The 75th derivative of y = cos(2x) can be found by dividing 75 by 4 to find the cycle it falls into due to the repeating pattern of cos and sin. Due to remainder 3 after division, the 75th derivative is equivalent to the 3rd derivative from the cycle, which is 8sin(2x), but scaled by 2 to the power of the number of completed cycles (18). This gives the final answer 2^18 * 8sin(2x).
Explanation:The process of finding the 75th derivative of a function can seem daunting or time-consuming, but with functions like cosines and sines, we can rely on the cycling pattern of these functions to simplify the task. This will significantly decrease the amount of computational effort needed.
When you find the derivative of y = cos(2x), the function cycles in a pattern every four times. The first derivative of y = cos(2x) is -2sin(2x), the second derivative is -4cos(2x), the third derivative is 8sin(2x), and the fourth derivative is 16cos(2x). As you can see, we've returned to the original function (scaled by a factor of 16).
So to find the 75th derivative, divide 75 by 4 to get remainder of 3. This means the 75th derivative is the same as the 3rd derivative, but scaled by 2 to the power of the number of full cycles (which is 18). Hence, the 75th derivative of y = cos(2x) is 2^18 * 8sin(2x).
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In 1943 the temperature in rapid city South Dakota fell about 45 degrees in 5 minutes what was the average drop in temperature per minute
Answer:-9 degrees
Step-by-step explanation:The average drop in temperature per minute is 9 degrees.
Explain in a minimum of 2 sentences how to graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½.
To graph an absolute value function with a given vertex and 'a' value, first plot the vertex. Then use the 'a' value to find and plot other points. Connect the points to create the graph.
Explanation:To graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½, you first plot the vertex on the graph. This point will be the lowest (if 'a' is positive) or highest (if 'a' is negative) point on the graph. The vertex of the absolute value function is the point of reflection. Next, create a table to find extra points on the graph. Because 'a' is ½, count over 1 and up (or down depending on if 'a' is positive or negative) half the distance. Similarly, count over 2 and up (or down) the distance to find more points. Once you've plotted these points, you'll see the absolute value function starting to take shape. Connect the dots to create the two arms of the absolute value function that point upwards or downwards depending on the value of 'a'. This will result in a 'V' shaped graph if 'a' is positive or an upside-down 'V' shape if 'a' is negative.
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One book costs 95p. How much do five books cost?
HELP QUICK!!! 3. There is a special sale at the pet store. You can buy a fish bowl and get 6 free goldfish. Carlos and Olivia each buy a bowl and get 6 fish. They want to keep track of their fishes’ growth, so they carefully measure each fish and record these lengths:
1 ¼ in
1 7/8in.
1 1/4in.
1 3/4in.
1 3/8 in.
1 7/8 in.
1 3/8 in.
1 1/4in.
1 4/8in.
1 6/8in.
1 7/8in.
1 3/4in.
(a) Plot the lengths of each of the 12 goldfish on the line plot.
(b) Which is greater: the amount of fish that measure less than 1 1/2 inches in length or the amount of fish with a length greater than 1 1/2 inches?
for a, make a dot on the line plot at each of the given lengths
b) there are more fishes greater than 1 1/2
A bag contains 450 blue and yellow marbles. The probability of drawing a yellow marble is 46%. How many blue marbles are in the bag?
1 _______=5,280 feet
"isotherms are drawn at regular intervals; on this map, the interval between successive isotherms is ______ fahrenheit degrees."
An isotherm on a geographic map is a type of equal temperature at a given date or time. And if we talk about thermodynamics, it is a curve on a Pressure – Volume diagram at a constant temperature.
Basing from the graph, we can actually see that the interval is:
10 Fahrenheit degrees
Please help! (Picture included)
may i please have some help?
A grocery store's receipts show that sunday customer purchases have a skewed distribution with a mean of $3030 and a standard deviation of $2121. suppose the store had 304304 customers this sunday. a) estimate the probability that the store's revenues were at least $9 comma 6009,600. b) if, on a typical sunday, the store serves 304304 customers, how much does the store take in on the worst 11% of such days?
a) The probability is approximately 0.9973.
b) The store takes in at most [tex]$\$ 15,600.00$[/tex].
a) To estimate the probability that the store's revenues were at least [tex]$\$9,500$[/tex], we need to find the z-score corresponding to this revenue value and then find the probability associated with that z-score in the standard normal distribution.
First, we calculate the z-score:
[tex]\[ z = \frac{X - \mu}{\sigma} = \frac{9500 - 3200}{2000} = \frac{6300}{2000} = 3.15 \][/tex]
Using a standard normal distribution table or a calculator, we find that the probability corresponding to [tex]$z = 3.15$[/tex] is approximately 0.9987.
So, the estimated probability that the store's revenues were at least [tex]$\$9,500$[/tex] is approximately 0.9987.
b) To find out how much the store takes in on the worst [tex]$10\%$[/tex] of such days, we need to find the revenue value corresponding to the [tex]$90\%$[/tex] percentile of the distribution.
Using the standard normal distribution table or a calculator, we find that the [tex]$90\%$[/tex] percentile corresponds to a z-score of approximately 1.28.
Now, we can find the revenue value:
[tex]\[ X = \mu + z \times \sigma = 3200 + 1.28 \times 2000 = 3200 + 2560 = 5760 \][/tex]
So, on the worst [tex]$10\%$[/tex] of such days, the store takes in at most [tex]$\$5,760.00$[/tex].
The correct question is:
A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of [tex]$\$ 32$[/tex] and a standard deviation of [tex]$\$ 20$[/tex]. Suppose the store had 294 customers this Sunday.
a) Estimate the probability that the store's revenues were at least [tex]$\$ 9,500$[/tex].
b) If, on a typical Sunday, the store serves 294 customers, how much does the store take in on the worst [tex]$10 \%$[/tex] of such days?
a) The probability is [tex]$\square$[/tex].
b) The store takes in at most [tex]$\$ \square$[/tex].
a right triangle has one angle that measures 23 degress.The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.What is the approximate area of the triangle?Round to the nearest tenth.Area of a triangle =1/2bh
Answer:
Area of the triangle will be 162.3 cm²
Step-by-step explanation:
From the figure attached,
In the triangle ABC angle ACB = 23°, side BC = 27.6 cm and hypotenuse AC = 30 cm
Now we have to calculate the area of the given right angle triangle.
Since area of a right angle triangle is represented by
Area = [tex]\frac{1}{2}\times b\times h[/tex]
Where b = adjacent side
h = opposite side
To calculate the opposite side of the triangle we will apply Pythagoras theorem in the ΔABC.
AC² = AB² + BC²
AB² = AC² - BC²
AB² = (30)² - (27.6)²
= 900 - 761.76
= 138.24
AB = √138.24
= 11.76
Area of the triangle = [tex]\frac{1}{2}(AB)(BC)[/tex]
= [tex]\frac{1}{2}(11.76)(27.6)[/tex]
= 162.28 cm² ≈ 162.3 cm²
Can someone help me with 2 and 4
Which value of b will cause the quadratic equation x2 + bx + 5 = 0 to have two real number solutions?
The Correct Answer is A:-5 :)
I HAVE 2 QUESTIONS:
1. if y = x^2 - x find the value of y when x = 3
2. if y = x^3 + x find the value of y when x = 5
After a concert for 1,200 people, only 9 people said they would not go to see the band again. What percent of the people who went to the concert said they would not go to see the band again? 0.75% 9% 75% 133%
divide 9 by 1200
9 / 1200 = 0.0075 = 0.75%
The isosceles triangle has a perimeter of 7.5m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
Answer:
2.1 +2x=7.5
Step-by-step explanation:
Bob has a dog who weighs 12 pounds. His cat weighs 2/3 as much as the dog. How many pounds does his cat weigh?
You take a trip by air that involves three independent flights. if there is an 76% chance each specific leg of the trip is on time, what is the probability all three flights arrive on time?
A rectangular table is 4 times as long as it is wide. If the area is 100ft^2, find the width and length of the table.
Nine fewer than half a number is a five more than a four times the number.define a varible, write an equation, and slove to find the number
0.5x-9 = 4x+5
add 9 to both sides
0.5x = 4x+14
subtract 4x from each side
-3.5x =14
x = 14/*3.5
x = -4
find the sum of all 3 digit whole numbers that arw divisible by 13 ?
The sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].
To find the sum of all 3-digit whole numbers that are divisible by 13, we can use the arithmetic series formula.
1. Identify the first and last 3-digit numbers divisible by 13:
- The smallest 3-digit number divisible by 13 is 104 (since [tex]\( 13 \times 8 = 104 \)[/tex]).
- The largest 3-digit number divisible by 13 is 988 (since [tex]\( 13 \times 76 = 988 \)[/tex]).
2. Calculate the number of terms in the series:
- Use the formula for the number of terms n in an arithmetic sequence:
[tex]\[ n = \frac{\text{last term} - \text{first term}}{\text{common difference}} + 1 \][/tex]
Here, the common difference d = 13:
[tex]\[ n = \frac{988 - 104}{13} + 1 = \frac{884}{13} + 1 = 68 + 1 = 69 \][/tex]
3. Find the sum of the arithmetic series:
- The sum [tex]\( S_n \)[/tex] of the first n terms of an arithmetic series is given by:
[tex]\[ S_n = \frac{n}{2} \times (\text{first term} + \text{last term}) \][/tex]
Substitute the values:
[tex]\[ S_{69} = \frac{69}{2} \times (104 + 988) \][/tex]
Simplify the calculation:
[tex]\[ S_{69} = \frac{69}{2} \times 1092 = 34.5 \times 1092 = 37674 \][/tex]
Thus, the sum of all 3-digit whole numbers that are divisible by 13 is [tex]\( \boxed{37674} \)[/tex].
The mean height of a group of students is 65.4 inches. A student joins the group who is 73 inches tall. How does this student’s height affect the mean?
A. The new mean height will still be 64.5 inches.
B. The new mean height will be greater than 65.4 inches.
C. The new mean height will be less than 65.4 inches.
D. The new mean height will be 73 inches.
Answer:
The new mean height will be greater than 65.4 inches.
Step-by-step explanation:
The mean height of a group of students is 65.4 inches. A student joins the group who is 73 inches tall.
Mean is 65.4 inches
A student joins the group who is 73 inches tall.
73 is greater than the means 64.4 inches
So mean will increase definitely
Mean will vary depends on the total number of students
The new mean height will be greater than 65.4 inches.
The length of the base of a rectangle is 6 less than 3 times the width. The perimeter of the rectangle is 52 inches. What is the length of the base?
Rearrange the formula A = \pi r ^ ( 2) for r
the ratio of girls to boys in the math club was 3.5. if there were 120 children altogether, how many girls were there?
3 girls to 5 boys
3+5 =8
120/8 = 15
3 *15 = 45 girls
What is the Measure Of arc WX in the diagram below?
Answer:
The correct option is A.
Step-by-step explanation:
Given information: Length of Arc TR is 116° and the measure of ∠WSX is 45°.
According to the angle of Intersecting Secants Theorem,
[tex]\text{Angle of Intersecting Secants}=\frac{1}{2}(\text{Major arc - Minor arc})[/tex]
Using this property we get
[tex]45^{\circ}=\frac{1}{2}(Arc(TR)-Arc(WX))[/tex]
[tex]45^{\circ}=\frac{1}{2}(116^{\circ}-Arc(WX))[/tex]
Multiply 2 on both the sides.
[tex]90^{\circ}=116^{\circ}-Arc(WX)[/tex]
[tex]Arc(WX)=116^{\circ}-90^{\circ}[/tex]
[tex]Arc(WX)=26^{\circ}[/tex]
The measure of arc WX is 26°. Therefore the correct option is A.
Pascal wants to find the sum of the measures of the interior angles of a polygon that has n sides. How could he do this?
Answer with explanation:
Smallest Polygon = Triangle , which has 3 sides
Sum of angles of triangle = 180°→→, Using the angle sum property of triangle.
We can find the Sum of angles of triangle, using the formula
= (n-2)×180°
= (3-2)×180°
= 1 × 180°
= 180°
A Quadrilateral has four sides.
Sum of angles of Quadrilateral = 360°
Or , using the formula
=(4-2)×180°
=2 × 180°
=360°
For, n sided Polygon
Sum of it's Interior angles = (n-2) × 180°
To prove this, we should divide that polygon into triangles, and multiply number of triangles by angle of 180°.
For, example, Quadrilateral can be divided into two triangles , sum of interior angles of Quadrilateral =2 × 180°=360°
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of drinks she needs to sell to earn $100.
1.25x + 1.49 = 100
What error did Barbara make in writing the equation?
Heather purchased an iPad mini on sale 20% off for 263.20 what's the original price of the iPad mini
Gina works at a diner. Earns $6.00 hour + $43.00 tips how much does she make all together?