Since f''(x) is always 0, f(x) is not concave upward on any interval.
On what interval is f concave upward?
The first derivative of f(x) is f'(x) = 6.
The second derivative of f(x) is f''(x) = 0.
The interval on which f(x) is increasing is when f'(x) > 0, which is when x is in the interval (-2,-5) U (1,60).
The interval on which f(x) is decreasing is when f'(x) < 0, which is when x is in the interval (-5,1).
The interval on which f(x) is concave downward is when f''(x) < 0, which is all values of x.
The interval on which f(x) is concave upward is when f''(x) > 0, which is no values of x.
To find the first derivative of f(x), we need to take the derivative of each term separately. The derivative of 3 is 0, the derivative of 6x is 6, and the derivative of -153 +3.2 is 0. Adding these up gives us f'(x) = 6.
To find the second derivative of f(x), we need to take the derivative of f'(x), which is a constant function. The derivative of a constant function is always 0, so f''(x) = 0.
To determine where f(x) is increasing, we need to find the values of x where f'(x) > 0. Since f'(x) is a constant function, it is always positive, so f(x) is increasing on the interval (-2,-5) U (1,60).
To determine where f(x) is decreasing, we need to find the values of x where f'(x) < 0. Since f'(x) is a constant function, it is always positive, so f(x) is decreasing on the interval (-5,1).
To determine where f(x) is concave downward, we need to find the values of x where f''(x) < 0. Since f''(x) is always 0, f(x) is concave downward on all values of x.
To determine where f(x) is concave upward, we need to find the values of x where f''(x) > 0. Since f''(x) is always 0, f(x) is not concave upward on any interval.
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The short leg of a triangle measures 17 and the long leg measures 32. What is the measure of the smaller acute angle of the triangle to the nearest tenth of a degree ? Draw a triangle to represent the problem. Be sure to show the trig equation you used when solving
The measure of the smaller acute angle of the triangle to the nearest tenth of a degree is 28.3 degrees.
Let's denote the smaller acute angle of the triangle as θ. We can use the tangent function to find the measure of this angle:
tan(θ) = opposite/adjacent
In this case, the opposite side is the length of the short leg (17) and the adjacent side is the length of the long leg (32). So we have:
tan(θ) = 17/32
Using a calculator, we can take the inverse tangent (tan^-1) of both sides to solve for θ:
θ = tan^-1(17/32) ≈ 28.3 degrees
So the measure of the smaller acute angle of the triangle is approximately 28.3 degrees.
Here's a diagram to illustrate the triangle:
/ l
/ l
17 / l opposite
/ l
/ θ l
/_______l
adjacent
32
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if the circumference is 24 inches what is the radius
Answer:
3.819inch
Step-by-step explanation:
Circumference(C)=24inch
radius(R)=?
Now,
C=2piR
24=2piR
12=piR
12/pi=R
R=3.819
Pls help immediately, and explain…
I did not do it correct pls help
Answer: x=20 y=43
Step-by-step explanation:
That little symbol in <1 means that the angle is a right angle, which is = to 90° so
<1 = 90°
133-y = 90 solve for y by subtracting 133 from both sides
-y = -43 divide by -1 on both sides
y=43
Because all 3 angles make a line, which is 180, and you know <1 = 90 then <2+<3=90 as well.
<2+<3=90
22 + x + 48 =90 simplify
70 + x =90 subtract 70 from both sides
x=20
If sin a = -4/5
and sec B =5/3
for a third-quadrant angle a and a first-quadrant angle Ã, find the following
(a)
sin(a + B)
(b)
tan(a + b)
(c) the quadrant containing a + B
O Quadrant I
O Quadrant II
O Quadrant III
O Quadrant IV
Since sin(a) is negative and a is in the third quadrant, we can use the Pythagorean identity to find cos(a):
[tex]cos^2(a) + sin^2(a) = 1[/tex]
[tex]cos^2(a) + (-4/5)^2 = 1[/tex]
[tex]cos^2(a) = 9/25[/tex]
cos(a) = -3/5 (since a is in the third quadrant)
Similarly, since sec(B) = 5/3, we can use the definition of secant to find cos(B):
sec(B) = 1/cos(B) = 5/3
cos(B) = 3/5
(a) To find sin(a + B), we can use the sum formula for sine:
sin(a + B) = sin(a) cos(B) + cos(a) sin(B)
= (-4/5)(3/5) + (-3/5)(4/5)
= -12/25 - 12/25
= -24/25
(b) To find tan(a + B), we can use the sum formula for tangent:
tan(a + B) = (tan(a) + tan(B)) / (1 - tan(a) tan(B))
To find tan(a), we can use the identity: [tex]tan^2(a) + 1 = sec^2(a)[/tex]
[tex]tan^2(a) = sec^2(a) - 1 = (5/3)^2 - 1 = 16/9[/tex]
tan(a) = -4/3 (since a is in the third quadrant)
To find tan(B), we can use the identity: tan(B) = sin(B) / cos(B) = 4/3
Plugging these values into the formula for tan(a + B), we get:
tan(a + B) = (-4/3 + 4/3) / (1 + (-4/3)(4/3))
= 0 / (1 - 16/9)
= 0
(c) To determine the quadrant containing a + B, we need to consider the signs of sin(a + B) and cos(a + B).
From part (a), we know that sin(a + B) is negative. To determine the sign of cos(a + B), we can use the Pythagorean identity:
[tex]sin^2(a + B) + cos^2(a + B) = 1[/tex]
Substituting sin(a + B) = -24/25, we get:
[tex](-24/25)^2 + cos^2(a + B) = 1[/tex]
[tex]cos^2(a + B) = 1 - (-24/25)^2[/tex]
cos(a + B) = ±7/25
Since cos(a + B) is positive in the first and fourth quadrants, and negative in the second and third quadrants, we can conclude that a + B is in the third quadrant, since cos(a + B) is negative and sin(a + B) is negative.
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h(x)=|2x|-8 domain and range
For the function "h(x) = |2x| - 8", the domain is (-∞, ∞) and the range is [-8, ∞).
The function h(x) = |2x| - 8 is defined for all real numbers x, so the domain of h(x) is the set of all real-numbers, or (-∞, ∞).
To find the range of the function, we determine set of all possible output values of function. Since the function involves the absolute value of 2x, the output can never be less than -8.
When "2x" is positive, |2x| = 2x. When 2x is negative, |2x| = -2x. This means that the function h(x) will have two branches depending on whether 2x is positive or negative.
⇒ When 2x is positive, h(x) = |2x| - 8 = 2x - 8. This branch of the function will have all non-negative values.
⇒ When 2x is negative, h(x) = |2x| - 8 = -2x - 8. This branch of the function will have all non-positive values.
Combining the two , we get the range of the function h(x) as [-8, ∞).
Therefore, the domain of h(x) is (-∞, ∞) and the range of h(x) is [-8, ∞).
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Mrs vilakazi is a retired consumer studies educator .she owns a small business of selling different types of cakes including scones.the cost price for ingredients plus water and electricity is r0,53 per scone .she sells scones at r2 ,00 each . calculate the profit mrs vilakazi will make if she bakes 204 scones and sells 171.
Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.
The profit is the difference between the total revenue and the total cost.
The total cost is the cost per scone multiplied by the number of scones baked:
total cost = r0,53/scone × 204 scones = r108,12
The total revenue is the selling price per scone multiplied by the number of scones sold:
total revenue = r2,00/scone × 171 scones = r342,00
Therefore, the profit is:
profit = total revenue - total cost
profit = r342,00 - r108,12
profit = r233,88
Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.
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Below is a table of hourly wages for receptionists working for various companies. What is the average wage for receptionists in this group? $9.67 $11.15 $11.60 $12.15 $14.50
The average wage for receptionists in this group is $11.60
How to calculate the average wageIt's important to note that "average wage" can be calculated in a few different ways, such as mean, median, and mode. Mean is the sum of all wages divided by the number of individuals, while median is the middle value in a range of wages. Depending on which method is used, the average wage figure can vary.
The table of hourly wages for receptionists working for various companies, the average wage for receptionists in this group will be:
= $58 / 5
= $11.60
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The area of a circular pizza is 2122.64 square centimeters. What is the diameter of the pizza?
Area of a circle = pi x r^2
---For the purposes of this problem, pi = 3.14
2122.64 = (3.14)(r^2)
676 = r^2
r = 26 cm
Diameter = 2 x radius
diameter = 2 x 26
diameter = 54 cm
Answer: diameter = 54 cm
Hope this helps!
Select the correct answer.
given a prism with a right triangle base and the dimensions h = x + 1, b = x, l = x + 7, and what is a correct expression for the volume of the prism?
The correct expression for the volume of the prism is:
V = (1/2)(x)(x + 7)(x + 1)
This expression is derived from the formula for the volume of a prism, which is V = Bh, where B is the area of the base and h is the height of the prism. For a right triangle base, the area is equal to half the product of the base and height, or (1/2)(b)(l). Substituting the given values, we get:
B = (1/2)(x)(x + 7)
h = x + 1
Multiplying B and h together and simplifying, we get:
V = (1/2)(x)(x + 7)(x + 1)
Therefore, this is the correct expression for the volume of the given prism.
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What is the probability that
both events will occur?
Two dice are tossed.
Event A: The first die is a 1 or 2
Event B: The second die is 4 or less
P(A and B) = P(A) • P(B)
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
The probability that both events will occur is 0.22.
How to calculate the probability?To work out the probability that both events occur, first, we shall calculate the probability of each event and then apply the multiplication operation on both.
Since there are 2 ways to get a 1 or 2 out of the 6 possible outcomes for a single roll of die, the probability of rolling a 1 or 2 on the first die = 2/6, or 1/3,
And the probability of rolling a 4 or less on the second die = 4/6, or 2/3, as 4 ways to get a number 4 or less from the 6 possible outcomes for single roll of die.
We would multiply the probabilities to find the probability of both events:
P(A and B) = P(A) * P(B) = (1/3) * (2/3) = 2/9 = 0.2222.
Therefore, the probability that both events A and B occur = 0.22 (rounded to the nearest hundredth).
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Question 1 4 pts 1 Details Suppose that the position of a particle is given by 8 = f(t) = 56° +61 +9. (a) Find the velocity at time t. m2 v(t) = 8 (b) Find the velocity at time t = 3 seconds. m (c) Find the acceleration at time t. a(t) = m 32 (d) Find the acceleration at time t = 3 seconds. m/s^2
The velocity at time t is 56 + 6 m/s, the velocity at time t = 3 seconds is 62 m/s, the acceleration at time t is 0 m/s², and the acceleration at time t = 3 seconds is 0 m/s².
Hi, I can help you with your question involving acceleration, time, and a particle.
(a) To find the velocity at time t (v(t)), take the first derivative of the position function f(t) = 56t + 6t + 9.
v(t) = d(56t + 6t + 9)/dt = 56 + 6
(b) To find the velocity at time t = 3 seconds, plug in t = 3 into the velocity function:
v(3) = 56 + 6 = 62 m/s
(c) To find the acceleration at time t (a(t)), take the first derivative of the velocity function v(t) = 56 + 6:
a(t) = d(56 + 6)/dt = 0
(d) To find the acceleration at time t = 3 seconds, since the acceleration is constant (a(t) = 0), it remains the same for all time:
a(3) = 0 m/s²
So, the velocity at time t is 56 + 6 m/s, the velocity at time t = 3 seconds is 62 m/s, the acceleration at time t is 0 m/s², and the acceleration at time t = 3 seconds is 0 m/s².
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Problem 3: enter the value of c when the expression 12.2x + c is
equivalent to 6.1(2x - 3.4).
The value of c that makes the two expressions equivalent is -20.74.
Let's start by simplifying the expression 6.1(2x - 3.4). To do this, we use the distributive property of multiplication, which states that a(b + c) = ab + ac. Applying this to our expression, we get:
6.1(2x - 3.4) = 6.1(2x) - 6.1(3.4) = 12.2x - 20.74
Now we can rewrite the equation we want to solve as:
12.2x + c = 12.2x - 20.74
To solve for c, we need to isolate it on one side of the equation. We can do this by subtracting 12.2x from both sides:
c = -20.74
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12. reasoning a rectangular piece of cardboard with dimensions 5 inches
by 8 inches is used to make the curved side of a cylinder-shaped
container. using this cardboard, what is the greatest volume the cylinder
can hold? explain.
answer asap
If a rectangular piece of cardboard with dimensions 5 inches by 8 inches is used to make the curved side of a cylinder-shaped container, the greatest volume the cylinder can hold is 80/π cubic inches.
To find the greatest volume the cylinder can hold, we need to determine the dimensions of the cylinder that can be made from the given cardboard.
First, we need to calculate the circumference of the cylinder using the length of the cardboard, which will be the height of the cylinder. The length of the cardboard is 8 inches, so the circumference of the cylinder will be 8 inches.
The circumference of a cylinder is given by the formula C = 2πr, where r is the radius of the cylinder.
Therefore, 8 = 2πr, or r = 4/π inches.
Next, we need to determine the length of the curved side of the cylinder, which is given by the formula L = 2πr.
So, L = 2π(4/π) = 8 inches.
Finally, we can calculate the volume of the cylinder using the formula V = πr²h, where h is the height of the cylinder, which is 5 inches.
V = π(4/π)²(5) = 80/π cubic inches.
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Question 3 of 10
What property does the equation show?
32 19
14
56
1 3
+
=
A. The associative property
B. The commutative property
OC. The distributive property
32 19
14 56
D. The identity property of multiplication
5 8
1 3
+
32
14
19
56
4
7
Answer:
C. The distributive property
WILL GIVE BRAINLIEST
Given the parent function g(x) = log2 x
What is the equation of the function shown
in the graph?
Answer:
To determine the equation of the function shown on the graph, we need to analyze its characteristics. From the graph, we can see that the function passes through the point (2, 0) and has a vertical asymptote at x = 1. This information allows us to conclude that the function is a transformation of the parent function g(x) = log2 x. Specifically, it appears to be a horizontal compression and a vertical translation.
To find the equation of the function, we can start by applying the horizontal compression. Let k be the compression factor, then the function can be written as f(x) = log2(kx). Next, we can apply the vertical translation by adding or subtracting a constant, let h be the vertical shift, then the equation becomes f(x) = log2(kx) + h.
To determine the values of k and h, we can use the point (2, 0) and the fact that the vertical asymptote is at x = 1. Setting k = 1/2 since 2k = 1 (corresponding to a horizontal compression by a factor of 1/2), we can find h by substituting the point (2,0) into the equation and solving for h:
0 = log2(1) + h
h = 0
Therefore, the equation of the function shown on the graph is f(x) = log2(1/2 x), which can also be written as f(x) = log2(x) - 1.
Answer:
log2 (x - 3) - 2
Step-by-step explanation:
When x = 4
log2 of (4 - 3) - 2
= log2 1 - 2
= 0 - 2
So we have the point
(4, -2)
and when x = 7
we have y = log2(7-3) - 2
= log2 4 - 2
= 2-2
= 0
- so we have the poin7 (7,0)
if it's 9:45 am what time would it be in 9 hours?
Answer:
6:45pm
Step-by-step explanation:
Given: The time is currently 9:45am
To find: The time in 9 hours
To do this, we have to add 9 hours to 9:45am.
9:45am+9 hours=
6:45pm
Hope this helps! :)
Escribe a cuáles de las bolsas anteriores corresponde la notación decimal aproximada a tres cifras
6.2 × 10⁴ in decimal notation is simply 62,000.
In scientific notation, a number is expressed as the product of a decimal number between 1 and 10 and a power of 10.
Now, let's talk about converting a number in scientific notation to decimal notation. Decimal notation simply means expressing a number in the standard way, using digits and a decimal point. To convert a number in scientific notation to decimal notation, we just need to evaluate the product of the decimal number and the power of 10.
In the case of 6.2 × 10⁴, the decimal number is 6.2, and the power of 10 is 4. To evaluate the product, we simply move the decimal point in 6.2 four places to the right, since the power of 10 is positive. This gives us:
6.2 × 10⁴ = 62,000
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Complete Question:
Convert to decimal notation: 6.2 × 10⁴
 A customer is comparing the size of oil funnels in a store. The funnels are cone shaped. One funnel has a base with a diameter of 8 in. And a slant height of 12 in. What is the height of the funnel? Round your answer to the nearest hundredth. 
The height of the funnel is 11.31, under the condition that one funnel has a base with a diameter of 8 in. And a slant height of 12 in.
Here we have to apply the Pythagorean theorem to evaluate the height of the funnel. The Pythagorean theorem projects that the square of the hypotenuse (the slant height) is equal to the sum of the squares of the other two sides (the radius and height).
Now, we have a cone that has a base diameter of 8 inches which says that the radius is 4 inches. The slant height is 12 inches. Then the height is
h² + r² = l²
h² + 4² = 12²
h² = 144 - 16
h² = 128
h = √(128)
h ≈ 11.31
Hence, 11.31 inches is the approximate height of the funnel after rounding to the nearest hundredth.
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Jack plus 1/3 pound of birdseed into his birthday. Every time he sells it how many times can jack sell his bird feeder with 4 lb of birdseed
Jack can sell 12 bird feeders with 4 lb of birdseed. We can use Proportion method to calculate this :
Assuming that Jack mixes 1/3 pound of birdseed for each bird feeder, we can find out how many bird feeders he can sell with 4 pounds of birdseed by using a proportion.
Let x be the number of bird feeders Jack can make with 4 pounds of birdseed. We can set up the proportion:
1/3 pounds of birdseed per bird feeder = 4 pounds of birdseed / x bird feeders.
Simplifying this equation, we get:
1/3 = 4/x
To solve for x, we can cross-multiply:
1x = 12
x = 12
Therefore, Jack can make and sell 12 bird feeders with 4 pounds of birdseed.
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Jess has $43 in her bank account. Destiny is negative 21. What's the difference between Jess and Destiny's account?
Answer:
$64
Step-by-step explanation:
This would be the answer because if we figure out what needs to be added to -21 to reach 43 we get 64.
(-21+64 - $43.)
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The equation The equation y=5,520x -1,091 was given for the line of best fit. What does the slope of the line mean in the context of this problem? was given for the line of best fit. What does the slope of the line mean in the context of this problem?
The slope of the line is 5,520 and it means the price of the diamond increases at a rate of 5,520 per diamond's weight.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this situation, it can be modeled by this linear equation:
y = mx + c
y = 5,520x - 1,091
By comparison, we have the following:
Slope, m = 5,520.
y-intercept, c = -1,091.
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Complete Question:
The function described by the equation y =5,520x - 1,091 is a model of the relationship between a diamond's weight and its price. What does the slope of the line mean in the context of this problem?
Which graphs represent functions?
4
←
4
•
4
4 -2
++
Graph A
4
2
2
2
4
4
2 4
Graph C
X
-4
-2
4
-2
2
-2-
4
Graph B
у
4-
2
-2
Graph D
4
4
Find dy/dt at x = – 1 if y = – 2x^2 + 4 and dx/dt = 4. dy/dt =?
Derivative of y w.r.t t is dy/dt = 16 at x = -1.
How to find dy/dt?We need to find dy/dt at x = -1, given y = -2x² + 4 and dx/dt = 4.
Step 1: Differentiate y with respect to x.
Since y = -2x² + 4, we have:
dy/dx = -4x
Step 2: Substitute x = -1 into the dy/dx equation.
When x = -1, we get:
dy/dx = -4(-1) = 4
Step 3: Use the Chain Rule to find dy/dt.
The Chain Rule states that dy/dt = (dy/dx)(dx/dt). We know dy/dx = 4 and dx/dt = 4, so we have:
dy/dt = (4)(4) = 16
Thus, dy/dt = 16 at x = -1.
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Liquid a has a density of 1.2 g/cm'
150 cm of liquid a is mixed with some of liquid b to make liquid c.
liquid c has a mass of 220 g and a density of 1.1 g/cm
find the density of liquid b.
Density of liquid b = 0.4 g/cm³.
How to find the density of liquid B?Density of liquid A = 1.2 g/cm³Volume of liquid A = 150 cm³Mass of liquid C = 220 gDensity of liquid C = 1.1 g/cm³Let the volume of liquid B added be V cm³.
The total volume of the mixture = Volume of A + Volume of B = 150 + V cm³
Using the formula:
Density = Mass/Volume
Density of C = (Mass of C) / (Volume of C)
1.1 = 220 / (150 + V)
Solving for V, we get:
V = 100 cm³
Therefore, the volume of liquid B added is 100 cm³.
The total mass of the mixture = Mass of A + Mass of B = (Density of A x Volume of A) + (Density of B x Volume of B)
220 = (1.2 x 150) + (Density of B x 100)
Solving for Density of B, we get:
Density of B = (220 - 180) / 100 = 0.4 g/cm³
Therefore, the density of liquid B is 0.4 g/cm³.
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THE ANSWER IS NOT 81!!!
The measures of the angles of a triangle are shown in the figure below solve for X
Tina is standing at the bottom of a hill. Matt is standing on the hill so that when Tina's line of sight is
perpendicular to her body, she is looking at Matt's shoes.
a. If Tina's eyes are 5 feet from the ground and 14. 5 feet from Matt's shoes, what is the angle of elevation of
the hill to the nearest degree? Explain.
The angle of elevation of the hill to the nearest degree is 44°.
The angle of elevation is the angle formed between the horizontal and an observer's line of sight to an object that is located above the observer. In this case, Tina is standing at the bottom of the hill and looking up at Matt who is standing on the hill. When Tina's line of sight is perpendicular to her body, she is looking at Matt's shoes.
This means that the line of sight forms a right angle with the ground.
To find the angle of elevation, we can use trigonometry. We know that the opposite side is the height of the hill (from Matt's shoes to the top of the hill), which is not given in the problem. However, we can use the Pythagorean theorem to find it.
Let h be the height of the hill. Then,
h^2 = (14.5)^2 - (5)^2
h^2 = 198.25
h ≈ 14.1 feet
Now, we can use the tangent function to find the angle of elevation.
tan θ = opposite/adjacent = h/14.5
tan θ = 14.1/14.5
θ ≈ 44.2°
Therefore, the angle of elevation of the hill to the nearest degree is 44°. This means that the hill slopes upward at an angle of 44° from the ground, as viewed from Tina's position at the bottom.
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Find f
f’’(θ) = sin (θ) +cos (θ), f(0) = 2, f’(0) = 4
F(θ) =
Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4
To find f, we need to integrate f''(θ) twice.
First, we integrate sin(θ) + cos(θ) with respect to θ to get f'(θ):
f'(θ) = -cos(θ) + sin(θ) + C1
where C1 is the constant of integration.
Next, we integrate f'(θ) with respect to θ to get f(θ):
f(θ) = -sin(θ) - cos(θ) + C1θ + C2
where C2 is the constant of integration.
Using the initial conditions given, we can solve for C1 and C2:
[tex]f(0) = -1 - 1 + C2 = 2[/tex]
C2 = 4
f'(0) = -1 + 0 + C1 = 4
C1 = 5
Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4
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The volume of a large is 210 It is 5 3/5 wide and 3 1/3 high. What is the length of the ?
Answer:
11.86 units
Step-by-step explanation:
Volume = length x width x height
We know that the volume is 210 and the width is 5 3/5 (or 5.6) and the height is 3 1/3 (or 3.33).
Substituting these values into the formula, we get:
210 = length x 5.6 x 3.33
To solve for the length, we can divide both sides of the equation by (5.6 x 3.33):
length = 210 / (5.6 x 3.33)
Simplifying this expression, we get:
length ≈ 11.86
Therefore, the length of the large box is approximately 11.86 units.
find the limit of the sequence \displaystyle a_n = \frac{(\cos n)}{7^n}.
The limit of the sequence a_n is 0. The sequence a_n = (cos n)/[tex]7^n[/tex] oscillates between -1/[tex]7^n[/tex] and 1/[tex]7^n[/tex] since the cosine function is bounded between -1 and 1. Therefore, by the squeeze theorem, the limit of the sequence is 0 as n approaches infinity.
The cosine function oscillates between -1 and 1, so we have:
-1/[tex]7^n[/tex] ≤ cos(n)/7^n ≤ 1/[tex]7^n[/tex]
Dividing each term by [tex]7^n[/tex], we obtain:
-1/[tex]7^n[/tex] ≤ a_n ≤ 1/[tex]7^n[/tex]
By the squeeze theorem, since -1/[tex]7^n[/tex] and 1/[tex]7^n[/tex] both approach zero as n approaches infinity, we have:
lim a_n = 0
Therefore, the limit of the sequence a_n is 0.
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To prove a
triangle is isosceles without the measures of each side , you need to know the?
You can use one of the following properties to prove that a triangle is isosceles without knowing the measure of each side.
How to prove isosceles traiangleAngle-Angle (AA): A triangle is equal if two angles of one triangle meet (equal in measure) two angles of another triangle. For an isosceles triangle, if you can prove that two angles are equal, then the triangle must be an isosceles triangle. This is because two right angles are the defining feature of an isosceles angle, as opposed to two congruent sides.
Base Angles: If the base angles of a triangle are equal (equal in measure), then the triangle is isosceles. This is because in an isosceles triangle, the base angles are always congruent.
Vertex angle bisection: If the vertex angle bisector of a triangle is also a perpendicular bisector of the opposite side (base), then the triangle is isosceles. This is because in an isosceles triangle, the two sides of the vertex angle always bisect the base and are perpendicular.
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