As per question,
The perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
[tex]AB+BC+AC=AC+CD+AD+12[/tex]
[tex]AB+BC=AD+CD+12\\AD+CD=BD+CD\\AB+BC=BC+12\\[/tex]
[tex]AB=12\rm\;{cm}[/tex]
Hence, the length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
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What's 24.67 to one significant figure?
Answers
A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form? A=–n2 + 3n + 5 B=n2 + 6n + 1 C=2n2 + 6n – 1 D=3n2 + 5
Answers
Multiplying out the first term: 2n^2 + 6n
Subtracting n^2-1: - (n^2 -1)
----------------------
n^2 + 6n + 1 (answer)
Answer:
B
Step-by-step explanation:
The diagram represents a reduction of a triangle by using a scale factor of 0.8.
What is the height of the reduced triangle?
4.0 inches
4.8 inches
5.2 inches
7.5 inches
Answers
The reduction factor of 0.8 means the lengths in the reduced triangle are 0.8 times those of the original.
Then the original 6 inch length is reduced to 0.8×6 inches = 4.8 inches in the reduced triangle.
Answer:
4.8 inches
Step-by-step explanation:
The scale factors are used to convert a figure into another one with similar characteristics but different lengths, in this example is a triangle, and in order to calculate the measure of the height you just have to multiply the original height by the scale factor:
6 inches * scale factor
6 inches* 0.8= 4.8 inches
So the resultant triangle will have a height of 4.8 inches.
30 POINTS: The art club had an election to select a president. 25% of the 76 members of the club voted in the election. How many members voted?
Answers
Answer:
19 members voted.
Step-by-step explanation:
Percentage problems can be solved by a rule of three.
25% of the 76 members of the club voted in the election. How many members voted?
So 76 is 100% = 1. How much is 0.25?
76 - 1
x - 0.25
[tex]x = 76*0.25[/tex]
[tex]x = 19[/tex]
19 members voted.
Use the chain rule to find dw/dt. w = xey/z, x = t7, y = 4 − t, z = 2 + 9t
Answers
[tex]w = xe^{y/z},\ x = t^7,\ y = 4 - t, \ z = 2 + 9t \\ \\ \frac{dw}{dt} = \frac{dw}{dx} \cdot \frac{dx}{dt} + \frac{dw}{dy} \cdot \frac{dy}{dt} + \frac{dw}{dz} \cdot \frac{dz}{dt} \\ \\ \frac{dw}{dx}=e^{y/z} \\ \\ \frac{dw}{dy}= \frac{x}{z} e^{y/z} \\ \\ \frac{dw}{dz}=- \frac{xy}{z^2} e^{y/z} \\ \\ \frac{dx}{dt}=7t^6 \\ \\ \frac{dy}{dt}=-1 \\ \\ \frac{dz}{dt}=9[/tex]
Thus,
[tex] \frac{dw}{dt}=e^{y/z}\cdot7t^6+\frac{x}{z} e^{y/z}\cdot(-1)+- \frac{xy}{z^2} e^{y/z}\cdot(9) \\ \\ =7t^6e^{y/z}-\frac{x}{z} e^{y/z}-9\frac{xy}{z^2} e^{y/z} \\ \\ =\left(7t^6-\frac{x}{z}-9\frac{xy}{z^2}\right)e^{y/z}[/tex]
The derivative[tex]\( \frac{dw}{dt} \) is \( \frac{7t^6 e^{4-t}}{2+9t} - \frac{t^7 e^{4-t}}{2+9t} - \frac{9t^7 e^{4-t}}{(2+9t)^2} \).[/tex]
To find [tex]\( \frac{dw}{dt} \)[/tex] using the chain rule for the given function[tex]\( w = \frac{x e^y}{z} \), where \( x = t^7 \), \( y = 4 - t \), and \( z = 2 + 9t \)[/tex], follow these steps:
1. **Express ( w ) in terms of ( t ):**
Substitute ( x ), ( y ), and ( z ) into ( w ):
[tex]\[ w = \frac{x e^y}{z} = \frac{(t^7) e^{(4 - t)}}{2 + 9t} \][/tex]
2. **Apply the chain rule:**
The chain rule states that for a function ( w(t) ) defined implicitly by ( w = f(x(t), y(t), z(t)) ), the derivative [tex]\( \frac{dw}{dt} \)[/tex] is given by:
[tex]\[ \frac{dw}{dt} = \frac{\partial w}{\partial x} \cdot \frac{dx}{dt} + \frac{\partial w}{\partial y} \cdot \frac{dy}{dt} + \frac{\partial w}{\partial z} \cdot \frac{dz}{dt} \][/tex]
3. **Compute partial derivatives of ( w ) with respect to ( x ), ( y ), and ( z ):**
[tex]\( \frac{\partial w}{\partial x} = \frac{e^y}{z} \)[/tex]
[tex]\( \frac{\partial w}{\partial y} = \frac{x e^y}{z} \)[/tex]
[tex]\( \frac{\partial w}{\partial z} = -\frac{x e^y}{z^2} \)[/tex]
4. **Compute [tex]\( \frac{dx}{dt} \), \( \frac{dy}{dt} \), and \( \frac{dz}{dt} \):**[/tex]
[tex]\( \frac{dx}{dt} = 7t^6 \)[/tex]
[tex]\( \frac{dy}{dt} = -1 \)[/tex]
[tex]\( \frac{dz}{dt} = 9 \)[/tex]
5. **Substitute these into the chain rule formula:**
[tex]\[ \frac{dw}{dt} = \frac{e^y}{z} \cdot 7t^6 + \frac{x e^y}{z} \cdot (-1) + \left(-\frac{x e^y}{z^2}\right) \cdot 9 \][/tex]
6. **Substitute[tex]\( x = t^7 \), \( y = 4 - t \), \( z = 2 + 9t \)[/tex] into the expression:**
[tex]\( e^y = e^{4 - t} \)[/tex]
Substitute these values into the formula for [tex]\( \frac{dw}{dt} \):[/tex]
[tex]\[ \frac{dw}{dt} = \frac{e^{4 - t}}{2 + 9t} \cdot 7t^6 - \frac{t^7 \cdot e^{4 - t}}{2 + 9t} - \frac{9t^7 \cdot e^{4 - t}}{(2 + 9t)^2} \][/tex]
Therefore, [tex]\( \frac{dw}{dt} \)[/tex] is:
[tex]{\frac{dw}{dt} = \frac{7t^6 e^{4 - t}}{2 + 9t} - \frac{t^7 e^{4 - t}}{2 + 9t} - \frac{9t^7 e^{4 - t}}{(2 + 9t)^2} } \][/tex]
Determine whether the function f : z × z → z is onto if
a.f(m,n)=m+n. b)f(m,n)=m2+n2.
c.f(m,n)=m.
d.f(m,n) = |n|.
e.f(m,n)=m−n.
Answers
b. No; [tex]m^2+n^2\ge0[/tex] for any integers [tex]m,n[/tex]
c. Yes; self-evident
d. No; similar to (b), because [tex]|n|\ge0[/tex] for any [tex]n\in\mathbb Z[/tex]
e. Yes; [tex]\mathbb Z[/tex] is closed under subtraction
What is the completely factored form of x3 – 64x? x(x – 8)(x – 8) (x-4)(x2+4x+16) x(x – 8)(x + 8) (x – 4)(x + 4)(x + 4)
Answers
After factoring x from both terms, you can factor the difference of two squares.
= x(x² -64)
= x(x -8)(x +8)
_____
It is worth remembering the "speciall form" that is the difference of two squares:
... a² - b² = (a -b)(a +b)
Answer:
x(x -8)(x +8)
Step-by-step explanation:
A, B, and C are mutually exclusive. P(A) = .2, P(B) = .3, P(C) = .3. Find P(A ∪ B ∪ C). P(A ∪ B ∪ C) =
Answers
In the question given above,
P (A) = .2
P (B) = .3
P (C) = .3
P (A U B U C) = .2 + .3 + .3 = .8
Therefore, P (A U B U C) = 0.8.
The function y = –3(x – 2)2 + 6 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog (in dollars). Find and interpret the zeros of this tion
A. Zeros at x = 2 and x = 6
B. Zeros at
C. The zeros are the hot dog prices that give $0.00 profit (no profit).
D. The zeros are the hot dog prices at which they sell 0 hot dogs.
Answers
the serose of the x value is where y=0,
that is where profit=0
the zeroes of the y value is where x=0
that's when the price is 0 dollars
ok
x zeroes
solve for when y=0
[tex]0=-3(x-2)^2+6[/tex]
[tex]-6=-3(x-2)^2[/tex]
[tex]2=(x-2)^2[/tex]
[tex]+/-\sqrt{2}=x-2[/tex]
[tex]2+/-\sqrt{2}=x[/tex]
x zeroes at [tex]x=2+\sqrt{2}[/tex] and [tex]x=2-\sqrt{2}[/tex]
y zeroes
x=0
[tex]y=-3(0-2)^2+6[/tex]
[tex]y=-3(-2)^2+6[/tex]
[tex]y=-3(4)+6[/tex]
[tex]y=-12+6[/tex]
[tex]y=-6[/tex]
the y zeroes are where they sell 0 hot dogs for 0 dollars, it is $-6 profit
the x zereoes are where you make 0 profit, that occurs when you sell [tex]2+\sqrt{2}[/tex] and [tex]2-\sqrt{2}[/tex] hot dogs
not sure which answer you want because it doesn't specify which zeroes we want
A is wrong tho
The zeros of the function y = -3(x - 2)² + 6 are x = 2 + √2 and x = 2 - √2, which represent the hot dog prices at which the hot dog stand makes $0.00 profit.
Explanation:The zeros of a function are the values of x that make the y-coordinate equal to zero. In this case, the function y = -3(x - 2)² + 6 represents the daily profit, and we need to find the x-values that result in a profit of $0.00. Setting the profit, y, to zero and solving for x, we get:
0 = -3(x - 2)² + 6
Adding 3(x - 2)² to both sides and simplifying the equation gives:
3(x - 2)² = 6
Dividing both sides by 3, we have:
(x - 2)² = 2
Take the square root of both sides, remembering to consider both the positive and negative square roots:
x - 2 = ±√2
Adding 2 to both sides gives us the final solutions:
x = 2 ± √2
So, the zeros of this function are x = 2 + √2 and x = 2 - √2. These are the hot dog prices at which the hot dog stand makes $0.00 profit.
Learn more about Zeros of a function here:https://brainly.com/question/31654173
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what is the answer of 9X23+3X39-28=n
Answers
n= 296
Answer: n=296
Step-by-step explanation: 9 x 23 + 3 x 39 - 28 + n = 296
Hope this helps! <3