Determine which statement is true about the graph of a function
Find the values of x on the curve y = cos x 2 + sin x at which the tangent is horizontal. (let n be an integer. enter your answers as a comma-separated list.)
To find the values of x on the given curve at which the tangent is horizontal, we need to find the points where the derivative of y with respect to x is equal to 0.
Explanation:To find the values of x on the curve y = cos x^2 + sin x at which the tangent is horizontal, we need to find the points where the derivative of y with respect to x is equal to 0. The derivative of y is -2x sin x + cos x.
Setting the derivative equal to 0, we have -2x sin x + cos x = 0. Solving this equation will give us the values of x at which the tangent is horizontal.
Unfortunately, it is not possible to find exact solutions to this equation analytically. We can, however, solve it numerically using methods such as Newton's method or the bisection method.
Find the area of the region bounded by the given curves. y = 9x2 ln(x), y = 36 ln(x)
The area of the region bounded by y = 9x2 ln(x) and y = 36 ln(x) is found by integrating the absolute difference of the two functions from x = 1 to x = 2, which yields ∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx.
Explanation:To find the area of the region bounded by the curves y = 9x2 ln(x) and y = 36 ln(x), you first need to find the points where they intersect. This means setting the two functions equal to each other and solving for x, i.e., 9x2 ln(x) = 36 ln(x).
This simplifies to x2 = 4 which yields two solutions x = 2 and x = -2. However, since the natural logarithm ln(x) is not defined for x < 0, we discard x = -2. So, the two curves intersect at x = 2.
The area between the curves from x = 1 to x = 2 is then obtained by integrating the absolute difference of the two functions from x = 1 to x = 2, which gives:
∫ from 1 to 2 (|36 ln(x) - 9x2 ln(x)|) dx. You can evaluate this integral with standard calculus techniques.
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rewrite vertically,then add
63,594+98,697+59,835
beth has a total of $6000 to invest, part at 6% simple interest and part at 8% simple interest. Her return for one year is $410. How much did she invest at each rate?
A square acre of land is 4840 square yards. Between which two integers is the length of one side? Pls show the steps or work.
Please help quickly first to answer gets bainliest
Which expression uses the greatest common factor and the distributive property to rewrite the sum 32 + 80?
A.16(2) + 80
B. 2(16 + 80)
C.16(2 + 5)
D.8(4 + 10)
Can somebody solve please?
The temperature changed from 5C at 6 p.m. to -2C at midnight. How much did the temperature decrease?
from 5 to 0 is a 5 degree change
then from 0 to -2 is a 2 degree change
5+2 = 7 degree change overall
Is (1,5) a solution to the equation y=x-2
Misty took a multiple choice test in science that had 50 questions. If the relationship between the number she got correct and the number she got incorrect is 7:3, and she got 9 incorrect, how many did she get correct?
The expression 4.95+0.07x models A household monthly long distance charges where x represents the number of minutes of long-distance calls during the month what are the monthly charges for each number of long distance minutes
The expression provided models the monthly long distance telephone charges, with a fixed fee of $4.95 plus $0.07 per minute of call time. To determine the monthly charge, multiply the number of minutes by $0.07 and add the result to the base charge of $4.95.
The given expression 4.95 + 0.07x represents a model for calculating a household's monthly long distance telephone charges, where x is the number of minutes of long-distance calls. To find the monthly charges for any number of minutes (x), we simply plug in the value of x and calculate the total cost.
If a household uses 0 minutes, the cost would be $4.95 (since 4.95 + 0.07(0) = 4.95).For 100 minutes of use, the cost would be $4.95 + (0.07 x 100) = $4.95 + $7.00 = $11.95.The formula incorporates a fixed fee of $4.95, which we can see as the base charge regardless of usage, plus a variable component that depends on the number of minutes used (0.07 times the number of minutes).
a diver is swimming 11 meters below the surface. The diver sees a shark 19 meters below him. how many meters from the surface is the shark?
A container holds 7 quarts of water. How much is this in gallons? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
In this problem, y = 1/(1 + c1e−x) is a one-parameter family of solutions of the first-order de y' = y − y2. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y(0) = − 1 8
Ruben bought six new books for his collection. This increased his collection by 12%. How many books did he have before his purchases?
20. Let x represent the amount of books he had:
x + 6 = 1.12x
Subtract x from both sides:
6 = 0.12x
Divide both sides by 0.12; x = 50
28. $6 + 0.025*$6 = $6 + $0.15 = $6.15
A store manager orders T-shirts so that 15 out of every 35 are a medium. How many medium T shirts would you expect to find when there are 126 T shirts on a rack
Solve for x: 2|2x − 2| + 4 = 20.
x = 5, x = −3
x = 5, x = −5
x = 3, x = −3
x = −5, x = 3
Mr. Abernathy bought a selection of wrenches for his shop and paid $78. He bought the same number of $1.50 and $2.50 wrenches, and half of that number of $4 wrenches. The number of $3 wrenches is one more than the number of $4 wrenches. How many of each did he buy?
In this algebraic word problem, equations were set up based on the prices and relationships between the numbers of wrenches bought, leading to the discovery that Mr. Abernathy purchased 12 wrenches each at $1.50 and $2.50, 6 wrenches at $4, and 7 wrenches at $3 to make a total of $78.
Mr. Abernathy's allocation of his $78 budget on wrenches can be formulated as an algebraic word problem where we define the number of wrenches bought at each price point and the total cost. Let us denote x as the number of $1.50 wrenches and also the number of $2.50 wrenches, so the number of $4 wrenches is x/2 since it is half of that number.
The number of $3 wrenches is x/2 + 1 because it is one more than the number of $4 wrenches. The total amount spent can be expressed as the sum of the products of the numbers of wrenches and their respective prices, which must equal $78.
The equation for the total amount spent on wrenches is therefore:
1.50x + 2.50x + 4(x/2) + 3(x/2 + 1) = 78
Solving this equation for x gives us the number of $1.50 and $2.50 wrenches, and then we can infer the quantities of the $4 and $3 wrenches.
After simplifying the equation, we solve for x, and by plugging x back into the previous expressions, we find out that Mr. Abernathy bought 12 wrenches at $1.50 each, 12 wrenches at $2.50 each, 6 wrenches at $4 each, and 7 wrenches at $3 each.
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?
Answer:
The slope is -3/2 and contains the point (0, −2). Which is b.
Step-by-step explanation:
(-3,-4) (3, 0)
slope = (0 +4) / (3 + 3) = 4/6 = 2/3
perpendicular so slope = -3/2
line on graph
y = mx + b
0 = 2/3 (3) + b
0 = 2+ b
b = -2
y intercept (0,-2)
A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. if the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours? 95% 68% 34% 99.7%
Approximately 99.7% of the light bulbs are expected to last between 600 and 900 hours, according to the empirical rule of normal distributions, as these values fall within +/- 3 standard deviations from the mean.
To determine what percent of the distribution of light bulbs will have a service life between 600 and 900 hours, we employ the empirical rule for normal distributions. If we know the mean (750 hours) and standard deviation (50 hours), we can calculate the number of standard deviations each of these values are from the mean:
(600 - 750) / 50 = -3 standard deviations (SD)
(900 - 750) / 50 = 3 standard deviations (SD)
According to the empirical rule (68-95-99.7 rule), approximately:
68% of the data falls within "+/- 1 SD"
95% of the data falls within "+/- 2 SD"
99.7% of the data falls within "+/- 3 SD"
Since 600 hours and 900 hours are three standard deviations away from the mean on either side, the percentage of light bulbs expected to last between these two values would be approximately 99.7%.
Write an expression for the following statement(s), and then list each operation
present (make sure you define any variables used).
A record company earns 25% of what a band collects in total sales. That
percentage is deducted from the band’s total sale
State your first and last name. use the letters in your first name and last name to write an equation of a line in slope-intercept form, y=mx + b as follows:
find the unit rate???
Answer:
500 kilobytes/ 1 min
Step-by-step explanation:
2,500 kilobytes/ 5 min
2,500 divide by 5 = 500 kilobytes
500 kilobytes/ 1 min
what is 69.12 rounded to the nearest tenth
Round 9.77 to the nearest tenth
Ed Callahan Is an executive at a local bank his annual salary is $75,530 if he receive a paycheck every two weeks what is his biweekly salary
His annual salary is $75,530. If Ed receives a paycheck every two weeks, his biweekly salary is $2905.
You will be paid every 2 weeks so is beginning on Sunday and ending on the second Saturday of the pay period. So you will be paid every two weeks, giving you a total 26 .
First you divide 75530 by 26 since its biweekly and that is how you get your answer.
how many times larger is the value of the 5 in 95,284 than the value 5 in 8,521
Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value $10.90. How many dimes and how many quarters does she have? [hint: use the decimal values of the c coins to write an equation.]
Rico is estimating 139 x 18 Find his mistake and correct it.
100 x 10 =1,000