Answer:
[tex]{ \underline{ \bf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}}[/tex]
Step-by-step explanation:
[tex]{ \bf{m = 3x + 1}} \\ { \sf{ \frac{dm}{dx} = 3 }} \\ \\ { \bf{y = \frac{5}{1 + {m}^{2} } }} \\ \\ { \tt{ \frac{dy}{dm} = \frac{ - 10m}{ {(1 + {m}^{2} )}^{2} } }}[/tex]
Using chain rule:
[tex]{ \boxed{ \bf{ \frac{dy}{dx} = \frac{dy}{dm}. \frac{dm}{dx} }}}[/tex]
[tex]{ \sf{ \frac{dy}{dx} = - \frac{10m}{ {(1 + {m}^{2}) }^{2} } \times 3}} \\ \\ { \sf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}[/tex]
[tex]{ \underline{ \sf{ \blue{christ \:† \: alone }}}}[/tex]
Answer:
Step-by-step explanation:
Never saw a problem presented in this way in all my years of teaching calculus. But I'm thinking that we need to sub that given expression for m into the equation for y and get everything into y in terms of x in order to find the derivative. I see no other way that makes sense. Can't find the derivative of y in terms of x if there's an m in there. Making that substitution:
[tex]y=\frac{5}{1+(3x+1)^2}[/tex] which simplifies to
[tex]y=\frac{5}{1+9x^2+6x+1}[/tex] and a bit more to
[tex]y=\frac{5}{9x^2+6x+2}[/tex] and now we're ready to find the derivative. Using the quotient rule:
[tex]y'=\frac{(9x^2+6x+2)(0)-[5(18x+6)]}{(9x^2+6x+2)^2}[/tex] which simplifies to
[tex]y'=\frac{-90x-30}{(9x^2+6x+2)^2}[/tex] or, equally:
[tex]y'=-\frac{90x+30}{(9x^2+6x+2)^2}[/tex]
FOR EASY BRAINLIEST ANSWER THESE QUESTIONS:
1.
2.
3.
4.
5.
Step-by-step explanation:
all answers and steps are in picture
The sum of the first n terms of an arithmetic series is 2n(n+3).
Find the first term of the series using the formula n/2(2a+(n-1)d)
Answer:
Sum:
[tex]{ \bf{S _{n} = \frac{n}{2} (2a + (n - 1)d) }} \\ \\ { \sf{2n(n + 3) = \frac{n}{2}(2a + (n - 1)d) }} \\ \\ { \sf{4 {n} + 12=2a + (n - 1)d }} \\ { \sf{2a = 4n - nd + d + 12}} \\ { \sf{2a = n(4 - d) + 12 + d}} \\ { \sf{a = \frac{1}{2}(n(4 - d) + 12 + d) }}[/tex]
Any help would be nice
Answer:
11. angles on a straight line add up to 180
so 180 -133 equal to b.b=47
12.Vertical opposite angles are equal.
therefore b=50
Write a short account on farmer with the help of statement given, it says that the Indian farmer is born in dept lives in dept and die in dept.
plese help. need help.
Answer:
sir Malcolm darling
Step-by-step explanation:
he has said Indian farmer is born in dept lives in dept and die in dept.
The graph of the invertible function g is shown on the grid below.
What is the value of g^-1(-8)
=======================================================
Explanation:
The result of [tex]g^{-1}(-8)[/tex] is the same as trying to find x in [tex]g(x) = -8[/tex]
Draw a horizontal line through -8 on the y axis. This horizontal line intersects the curve at point P. From point P, move upward until you reach the x axis. You should get to 7 on the x axis. Therefore, the solution to [tex]g(x) = -8[/tex] is [tex]x = 7[/tex]. In other words, [tex]g(7) = -8[/tex]. This ultimately means [tex]g^{-1}(-8) = 7[/tex]
Refer to the diagram below.
Given the function g(x) = x2 + 5x + 1, determine the average rate of change of
the function over the interval -9 < x < -2.
Answer:
-6
Step-by-step explanation:
The average rate of change of a function, f(x), on interval [a,b] is (f(b)-f(a))/(b-a).
So the avereage rate of change of a function, f(x)=x^2+5x+1, on [-9,-2] is
(f(-2)-f(-9))/(-2--9)
(f(-2)-f(-9))/(7)
Stop!
To find f(-2), you replace x in f(x) = x^2 + 5x + 1, with (-2) giving you f(-2)=(-2)^2+5(-2)+1=4-10+1=-6+1=-5.
To find f(-9), you replace x in f(x) = x^2 + 5x + 1, with (-9) giving you f(-2)=(-9)^2+5(-9)+1=81-45+1=36+1=37.
Continue!
(f(-2)-f(-9))/(7)
=(-5-37)/7
=(-42)/7
=-42/7
=-6
Which numbers are a distance of 2 units from 8 on a number line?
++++++++++
-10-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9 10
Select each correct answer.
0-2
06
O 8
0 10
0-6
0-8
Step-by-step explanation:
0 10
0-6
this is the answer. I am sure
The value of numbers are 6 and 10 which are a distance of 2 units from 8 on a number line.
What is mean by Number line?Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
We have to given that;
Number line is shown in figure.
And, We have to find the value of numbers which are a distance of 2 units from 8 on a number line.
Now,
We can find the value of numbers as;
⇒ | 8 - 2 | = 6
⇒ | 8 + 2 | = 10
Therefore, The value of numbers are 6 and 10 which are a distance of 2 units from 8 on a number line.
Learn more about the number line visit:
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PLEASE HEL URGENT 25 POINTS!!!
Write 0.0000012 in scientific notation
Answer:
0.0000012 = 1.2 x 10⁶ (that is the scientific notation)
Step-by-step explanation:
The decimal moves 6 places to the right
The 6 then becomes the exponent in a* 10^b
And (a) must be a 10 > number > 1
b = number of places the decimal moves
Answer:
1.2 * 10 ^6
Step-by-step explanation:
0.0000012
Move the decimal 6 places to the right
The 6 becomes the exponent in
a* 10^b a must be a number 1 or greater but less than 10
b is the the number of places the decimal moves (+ to the right, - to the left)
000001.2
Then the number becomes 1.2 * 10 ^6
11. The student government is selling flowers for homecoming. The project costs them $20 for advertising and
$3 for each flower sold.
a. Evaluate the expressions 3n+20 and 3(n+20) when n = 4.
b. Which expression shows their total cost? How do you know?
Answer:
32
Step-by-step explanation:
3(n+20) = 3(4+20) = 3(24) = 723n+20 = 3(4)+20= 12+20=32If n represents the amount of flowers they sold, then the correct answer should be 32. The cost for each flower they sold would be 3 x 4 and then add $20 for advertising.
If the density of the wood is 3 pounds per cubic foot and if the weight of the solid is
360 pounds, what is the width, w, in feet, of the solid?
(A) 5.0
(B) 2.5
(C) 2.4
(D) 1.5
The area of the triangular face of the solid is 48 if that helps
The width in feet of the given solid is 1.136
Density is defined as the ratio of the mass per unit volume
Density = Mass/Volume
Given
Weight = 360 pounds
Density = 3 pounds per cubic foot
Get the mass;
Since W = mg
m = W/g
m = 360/2.2
m =163.64 lbm/kg
Get the volume
From the formula;
Volume = Mass/Density
Volume = 163.64 /3
Volume = 54.55 ft³
Next is to get the width
Volume of the triangular prism = Base Area * Width
Base Area = 48ft²
54.55 = 48w
w = 54.55/48
w = 1.136
Hence the width of the solid in feet is 1.136ft
Learn more on how to calculate density here https://brainly.com/question/17887628
Does this graph represent a function (scatter)
A. Yes
B. No
Answer:
A. Yes
Step-by-step explanation:
it is always yes because no os negative
Answer
a
Step-by-step explanation:
it does represent a function
9) What is the area of a square with a side length of 120 cm?
Area of square = Side × Side
Side of square is 120 Cm.⇛Area = 120 cm × 120 cm
⇛Area = 14400 cm²
Hence , the area of square is 14400 cm²
Answer:
14400
Step-by-step explanation:
Area for square formula: B × H
Since a square has equal sides for each side, you will multiply 120 by itself.
120 × 120 = 14400
The area of the square is 14400.
Hope this helped.
8.
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0
A. 2
B. cannot be determined
C. 0
D. 1
sin^6x + cos^6x = 1/4
Answer:
[tex]\displaystyle x = \frac{\pi}{4} + k\, \pi[/tex] for integer [tex]k[/tex] (including negative numbers.)
Step-by-step explanation:
Pythagorean Identity: [tex]\sin^{2}(x) + \cos^{2}(x) = 1[/tex]. Equivalently, [tex]\cos^{2}(x) = 1 - \sin^{2}(x)[/tex].
Rewrite the original equation and apply this substitution to eliminate [tex]\cos(x)[/tex]:
[tex]\displaystyle \sin^{6}(x) + \cos^{6}(x) = \frac{1}{4}[/tex].
[tex]\displaystyle (\sin^{2}(x))^{3} + (\cos^{2}(x))^{3} = \frac{1}{4}[/tex].
[tex]\displaystyle (\sin^{2}(x))^{3} + (1 - \sin^{2}(x))^{3} = \frac{1}{4}[/tex].
Let [tex]y = \sin(x)[/tex] ([tex]-1 \le y \le 1[/tex].) The original equation is equivalent to the following equation about [tex]y[/tex]:
[tex]\displaystyle y^{6} + (1 - y^{2})^{3} = \frac{1}{4}[/tex].
Expand the cubic binomial in the equation:
[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, (y^{2})^{2} - (y^{2})^{3} = \frac{1}{4}[/tex].
[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, y^{4} - y^{6} = \frac{1}{4}[/tex].
Simplify to obtain:
[tex]\displaystyle 1 - 3\, y^{2} + 3\, y^{4} = \frac{1}{4}[/tex].
Rearrange and simplify:
[tex]12\, y^{4} - 12\, y^{2} + 3 = 0[/tex].
[tex]3\, (2\, y^{2} - 1)^{2} = 0[/tex].
[tex]2\, y^{2} - 1 = 0[/tex].
[tex]\displaystyle y^{2} - \frac{1}{2} = 0[/tex].
Solve for [tex]y[/tex]:
Either [tex]\displaystyle y = \frac{1}{\sqrt{2}}[/tex] or [tex]\displaystyle y = -\frac{1}{\sqrt{2}}[/tex].
If [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{\pi}{4} + 2\, k\,\pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].
On the other hand, if [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{3\, \pi}{4} + 2\, k\,\pi = \frac{\pi}{4} + (2\, k + 1) \, \pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].
Combine both situations to obtain:
[tex]\displaystyle x = \frac{\pi}{4} + 2\, k\, \pi[/tex] for all [tex]k \in \mathbb{Z}[/tex].
If sin 115° ≈ 0.91 and cos 115° = -0.42, then sin -115° =
Answer:
sin -115° = -0.91
Step-by-step explanation:
Point A is (cos 115°, sin 115°). Since cos 115° = -0.42 and sin 115° ≈ 0.91, it means that the coordinates at point A is (-0.42, 0.91).
As for point B which was revolved around -115°,
the coordinates will be similar to point A but you just have to change the negative.
B(cos -115°, sin -115°) = B(0.42, -0.91)
Answer:
PLATO ANSWER
-0.91; -0.42
Step-by-step explanation:
The sine function is an odd function, meaning that sin -x = -sin x. Because sin 115° ≈ 0.91, sin -115° ≈ -0.91.
The cosine function is an even function, meaning that cos -x = cos x. Because cos 115° = -0.42, cos -115° = -0.42.
Use substitution to solve the following system of equations. What is the value of y?
Answer:
y = 6Step-by-step explanation:
Use the second equation:
2x - y = 2 ⇒ y = 2x - 2Substitute this into first equation:
3x + 4(2x - 2) = 363x + 8x - 8 = 3611x = 44x = 4Now find y:
y = 2*4 - 2 y = 8 - 2y = 6It is given that,
→ 2x - y = 2
Convert the equation as,
→ y = 2x - 2
First we should,
find the required value of x.
→ 3x + 4(2x - 2) = 36
→ 3x + 8x - 8 = 36
→ 11x = 44
→ [x = 4]
Let's find the required value of y,
→ y = 2x - 2
→ y = (2 × 4) - 2
→ y = 8 - 2
→ [y = 6]
Therefore, the value of y is 6.
A random sample of 23 items is drawn from a population whose standard deviation is unknown. The sample mean isx⎯ ⎯ x¯ = 840 and the sample standard deviation is s = 15. Use Appendix D to find the values of Student's t. (a) Construct an interval estimate of μ with 98% confidence. (Round your answers to 3 decimal places.) The 98% confidence interval is from to
Answer:
[tex](832.156, \ 847.844)[/tex]
Step-by-step explanation:
Given data :
Sample standard deviation, s = 15
Sample mean, [tex]\overline x = 840[/tex]
n = 23
a). 98% confidence interval
[tex]$\overline x \pm t_{(n-1, \alpha /2)}. \frac{s}{\sqrt{n}}$[/tex]
[tex]$E= t_{( n-1, \alpha/2 )} \frac{s}{\sqrt n}}[/tex]
[tex]$t_{(n-1 , \alpha/2)} \frac{s}{\sqrt n}$[/tex]
[tex]$t_{(n-1, a\pha/2)}=t_{(22,0.01)} = 2.508$[/tex]
∴ [tex]$E = 2.508 \times \frac{15}{\sqrt{23}}$[/tex]
[tex]$E = 7.844$[/tex]
So, 98% CI is
[tex]$(\overline x - E, \overline x + E)$[/tex]
[tex](840-7.844 , \ 840+7.844)[/tex]
[tex](832.156, \ 847.844)[/tex]
I need help ASAP!!Please explain how you got the answer
Answer:
348 km³
Does the answer help you?
256x²+² - x²y² + 49y²+²
[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49y^2x^2[/tex]
[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49x^2y^2[/tex]
[tex]\\ \sf\longmapsto (256-1+49)x^2y^2[/tex]
[tex]\\ \sf\longmapsto 304x^2y^2[/tex]
If tanA=1/7 and tanB=1/3 prove that cos2A=sin4B
Answer:
{4 |8}. 96. 24
sin4B{3. |9}= ___. = ___ = cos2A
{10|10} 100. 25
{9 |9}
Help me quick i need helppp
[tex]\\ \sf\longmapsto (m-8)+(m-8)+(m-8)+(m-8)+(m-8)+(m-8)=12[/tex]
[tex]\\ \sf\longmapsto 6(m-8)=12[/tex]
[tex]\\ \sf\longmapsto 6m-48=12[/tex]
[tex]\\ \sf\longmapsto 6m=12+48[/tex]
[tex]\\ \sf\longmapsto 6m=60[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{60}{6}[/tex]
[tex]\\ \sf\longmapsto m=10[/tex]
Answer:
M=14
Step-by-step explanation:
First make an equation - m÷6 =8Then shift 6 to 8 - m=6×8Answer - m=14HELP ME PLEASE i need this thing really fast
Answer:
[tex]h(x - 1) + 2[/tex]
[tex]h( - 3+ 1) + 2[/tex]
[tex]h \times - 4 + 2[/tex]
[tex] - 4h + 2[/tex]
which of the following represents x= 1/2 y written in general form?
2x-y = 0
=============================================
Work Shown:
x = (1/2)y
2x = y ... multiply both sides by 2
2x-y = 0 ... subtract y from both sides
This is in standard form Ax+By = C, where A,B,C are integers. In this case, A = 2, B = -1, C = 0.
PLS HELP ME I WILL MARK YOU AS BRAINLIEST!!!
Answer:
Option B, 187.5 cm³
Step-by-step explanation:
Volume of the triangular prism,
base area × height
= (10×7.5/2)×5
= 187.5 cm³
x²+y²+6x+8y+24=0 asap reply plss.. Sana umabon ng 1 makasagot
Answer:
3
Step-by-step explanation:
If x = 3 and y = 5 then which of the following expression has the value ( -8)
당신에게 도움이됩니다
[tex]( - 3) - 5 \\ = ( - 8)[/tex]
A piece of wire, 12.55m long is cut into 50 pieces of equal length. How long is each piece?
Answer:
Each wire is 0.251 m
Step-by-step explanation:
[tex] = \frac{12.55}{50} \\ \\ = 0.251[/tex]
Answer:
length of wire= 12.55m= 1255cm
Number of pieces= 50
length of each piece=?
length of each piece = 1255/ 50
length of each piece= 25.1cm= 0.251m
2. Find the measure of angle J.
(x^2+12x+36)-(x-1)^2
x^2-4xy+4y^2
16x^2-8x+1
x^2+4x+4
4x^2+12xy+9y^2
x^2-8x-16
4x^2-16
x^2-1
x^2+6x+9
9x^2-25y^4
16x^2-8x+1
Answer:
Hey I'm sorry I didn't get to answer your question it's just that I need the points because I don't have enough to get help with my question. I hope you get the answer that you need for you question. Good Luck :)
Step-by-step explanation:
BRAINLIEST Which equation could be solved using this application of the quadratic formula?
A.
x2 + 1 = 2x − 3
B.
x2 – 2x − 1 = 3
C.
x2 + 2x − 1 = 3
D.
x2 + 2x − 1 = -3
The quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.
What is the quadratic formula?A standard quadratic equation of the form ax² + bx + c = 0, can be solved using the quadratic formula, which is given as:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
How to solve the question?In the question, we are asked for the quadratic equation, which could be solved using this application of the quadratic formula:
[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]
To find the quadratic equation for which we use the quadratic formula
[tex]x = \frac{-2\pm\sqrt{2^2-4(1)(-4)} }{2(1)}[/tex]
we compare this equation with the standard quadratic formula,
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
to get a = 1, b = 2, and c = -4, to get the standard quadratic equation, ax² + bx + c = 0, as (1)x² + (2)x + (-4) = 0, or x² + 2x - 4 = 0.
Now, we convert the given options in the standard form to check for the correct choice:
A. x² + 1 = 2x - 3 ⇒ x² - 2x + 4 = 0, which is not the correct choice.B . x² - 2x - 1 = 3 ⇒ x² - 2x - 4 = 0, which is not the correct choice.C. x² + 2x - 1 = 3 ⇒ x² + 2x - 4 = 0, which is the correct choice.D. x² + 2x - 1 = -3 ⇒ x² + 2x + 2 = 0, which is not the correct choice.Thus, the quadratic equation that could be solved using the given application of the quadratic formula is x² + 2x - 1 = 3, which in standard form is x² + 2x - 4 = 0. Hence, option C is the right choice.
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