Answer:
[tex]\frac{dy}{dx}[/tex] = 2x + 3
Step-by-step explanation:
Differentiate each term using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
y = x² + 3x
[tex]\frac{dy}{dx}[/tex] = 2[tex]x^{(2-1)}[/tex] + 3[tex]x^{(1-1)}[/tex]
= 2x + 3[tex]x^{0}[/tex]
= 2x + 3
I need this question
If 2^x-4 = 4^x-6 , then value of x is?
Answer: [tex]x=1[/tex]
Step-by-step explanation:
[tex]2^x-4=4^x-6[/tex] is the equation that you've given us.
Now if we plot these two equations on the graph we notice there's an intersection at (1,-2). Therefore meaning that [tex]x=1[/tex].
We can prove that by doing the following calculations to prove that both sides are equal to each other.
The left side of the equal sign:
Step 1: Write the equation down:
[tex]2^x-4[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]2^1-4[/tex]
Step 3: Find the square of [tex]2^1[/tex], which is itself, 2.
[tex]2-4[/tex]
Step 4: Subtract 2 from 4. Which is a negative number, thus being -2.
[tex]-2[/tex]
The right side of the equal sign:
Step 1: Write the equation down:
[tex]4^x-6[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]4^1-6[/tex]
Step 3: Find the square of [tex]4^1[/tex], which is itself, 4.
[tex]4-6[/tex]
Step 4: Subtract 4 from 6. Which is a negative number, thus being -2.
[tex]-2[/tex]
We know that [tex]x=1[/tex] because when substituting x with 1, we get -2 on both sides. Therefore making this statement true and valid.
[tex]-2=-2[/tex]
These circles are:
A. tangent
B. congruent
C. congruent
D. none of these
Answer:
A. tangent
Step-by-step explanation:
Hi there!
Tangent circles are circles that intersect (or "touch") at exactly one point. These circles appear to have this characteristic.
I hope this helps!
Yet another calculus question :)
Given [tex]y = x^3 - 2x[/tex] for [tex]x \geq 0[/tex], find the equation of the tangent line to y where the absolute value of the slope is minimized.
I have tried taking both the first and second derivatives and setting them equal to 0 and using that as the answer, but they're incorrect. Could somebody please explain how to complete the question correctly? Thank you so much!
Answer: y = (-4/3)*sqrt(2/3)
This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]
============================================================
Explanation:
The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.
Your teacher has given you
y = x^3 - 2x
which differentiates into
dy/dx = 3x^2 - 2
after using the power rule
The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.
dy/dx = 0
3x^2 - 2 = 0
3x^2 = 2
x^2 = 2/3
x = sqrt(2/3)
Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]
-------------------------
Now plug this x value back into the original equation to find its corresponding y coordinate.
y = x^3 - 2x
y = x(x^2 - 2)
y = sqrt(2/3)*( 2/3 - 2 )
y = sqrt(2/3)*( -4/3 )
y = (-4/3)*sqrt(2/3)
Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.
-------------------------
Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)
All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).
In the following diagram, BAC = 46 degrees, and AD is the bisector of BAC. Find BDA
Answer:
67 degrees
Step-by-step explanation:
We have a right triangle with the following known values:
B = 90
A = 23 (46/2=23 since AD is the angle bisector)
D = ?
180 = 90 + 23 + D and we solve
67 = D
what is the equation of the axis of symmetry do the quadratic function f(x) = -(x+4) (x-1)
9514 1404 393
Answer:
x = -3/2
Step-by-step explanation:
The zeros of the function are the values of x that make the factors zero:
x = -4, x = 1
The axis of symmetry is the vertical line halfway between these zeros.
x = (-4 +1)/2 = -3/2
The equation of the axis of symmetry is x = -3/2.
Steve works two different jobs for a total of 60 hours every Monday through Friday schedule is the same each day and he works three hours a day at his first job how many hours a day does he work at his second job
Answer:
Step-by-step explanation:
Steve works:
- 60 hour per week = 12 hours per day (60/5)
- first job: 3 hours per day = 15 hours per week
- x = second job hours per day
equitation:
1st option to calculate:
12 (total hours per day) = 3 (hours per day on first job) + X
9 = X
2nd option to calculate:
60(total hours per week) = 15 (3 hours per day x 5) + x
45 = x
you need to divide 45 / 5 to get the daily hours which is 9
find the missing length indicated
Answer:
192
Step-by-step explanation:
According to Euclidian theorem
x^2 = 144*(400-144)
x^2 = 144*256
x^2 = 36864 find the root of both
x = 192
Density of wood is a very important trait for furniture making. There are two main important mechanical properties: strength and stiffness. Research has shown that a increase density equals an increase strength, hardness and stiffness of sawn timber.
A carpenter has two pieces of wood. He wants to find the density of each piece.
The first piece came from a birch tree. The piece of birch wood measures 2 meters by 4 meters by 3 meters and weighs (mass) 16 kilograms.
The second piece came from a cypress tree. The piece of cypress wood measures 3 meters by 5 meters by 2 meters and weighs (mass) 15.3 kilograms.
Which piece of wood has a greater density? You must show your work in order to receive credit.
Step-by-step explanation:
The Birch tree has a greater density.
Work out an estimate for the value of
41.2 x 19.8
——————-
0.49
Answer:
820
Step-by-step explanation:
41.2 * 19.8 = 41 *20 = 820
41.2
In this tenth value is 2 which is less than 5. So ignore it and write the whole number alone. 41
19.8
In this tenth value is 8 awhich greater than 5. So add 1 to whole part and write.
19+1 = 20
Provide a rule to describe the relationship between the number in the sequence
1,4,9,16
Answer:
add 3, add 5, add 3
Step-by-step explanation:
1, 4, 9, 12
add 3, add 5, add 3
Answer:
x^2
Step-by-step explanation:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
And so on.
So, the rule is x^2.
factor: 3x^(2)-16x+16
Answer:
[tex]3 {x}^{2} - 16x + 16 \\ 3 {x}^{2} - 12x - 4x + 16 \\ 3x(x - 4) - 4(x - 4) \\ (3x - 4)(x - 4)[/tex]
Step-by-step explanation:
I hope it helped U
stay safe stay happy
31. Which choice describes the value of m when -5(m + 1) = 23?
А
B.
m 2-3
ms-
6 m2
D.ms-
Answer:
The correct choice is Option A. m ≥ -28/5
Step-by-step explanation:
Find the 8th term of the geometric sequence 7,−21,63,
Answer:
8th term is -15309
Step-by-step explanation:
[tex]{ \boxed{ \bf{u_{n} = a( {r}^{n - 1} ) }}} \\ { \tt{u_{8} = 7( {( - 3)}^{8 - 1}) }} \\ { \tt{u_{8} = 7( - 2187)}} \\ { \tt{u _{8} = - 15309}}[/tex]
r is the common difference, r = -21/7 = -3
Answer:
a₈ = - 15309
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{7}[/tex] = - 3 , then
a₈ = 7 × [tex](-3)^{7}[/tex] = 7 × - 2187 = - 15309
1 upon sec A -tan a minus one upon cos A is equal to 1 upon Cos A minus one upon sec a + tan a prove it
Step-by-step explanation:
1/(seca-tana) - 1/cosa=1/cosa -1/(seca+tana)
There are many ways to solve this, let's take a look at a simple one
1/(seca-tana) + 1/(seca+tana) =1/cosa + 1/cosa
((seca-tana)+(seca+tana))/(sec^2a-tan^2a)=2/cosa
(seca-tana+seca+tana)/1=2*1/cosa
2seca=2seca
Please help me this on the picture
Answer:
Step-by-step explanation:
please help geometry surface area
Answer: 159
Step-by-step explanation:
We have to find the surface area of two triangles and 3 rectangles
To find the surface areas of the triangles, we use the formula: base x height / 2
6 x 5.5 / 2 = 16.5
Multiply that by 2 since there are 2 of them
16.5 x 2 = 33
To find the surface area of the rectangles, we multiply the length and width
7 x 6 = 42
Multiply that by 3 since there are 3 of them
42 x 3 = 126
Add up all the surface areas
126 + 33 = 159
I’m very confused abt this question: Look at the pic for clarification.
Answer:
8A
Step-by-step explanation:
We are multiplying the matrix by a scalar
Each term in the first matrix is multiplied by 2
[tex]\left[\begin{array}{ccc}2l&2m&2n\\2p&2q&2r\\2s&2t&2u\end{array}\right][/tex]
Factor out 2
[tex]2\left[\begin{array}{ccc}l&m&n\\p&q&r\\s&t&u\end{array}\right][/tex]
We know that the determinant of a matrix when multiplied by a scalar is found by
det ( a A) =a^n * det (A)
The scalar in this case is 2 and n is the number of rows ( or columns) since the matrix must be square
det (2A) = 2^3 det(A) = 8A
Answer:
(A)
Step-by-step explanation:
Factor the 2 out and do 2/1=x/A
X=2A
in triangle ABC the measure of angle A is 90. the length of AB is 1 unit the length of AC is 8 unit, find the legth of BC
Answer:
8.06
Step-by-step explanation:
by using pythagoras
BC^2=1^2+8^2
BC^2=1+64
BC^2=65
BC=√65
BC=8.06
125 + (a-b)³ help me
Answer:
(5 + a - b)(a² + b² - 2ab - 5a + 5b + 25)
Step-by-step explanation:
125 + (a - b)³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
Then
125 + (a- b)³
= 5³ + (a - b)³
with a = 5 and b = (a - b)
= (5 a a - b)(5² - 5(a - b) + (a - b)² )
= (5 + a - b)(25 - 5a + 5b + a² - 2ab + b²)
= (5 + a - b)(a² + b² - 2ab - 5a + 5b + 25)
Hey can someone help me figure out what 3/4(x-8)=12
Answer:
x=24
Step-by-step explanation:
3/4(x-8)=12
Multiply each side by 4/3
4/3*3/4(x-8)=12*4/3
x-8 = 16
Add 8 to each side
x-8+8 = 16+8
x=24
Answer:
x = 24
Step-by-step explanation:
Essentially, you need to break this apart.
You need to isolate the x to figure it out with division or something.
To isolate, you need to get rid of the numbers around it.
To get rid of the 3/4, you can convert it to a decimal to make it easier, and then divide both sides by 0.75 to get rid of it on the x's side.
You now have
x-8 = 12/0.75
You can quickly punch the right side into a calculator to make it easier.
x - 8 = 16
You then add 8 to both sides to finish off the x, to get
x = 24
pls help !! answer both 1a and 1b pls
Answer:
KM = 50 mm , ∠ K = 104°
Step-by-step explanation:
Note that KM = KL = 50mm ( congruent legs )
This indicates the triangle is isosceles with base angles congruent, both 38°
∠ K = 180° - (38 + 38)° = 180° - 76° = 104°
Answer:
So the answer is 398°
Step-by-step explanation:
hope it helps
Factor the following expression completely. 16x^5-x^3
Answer:
x³ (4x + 1)(4x - 1)
Step-by-step explanation:
Answer:
x^3 (4x-1)(4x+1)
Step-by-step explanation:
16x^5-x^3
Factor out x^3
16* x^2*x^3 - x^3
x^3(16x^2 -1)
The term inside the parentheses is the difference of squares
a^2 - b^2 = (a-b)(a+b)
x^3 ( (4x)^2 -1^2)
x^3 (4x-1)(4x+1)
Setting y = 0 allows you to determine the what
of a graph
[tex]y=0[/tex] allows you to determine the x-intercept of a graph.
x-intercept and y-intercept:The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept. Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.When y is 0, the x-intercept is reached. The graph's intersection with the y-axis, or (0, b), is known as the y-intercept. When x is 0, the y-intercept is reached. When y is 0, the x-intercept is reached.Therefore, [tex]y=0[/tex] allows you to determine the x-intercept of a graph.
Know more about x-intercept and y-intercept here:
https://brainly.com/question/24363347
#SPJ2
Simplify [2(5 – 4) + 6(7 – 3)] ÷ 2
I'LL MARK BRAINLY PLEASE HELP ME I'M STRUGGLING
Answer:
13
Step-by-step explanation:
[2×1+6×4]÷2
[2+24]÷2
26÷2
13
Please help explanation if possible
Answer:
y=-3x+5
Step-by-step explanation:
concepts: y=mx+b is slope intercept equation formula
m=slope
b= y intercept
Therefore we need to find the slope and y intercept
first find slope
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
let y2 be 2
let y1 be -4
let x2 be 1
let x1 be 3
[tex]\frac{2-(--4)}{1-3}[/tex]
6/-2 = -3
m=-3
slope is -3
y= -3x+ b
we need find y intercept now
just plug in (1,2) into that equation
2=-3(1)+b
b=5
y=-3x+5
Which regular polygon can be used to form a tessellation?
I need help
Answer: Option 4 (Hexagon)
Step-by-step explanation:
A equilateral triangle, square and hexagon can be used to form a tessellation.
Please click thanks and mark brainliest if you like
10,4,7
The above set 4 numbers have a mean of 8
what could the mystery number
11 is the mystery number
Answer:
The mystery number is 11
Step-by-step explanation:
→ Set up an equation
( 10 + 4 + 7 + x ) ÷ 4 = 8
→ Multiply both sides by 4
21 + x = 32
→ Minus 21 from both sides
x = 11
solve this questions
Answer:
3 a) solution:-
Discount=Rs 1,200
S .P =RS 4,000
M P=?
we know that,
Discount= M.P - S.P
or, Rs 1,200= M.P - Rs 4,000
or, M.P = RS (4,000-1,200 )
M.P = RS 2,800
In no. 3 all we have to make like this .........
Hope it helps
Answer:
Step-by-step explanation:
2)a) M.P =₹ 5000
S.P = ₹4000
Discount amount = M.P - S.P
= 5000 - 4000
= ₹1000
Discount percent = [tex]\frac{discount \ amount}{M.P}*100[/tex]
[tex]= \frac{1000}{5000}*100\\[/tex]
= 20%
3)a) Discount = ₹ 1200
S.P = ₹ 4000
M.P = S.P + discount
= 4000 + 1200
= ₹ 5200
4)a ) Discount rate = 15%
S.P= ₹ 4000
[tex]M.P = \frac{100+Discount rate}{100}*S.P\\\\=\frac{115}{100}*4000[/tex]
= ₹ 4600
What number line shows Point A at -4, Point B at 2.5, Point C at -2 1/2, and Point D, which is the opposite of Point A.
Answer: Choice A
Explanation:
Since -3/5 > -0.8, this means -3/5 is to the right of -0.8
Larger stuff is to the right of smaller stuff. Another example would be 10 > 7, meaning we have 10 to the right of 7 since 10 is larger.
Any negative value is always to the left of 0, so -3/5 is to the left of 0.
That's why the answer is choice A.
