The area of Square 4 is a2+2ab+b2
The area of Square 5 is 2ab+c2
Setting them equal to one another (a2+2ab+b2=2ab+c2) and simplifying yields that a2+b2=c2 (note that 2ab is what they have in common), which is Pythagoras' theorem.
Consider the function defined by f(x) lnx/x^4 for x > 0 and its graph y = f(x).
The graph of f has a horizontal tangent at point P. Find the coordinates of P.
Answer:
[tex]\sqrt[4]{e};\frac1{4e}[/tex]
Step-by-step explanation:
The first derivative of [tex]f(x)[/tex] will give, for each x, the slope of the tangent at that specific x. Let's calculate the derivative, applying the quotient rule.
[tex]D(\frac AB) = \frac{A'B-AB'}{B^2}\\f'(x)= \frac1{x^8}[(\frac1x)x^4-(lnx)(4x^3)]=\frac1{x^8}[x^3(1-4lnx)]=\frac{1-4lnx}{x^5}[/tex]
Now, to find the point with an horizontal tangent (called "stationary points"), we set the first derivative equal to 0. Considering that we're working with [tex]x > 0[/tex] we deal only with the numerator.
[tex]1-4lnx = 0 \rightarrow lnx= \frac14\\x=e^\frac14 =\sqrt[4]{e}[/tex]
At this point we Replace the value we found in the equation to find it's y coordinate
[tex]f(\sqrt[4]e) = \frac{ln\sqrt[4]e}{\sqrt[4]e^4}= \frac{\frac14}{e} = \frac1{4e}[/tex]
PLS HELP WILL GIVE BRAINLIEST
Answer:
y = 1/2x - 1
Step-by-step explanation:
The x value is divided by 2 and then has 1 subtracted from it.
also for future posts, put the question in the title that way people know what you need and can click if they know the answer.
Write the following series in sigma notation.
7 + 16 + 25 +34 +43 +52 + 61
The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series
The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]
How to write the series in sigma notation?The series is given as:
7 + 16 + 25 +34 +43 +52 + 61
The above series is an arithmetic series, with the following parameters
First term, a = 7Common difference, d = 9Number of terms, n = 7Start by calculating the nth term using:
a(n) = a + (n - 1) * d
This gives
a(n) = 7 + (n - 1) * 9
Evaluate the product
a(n) = 7 - 9 + 9n
Evaluate the difference
a(n) = 9n - 2
So, the sigma notation is:
[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]
Read more about arithmetic series at:
https://brainly.com/question/6561461
Which of the following is true? there is a phase shift to the left. there is a phase shift to the right. the graph is reflected across the x-axis the graph is stretched horizontally. the graph is compressed horizontally.
Answer:
a. There is a phase shift to the left
Step-by-step explanation:
The correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: [tex]y=f(x+c)[/tex]output, but c units earlier)Right shift by c units: [tex]y=f(x-c)[/tex] (same output, but c units late)Vertical shift:
Up by d units: f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, the parent function y = cos(x) is transformed to make the function y = cos (x + pi/6)
Thus, there is left shift of the graph of the function y =cos(x).
The graphs of both functions (parent function in red color and transformed function in blue color) is given below.
Thus, the correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
Learn more about transforming functions here:
https://brainly.com/question/17006186
Can anyone solve this?
Answer:
54 cubic inches
Step-by-step explanation:
Just as the area of a triangle is half the area of a rectangle with the same dimensions, the volume of a triangular prism is half the volume of a rectangular prism with the same dimensions:
V = 1/2(LWH)
V = (1/2)(9 in)(4 in)(3 in) = 54 in³
The volume of Phil's block of cheese is 54 in³.
Solve the equation for x
Answer:
5x-18=4x+7 ( vertical opposite angle)
5x-4x=7+18
x=25
you buy a sandwich for $6.965, a salad for $3.25, and a drink for $1.79. if sales tax is 7%, how much change do you receive from $20 bill, rounded to the nearest cent?
6.965 + 3.25 + 1.79 = 12.005, now, let's apply a 7% taxation on that
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 12.005}}{\left( \cfrac{7}{100} \right)12.005}\implies 0.84035~\hfill \underset{total~bill}{\stackrel{12.005~~ + ~~0.8435}{12.84535}} \\\\\\ 20~~ - ~~12.84535\implies 7.15465~~\approx ~~ \$7.15[/tex]
Please help me!!! I don't know!
txcfygvubhjnlkm
Answer:
See explanation
Step-by-step explanation:
look photo
Y+1.27=7.23 solve for y
Answer:
y=5.96
Step-by-step explanation:
You can do a reverse equation and do 7.23 - 1.27 = 5.96
PLS HELP I am giving 25 points here is the question
A shopkeeper sold 12 bags of potatoes for $2.99 each. He bought the potatoes for $1.90 for each bag what was his total profit
Find theFind tha amount of profit per bag by subtracting:
2.99 - 1.90 = 1.09
He made $1.09 profit per bag.
Now multiply the profit per bag by the number of bags:
1.09 x 12 = 13.08
Total profit = $13.08 amount of profit per bag by subtracting:
2.99 - 1.90 = 1.09
He made $1.09 profit per bag.
Now multiply the profit per bag by the number of bags:
1.09 x 12 = 13.08
Total profit = $13.08
What is 8 * 8?
8*8 =
A. 64
B. 24
C. 91
D. 8
Answer: A. 64
Step-by-step explanation:
8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 64
(PLS help I’ll give brainliest to whoever can answer right nobody has been able to. )
A company makes piñatas for special events such as birthday parties. One of their piñatas is in the form of a cone-shaped hat. How much space do they have inside the piñata for candy if the piñata is 2 feet tall and 1.5 feet wide? Round to the nearest hundredth.
Note: Images may not be drawn to scale
Square A'BC V' is a ditation of square ABCD.
What is the scale factor?
Enter your answer in the box
C
Be
7
8
9
11
4
5
6
6
1
2
3
V
:
$
0
*
Answer:
1/3
Step-by-step explanation:
The scale factor is the ratio of image lengths to original lengths. For this pair of figures, the scale factor is ...
A'B'/AB = 2/6 = 1/3
The scale factor is 1/3.
12 , − 7 , − 20 , − 9 , − 5 , 6 , 2 , − 12 , 15 , 16 State the median.
To find the median, we must order the numbers from least to greatest and find the middle number which will be the median.
List in order: -20, -12, -9, -7, -5, 2, 12, 15, 16
The number in the middle position is -5 <-- median
Hope that helps!
please help i dont take links or files
What do all of the numbers have in common
1.) 13%
2.) 0.125
3.) 1
----
5
4.) 10%
PLEASE HELP I DONT TAKE LINKS OR FILES AND PLEASE SHOW YOUR WORK
Answer: They are all less than 1
13% = 0.13 is less than 1
So is 0.125
And so is [tex]\frac{1}{5} = 0.2[/tex]
Same goes for 10% = 0.10
I don't know how to solve this
Answer:
7
Step-by-step explanation:
List out possible numbers that would add to the answer choices and see which has most possibilities
7
3 + 4
5 + 2
1 + 6
10
5 + 5
4 + 6
11
5 + 6
12
6 + 6
how to multiply and divide decimals with whole numbers
Name the circle
Will give a lot of points!!! ASAP
Circle KJI center L, radius LK/diamter KI?
Which of the following notes is G?
CAN SOMEBODY SOLVE THE PROBLEM IVE BEEN STUCK ON IT I WILL GIVE BRAINIEST
The diameter of a cylinder is 3 yd. The height is 12 yd.Find the volume of the cylinder.
Answer:
84.78cube.yd
Step-by-step explanation:
Volume of cylinder= πr^2h
3.14 × 1.5 × 1.5 × 1284.78 cube.ydCan an isosceles triangle be a right triangle? Why or why not?
Answer: Yes
Step-by-step explanation:
It can have angles of 90 degrees, 45 degrees, and 45 degrees.
Yes, a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.
What is the isosceles triangle?The Isosceles Right Triangle has one of the angles exactly 90 degrees and two sides, which are equal to each other.
Since the two sides are equal it makes the corresponding angle congruent.
An Isosceles triangle is a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.
Hence, Yes, a triangle in which at least two sides are equal. Since the two legs of the triangle are equal, which makes the corresponding angles are equal to each other.
Read more on isosceles triangle;
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how do i find slope in standard form?
Answer:
The standard form of a linear equation is Ax + By = C. When we want to find the slope of the line represented by this equation, we have two options. We can put the equation in slope-intercept form and identify the slope that way, or we can use the formula m = -A/B.
Answer:
m = -A/B
The standard form of a linear equation is Ax + By = C.
[tex]hope \: it \: will \: help \: [/tex]
In the following figure, the square ABCD is inscribed in the circle centered at point P. What is the area of the circle?
Answer:
[tex]A_{Circle} \approx 39.24\: units^2[/tex]
Step-by-step explanation:
Square ABCD is inscribed in a circle with center P such that BC = 5 units.
BD will be diagonal of the square as well as diameter of the circle.
[tex]BD = BC\times\sqrt 2[/tex]
[tex]\implies BD = 5\sqrt 2[/tex]
-> Diameter of the circle [tex](d) = 5\sqrt 2[/tex]
-> Radius of the circle [tex](r) = 2.5\sqrt 2=3.535\: units[/tex]
[tex]A_{Circle} =\pi(r)^2[/tex]
[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]
[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]
[tex]\implies A_{Circle} =39.2381465[/tex]
[tex]\implies A_{Circle} \approx 39.24\: units^2[/tex]
Constants are numbers without letters attached.
What is the constant in the equation x/2 - 3?
answers:
2
-3
Answer:
constant = - 3
Step-by-step explanation:
[tex]\frac{x}{2}[/tex] - 3 = [tex]\frac{1}{2}[/tex] x - 3
the number without letters attached is the constant - 3
Answer:
-3
Step-by-step explanation:
The answer is -3 because 2 has a letter attached to it which is x/2 -3 is without a letter.
hope dis helps):
Solve for x: √(32^0 + 2/3)=(0.6)^2-3x
Step-by-step explanation:
Given: √{32⁰ + (2/3)} = (0.6)²⁻³ˣ
Asked: Find the value of x = ?
Solution: Given that √{32⁰ + (2/3)} = (0.6)²⁻³ˣ
⇛√{1 + (2/3)} = (0.6)²⁻³ˣ
⇛√{(1/1) + (2/3) = (0.6)²⁻³ˣ
⇛√{(1*3 + 2*1)/3} = (0.6)²⁻³ˣ
⇛√{(3 + 2)/3} = (0.6)²⁻³ˣ
⇛√(5/3) = (0.6)²⁻³ˣ
Squaring on both sides then
⇛{√(5/3)}² = {(0.6)²⁻³ˣ}²
⇛√(5²/3²) = {0.6}(²⁻³ˣ)²
⇛√{(5*5)/(3*3)} = {0.6}(²⁻³ˣ)²
⇛5/3 = {0.6}(²⁻³ˣ)²
[[tex]\mathsf{\because}[/tex] (aᵐ)ⁿ = aᵐⁿ]
⇛5/3 = (0.6)²*²⁻³ˣ*²
⇛5/3 = (0.6)⁴⁻⁶ˣ
⇛5/3 = (6/10)⁴⁻⁶ˣ
⇛5/3 = {(6÷2)/(10÷2)})⁴⁻⁶ˣ
⇛5/3 = (3/5)⁴⁻⁶ˣ
⇛(3/5))⁻¹ = (3/5)⁴⁻⁶ˣ
[[tex]\mathsf{\because}[/tex] a⁻ⁿ = 1/aⁿ]
Base are the same, so the exponents must be equal.
[tex]\mathsf{\therefore}[/tex] -1 = 4 - 6x
Shift the number 4 from RHS to LHS, changing it's sign.
⇛-1 - 4 = -6x
⇛-5 = -6x
⇛x = {(-5)/(-6)}
[tex]\mathsf{\therefore}[/tex] x = 5/6
Answer: Hence, the value of x for the given problem is 5/6.
also read similar questions: (1/3)^-2 + (1/4)^-2 = (125)^x Find the value of x? https://brainly.com/question/25746379?referrer
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Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (0, ∞).
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (0, ∞).
The function is increasing on the interval (–∞, 0).
Using translation concepts, it is found that the correct statement about h(x) is:
The function is decreasing on the interval (0, ∞).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is:
[tex]f(x) = \sqrt{x}[/tex]
Which is increasing on (0, ∞).
After the translation, the function is:
[tex]h(x) = -2\sqrt{x}[/tex]
It was multiplied by a negative number, which means that it was reflected over the x-axis, and it will be decreasing on the interval (0, ∞).
More can be learned about translation concepts at https://brainly.com/question/4521517
What is the slop of the line?
5(y+2)=4(x-3)
A. 3/2
B. 2/3
C. 4/5
D. 5/4
Answer:
c. 4/5
Step-by-step explanation:
Write x=2 in Slope intercept form
Answer:
y= 2/1 + 0
Step-by-step explanation:
If there's not a y-int. it'll be 0.
James has 13. 7 ounces of trail mix. He shares the trail mix equally with his sister. How much trail mix does each person get?
6. 35 oz
6. 85 oz
7. 35 oz
7. 7 oz
Step-by-step explanation:
13.7 divide by 2 because he and his sister are sharing the trail mix.13.7 = 2x6=12 so 13-12=1 and bring down the 7 so 2x8=16 17-16=11 so 2x5=10 11-10=1. But don't put 6.851 put 6.85 ounces.I need the assistance of smarter beings than I..... I'm so lost.....
Answer:
[tex]\sf \bold{ 1 * (-3)^{n-1}}[/tex]
Explanation:
first term, a₁ = 1
difference between the terms: -3
used geometric formula : [tex]\bold{\sf a_1 * (r)^{n-1}}[/tex]where "a₁ is first term" and "r refers to common difference"
formula for this nth term: [tex]\sf \bold{ 1 * (-3)^{n-1}}[/tex]