Use the chain rule:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\cdot\dfrac{\mathrm dt}{\mathrm dx}[/tex]
So we have
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}[/tex]
[tex]x=t^2+4\implies\dfrac{\mathrm dx}{\mathrm dt}=2t[/tex]
[tex]y=t^3+3t\implies\dfrac{\mathrm dy}{\mathrm dt}=3t^2+3[/tex]
[tex]\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3t^2+3}{2t}[/tex]
Now write [tex]f(t)=\dfrac{\mathrm dy}{\mathrm dx}[/tex]. Then by the chain rule,
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{\mathrm dy}{\mathrm dx}\right]=\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dt}\cdot\dfrac{\mathrm dt}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}[/tex]
so that
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac{\mathrm d}{\mathrm dt}\left[\frac{3t^2+3}{2t}\right]}{2t}=\dfrac{3(t^2-1)}{4t^3}[/tex]
The curve is concave upward when the second derivative is positive:
[tex]\dfrac{3(t^2-1)}{4t^3}>0\implies t^2>1\implies\sqrt{t^2}>\sqrt1\implies|t|>1[/tex]
or equivalently, when [tex]t<-1[/tex] or [tex]t>1[/tex].
The dy/dx is equal to 1 + 3/2t, and the d2y/dx2 is 3/2t. The curve is concave upward for t values in the (0, Infinity) interval.
Explanation:To answer your question, we first need to take the derivatives of x and y with respect to t. The derivatives of x = t^2 + 4 and y = t^2 + 3t by t yield dx/dt = 2t and dy/dt = 2t + 3. Now, dy/dx = (dy/dt) / (dx/dt) = (2t + 3) / 2t = 1 + 3/2t.
Next the second derivative d2y/dx2 (concavity), is obtained as the derivative of dy/dx = 1 + 3/2t with respect to t, which is 3/2t. Now, the curve will be concave upward whenever d2y/dx2 > 0. Solving 3/2t > 0 gives the interval for t as (0, Infinity), which indicates the values of t for which the curve is concave upward.
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The right rectangular prism is packed with unit cubes of the appropriate unit fraction edge lengths. Find the volume of the right rectangular prism in centimeters. (Figure not to scale)
Answer:
The volume is equal to [tex]112\frac{1}{2}\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=LWH[/tex]
we have
[tex]L=4\frac{1}{2}\ cm=\frac{4*2+1}{2}=\frac{9}{2}\ cm[/tex]
[tex]W=5\ cm[/tex]
[tex]H=5\ cm[/tex]
substitute the values
[tex]V=(\frac{9}{2})(5)(5)[/tex]
[tex]V=112.5\ cm^{3}[/tex]
Convert to mixed number
[tex]112.5\ cm^{3}=112\frac{1}{2}\ cm^{3}[/tex]
Answer:
D
Step-by-step explanation:
Todd's cube has an edge that measures5 inches. Kara's cube has an edge of3 inches. If Kara's cube was stackedon top of Todd's cube, what wouldbe the total volume of the combinedsolid? ?
Answer:
152 in³
Step-by-step explanation:
Each cube's volume is the cube of its edge length, so the total volume is ...
(5 in)³ + (3 in)³ = 125 in³ +27 in³ = 152 in³
. A man is 25 years old. His mother is exactly three times his age. How old will the man's mother be when he is 35 years old?
Answer:
Step-by-step explanation:
105 years old. Since if he 35 the mother is 105>>------->(35 x 3= 105)
85 years old. 25•3=75 the difference between 75 and 25 is 50, which means she is 50 years older than him. 35+50=85.
A square patio was enlarged by adding 9 feet to the length and width of the original square patio. If the area of the enlarged patio is 441 ft.2, what was the side length of the original patio?
Answer:
The side length of the original patio was [tex]12\ ft[/tex]
Step-by-step explanation:
Let
x----> the side length of the original square patio
we know that
[tex]441=(x+9)^{2}\\ \\x^{2} +18x+81=441\\ \\ x^{2} +18x- 360=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=12\ ft[/tex]
see the attached figure
Answer:
for study island it is 11 feet
Step-by-step explanation:
You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads. Write an equation for the number of minutes you read, y, when your brother reads x number of minutes. How many minutes will you read if your brother reads for 15minutes?
the equation would be y = 30 + x and if your brother will read for 15 minutes then you'll read for 45 minutes i believe.
The equation for the number of minutes you read, y, when your brother reads x number of minutes is y = x + 30. Therefore, if your brother reads for 15 minutes, you will read for 45 minutes.
To write an equation for the number of minutes you read, y, when your brother reads x number of minutes and you decide to read 30 minutes longer than him, you can represent this relationship as y = x + 30. This equation signifies that your reading time (y) is equal to your brother's reading time (x) plus an additional 30 minutes.
If your brother reads for 15 minutes (x=15), you can determine how many minutes you will read by substituting 15 into the equation for x, obtaining y = 15 + 30 = 45 minutes. Therefore, if your brother reads for 15 minutes, you will read for 45 minutes to stay ahead.
If Jamaal will be paid $5.00 an hour for delivering pizzas, and he works for 4 hours, how much will he be paid?
Answer:
$20
Step-by-step explanation:
4×5=$20
this is random do not look
Maurice bought 3 sodas and 4 candy bars for $10.17. Larry bought 2 sodas and 5 candy bars for $10.28. How much does a candy bar cost?
Answer:
The cost of a candy bar is [tex]\$1.5[/tex]
Step-by-step explanation:
Let
x----> the cost of a soda
y----> the cost of a candy bar
we know that
[tex]3x+4y=10.17[/tex]-----> equation A
[tex]2x+5y=10.28[/tex]-----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point [tex](1.39,1.5)[/tex]
see the attached figure
therefore
The cost of a soda is [tex]\$1.39[/tex]
The cost of a candy bar is [tex]\$1.5[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
A spinner is divided into 4 sections. The spinner is spun 100 times.
The probability distribution shows the results.
What is P(2 ≤ x ≤ 4) ?
Enter your answer, as a decimal, in the box.
Answer: 0.80
Step-by-step explanation:
P (2 ≤ x ≤ 4) is: P(X = 2) + P(X = 3) + P(X = 4)
= 0.36 + 0.12 + 0.32
= 0.48 + 0.32
= 0.80
It can also be calculated as: 1 - P(X = 1)
= 1 - 0.20
= 0.80
help please will give brainliest thank you
Independent, means the first event won't affect the second event.
The independent events would be :
A, B, E, F
You drink a beverage with 100 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%.
a. after 5 hours, how many caffeine left in your system.
b. How long until you have 50mg of caffeine?
Answer:
a. The amount of caffeine left is 52.77 mg
b. It will take about 5.42 hours
Step-by-step explanation:
* Lets solve it as an exponential decay
- Exponential decay: If a quantity decrease by a fixed percent at
regular intervals, the pattern can be depicted by this functions
y = a(1 - r)^x
# a = initial value (the amount before measuring growth or decay)
# r = growth or decay rate (most often represented as a percentage
and expressed as a decimal)
# x = number of time intervals that have passed
* Now lets solve the problem
∵ The initial amount of caffeine is 100 mg
∴ a = 100 mg
∵ The caffeine decreases by about 12% each hour
∴ r = 12/100 = 0.12
* Lets solve a.
a. ∵ x = 5 ⇒ the time interval
∵ The amount of caffeine left = a(1 - r)^x
∴ The amount of caffeine left = 100(1 - 0.12)^5
∴ The amount of caffeine left = 100(0.88)^5= 52.77 mg
* To find the time x use the linear logarithmic function
b. ∵ The amount of caffeine is 50 mg
∴ 50 = 100(1 - 0.12)^x ⇒ divide both sides by 100
∴ 50/100 = (0.88)^x
∴ 0.5 = (0.88)^x ⇒ take ln for each side
∴ ln(0.5) = ln(0.88)^x
∵ ln(a)^n = n ln(a)
∴ ln(0.5) = x ln(0.88) ⇒ divide both sides by ln(0.88)
∴ x = ln(0.5)/ln(0.88) = 5.4 years
* It will take about 5.42 hours
After 5 hours, approximately 54.47 mg of caffeine would remain in your system. It would take approximately 3.72 hours for the caffeine level to reach 50 mg.
Explanation:To find the remaining amount of caffeine after 5 hours, we need to calculate the decreasing amount of caffeine each hour. The decrease in caffeine can be calculated by multiplying the previous amount of caffeine by 0.88 (1 - 0.12). So, after 5 hours, the remaining caffeine can be found using the formula:
Initial amount of caffeine: 100 mgRemaining caffeine after 5 hours: 100 mg * (0.88)5 = 54.47 mgTo find the time it takes to have 50 mg of caffeine remaining, we can set up an equation and solve for time:
Initial amount of caffeine: 100 mgRemaining caffeine: 50 mgDecay rate: 0.88 (1 - 0.12)Equation: 100 mg * (0.88)t = 50 mgSolving for t, we get:t = log0.88(50/100) ≈ 3.72 hoursTherefore, after 5 hours, approximately 54.47 mg of caffeine would remain in your system. It would take approximately 3.72 hours for the caffeine level to reach 50 mg.
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select all the statements that apply to this figure
B, C, and D is the answer
This question most likely pertains to a mathematical figure or diagram. The student is asked to identify true statements applying to the figure, which might illustrate a problem-solving process or the form of a disjunctive syllogism. Without the actual figure, a more detailed analysis isn't possible.
Without having the actual figure to analyze it's difficult to state definitively, but from the context provided, it sounds like this could be a diagram or figure related to problem-solving in mathematics. Figures are often used in mathematics to illustrate complex concepts and provide visual representation to support understanding. It seems like the figure might be used to demonstrate the process of solving mathematical problems or possibly, the process of argumentation using a disjunctive syllogism. Based on this information, the student may have to identify true statements about the figure in question. Potential statements could relate to the type of problem the figure represents, the process it illustrates, or specific features or attributes depicted in the figure itself.
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Help! Anyone can you explain?
A goblet contains 3 red balls, 2 green balls, and 6 blue balls.
If we choose a ball, then another ball without putting the first one back in the goblet, what is the probability that the first ball will be red and the second will be blue?
Answer:
[tex]\texttt{Probability that the first ball will be red and the second will be blue = }\frac{9}{55}[/tex]
Step-by-step explanation:
Total number of balls = 3 + 2 + 6 = 11
Probability is the ratio of number of favorable outcome to total number of outcomes.
[tex]\texttt{Probability that the first ball will be red = }\frac{\texttt{Total number of red balls}}{\texttt{Total number of balls}}\\\\\texttt{Probability that the first ball will be red = }\frac{3}{11}[/tex]
Now we have 10 balls in which 6 are blue.
[tex]\texttt{Probability that the second ball will be blue = }\frac{\texttt{Total number of blue balls}}{\texttt{Total number of balls}}\\\\\texttt{Probability that the first ball will be red = }\frac{6}{10}=\frac{3}{5}[/tex]
[tex]\texttt{Probability that the first ball will be red and the second will be blue = }\frac{3}{11}\times \frac{3}{5}\\\\\texttt{Probability that the first ball will be red and the second will be blue = }\frac{9}{55}[/tex]
Solve the system by using a matrix equation
Answer:
Option A is correct (17,11).
Step-by-step explanation:
6x - 9y = 3
3x - 4y =7
it can be represented in matrix form as[tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right][/tex]
A= [tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] [/tex]
X= [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex]
B= [tex] \left[\begin{array}{c}3\\7\end{array}\right][/tex]
i.e, AX=B
or X= A⁻¹ B
A⁻¹ = 1/|A| * Adj A
determinant of A = |A|= (6*-4) - (-9*3)
= (-24)-(-27)
= (-24) + 27 = 3
so, |A| = 3
Adj A= [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex]
A⁻¹ = [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex]/3
A⁻¹ = [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] [/tex]
X= A⁻¹ B
X= [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}-4+21\\-3+14\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}17\\11\end{array}\right][/tex]
x= 17, y= 11
solution set= (17,11).
Answer:
a. (17,11)
Step-by-step explanation:
The given system is ;
[tex]6x-9y=3[/tex]
[tex]3x-4y=7[/tex]
The augmented matrices is
[tex]\left[\begin{array}{ccc}6&-9&|3\\3&-4&|7\end{array}\right][/tex]
Divide Row 1 by 6
[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\3&-4&|7\end{array}\right][/tex]
Subtract 3 times Row 1 from Row 2
[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&\frac{1}{2}&|\frac{11}{2}\end{array}\right][/tex]
Divide Row 2 by [tex]\frac{1}{2}[/tex]
[tex]\left[\begin{array}{ccc}1&-\frac{3}{2}&|\frac{1}{2}\\0&1}&|11\end{array}\right][/tex]
Add [tex]\frac{3}{2}[/tex] times Row 2 to Row 1
[tex]\left[\begin{array}{ccc}1&0&|17\\0&1}&|11\end{array}\right][/tex]
Hence the solution is (17,11)
Which expressions are equivalent to 6^16 ? Check all that apply
For this case we will indicate expressions equivalent to 6 ^ {16}:
We can write the following:
[tex]6 ^ {16} = 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6\\6 ^ {16} = (6 ^ 8) ^ 2\\6 ^ {16} = 6 ^ {\frac {32} {2}}[/tex]
Answer:
The equivalent expressions are shown in the previous part.
Answer:
3,4,6Step-by-step explanation:
What is the surface area of the cone below?
For this case we have that by definition, the surface area of a cone is given by:
[tex]SA = \pi * r * S + \pi * r ^ 2[/tex]
Where:
SA: It is the surface area
A: It's the radio
S: It's slant height
Then, replacing the values of the figure in the formula we have:
[tex]SA = \pi * 6 * 15 + \pi * 6 ^ 2\\SA = 90 \pi + 36 \pi\\SA = 126 \pi \ units ^ 2[/tex]
ANswer:
Option A
What are the domain and range of the exponential function below?
[tex]F(x) = 5^x+6[/tex]
Answer:
B
Step-by-step explanation:
The domain is the set of x values for which the function is defined.
The range is the set of y values for which the function is defined.
Attached is the graph of the exponential function.
It is the basic graph of exponential function of y = 5^x which is shifted 6 units above (because of +6 at the end).
Looking at the graph, the domain is the set of all x values.
The range is anything above 6.
Correct answer is B.
Answer: b
Step-by-step explanation:
A P E X
Type the correct answer in the box. If necessary, use / for the fraction bar. A fair coin is tossed 5 times in a row. The exact probability of the coin landing heads exactly 2 times is .
Answer:
The probability is [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
Given is that a fair coin is tossed 5 times in a row.
This gives total number of outcomes as = [tex]2\times2\times2\times2\times2=32[/tex]
As its needed that heads comes exactly 2 times, so favorable outcomes are = 5C2
[tex]\frac{5!}{2!(5-2)!}[/tex]
Solving this we get 10
Therefore, the probability of getting heads exactly 2 times is =
[tex]\frac{10}{32}=\frac{5}{16}[/tex]
Answer:
5/16
Step-by-step explanation:
Use the equation below to identify the value fo each variable for the circle.
Standard form equation of a Circle
[tex](x-h)^2+(y-v)^2=r^2[/tex]
(h,v) = center
r = radius
h= ???
v = ???
r = ???
Then, write the standard form equation of the circle.
Answer:
The equation of the circle in standard form is: (x - 2)² + (y - 4)² = 9
Step-by-step explanation:
* Lets revise the standard form of the equation of the circle
- If the center of the circle is point (h , v) and the radius of the
circle is r, then the standard form of the equation of the circle
is (x - h)² + (y - v)² = r²
- (x , y) a general point on the circle
* Lets look to the picture
- The center of the circle is point (2 , 4)
- The highest point on the circle is (2 , 7) and the lowest point
on the circle is (2 , 1)
∴ The diameter of the circle = 7 - 1 = 6
∵ The radius = 1/2 the diameter
∴ The radius of the circle = 1/2 × 6 = 3
* Now we can write the equation of the circle
∵ h = 2 and v = 4
∵ r = 3
∴ (x - 2)² + (y - 4)² = 3²
∴ The equation of the circle in standard form is:
(x - 2)² + (y - 4)² = 9
The vertices of the feasible region represented by a system are (0, 100), (0, 80), (80, 60), (80, 0), and (120, 0). What are the minimum and maximum values of the objective function F = 8x + 5y? M
Answer:
[tex]\boxed{\text{Min = 400; Max = 960}}[/tex]
Step-by-step explanation:
F = 8x + 5y
At (0, 100): F = 8×0 + 5×100 = 0 + 500 = 500
At (0, 80): F = 8×0 + 5×80 = 0 + 400 = 400 — MINIMUM
At (80, 60): F = 8×80 + 5×60 = 640 + 300 = 940
At (80, 0): F = 8×80 + 5×0 = 640 + 0 = 640
At (120, 0): F = 8×120 + 5×0 = 960 + 0 = 960 — MAXIMUM
The minimum value is [tex]\boxed{ 400}[/tex]and the maximum value is [tex]\boxed{ \text{ 960}}[/tex].
Answer:
Minimum; 400
Maximum; 960
☆
EDGE2022; Good Luck :D
A bag contains 8 blue marbles, 6 green marbles, 12 yellow marbles and 10 orange marbles. A marble is drawn from at randm of the bag, what is the probibilty that the marble will not be blue?
8+6+12+10 = 36
6+12+10 = 28
28/36
7/9
Hope this helps ❤️
What function is the square root parent function, F(x) = [tex]\sqrt{x}[/tex] the inverse of?
A. [tex]F(x) = x^2[/tex], where [tex]x[/tex] ≥ [tex]0[/tex]
B. [tex]F(x) = |x|[/tex]
C. [tex]F(x)=\frac{1}{\sqrt{x} }[/tex]
D. [tex]F(x) = x^2[/tex]
You can think of an inverse function as a function that “unwraps” x from whatever operations are attached to it. In the case of F(x) = √x, we can ”unwrap” x by squaring it. This narrows our options down to either A or D. Keep in mind that since there are no real number solutions to the square root of a negative number, we need to limit our domain to non-negative values. In other words, x ≥ 0. With that restriction, our answer is A.
The answer is:
The inverse of the given function is:
A. [tex]f(x)^{-1}=x^{2}[/tex]
Where,
[tex]x\geq 0[/tex]
Why?Inversing a function involves inversing the function variables. If we want to inverse a function, we need to rewrite the variable "x" with "y" and rewrite the variable "y" with "x", and then, isolate the variable "y".
Also, the domain of the original function will be the range of its inverse function, and the range of the original function, will be the domain of the its inverse function.
We are given the function:
[tex]f(x)=\sqrt{x}[/tex]
[tex]f(x)=y=\sqrt{x}[/tex]
So, inversing we have:
[tex]y=\sqrt{x}[/tex]
[tex]x=\sqrt{y}[/tex]
[tex](x)^{2}=(\sqrt{y})^{2}\\\\x^{2}=(y^{\frac{1}{2}})^{2}\\\\x^{2}=y^{\frac{2}{2} }\\\\x^{2}=y[/tex]
So, we have that the given function is only "part" of its inverse function, since negative square roots does not exist, it means that the domain of the given function starts from the number 0 taking only positive numbers.
Hence, we have that the answer is:
A. [tex]F(x)=x^{2}[/tex]
Where,
[tex]x\geq 0[/tex]
Have a nice day!
pleaseeeeee help thanks!
I think it's C. Trout increased its predicted average population.
Answer:
b
Step-by-step explanation:
because it increases the most
If 33 laptops cost 30,000 in dollars, which proportion could be used to determine the cost of 11 laptops?
The cost of 11 laptops is 11c
Using the parameters given :
Number of laptops = 33Cost of 33 laptops = 30000The expresssion to determine the cost is :
Number of laptops = Cost of laptopsNow we have;
33 = 30000
11 = c
cross multiply
33c = 330000
c = 10000
The cost of 11 laptops : 11*c
Please show all of your work! I will mark the brainliest nd gve thanks!
1.Find the standard equation of a circle with its center at (2, 8) and a radius of 10.
2. Find the standard equation of a parabola with its vertex at (2, 2) and a focus at (2, 5).
3. Find the standard equation of a parabola with its vertex at (5, 2) and a directrix x =3.
Answer:
Step-by-step explanation:
1. Equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
If (h, k) is (2, 8) and r = 10:
(x - 2)² + (y - 8)² = 100
2. The vertex and focus have the same x-coordinate, so this is a vertical parabola. Equation of a vertical parabola is:
y = 1/(4p) (x - h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
If (h, k) is (2, 2) and p = 5-2 = 3:
y = 1/12 (x - 2)² + 2
3. The directrix is a vertical line, so this is a horizontal parabola. Equation of a horizontal parabola is:
x = 1/(4p) (y - k)² + h
The distance between the directrix and the vertex is the same as p.
If (h, k) is (5, 2) and p = 5-3 = 2:
x = 1/8 (y - 2)² + 5
Help me please!!!!!!!!
Answer:
82
Step-by-step explanation:
The sum resolves to ...
13 + 18 + 23 + 28 = 82
_____
for n=2, the term is 5·2 +3 = 10+3 = 13
The coefficient of n is 5, so you know the next term will be 5 more than this:
for n=3, the term is 5·3 +3 = 15+3 = 18
Additional terms are each 5 more than the one before. Since there are so few terms, you can add them up directly as quickly as you can use any other formula. For a longer series, you might find the average term (here, 41/2), then multiply by the number of terms (here, 4). The result is the sum of the series:
4·(41/2) = 82
HELP!! THIS TEST WORTH 36 POINTS!!! WILL MARK BRAINLEIST!!!!
Natalie applied for a new credit card.
Which information about Natalie could appear on her credit report?
Choose all answers that are correct.
A. her savings account number
B. amount of available credit on her credit cards
C. amount she owes on her mortgage
D. her gender
Answer:
A, B, C
Step-by-step explanation:
What is the value of X if 5^x^+^2=5^9?
X=-11
X=-7
X=7
X=11
Answer:
[tex]\large\boxed{x=7}[/tex]
Step-by-step explanation:
[tex]5^{x+2}=5^9\iff x+2=9\qquad\text{subtract 2 from both sides}\\\\x+2-2=9-2\\\\x=7[/tex]
The value of x if 5ˣ⁺²=5⁹ is 7. Therefore, the correct answer is option C.
The given equation is 5ˣ⁺²=5⁹.
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
We know that, when the bases are equal their exponents are equal.
x+2=9
x=9-2
x=7
Therefore, the correct answer is option C.
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Let a[0 . . . n] be an array of n + 1 natural numbers not exceeding n. let k < n be an integer such that the values of any two successive entries of a differ at most by k, i.e., |a[j] − a[j + 1]| ≤ k for all j ∈ {0, . . . , n − 1}. 1. prove that there exist an index j such that |a[j] − j| ≤ (k + 1)/2. 2. given the number k, find an o(log n) divide and conquer algorithm that finds such an index.
Answer:
i really have no clue but if i put this i get points so good luck on your test
What is the leading coefficient of this polynomial?
[tex]f(x)=3x^2-0.2x^5+7x^3[/tex]
The leading coefficient is the number in front of the variable with the highest degree(exponent)
The highest degree (exponent) is 5, so the leading coefficient = -0.2
ANSWER
The leading coefficient of the given polynomial is -0.2
EXPLANATION
The given polynomial function is
[tex]f(x)=3x^2-0.2x^5+7x^3[/tex]
We rewrite in standard form to obtain,
[tex]f(x)=-0.2x^5+7x^3+3x^2[/tex]
Note that writing in standard form means writing in descending powers of x.
The coefficient of the leading term is -0.2.
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Evaluate the expression:
v ⋅ w
Given the vectors:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
Multiply corresponding components, then add the products:
[tex]v\cdot w=3(-4)+(-8)(-2)+(-3)(-6)=22[/tex]
The resultant of the dot product of two vectors is:
[tex]v\cdot w=22[/tex]
Step-by-step explanation:We are asked to find the dot product of the two vectors v and w.
The vectors are given by:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
This means that in the vector form they could be written as follows:
[tex]r=8\hat i+8\hat j -6\hat k\\\\v=3\hat i-8\hat j -3\hat k\\\\w=-4\hat i-2\hat j -6\hat k[/tex]
Hence, the dot product of two vectors is the sum of the product of the entries corresponding to each direction component.
i.e. the x-component get multiplied to each other, y-component get multiplied to each other and so happens with z.
Hence, the dot product of v and w is calculated as:
[tex]v\cdot w=3\times (-4)-8\times (-2)-3\times (-6)\\\\i.e.\\\\v\cdot w=-12+16+18\\\\i.e.\\\\v\cdot w=22[/tex]