Answer:
[tex]1296 = 6 \times 6 \times 6 \times 6 = {6}^{4} = {2}^{4} \times {3}^{4} [/tex]
This is for AP CALCULUS. I really need help on this. I’m trying to find the first and second derivative of these three functions.
Review Material:
[tex]\sqrt[n]{x^m} = x^{\frac{m}{n}}[/tex]
[tex]\frac{d}{dx}[x^n]=nx^{n-1}\\[/tex]
[tex]\frac{d}{dx}[\sin(x)]=\cos(x)\\[/tex]
[tex]\frac{d}{dx}[\cos(x)]=-\sin(x)\\[/tex]
[tex]\frac{d}{dx}[constant]=0\\[/tex]
Step-by-step explanation:
(a)
[tex]F(x) = -2\cos(x) +x^{\frac{4}{3}} -3e\\ \text{Note: 3e is a constant}\\F'(x) = 2\sin(x) + \frac{4}{3}x^{\frac{1}{3}}\\F''(x) = 2\cos(x) + \frac{4}{9}x^{-\frac{2}{3}}[/tex]
(b)
[tex]F(x) = x^{-3} + \frac{1}{2}x^2-\sin(x)\\F'(x)=-3x^{-4} + x - \cos(x)\\F''(x) = 12x^{-5} + 1 + \sin(x)[/tex]
(c)
[tex]F(x) = 2x^{-3}+x^{\frac{3}{4}}-4x\\F'(x) = -6x^{-4} + \frac{3}{4}x^{-\frac{1}{4}}-4\\F''(x)= 24x^{-5} - \frac{3}{16}x^{-\frac{5}{4}}[/tex]
Solve 12x + 6>9x+ 12.
Ο Α. x>6
Ο Β. x<2
Ο C. X>2
O D. X<6
Answer:
x>2
Step-by-step explanation:
-Subtract 6 from both sides
-Simplify
-Subtract 9x from both sides
-Simplify
-Divide both sides by 3
-Simplify
Please Help its a math problem amber has done 3 projects this year in Social Studies and wants a mean project grade of 92. Her first three project grades are 92, 93 and 89. What does she need to make on the fourth project to meet her goal?
Question 5 options:
94
90
95
92
Answer:
a) 94
Step-by-step explanation:
92 + 93 + 89 + 94 = 368/4= 92
Answer:
94
explanation:
because common sense
What is the quotient of (x cubed 3 x squared minus 4 x minus 12) divided by (x squared 5 x 6)? x 2 x – 2 x – 8 x 8
The quotient of the given expression is x-2. The correct option is the second option- x – 2
Simplification of fractionsFrom the question, we are to determine the quotient
The given expression is
[tex]\frac{x^{3}+3x^{2} -4x-12 }{x^{2} +5x+6}[/tex]
The numerator can be expressed as
[tex](x-2)(x^{2} +5x+6)[/tex]
Then, the fraction becomes
[tex]\frac{x^{3}+3x^{2} -4x-12 }{x^{2} +5x+6}[/tex] = [tex]\frac{(x-2)(x^{2} +5x+6)}{x^{2} +5x+6}[/tex]
Simplifying
[tex]\frac{(x-2)(x^{2} +5x+6)}{x^{2} +5x+6} = x-2[/tex]
Hence, the quotient of the given expression is x-2. The correct option is the second option- x – 2
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Here is the complete and correct question:
What is the quotient of (x cubed + 3 x squared minus 4 x minus 12') divided by (x squared + 5 x + 6)? x + 2 x – 2 x – 8 x + 8
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what is the absolute vale of |35|
Answer:
Absolute value of any number is positive. so the absolute value of (-35) is 35.
Step-by-step explanation:
What does each line on the protractor stand for?
Answer:
There are two sets of degrees going in opposite directions along an arc. The top of the arc shows degrees from 0º to 180º from left to right. The bottom of the arc shows degrees from 180º to 0º from left to right. The smallest "tick marks" along the edge of the protractor represent 1º intervals.
Step-by-step explanation:
hlp!
options:
A. [tex]x\leq -5[/tex]
B. [tex]x\geq -5[/tex]
C.[tex]x\geq 2[/tex]
D.[tex]x=4[/tex]
Answer:
Option B
x ≥ (-5)
Step-by-step explanation:
Given;-3(x + 4) ≥ x + 8So,
-3(x + 4) ≥ x + 8
-3x – 12 ≥ x + 8
Add both sides 12 we get,
-3x – 12 + 12 ≥ x + 8 + 12
-3x ≥ x + 20
Similarly, subtract x from both sides we get,
-3x – x ≥ x – x + 20
-4x ≥ 20
Then, divide both sides by (-4) we get,
-4x/(-4) ≥ 20/(-4)
x ≥ -5
Thus, The answer is x ≥ (-5).
Julio says "If you subtract 16 from my number and multiply the difference by -3, the result is 69." What is Julio's number?
Julio's number is 3.
What is Algebra?
Algebra is a branch of mathematics that deals with symbols or variables and uses arithmetic operations (+, –, ×, ÷) to find the unknown quantities represented by these variables.
Let us consider the number is 'x'
Julio's number be,
-3(x-16)=69
x-16=-13
x= -13+16
x= 3
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Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
The graph shows a curve with an end point at 2 comma 3 that increasing to the right
The graph shows a curve with an end point at 3 comma 2 that increasing to the right
The graph shows a curve with an end point at negative 3 comma negative 2 that increasing to the right
The graph shows a curve with an end point at negative 2 comma negative 3 that increasing to the right
The obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis. None of the option is correct.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
The given equation of the function is;
[tex]y = -(x+2)^{1/3}+5[/tex]
Hence,the obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis.
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Answer:
The function f(x) = sqrt(x - 2) + 3 represents a square root function that is shifted 2 units to the right and 3 units up from the parent function f(x) = sqrt(x).
The endpoint of the function occurs when the radicand (x - 2) is equal to zero, which means x = 2. So, the function has an endpoint at (2, 3).
Since the function involves a square root, the value of y cannot be negative. Therefore, the function is increasing to the right.
The correct graph that represents the function f(x) = sqrt(x - 2) + 3 is the one that shows a curve with an endpoint at (2, 3) that increases to the right.
Therefore, the answer is: The graph shows a curve with an endpoint at 2 comma 3 that increases to the right. A.
POINTS!!! Answer both 3 and 4 PLEASE
Answer:
yes not function because 1 is repeated
How do I answer this?
Answer:
I dontknow what ur question is but I think u just have to measure the length of 50 ° on ur protector use a compass
Question 4 (Essay Worth 10 points)
(04.05 MC)
The graph represents the journey of a bus from the bus stop to different locations:
Bus Journey
Distance
(miles)
Time (hours)
Part A: Use complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey. (4 points)
Part B: In which parts of the graph is the function increasing, decreasing, and constant? (4 points)
Part C: Is the graph linear or non-linear? Explain your answer. (2 points)
5
1 and 3 are increasing, 2 and 4 are constant, and 5 is decreasing. And the graph is non-linear.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The graph represents the journey of a bus from the bus stop to different locations:
Complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey.
1 and 3 show that the bus is going to the last station, 2 and 4 show the holding time of the bus at a station, and 5 shows that the bus is returning.
1 and 3 are increasing, 2 and 4 are constant, and 5 is decreasing.
The graph is non-linear.
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Determine the next two terms in the arithmetic sequence.
5, 11, 17, 23,
The sequence is add 6 so the answer is 29 and 35
Answer:
Next two will be 41, 47
Step-by-step explanation:
5+6= 11
11+6= 17
17+6= 23
23+6= 29
29+6= 35
35+6= 41
41+6= 47
Answer:
29 and 39
Step-by-step explanation:
A cylindrical well has a radius of 6 feet and a height of 12 feet. How many cubic feet of water will it take to fill the well?
Assume that π = 3.14 and round to the nearest tenth when necessary.
maybe 1375 cubic feet of water will take to fill the well
Simone travels 90 miles at an average speed of 40 mph.
She then travels a further 30 miles.
The average speed for the entire journey is 43 mph.
Assuming Simone didn't stop, what was her average speed for the final 30 miles to 2 dp?
Using the relation between velocity, distance and time, it is found that her average speed for the final 30 miles is of 55.56 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
Simone travels 90 miles at an average speed of 40 mph, hence the time is given by:
[tex]t_1 = \frac{90}{40} = 2.25[/tex]
She then travels a further 30 miles, with an average speed for the journey of 43 mph. Hence, she traveled 90 + 30 = 120 miles, and the total time is given by:
[tex]t = \frac{120}{43} = 2.79[/tex]
Hence, in the second part, she traveled 30 miles in 2.79 - 2.25 = 0.54 hours, so the velocity is given by:
[tex]v = \frac{d}{t} = \frac{30}{0.54} = 55.56[/tex]
Her average speed for the final 30 miles is of 55.56 mph.
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Please answer quickly
[tex]\dfrac{4+3\sqrt 5}{4-3\sqrt 5}\\\\\\=\dfrac{\left(4+3\sqrt 5 \right)\left(4+3\sqrt 5 \right)}{\left(4-3\sqrt 5 \right)\left(4+3\sqrt 5 \right)} \\\\\\=\dfrac{\left(4+3\sqrt 5 \right)^2}{4^2 - \left( 3 \sqrt 5 \right)^2}\\\\\\=\dfrac{4^2 + 2\cdot 4 \cdot 3\sqrt 5 + \left( 3\sqrt 5 \right)^2}{16-9\cdot 5}\\\\\\=\dfrac{16+24\sqrt 5 + 45}{16-45}\\\\\\=\dfrac{61+24\sqrt5}{-29}\\\\\\=-\dfrac{61}{29}-\dfrac{24}{29}\sqrt 5\\\\\\=-\left(\dfrac{61}{29}\right) + \left(- \dfrac{24}{29} \right) \sqrt 5[/tex]
[tex]\text{It is now in a form of}~ a+b\sqrt 5~, \text{where}\\ \\a=-\dfrac{61}{29}~~ \text{and}~~ b =- \dfrac{24}{29}[/tex]
You decide that you will only sell two different types of frozen treats in your
ice-cream cart. You use the following criteria to help you make your decision:
• You will purchase 550 frozen treats for your cart.
• You have a budget of $450.
• Your goal is to make a profit of at least $700.
Which two frozen treats will you sell in your ice-cream cart, and how many of
each treat will you purchase? Show that your combination of frozen treats
meets the criteria.
Based on the given scenario above, the purchase decision will be I will chose Ice cream bar fruit and frozen bar fruit.
What is Purchase decision?This is know to be the thought method or act that helps a consumer to identify a need, gather options, and choosing a given product and brand.
Note that Based on the given scenario above, the purchase decision will be I will chose Ice cream bar fruit and frozen bar fruit.
If I am to purchase 550 frozen treats, I will buy:
Ice cream bar fruit = 300
Frozen bar fruit = 250
Therefore, for Ice cream bar fruit , it will be = amount x cost price
300 x 0.85 = 255
For Frozen bar fruit = 250 x 0.50
= 125
Add up the total cost= 255 + 125
Total amount spent will be= 380
Therefore we can see that the total price spent falls within the budget allocated and so I will choose both Ice cream bar fruit and frozen bar fruit.
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can someone help me here
NONSENSE=REPORT
topic: Circles and its Concept
Answer:
Step-by-step explanation:
Circumference of a circle: 2πrArea of a circle: πr²π = 3.14r (radius) = d/21. Circumference: 2(3.14)(4.2) = 26.38 in.
Area: πr² = 3.14(4.2)² = 55.39 in.²
2. Circumference: 2(3.14)(1) = 6.28 m.
Area: πr² = 3.14(1)² = 3.14 m.²
Hope this helps!
what is 4x^2 -40-120 is equivalent to
Answer:
Step-by-step explanation:
4x^2-40-120
4x^2-160
4x^2=160
x^2=40
sqrt40=6.32
Pls find equation of parabola
Answer:
y = - 3x² + 6x + 9
Step-by-step explanation:
given the zeros of a parabola x = a , x = b , then the factors are
(x - a) , (x - b)
here the zeros are x = - 1 and x = 3 , then
factors are (x + 1) and (x - 3)
the equation of the parabola is then the product of the factors, that is
y = a(x + 1)(x - 3) ← a is a multiplier
to find a substitute the point (0, 9 ) into the equation
9 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )
- 3 = a
then equation is
y = - 3(x + 1)(x - 3) ← expand factors using FOIL
= - 3(x² - 2x - 3) ← distribute parenthesis by - 3
y = - 3x² + 6x + 9
Which of the following expressions is true?
2^4•2^4>2^7
3^2•3^6=3^7
4^3•4^5<4^8
5^2•5^3=5^6
Answer:
2^4•2^4>2^7
Step-by-step explanation:
Hope it helps you in your learning process.
2. Every morning, Desiree walks around her pool to get some morning exercise. She doesn't remember
the width of the pool, but she knows that the length of the pool is three less than twice the width.
Her father tells her that when he built the border of the pool, it had a perimeter of 48 feet. What is
the width of the pool?
José tiene una tabla de: (x² -4x + 4) cm de largo y (x+4) cm de ancho ¿Cuál es el área de la tabla?
Answer:
x³ - 12x + 16
Step-by-step explanation:
(x² -4x + 4) × (x+4) =
= x³ + 4x² - 4x² - 16x + 4x + 16
= x³ - 12x + 16
Graph and label each figure and it’s image under the given translation. Give the coordinates of the image.
Answer:
New coordinates:
A'(-3, 3)
B'(4, -1)
C'(-2, 0)
Step-by-step explanation:
It tells you (x-3, y-4), which means you have to subtract 3 from every x coordinate, and 4 from every y coordinate.
Hope this helps <3
Answer:
See below ~
Step-by-step explanation:
New coordinates
A' = (0 - 3, 7 - 4) = (-3, 3)B' = (7 - 3, 3 - 4) = (4, -1)C' = (1 - 3, 4 - 4) = (-2, 0)If the hypotenuse of the triangle below is 8√2, what is the leg?
Answer:
8
Step-by-step explanation:
The side lengths of this special right triangle is as follows:
The side length that sees angle measure 90 (hypotenuse) is represented with x[tex]\sqrt{2}[/tex]
and
the side length that sees angle measures 45 (the legs) is represented with x
hypotenuse is given as 8[tex]\sqrt{2}[/tex] so we can easily find the value of x and legs in this case
x = 8
If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____.
Using the z-distribution, the confidence coefficient for the 90% confidence interval is of 1.645.
What is the critical value for a 90% confidence interval?In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.95[/tex], and the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
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35-40 evaluate the integral by interpreting it in terms of areas.
39. [tex]\int_{-4}^{3}\left|\frac{1}{2} x\right| d x[/tex]
The value of the definite integral corresponds to the total area of two triangles (see attached plot).
[tex]\displaystyle \int_{-4}^3 \left|\frac x2\right| \, dx = \dfrac12 \times 2 \times 4 + \dfrac12 \times 3 \times \dfrac32 = \boxed{\frac{25}4}[/tex]
A cooler is filled with different juices. There are 6 bottles of juice:
1 orange juice, 2 apple juice, 2 cranberry juice, and 1 grape juice.
What is the probability of randomly choosing 1 orange juice and then 1 apple juice
without replacing the first juice?
Answer:
1/15
Step-by-step explanation:
Total = 6 bottles
1 orange and apple
Without replacement:
P(orange and apple) = 1/6 x 1/5 = 1/15
Answer: Probability = 1/15
which expression is equivalent to 2^2 x 2/24
a. 2^-2
b.2^-1
c.2^6
d.2^7
Answer:
noneStep-by-step explanation:
which expression is equivalent to 2^2 x 2/24
a. 2^-2
b.2^-1
c.2^6
d.2^7
2^2 * 2/24 =
4 * 2/24 =
4 * 1/12 =
1/3
then
1/3 = 0.33
find equivalent
a) 2^-2 = 0.25
b) 2^-1 = 0.5
c) 2^6 = 64
d) 2^7 = 128
Find the volume of this triangular prism. Be sure to include the correct unit in your answer. 7m 5m 9m? Thank u!!