Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
Question 1 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(4x^{3})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 4(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 12x^{2}}[/tex]
Question 2 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{2}{x^{4}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(2x^{-4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 2(-4)x^{-4-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -8x^{-5}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{8}{x^{5}}}[/tex]
Question 3 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3\sqrt{x})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3(x)^{\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(\frac{1}{2})x^{\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2}x^{-\frac{1}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2\sqrt{x}}}[/tex]
Question 4 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{3}{\sqrt{x}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{-\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(-\frac{1}{2})x^{-\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2}x^{-\frac{3}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2x\sqrt{x}}}[/tex]
Question 5 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{x^{3}}{4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{1}{4}(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{4}x^{2}}[/tex]
Question 6 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{5})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(5)x^{5-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 15x^{4}}[/tex]
What is the value for y?
Enter your answer in the box.
Answer:
angle A=angleB .…(समदिबाहु त्रिभुज भएर)
34°=(x-5)°
or, 34=34
angleA+angleB+angleC=180°
or, 34+34+4y=180
or, 68+4y=180
or, 4y=180-68
or, 4y=112
or, y=112÷4
or, y=28
Which calculation correctly uses prime factorization to write square root of 48 in simplest form?
The simplest form of the square root of 48 is 4√3
Simplifying rational functionsGiven the following rational function √48
The correct prime factorization is given as;
√48 = √3×16
√48 = √16 × √3
Since the square root of 16 is 4, hence;
√48 = 4√3
Hence the simplest form of the square root of 48 is 4√3
Learn more on prime factorization here: https://brainly.com/question/92257
#SPJ1
Scalar and Matrix Multiplication
Answer:
multiply 1/2 by each element in the matrix
Step-by-step explanation:
6. 32
39 15
Which of the following rational functions is graphed below?
Answer:
B
Step-by-step explanation:
The vertical asymptotes are the red dashed lines. They are x = -4 and x = 0. Think of them as electric fences that the graph cannot touch or cross. The curve can only get closer and closer.
This question has already been posted, so all credit goes to jimthompson5910.
https://brainly.com/question/20689400
Subtract-3x - 8 from 4x² - 7x - 2.
[tex]( {4x}^{2} - 7x - 2) - (3x - 8) \\ \\ {4x}^{2} - 7x - 2 - 3x + 8 \\ \\ {4x}^{2} - 10x + 4.[/tex]
Use the following information for problems 5-8.
f(2, 33) = 5.5, p < 0.01
1) how many groups were in this study?
a) 34
b)33
c) 3
d) 2
how many participants were in this study?
a) 36
b) 33
c) 3
d) 2
what is the f ratio?
a) 5.5
b) 2
c) 33
d) 0.01
The number of groups is 3, the number of participants is 36, and the f ratio is 5.5.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
f(2, 33) = 5.5, p < 0.01
From the above details, we can find the number of groups:
5) Number of groups = df for groups + 1
Number of groups = 2+ 1 = 3
Option (c) is correct.
6) Number of participants =2 + 33 + 1 = 36
Option (a) is correct.
7) f ratio = 5.5
Option (a) is correct.
8) True; as the p-value is less than the 0.01 level.
Thus, the number of groups is 3, the number of participants is 36, and the f ratio is 5.5.
Learn more about the null hypothesis and alternative hypothesis here:
brainly.com/question/27335001
#SPJ1
Find a rational number between -1/3 and 1/2
Answer:
1/6
Step-by-step explanation:
Rational numbers between two rational numbers:
First find the Least Common Denominator for 2 and 3Then find equivalent fractions with the LCD.LCD of 2 and 3 = 6
[tex]\sf \dfrac{-1}{3}=\dfrac{-1*2}{3*2}=\dfrac{-2}{6}\\\\\dfrac{1}{2}=\dfrac{1*3}{2*3}=\dfrac{3}{6}[/tex]
[tex]\sf Rational \ number \ between \ \dfrac{-2}{6} \ and \ \dfrac{3}{6} \ is \ \bf \dfrac{1}{6}[/tex]
I
1
8 in
Find h.
13 in
= √[?] in.
as the following pic you can see the answer.
#diameter is 8 so radius is 4
A plane flies at 350 mph in the direction 40° north of east, with a wind blowing at 40 mph in the direction 30° south of east. What is the plane’s drift angle?
5.90°
6.38°
45.89°
46.38°
If the plane flying in direction of 40° north of east at a speed of 350 mph and wind is blowing at 40 mph in the direction 30° south of east. then the drift angle will be 5.9 °.
Let's assume east as x axis and north as y axis.
Breaking velocity of plane into components
350 cos40° î + 350 sin40° ĵ
(350 × 0.76604) î + (350 × 0.64278) ĵ
268 î + 225 ĵ
Breaking velocity of wind into components
40 cos30° î - 40 sin30° ĵ
(40 × 0.86602) î - (40 × 0.5) ĵ
34.64 î - 20 ĵ
Now adding velocity of wind to velocity of plane as
The resultant velocity of the plane = initial velocity of plane + velocity of wind
( 268 + 34.64 ) î + ( 225 - 20 ) ĵ
302.64 î + 205 ĵ
So the final velocity of plane will be 302.64 î + 205 ĵ
Lets assume the angle of final velocity from east be θ
So Tan θ = perpendicular / base
So Tan θ = 205 / 302.64
Tan θ = 0.677
θ = Tan⁻¹(0.677)
θ = 34.12 °
As we know,
Drift angle is the difference of initial and final angle of the object measured from same reference.
Drift angle=| Initial angle of plane from east - final angle of plane from east |
Drift angle= | 40 - 34.12 |
Drift angle= 5.87 ° ≈ 5.9 °
So we used the concepts of vectors to solve the above question, first we find out the the final angle of plane from east and then takes the difference of initial and final angle from east to find the drift angle and that we got as 5.9 °.
Learn more about Vectors here:
brainly.com/question/25705666
#SPJ10
Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k.
k=______.
Answer:
5
Step-by-step explanation:
Look at one of the coordinates to find k. For this example I'll look at the y-intercepts (0, 3) (for g(x)) and (0, -2) (for f(x))
g(0) = 3
g(0) = f(0) + k
3 = -2 + k
5 = k
Round the number to the nearest ten-thousands:
388,725
a. 400,000
b.390,000
c. 388,800
d. 389,000
Answer:
B is the correct answer
Step-by-Step:
Jim thinks of a number (n). He adds 5 to the
number then multiplies the result by 7.
(a) Write this as a expression.
The answer Jim gets is 91.
(b) Work out the number Jim thought of.
Show all your
working.
Answers + Step-by-step explanation :
a) the equation should be:
7(n + 5) = 91 since you first add 5 to n and then multiply it by 7. The answer is 91 so that is on the other side of the equal sign
b) we can solve our equation to find for n, the number jim thought of
7(n + 5) = 91
I will use the distributive property.
7n + 35 = 91
Subtract 35 on both sides
7n = 56
Now divide 7 on both sides to find n
n = 8
The number Jim was thinking of was 8! this should be correct, hope this helps!
PLEASS HELP!!
3 folders cost $2.91.
Which equation would help determine the cost of 2 folders?
Answer:
The answer is B
Step-by-step explanation:
By proportion , 3 : 2.91 = 2: x . then you write it in fraction
It takes 15 men, 48 days to weed a plot of land. How
의
plot of land in 16 days, if
mary men can weed the same
kry work at the sametime?
Answer:
it takes 48 days for 15 men to work
it takes 16 days for 15/48*16
the answer is 5 men
Answer:
45 men
Step-by-step explanation:
If you 1/3 the amount of time (from 48 to 16 ) to weed the plot, you will need to TRIPLE the number of men to 45 men
Tariq also designs hot tubs. The diameter of the hot tub is 3 meters. What is the area of the deck that surrounds the hot tub? If necessary, round to the nearest tenth.
The area of the deck that surrounds the hot tub is 17.93 m²
What is Area?
The area is the amount of space within the perimeter of a 2D shape.
radius = 3/2 = 1.5 m
Area of deck,
=Area of square - area of circle
= side side- πr²
=5*5 - 3.14* 1.5*1.5
= 25- 7.065
= 17.93 m²
Learn more about this concept here:
https://brainly.com/question/12744368
#SPJ1
please evaluate the equation
Step-by-step explanation:
[tex] = \sum \limits_{n = 1}^{7} ( - 2. {6}^{n - 1} )[/tex]
[tex] = \sum \limits_ {n = 1}^{n_{ \text{max}}} (a_1. {r}^{n - 1} )[/tex]
[tex] \: [/tex]
[tex]a_1 = - 2[/tex]
[tex]n = 7[/tex]
[tex]r = 6 \to r >1[/tex]
[tex] \: [/tex]
• Find S7.
[tex]s_n = a_1.( \frac{ {r}^{n} - 1}{r - n} )[/tex]
[tex]s_7 = - 2.( \frac{ {6}^{7} - 1 }{6 - 1} )[/tex]
[tex]s_7 = - 2.( \frac{279.936 - 1}{5} )[/tex]
[tex]s_7 = - 2.( \frac{279.935}{5} )[/tex]
[tex]s_7 = - 2 \: . \: 55.987[/tex]
[tex]s_7 = - 111.974[/tex]
The answer is B.
a company's stock begins the week with a price of 43.85 per share the price changes by 2.70 each day for 2 days then the price changes by -1.10 each day for 2 days on the last day the price changes by -4.45 what is the price per share of the company's stock after those 5 days
Step-by-step explanation:
so, in other words, the price is
43.85 + 2.7 + 2.7 - 1.1 - 1.1 - 4.45 =
= 43.85 + 5.4 - 2.2 - 4.45 = 43.85 + 3.2 - 4.45 =
= 43.85 - 1.25 = 42.60
Given: JLM is equilateral. Z is the midpoint of JM.
Prove: JZL is congruent to MZL.
There are multiple ways to prove congruence between two triangles:
SSS - three sides are congruentSAS - two sides and the angle in between are congruentASA - two angles and the side in between are congruentAAS - two angles and one side are congruentHL - (applies only to right triangles) the hypotenuse and one leg are congruent.Keep in mind that the order of the letters matters.
Solving the Question
Given triangle JLM, we know that
S - Z is the midpoint of JM, meaning JZ is congruent to MZ.S - Both triangles share side LZ.S - Because JLM is an equilateral triangle, LJ is congruent to LM.This is only one of the ways to prove congruence with these two triangles.
Which equation is equivalent to the given equation?
-4(X - 5) + 8x = 9x - 3
Answer:
-5x=-23
Or
X=23/5
Step-by-step explanation:
If p() = x2 - 1 and q(x) - 5(x-1), which expression is equivalent to (p - q)(x)?
Answer:
[tex]\text{If p(x) = x2 - 1 and q(x) = 5(x - 1), the expression which is equivalent to}[/tex] [tex]\text{ (p - q)(x) is (x2 - 1) - 5(x - 1).}[/tex]
Step-by-step explanation:
Given:
p(x) = 2x2 - 1q(x) = 3(x - 1)To find:
(p - q)(x)We know:
(p - q)(x) = p(x) - q(x)Substitute
(2x^2 - 1) - 3(x - 1)[tex]\text{Therefore, the expression equivalent to (p - q)(x) is (2x2 - 1) - 3(x - 1).}[/tex]
The graph below shows point P and line A. If line B is drawn such that it passes through point P and is parallel to line A, what is the equation of line B? Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms. The graph below shows point P and line A. If line B is drawn such that it passes through point P and is parallel to line A , what is the equation of line B ? Give your answer in the form y = mx + c , where m and care integers or fractions in their simplest forms .
Answer:
Step-by-step explanation:
If line A is parallel to line B passes through the point (2,7), the equation of line B will be y=3x+1.
What is 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:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that the points are (2,7)
The slope of line A is,
m = 6/2
m=3
The equation of the line is,
y-(-1)=3x
y=3x+1
Since the line B is parallel to A the slope of the line is the same,
y-(-7)=3(x-2)
y=3x+1
Thus, if line A is parallel to line B passes through point (2,7), the equation of line B will be y=3x+1.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ2
Help Me. I need to get back on track on common factors and factors.
Answer:
A) 1, 2, 4
Hope this helps you!
Answer:
A. 1, 2, 4
Step-by-step explanation:
32= 1*32, 2*16, 4*8
36* 1*36, 2*18, 3*12, 4*9, 6*6
Common factors: 1, 2, 4
So the Answer is A.
Identify the inverse g(x) of the given relation f(x).
f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}
g(x) = {(–4, –3), (0, –1), (4, 1), (8, 3)}
g(x) = {(–8, –3), (–4, 1), (0, 1), (4, 3)}
g(x) = {(8, –3), (4, –1), (0, 1), (–4, 3)}
g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}
Answer:
Last choice
Step-by-step explanation:
The basic definition of inverse function is both domain and range are swapped.
The domain is defined as set of all x-values while range is defined as set of all y-values.
If we have set of function h = {(1,2), (3,4), (5,6)} then the inverse will be {(2,1), (4,3), (6,5)}. Thus, if set of (x,y) is original function then set of (y,x) will be inverse of set of (x,y).
Henceforth, the inverse of f(x) will be g(x) = {(3,8), (1,4), (-1,0), (-3,-4)}.
Answer:
D. g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}
Step-by-step explanation:
hope this helps:)
Please help!!!
What is the area of , given that θ=π/3 radians? Express your answer in terms of π and as a decimal rounded to the nearest tenth. Show all your work.
Answer:
A = 1.5 π in² ≈ 4.7 in²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{\frac{\pi }{3} }{2\pi }[/tex]
= π × 3² × [tex]\frac{1}{6}[/tex]
= 9π × [tex]\frac{1}{6}[/tex]
= 1.5π in²
≈ 4.7 in² ( to the nearest tenth )
Which equation has a graph that lies entirely above the x-axis?
y = -(x + 7)² + 7
y= (x-7)²-7
y= (x-7)² +7
y= (x-7)²
Heyo!
The equation when displayed on a graph that lies entirely above the x-axis would be Option 4) y = (x - 7)^2.
Hope this helps! If so, please lmk! Also, if you have any questions, feel free to comment below. Good luck!
Answer:
Step-by-step explanation:
Use the tables below to answer the following questions: a. f(h(2)) b. g(h(f(1))) c. g(g(4))
Answer:
19-73 19-73 and the other half way back home from the
to ghana 5hjgf and to the 8
I need this due by tonight what is 45+x=75
Answer:30
Step-by-step explanation: jus subtract total number by 45 to c what u missin
Given: [tex]\textsf{45 + x = 75}[/tex]
Need: [tex]\textsf{The value of the unknown x}[/tex]
Solution: In order to solve for the unknown we must subtract 45 from both sides which would isolate x and given us the value.
Subtract 45 from both sides
[tex]\textsf{45 - 45 + x = 75 - 45}[/tex][tex]\textsf{x = 75 - 45}[/tex][tex]\textsf{x = 30}[/tex]After simplifying the expression we were able to determine that x is equal to 30.
If a/b = 3b, what is the value of 6b/a ?
A = 2/a
B = 2/b
C = 2a
D = 2b
Answer:
2/b
Step-by-step explanation:
a/b=3b
a=3b*b
a=3b^2
6b/a=6b/(3b^2)=2/b
Mr. Gaffy asked his students to pick a number, add
3 to it, multiply by 5 and then reduce it by 12.
Jermaine calls out his answer of 15. What number
did Jermaine start with?
Answer:
2.4
Step-by-step explanation:
We must do the inverse of every operation:
15 + 12 = 27
27/5 = 5.4
5.4 - 3 = 2.4
Damek has five number cards lying on the table. There are two number cards with digit 1, two number cards with digit 2 and one number card with 0. How many different three-digit numbers can Damek form? (Number cannot being with 0).
(P.S. Is there a way to find the answer without listing all the possibilities?)
Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.
There are five number cards on the table.
2- digit 1 card
1- digit 0 card
2- digit 2 card
There is a possibility of putting 1 or 2 in the hundredth place.
If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2
If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place
If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place
If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.
So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.
Similarly, there will be 7 possibilities that the hundredth place is filled by 2.
Hence, there are 14 possibilities as required by the problem.
So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.
Learn more about permutation here-
brainly.com/question/1216161
#SPJ10