Answers
[tex]\textbf{(i)}\\\\~~~~~~~y= e^{3x} \sin 2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx} \left( e^{3x} \sin 2x \right)\\\\\\~~~~~~~~~~~~=e^{3x} \dfrac{d}{dx} \sin 2x + \sin 2x \dfrac{d}{dx} e^{3x}\\\\\\~~~~~~~~~~~~=2e^{3x} \cos 2x + 3e^{3x}\sin 2x \\\\\\[/tex]
[tex]\textbf{(ii)}\\\\~~~~~~~~y = \dfrac{e^{3x}}{\cos 2x}\\\\\\\implies \dfrac{dy}{dx} = \dfrac d{dx} \left(\dfrac{e^{3x}}{\cos 2x} \right)\\\\\\~~~~~~~~~~~=\dfrac{\cos 2x \dfrac{d}{dx}\left(e^{3x} \right) -e^{3x} \dfrac{d}{dx}( \cos 2x) }{\cos^2 (2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x+2e^{3x}\sin2x }{\cos^2(2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x}{ \cos^2(2x)} + \dfrac{2e^{3x} \sin 2x}{\cos^2(2x)}\\\\\\~~~~~~~~~~~=3e^{3x}\sec (2x) + 2e^{3x}\sec (2x) \tan (2x)[/tex]
[tex]\textbf{(iii)}\\\\~~~~~~~~~y=( 3x+2)^3\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx}(3x+2)^3\\\\\\~~~~~~~~~~~=3(3x+2)^2 \dfrac{d}{dx} (3x+2)\\\\\\~~~~~~~~~~~=3(3x+2)^2 \cdot 3\\\\\\~~~~~~~~~~~=9(3x+2)^2[/tex]
[tex]\textbf{(iv)}\\\\~~~~~~~~~x^2 +y^2 = 5xy\\\\\\\implies \dfrac{d}{dx}(x^2 +y^2) = 5\dfrac{d}{dx} (xy)\\\\\\\implies 2x + 2y \dfrac{dy}{dx} = 5\left(x \dfrac{dy}{dx} +y\right)\\ \\\\\implies 2x +2y \dfrac{dy}{dx} = 5x \dfrac{dy}{dx} +5y\\\\\\\implies 2y \dfrac{dy}{dx} - 5x \dfrac{dy}{dx} = 5y-2x\\\\\\\implies (2y-5x) \dfrac{dy}{dx} = 5y-2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{5y-2x}{2y-5x}[/tex]
Related Questions
6. Find the height of a triangle with a
base of 4 cm and a hypotenuse of
11 cm. Round to the nearest tenth
of a centimetre. Show your work..
Answers
Answer:
Hope the picture will help you..............
Need help! Need Urgent
Answers
The amount of paper that Lemon needs for the actual poster will be 8 square feet.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
The dimension of the poster is 10 cm by 20 cm.
And the scale factor will be 5 cm is equal to 1 ft.
Then the dimension of the poster will be 2 ft by 4 ft.
Then the amount of the paper that Lemon needs for the actual poster will be
Area = 2 × 4
Area = 8 ft²
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Equation for a line perpendicular to 3y-9x=9 and passing through the point(-3,2)
Answers
Answer:
Step-by-step explanation:
3y-9x=9
3y-9x+9x=9+9x
3y=9x+9
y=3x+3
If a line is perpendicular to an equation, the slope is flipped.
So, 3x would equal to -3x.
The final equation is y=-3x+3
how many liters each of a 50% acid solution and a 65% acid solution must be used to produce 60 liters of a 55% acid solution?
Answers
Answer:
178
Step-by-step explanation:
100 plus 78 equal s 179
Determine the equation of the line tha has an x-intercept of 4 and a y intercept of-3
Answers
Answer:
[tex]y=\frac{3}{4} x-3[/tex]
Step-by-step explanation:
Given information: x-int: 4 and y-int:-3
x-int point : (4,0).
y-int point : (0,-3).
Plug this information to point-slope form to solve for m and then convert that to slope-intercept form.
[tex]y-y_0=m(x-x_0)\\0-(-3)=m(4-0)\\3=4m\\m=\frac{3}{4} \\[/tex]
[tex]y-y_0=m(x-x_0)\\y-(-3)=\frac{3}{4} (x-0)\\y+3=\frac{3}{4}x\\y=\frac{3}{4}x-3[/tex]
What is the definition of cause and effect structure?
A. Describes a problem as well as its causes and suggests solutions
B. Shows how two or more things are alike andlor different
C. Shows relationship between events, explains how one thing happens as a result of another
D. Describes a topic, idea, person, place or thing
Answers
Answer:
Method of paragraph or essay development in which a writer analyzes the reason for - and / or the consequences of - an action , event, or decision
Answer:
C. Shows relationship between events, explains how one thing happens as a result of another
Step-by-step explanation:
11 BAP-Z
Question
Find the volume of the solid figure.
1 cm
3 cm
6 cm
2 cm
3 cm
8 cm
9 cm
Answers
Answer:
168 [tex]cm^{3}[/tex]
Step-by-step explanation:
Start by finding the whole prism's volume. 9 x 3 x 8 = 216 Then find the volume of the missing part. 8 x 6 x 1 = 48. Subtract the missing volume from the whole volume. 216 - 48 = 168
Urgent help!!!
Write equation in slope intercept form.
1.25 (25) = 31.25
Answers
The equation in slope intercept form is,[tex]31.25 = 1.25 \times 25 +0[/tex]. The given equation is obtained by comparing the standard equation of the straight line.
What is a slope of a straight line?
A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The given equation is;
1.25 (25) = 31.25
31.25=1.25 (25)
The standard equation of the slope intercept form. is;
[tex]\rm y = mx +x[/tex]
On comparing the given equation with the above equation, we get;
y=31.25
m=1.25
x=25
c=0
The equation in slope intercept form is;
[tex]31.25 = 1.25 \times 25 +0[/tex]
Hence, the above equation is the slope intercept form.
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Figure ABCD is a parallelogram.What are the lengths of line segments AB and BC?
Answers
Answer:
I need an image
Step-by-step explanation:
Answer:CPCTC
Step-by-step explanation:
6. AB ≅ CD Corresponding Parts of Congruent triangles are Congruent(CPCTC)
Hope it helps:)
A 30-foot ramp is used to move product to a loading dock. The ramp makes a 24° angle with the horizontal. The ramp is to be replaced with a ramp that is 50 feet long. What angle does this replacement ramp make with the horizontal? Round your answer to the nearest tenth of a degree.
Answers
Check the picture below.
[tex]sin(\theta )=\cfrac{\stackrel{opposite}{30\cdot sin(24^o)}}{\underset{hypotenuse}{50}}\implies sin^{-1}[sin(\theta )]=sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right] \\\\\\ \theta =sin^{-1}\left[ \cfrac{30\cdot sin(24^o)}{50} \right]\implies \theta \approx 14.1^o[/tex]
The value of angle does this replacement ramp make with the horizontal is,
⇒ θ = 14.1°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
A 30-foot ramp is used to move product to a loading dock.
The ramp makes a 24° angle with the horizontal.
And, The ramp is to be replaced with a ramp that is 50 feet long.
Hence, By given figure;
We have;
⇒ sin θ = 30 × sin 24° / 50
⇒ θ = sin ⁻¹ (30 × sin 24° / 50)
⇒ θ = 14.1°
Thus, The value of angle does this replacement ramp make with the horizontal is,
⇒ θ = 14.1°
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Make up a question that you need to use 6 fractions to solve! It needs to involve subtraction. It can involve addition too.
Answers
Answer:
6/4-3/2(12/8+27/4)9/8x30/12=
PLEASE HELP ME FOR BRAINLIEST
Answers
Answer: The answer is d
Step-by-step explanation:
let f(x) = x-3 and g(x) =x^2 find f(g(4))
Answers
Answer:
f(g(4)) = 13.
Step-by-step explanation:
g(4) = 4^2 = 16
so f(g(4)) = f(16)
= 16 - 3
= 13.
Determine the percentage (%) of your total daily intake:
% kcal from carbs=
% kcal from fat=
% kcal of protein=
explain please
Answers
Answer & Step-by-step explanation:
USDA's Dietary Guidelines for Americans provide percent ranges for each macronutrient. For adults, the organization recommends consuming 10%–35% of calories from protein, 45%–65% from carbohydrates, and 20%–35% of calories from fat. They also suggest consuming less than 10% of total calories from saturated fat.
Find F Write your answer in simplest radical form.
Answers
Side lengths of a 30-60-90 triangle are x xsqrt3 and 2x
Answer:
f= 5.2 or 3[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Cot(60) = 3/f
0.58 =3/f
0.58f = 3
f= 5.2 or 3[tex]\sqrt{3}[/tex]
im stuck need help me i don't get it
Answers
Answer:
J. 12 : 18
Step-by-step explanation:
Amy used 2 tea bags for every 3 cups of water to make iced tea
the ratio here is 2:3
x = 2:3
lets simplify our ratios
6 : 10 = 3 : 5 ≠ 2 : 3
5 : 6 = (doesn't simplify evenly) ≠ 2 : 3
9 : 15 = 3 : 5 ≠ 2 : 3
12 : 18 = 2 : 3 = 2 : 3
Simplifying
find their highest common factor and divide both the numbers by the same amount (HCF).
Ex.
12 : 18
12 ÷ 6 = 2
18 ÷ 6 = 3
2 : 3
Anthony's Muffin Shop recently sold 4 blackberry muffins and 6 other muffins. Considering this data, how many of the next 20 muffins sold would you expect to be blackberry muffins?
Answers
Answer:
there should be 8 blackberry muffins
Answer:
8 Black berry muffins
Step-by-step explanation:
Trust me
WILL GIVE BRAINLIEST 50 POINTS
∆ABC is mapped to ∆A'B'C' using each of the given rules in the table below. Place a checkmark in the correct column for each mapping to state if the resulting mapping would make ∆ABC congruent or not congruent to ∆A'B'C'.
∆ABC is congruent to ∆A^' B^' C'
∆ABC is NOT congruent to ∆A^' B^' C'
(x,y) → (x+5,y)
(x,y) → (5x,5y)
(x,y) → (.5x,.5y)
(x,y) → (x,-y)
(x,y) → (-x,-y)
Answers
Answer:
(x+5,y) = Yes
(5x,5y) = No
(.5x,.5y) = No
(x,-y) Yes
(-x,-y) Yes
Step-by-step explanation:
What is the volume of this figure?
Answers
Answer:
4,105 yd cubed
Step-by-step explanation:
This can be divided into three rectangular prisms, one of which is constructed from triangular prisms
19*9*10 = 1,170 yd
30*9*7 = 1,890 yd
10*5.5*9 = 1,045 yd
Adding them all together gets
4,105 yd cubed
Hey! pls help me with this question on angles. would really be appreciated. have a nice day.
Answers
Using supplementary angles, it is found that the measures of the angles are given as follows:
m<a = 30º.m<b = 90º.What are supplementary angles?Supplementary angles are two angles whose sum is of 180º.
An interior angle is supplementary with it's exterior angle, hence:
m<a + 150º = 180º -> m<a = 30º.
The sum of the three interior angles of a triangle is of 180º, hence:
30º + m<b + 60º = 180º
90º + m<b = 180º
m<b = 90º.
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A line passes through the points (-4,8) and (3,-7). Answer all parts of the question. Part A: what is the slope of the line that passes through these points (-4,8) and (3,-7).
Answers
Answer: [tex]y=\frac{-15}{7}x-\frac{4}{7}[/tex]
Slope: -15/7
y-int:-4/7
Step-by-step explanation:
slope: rise/run
[tex]\frac{x^2-x^1}{y^2-y^1}[/tex]
[tex]\frac{-7-8}{-4-3}=\frac{-15}{-7} =\frac{-15}{7}[/tex]
thats the answer :)
~rere
How to simplify the problem in the photo?
Answers
Answer:
2^3 a^5 b^4
4b^2 c^3
2^(3-2) a^5 b^(4-2)
c^3
2a^5 b^2
2a^5 b^2 c^3
Can someone help me with this?
Answers
Answer:
B
Step-by-step explanation:
4x4= 8
10x10= 20
8+20= 28
5x2= 10
9x2= 18
10+18= 28
Answer:
[tex]4x + 10y = 28 \\ 5x + 9y = 28 \\ 10y = 28 - 4x \\ y = \frac{28 - 4x}{10} \\ y = 2.8 - 0.4x \\ 5x + 9(2.8 - 0.4x) = 28 \\ 25.2 - 3.6x + 5x = 28 \\ 1.4x = 2.8 \\ x = 2 \\ [/tex]
[tex]y = 2.8 - 0.4 \times 2 \\ y = 2[/tex]
B
You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total of $858. This year, the first fund paid a 10% dividend and the second only 1%, and you received a total of $867. How much money did you invest in each fund?
Answers
The amount that was invested in the first fund is $8300.
The amount that was invested in the second fund is 3700.
What are the linear equations that represent the question?0.09a + 0.03b = $858 equation 1
0.1a + 0.01b = $867 equation 2
Where:
a = amount invested in the first fund b = amount invested in the second fund How much was invested in the second fund?Multiply equation 2 by 0.9:
0.09a + 0.009b = 780.30 equation 3
Subtract equation 1 from equation 3
0.021b = 77.70
Divide both sides by 0.021
b = $3700
How much was invested in the first fund?
Substitute for b in equation 1: 0.09a + 0.03(3700) = $858
0.09a + 111 = 858
a = (858 - 111) / 0.09
a = $8300
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
the last 2 answer options are completely useless and outright nonsense, because all limits are going against +4.
so, an asymptote at x = -4 is not an option anywhere.
g(x) is always y, and the limit of the function is the limit of the y values.
we just evaluate for what x value is then y reaching that limit. but the sign of the y limit has no direct impact on the sign of the x value.
it is true that the case x = -4 needs to be checked too, but it turns out this just delivers g(-4) = 0.
now, about x = 4 :
when coming from the left side of +4 (increasing x), what is the sign of the function ?
we can simply use x = 3 to test this :
g(3) = 2(3+4)²/(3² - 16) = 2×49/-7
so, it is negative.
that means when getting closer and closer to +4 coming from that side we what get negative values, and the limit is -infinity.
when coming from the right side of +4 (decreasing x), what is the sign of the function ?
we can simply use x = 5 to test this :
g(3) = 2(5+4)²/(5² - 16) = 2×81/9
so, it is positive.
that means when getting closer and closer to +4 coming from that side we what get positive values, and the limit is +infinity.
so, the second answer option is correct.
because of these y limits, there is a vertical asymptote at x = 4 that kind of "connects" -infinity and +infinity in y direction at that location and symbolizes the limits of y.
This figure represents a small keepsake box. Holly wants to cover 35 of the surface with stickers.
How much of the total surface will be covered with stickers?
Enter your answer as a decimal or mixed number in simplest form in the box.
Answers
The amount of the surface area covered with stickers is 0.6 or 60%
How to determine the covered area?The amount of area to cover is given as:
Covered area = 3/5
Express as percentage
Covered area = 3/5 * 100%
Divide 3 by 5
Covered area = 0.6 * 100%
Evaluate the product
Covered area = 60%
Hence, the amount of the surface area covered with stickers is 0.6 or 60%
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Answer:
135.93
Step-by-step explanation:
I took the test
Joey is putting all of his trophies onto 7 shelves. If he places 7 trophies on each shelf but still has 4 trophies left over, how many
trophies does he have?
OA. 53
OB. 35
OC. 18
OD. 49
Answers
Answer:
53
Step-by-step explanation:
7 * 7 = 49 + 4 = 53
Answer:
A. 53
Step-by-step explanation:
Find number of trophies on shelves:
7 shelves x 7 trophies each = 49 trophies on shelves
Find total number of trophies:
49 trophies on shelves + 4 leftover = 53 trophies overall
So the answer is A. 53
How do the values compare? Order the values from least to greatest.
|1 1/4|
|-1 3/4|
3/4
-2 1/4
-1 1/4
|-2 1/4|
Answers
Answer:
see below
Step-by-step explanation:
For absolute values | x | just drop the sign of the number and make it positive
example : | -3| = 3
so for this Q
-2 1/4 - 1 1/4 3/4 1 1/4 1 3/4 2 1/4
125% of what number is 45?
Answers
Answer:
36
Step-by-step explanation:
125%*x=45
125%x=45
x=36
write two equations that when graphed look like this *see image*. please help its due soon and i will give ya 75 points for answering CORRECTLY thanks, 5 stars, and brainlist. Thank ya
Answers
The graph is showing the equation of circle x²+y²=4
What is a circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The given graph in the question represents the equation of the circle cutting the points on the x-axis and y-axis at 4 which is the radius of the circle.
The equation will be as follows:-
x²+y²=4
Hence the graph is showing the equation of circle x²+y²=4
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