So, the final answer is:
(1/2)(-√(4 - x^2) / x) + C. To evaluate the integral ∫dx / (x^2√(4-x^2)), we will use the trigonometric substitution x = 2sin(θ). This substitution is chosen because it simplifies the expression under the square root, as 4 - x^2 becomes 4 - 4sin^2(θ) which can be factored into 4cos^2(θ).
Now, we need to find dx in terms of dθ. Differentiating x with respect to θ, we get:
dx/dθ = 2cos(θ) => dx = 2cos(θ)dθ
Substituting x = 2sin(θ) and dx = 2cos(θ)dθ into the integral:
∫(2cos(θ)dθ) / ((2sin(θ))^2√(4(1-sin^2(θ))))
= ∫(2cos(θ)dθ) / (4sin^2(θ)√(4cos^2(θ)))
Simplifying the integral, we get:
= (1/2) ∫(cos(θ)dθ) / (sin^2(θ)cos(θ))
= (1/2) ∫dθ / sin^2(θ)
Now, use the identity csc^2(θ) = 1/sin^2(θ) and integrate:
= (1/2) ∫csc^2(θ) dθ
= (1/2)(-cot(θ)) + C
To find cot(θ), we draw a right triangle with the opposite side x, the adjacent side √(4 - x^2), and the hypotenuse 2:
cot(θ) = adjacent / opposite = √(4 - x^2) / x
So, the final answer is:
(1/2)(-√(4 - x^2) / x) + C
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Jessica has 300 cm of matenal. She uses 12. 6 cm to make a nght triangular prism She wants to make a second prism that is a
dilation of the first prism with a scale factor of 3
How much more material does Jessica need in order to make the second prism?
Select from the drop-down menu to correctly complete the statement
cm of material to make the second prism
Jessica needs an additional Choose
To make the second prism, Jessica needs an additional 25.2 cm of material.
To answer your question, since Jessica wants to create a second triangular prism with a scale factor of 3, she will need 3 times the material used for the first prism.
She used 12.6 cm for the first prism, so for the second prism, she would need 12.6 cm × 3 = 37.8 cm of material.
Jessica already has 300 cm of material, so to find out how much more she needs, subtract the amount used for the first prism: 37.8 cm - 12.6 cm = 25.2 cm.
Jessica needs an additional 25.2 cm of material to make the second prism.
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What is the measure of “?”
The part of the figure marked ? is solved to be
113 degrees
How to find the question markThe part of the circle marked by a question mark is solved using the relation as shown below
given angle formed by the tangents = 180 degrees - minor arc GE
information given in the problem includes
given angle formed by the tangents = 67 degrees
minor arc GE = ?
plugging in these values results to
67 degrees = 180 degrees - ?
rearranging the equation
? = 180 degrees - 67
? = 113
hence the required side is 113 degrees
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You have $20 to spend. You go to the store and buy a bouncy ball for an unknown amount of money and then you buy a glider airplane for $3. If you have $15 left over, how much did you spend on the bouncy ball?
Answer: Let's start by subtracting the cost of the glider airplane from the total amount of money you started with:
$20 - $3 = $17
We know that you spent $15 of that $17 on the bouncy ball, since you had $15 left over after buying both items:
$17 - $15 = $2
Therefore, you spent $2 on the bouncy ball.
Answer: $2.
Step-by-step explanation:
Write an appropriate and interesting word for 15000 and 3000.solve it
An appropriate and interesting word for 15,000 is "fifteen thousand," while for 3,000, it is "three thousand."
To solve this question, we need to write the numbers 15,000 and 3,000 as words. To do this, first, we look at the place values of each digit. In 15,000, the "15" is in the thousands place, so we write it as "fifteen thousand." Similarly, in 3,000, the "3" is in the thousands place, so we write it as "three thousand."
By doing this, we have expressed the numbers using their word forms, which helps in understanding and communicating numerical values more effectively, especially in written or spoken contexts. Remember, when writing large numbers as words, we use the place values to guide us in expressing them accurately and understandably.
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The function f(z) = 1 + 6x + 96x^-1 has one local minimum and one local maximum.
This function has a local maximum at x?
The function f(z) = 1 + 6x + 96x^-1 has one local minimum and one local maximum. This function has a local maximum at x. The function f(x) = 1 + 6x + 96x^(-1) has a local maximum at x = -4.
To find the local maximum of the function f(x) = 1 + 6x + 96x^(-1), we first need to find the critical points. We do this by finding the first derivative of the function and setting it equal to zero.
Step 1: Find the derivative of the function
f'(x) = d/dx (1 + 6x + 96x^(-1))
f'(x) = 6 - 96x^(-2)
Step 2: Set the derivative equal to zero and solve for x
6 - 96x^(-2) = 0
Step 3: Solve for x
96x^(-2) = 6
x^(-2) = 6/96
x^(-2) = 1/16
x^2 = 16
x = ±4
Step 4: Determine which of the critical points is a local maximum. To do this, we will examine the second derivative of the function.
f''(x) = d^2/dx^2 (1 + 6x + 96x^(-1))
f''(x) = 192x^(-3)
Now we will evaluate the second derivative at each critical point:
f''(4) = 192(4)^(-3) = 3 > 0, so x = 4 is a local minimum.
f''(-4) = 192(-4)^(-3) = -3 < 0, so x = -4 is a local maximum.
Therefore, the function f(x) = 1 + 6x + 96x^(-1) has a local maximum at x = -4.
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(1 point) Calculate T..T,, and n(u, v) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point. (u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v) = . The tangent plane: = 92
Given points:
(u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v)
the equation of the tangent plane at the point (u, v) = (24, 9) is:-8x + z = -183T
Process of finding equation:
To start, let's find T..T,, which represents the magnitude of the tangent vector at the given point:
T..T, = ||n(u, v)|| = ||n(24, -31, 72)|| = ||<48, -62, 144>|| = sqrt(48^2 + (-62)^2 + 144^2) = sqrt(11668) ≈ 108.03
Next, let's find the normal vector n(u, v) at the given point:
n(u, v) =
where f_u and f_v are the partial derivatives of the surface equation with respect to u and v, respectively.
In this case, we have:
f(u, v) = (24 + 0,u - 40, 8u)
f_u = <0, 1, 8>
f_v = <1, 0, 0>
Therefore, at the point (u, v) = (24, 9), we have:
n(u, v) = <0, 1, 8> x <1, 0, 0> = <-8, 0, 1>
Finally, let's find the equation of the tangent plane at the point (u, v) = (24, 9). The equation of a plane can be written as:
Ax + By + Cz = D
where A, B, and C are the components of the normal vector, and D can be found by plugging in the coordinates of the point on the plane. In this case, we have:
A = -8
B = 0
C = 1
D = -8(24) + 1(9) = -183
Therefore, the equation of the tangent plane at the point (u, v) = (24, 9) is:
-8x + z = -183
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The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is
The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is undefined. This is because as x approaches 2, the denominator (x^2-4) approaches 0, which means that the fraction as a whole is undefined. Therefore, there is no value that the limit can approach.
The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is:
Step 1: Recognize that the given expression can be simplified. Notice that the denominator, x^2 - 4, is a difference of squares, so it can be factored as (x-2)(x+2).
Step 2: Simplify the expression by canceling the common factors in the numerator and the denominator: (x-2)(x+2) / (x-2)(x+2) simplifies to 1, because the factors (x-2)(x+2) cancel each other out.
Step 3: Now that the expression is simplified, substitute x = 2 to find the value of the limit: lim x->2 | 1 = 1.
Your answer: The value of the limit lim x->2 | (x-2)(x+2)/(x^2-4) is 1.
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Shaunda measures the diameter of a ball as 12 in. How many cubic inches of air does this ball hold? Round your answer to the nearest tenth
To find the volume (cubic inches) of the ball, we first need to find its radius, which is half the diameter.
Radius = 12 in / 2 = 6 in
Now we can use the formula for the volume of a sphere:
Volume = (4/3) x π x radius^3 cubic inches
Volume = (4/3) x π x 6^3
Volume ≈ 904.8 cubic inches
So the ball holds approximately 904.8 cubic inches of air. Rounded to the nearest tenth, the answer is 904.8.
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What are the 2 terms that are associated with input?
The two terms that are commonly associated with input are input device and input data.
Input Bias are essential factors of computer systems as they enable druggies to interact with the machine and give data or information that the computer processes to produce affair. There are several types of input bias, each designed to feed to specific requirements and conditions. For illustration, a keyboard is a common input device used to input textbook and commands, while a microphone is used to input audio data.
Input data, on the other hand, can come in colorful forms and formats. It can be entered manually by a stoner or automatically collected by detectors, bias, or other systems. Input data can also be stored in colorful train formats, similar as textbook, audio, videotape, images, or databases. It's reused by the computer system using algorithms, software programs, and tackle factors to induce affair data, results, or conduct.
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Segment cd is the mid segment of trapezoid wxyz what is the value of xy?
Since segment CD is the mid-segment of trapezoid WXYZ, it means that segment CD is parallel to both bases WX and YZ and it is also half the length of their sum. Therefore, we can use the mid-segment formula which states that the length of segment CD is equal to the average of the lengths of the bases WX and YZ.
So, we can write:
CD = (WX + YZ)/2
Since we want to find the value of XY, we need to know its length in terms of WX and YZ.
If we draw a diagonal of the trapezoid, say diagonal WZ, it will divide the trapezoid into two triangles, namely triangle WXY and triangle ZYX.
We know that the mid-segment CD is also the median of triangle WZY, so it divides it into two equal areas.
Therefore, the area of triangle WXY is equal to the area of triangle ZYX.
We can write:
1/2 * WX * CD = 1/2 * YZ * CD
Simplifying this equation by dividing both sides by CD, we get:
1/2 * WX = 1/2 * YZ
Multiplying both sides by 2, we get:
WX = YZ
Therefore, the trapezoid WXYZ is actually an isosceles trapezoid with equal bases WX and YZ.
So, we can substitute WX for YZ in the formula for CD:
CD = (WX + WX)/2
Simplifying this equation, we get:
CD = WX
Therefore, the length of segment XY is equal to the length of the shorter base of the trapezoid, which is WX.
So, the value of XY is equal to the value of WX, and we can conclude that XY = WX.
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I need help on this question, and please explain how you did it.
The expression for AB in terms of x and √3 is:
AB = x√3.
What is an expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
In a right triangle ABC, if sin B = 0.5, then we know that:
sin B = opposite / hypotenuse
So, we can write:
0.5 = AB / CB
We also know that:
CB² = AB² + AC²
Substituting the value of AC, we get:
CB² = AB² + (3x)²
CB² = AB² + 9x²
Now, we can substitute the value of CB² from the first equation:
(AB / 0.5)² = AB² + 9x²
4AB² = AB² + 9x²
3AB² = 9x²
AB² = 3x²
The expression for AB in terms of x and √3 is:
AB = x√3
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A line that passes through the point (x,y) with a y-intercept of b and a slope of m can be represented by the equation y = mx + b.
Joe drew a line on the coordinate plane that passes through the point (-10,52) and has a slope of -6.5. The y-intercept of the line is
The y-intercept of the line is -13.
To find the y-intercept of the line, we can use the slope-intercept form of the equation of a line: y = mx + b,
where m is the slope and b is the y-intercept.
Given that the line passes through the point (-10, 52) and has a slope of -6.5, we can substitute these values into the equation:
52 = -6.5(-10) + b
Simplifying the equation:
52 = 65 + b
To isolate b, we subtract 65 from both sides:
52 - 65 = b
Simplifying further:
b = -13
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CopyCat Pear-Apple wants to get into the tablet business. They want to make tablets similar to Apple's iPad Mini 2. If Pear-Apple applies a scale factor of 1. 25 to the iPad Mini 2 to make a new tablet called the BigMini, what would be the new volume in cubic inches?
The new volume of the BigMini tablet is about 22.18 cubic inches.
How to calculate the new volume of the BigMini tablet?The volume of a three-dimensional object, such as a tablet, is calculated by multiplying its length, width, and height.
Assuming that the scale factor of 1.25 is applied uniformly to all three dimensions of the iPad Mini 2, the new dimensions of the BigMini tablet would be:
Length: 1.25 x 7.87 inches = 9.84 inches
Width: 1.25 x 5.3 inches = 6.63 inches
Height: 1.25 x 0.29 inches = 0.36 inches
The new volume of the BigMini tablet can be calculated as:
9.84 x 6.63 x 0.36 = 22.18 cubic inches
Therefore, the new volume of the BigMini tablet would be approximately 22.18 cubic inches.
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Question 6 of 20 :
Select the best answer for ige question. 6. Simplify (4x 4)-3. O B. 2
O C. -8x12
0D. -64x9
The correct answer is (C) -8x12.
To simplify (4x^4)^-3, we use the power of a power rule which states that (a^m)^n = a^(mn), where a is a non-negative number and m and n are integers. Applying this rule, we get:
(4x^4)^-3 = 4^(-3) x^(4 x -3) = (1/64)x^(-12) = -8x^12 (using the negative exponent rule, which states that a^(-n) = 1/a^n)
Therefore, the simplified form of (4x^4)^-3 is -8x^12.
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In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 10 recent loans is taken. The average calculated from this sample is 6. 40%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a population standard deviation of 0. 5%. Compute 95% and 99% confidence intervals for the population mean 30-year fixed mortgage rate
The 95% confidence interval for the population mean 30-year fixed mortgage rate is (6.091%, 6.709%), and the 99% confidence interval is (5.993%, 6.807%).
To estimate the mean 30-year fixed mortgage rate for a home loan in the United States using a random sample of 10 recent loans with an average of 6.40% and a population standard deviation of 0.5%, you can compute the 95% and 99% confidence intervals as follows:
1: Identify the sample mean (x), sample size (n), and population standard deviation (σ).
x = 6.40%
n = 10
σ = 0.5%
2: Calculate the standard error (SE) using the formula SE = σ/√n.
SE = 0.5%/√10 ≈ 0.158%
3: Determine the critical z-values for 95% and 99% confidence intervals.
For a 95% confidence interval, z = 1.96 (from the z-table)
For a 99% confidence interval, z = 2.576 (from the z-table)
4: Calculate the margin of error (ME) using the formula ME = z * SE.
For 95% CI,
ME = 1.96 * 0.158% ≈ 0.309%
For 99% CI,
ME = 2.576 * 0.158% ≈ 0.407%
5: Compute the confidence intervals by adding and subtracting the ME from the sample mean.
95% CI:
(6.40% - 0.309%, 6.40% + 0.309%) = (6.091%, 6.709%)
99% CI:
(6.40% - 0.407%, 6.40% + 0.407%) = (5.993%, 6.807%)
So, the 95% confidence interval and 99% confidence interval is (6.091%, 6.709%) and (5.993%, 6.807%) respectively.
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Find the mass of a ball of radius R if the mass density is proportional to the product of the distance to the origin multiplied the distance to an equatorial plane. Note that: (ib A ball is a solid whose edge is a sphere. (ii) An equatorial plane is any plane that contains the center of the sphere. (iii) It is convenient to look for a coordinate system that facilitates the task. By For example, the center of the ball can be placed at the origin. And the equatorial plane? (iv) What type of coordinates is the most suitable for problem?
The mass density is proportional to the product of the distance to the origin multiplied the distance to an equatorial plane.The center of the ball can be placed at the origin.
The mass of ball is M = (2/5)MR^2
Process of finding mass:
To find the mass of a ball of radius R with a mass density that is proportional to the product of the distance to the origin multiplied by the distance to an equatorial plane, we need to first find the equation for the mass density.
In spherical coordinates, a point is described by its distance from the origin (r), its polar angle (θ), and its azimuthal angle (φ).
Using this coordinate system, we can write the mass density as:
ρ(r,θ,φ) = k r^2 sinθ
where k is a constant of proportionality.
To find the mass of the ball, we need to integrate the mass density over the entire volume of the ball. The volume element in spherical coordinates is given by:
dV = r^2 sinθ dr dθ dφ
Integrating the mass density over this volume gives us:
M = ∫∫∫ ρ(r,θ,φ) dV
= k ∫0^R ∫0^π ∫0^2π r^4 sin^3θ dr dθ dφ
= 2πk/5 R^5
where R is the radius of the ball.
To find the value of k, we can use the fact that the total mass of the ball is given by:
M = (4/3)πρavg R^3
where ρavg is the average mass density of the ball. From this equation, we can solve for k:
k = (3/4πρavg) = (3/4πR^3)M
Substituting this value of k into our expression for the mass of the ball, we get:
M = (2/5)MR^2
Therefore, the ball's mass is proportional to its radius's square.
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John rides his bike 68 km south and then 6 km went. How far is he from his starting point?
John is approximately 68.26 km away from his starting point after riding 68 km south and then 6 km west.
To find out how far John is from his starting point after riding 68 km south and then 6 km west, we will use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we will consider the 68 km south as one side, and the 6 km west as the other side, with the distance from the starting point being the hypotenuse.
Step 1: Square the lengths of the two given sides.
68^2 = 4624
6^2 = 36
Step 2: Add the squared values together.
4624 + 36 = 4660
Step 3: Find the square root of the sum to get the length of the hypotenuse (distance from the starting point).
√4660 ≈ 68.26 km
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A 100 g blackbird is flying with a speed of 12 m/s directly toward a 30 g bluebird, who is flying in the opposite direction at a speed of 40 m/s
Answer: 0 g * m/s
Step-by-step explanation:
You first want to multiply 100g, by 12 m/s. This gives you the momentum of the first bird, the answer being 1200 g * m/s
Second, You was to multiply 30g, by 40 m/s. This gives you the momentum of the second bird, The answer also being 1200 g * m/s.
Then, subtract The final answers, and you get 0 g * m/s.
=(100 g)(12 m/s)+(30 g)(−40 m/s)
=1200 g⋅ m/s+(−1200 g⋅ m/s)
=0 g⋅ m/s
I am not an expert, so I may have gotten some things incorrect.
If this doesn't make sense please consult an expert :,)
The relative speed of the birds is 52 m/s.
We are given that;
Number of blackbirds= 100g
Speed= 12m/s
Now,
The relative speed of the blackbird as seen by the bluebird is:
vblackbird relative to bluebird=vblackbird−vbluebird
vblackbird relative to bluebird=−12−40
vblackbird relative to bluebird=−52 m/s
This means that the blackbird is moving to the left at 52 m/s as seen by the bluebird. The relative speed of the bluebird as seen by the blackbird is:
vbluebird relative to blackbird=vbluebird−vblackbird
vbluebird relative to blackbird=40−(−12)
vbluebird relative to blackbird=52 m/s
This means that the bluebird is moving to the right at 52 m/s as seen by the blackbird. The relative speed of either bird is equal to the magnitude (absolute value) of their relative velocity.
Therefore, by the speed the answer will be 52 m/s.
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Solve the following inequality for r. Write your answer in simplest form. -5r - 2(-10r - 9)<=-6r + 8 - 9
Distribute on the left side:-5r + 20r + 18 ≤ -6r - 1
Combine like term on the left side:15r + 18 ≤ -6r -1 (Add 6 to both sides)21r + 18 ≤ -1 (Subtract 18 from both sides)21r ≤ -1921r/21 ≤ -19/21 (Divide by 21)Get Solution r ≤ -19/21Solution:r ≤ -19/21
Which of the following is a typical characteristic of debit cards? (1 point)
O Your bank may charge you a very large fee each time you use one.
O When you buy something from a store, you may be offered a discount if you open one with the store.
O They usually charge a lower interest rate than credit cards.
They are tied directly to your bank account.
A typical characteristic of debit cards is expressed by option D, they are tied directly to your bank account, since money has to be deducted for a purchase to be made.
How debit cards functionWhen you use a debit card to make a purchase, the money is deducted directly from your bank account. Debit cards do not typically charge interest like credit cards do, so C is not correct.
A is also not correct since most banks do not charge a fee for using a debit card, although some may charge fees for using an out-of-network ATM or overdraft fees if you spend more than you have in your account. B is not a typical characteristic of debit cards either, as there is generally no connection between a store's loyalty program or discounts and using a debit card for payment.
Therefore, it is possible to conclude that debit cards have option D as their characteristic. Since they require money in the bank to make the purchase, they are connected to one's account.
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1. $4,076.92
2. Assets = Liabilities + Equity
3. They can be used to make online purchases.
4. by using an emergency fund for this unplanned expense
5. a fund with a minimum investment that tracks the value of cash
6. 1930s
7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.
8. their vacation cabin
9. You should shop around for the best overall deal.
10. If you use a credit card, it is easy to run up huge debts.
11. They are tied directly to your bank account.
12. preventative care
13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage
14. how long the coverage lasts, how much the premium costs, and the cash value
15. 1-year renewable group term life
16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.
17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.
18. 2 year in state community college degree
19. tuition assistance
20. -a sundae, -movie tickets
Explanation: All of these answers are correct!
Personal Finance Semester Exam
5/11/2023
In building a brick staircase, we need 200 bricks for the bottom step and 84 bricks for the top step. If, beginning with the bottom step, each successive step requires four fewer bricks, how many bricks will be required to build the staircase?
The number of bricks that will be required to build the staircase is: 30 bricks
How to find the nth term of an arithmetic sequence?An arithmetic sequence is defined as one where you get the next term by adding a constant, called the common difference, to the previous term. A lot of formulas come from this simple fact. and they allow us to solve for any term in the sequence and even the sum of the first few terms.
The formula for the nth term of an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where:
a₁ is first term
d is common difference
n is nth term
We are given:
a₁ = 200
d = -4
aₙ = 84
Thus:
84 = 200 + (n - 1)(-4)
84 - 200 = -4n + 4
-4n = -120
n = 30
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The Greens bought a condo for $110,000 in 2005. If its value increases at 6% compounded annually, what will the value be in 2020?
Answer:
$264,000
Step-by-step explanation:
PV = $110,000
i = 6%
n = 15 years
Compound formula:
FV = PV (1 + i)^n
FV = 110,000 (1 + 0.06)^15
FV = 110,000 · 2.40(rounded) = $264,000
HERE IS A HARD QUESTION , COULD U PLEASE ANSWER B PLEASE? I DID A ! 1ST ANSWER WOULD BE MARKED BRAINLIEST AND GET 5/5 WITH A THANKS! ILL ALSO COMMENT ON YOUR ANSWER ! BUT IF IT ISNT CORRECT , I WONT MARK BRAINLIEST! Thank you for your answers!!!!
Answer:
D(6,4).
Step-by-step explanation:
The shape ABCD is a square.
By definition, the diagonals are equal.
The diagonal from A to C is 6 units long. Therefore, you should get your point D by drawing across from B to the right by 6.
D(6,4).
What is the sine ratio for angle A?
A. 10/8
B. 8/10
C. 6/10
D. 6/8
Answer:
C. 6/10
Step-by-step explanation:
Sin A = 6/10
What is the exact circumference of a circle with a radius of 15 cm?
Responses
10π cm
10 pi, cm
15π cm
15 pi, cm
30π cm
30 pi, cm
60π cm
Answer:
30π cm
Step-by-step explanation:
if r = 15 cm
circumference = π2r
= π × 2 × 15
= 30π cm
#CMIIWCasho went shopping for a new pair of sneakers because of a sale. The price on the tag was $25, but Casho paid $22. 50 before tax. Find the percent discount
The percent discount on the sneakers is 10%
Casho paid $22.50 before tax, despite the item's $25 tag price. The discount is the difference between the original price and the sale price, which is $25 - $22.50 = $2.50.
The discount is the difference between the original price and the discounted price, expressed as a percentage of the original price.
To find the percent discount, we divide the discount by the original price and multiply by 100:
Percent discount = (discount / tag price) x 100
Percent discount = ($2.50 / $25) x 100
Percent discount = 0.1 x 100
Percent discount = 10%
Therefore, the percent discount on the sneakers is 10%
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A tank in the shape of a hemisphere has a diameter of 8 feet. If the liquid that fills the tank has a density of 86 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
209.07 pounds
Step-by-step explanation:
radius= 8÷2=4 feet
volume of hemisphere=((4/3)×(22/7)×r^3)/2
=134.09 cubic feet
Mass=density × volume
=86×134.09
=209.07 pounds
5. Rita has a circular hot tub. The hot tub has a circumference 25. 12 feet. It is 3. 5 feet deep.
a. Find the radius of the hot tub. Use 3. 14 for pi
b. How much water can the hot tub hold?
c. The hot tub manual recommends filling the hot tub to 80% of its full capacity. How
much water should rita put in the hot tub in order to follow the recommendation?
a.The radius of the hot tub is 4 feet. b. The amount of water that the hot tub can hold is 176.96 cubic feet c. The amount of water that Rita should put in the hot tub in order to follow the recommendation is 141.57 cubic feet.
a. Find the radius of the hot tub.
Given: Circumference = 25.12 feet
Formula: Circumference = 2 * pi * radius
1: Plug in the given circumference and the value of pi.
25.12 = 2 * 3.14 * radius
2: Solve for the radius.
radius = 25.12 / (2 * 3.14)
radius ≈ 4 feet
So, the hot tub's radius is 4 feet.
b. How much water can the hot tub hold?
Given: Radius = 4 feet, Depth = 3.5 feet
Formula: Volume = pi * radius^2 * depth
1: Plug in the radius, depth, and the value of pi.
Volume = 3.14 * (4^2) * 3.5
2: Calculate the volume.
Volume ≈ 176.96 cubic feet
So, the hot tub can approximately hold 176.96 cubic feet.
c. How much water should Rita put in the hot tub to follow the recommendation?
Given: Recommended capacity = 80% of full capacity
Formula: Recommended water = 0.8 * full capacity
1: Plug in the full capacity (volume) calculated in part b.
Recommended water = 0.8 * 176.96
2: Calculate the recommended water amount.
Recommended water ≈ 141.57 cubic feet
So, Rita should put approximately 141.57 cubic feet of water in the hot tub to follow the recommendation.
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Suppose f'(x) = 833 + 12x + 2 and f(1) = -4. Then f(-1) equals (Enter a number for your answer)
To find f(-1), we can use the fact that the derivative of a function f(x) gives us the slope of the tangent line to the graph of f(x) at any point x. We can use this information along with the given value of f(1) to find the equation of the tangent line at x=1, and then use that equation to find the value of f(-1).
First, we find the equation of the tangent line at x=1:
- The slope of the tangent line at x=1 is f'(1) = 833 + 12(1) + 2 = 847
- The point (1, f(1)) lies on the tangent line, so we can use the point-slope form of the equation of a line to write the equation of the tangent line:
y - (-4) = 847(x - 1)
y + 4 = 847x - 847
y = 847x - 851
Now we can use this equation to find f(-1):
- The point (-1, f(-1)) also lies on the tangent line, so we can substitute x=-1 and solve for y:
f(-1) + 4 = 847(-1) - 851
f(-1) + 4 = -1698
f(-1) = -1702
Therefore, f(-1) = -1702.
To find f(-1), we first need to determine the function f(x). We know f'(x) = 833 + 12x + 2. To find f(x), we need to integrate f'(x) with respect to x:
∫(833 + 12x + 2) dx = 833x + 6x^2 + 2x + C
Now, we use the given condition f(1) = -4 to find the constant C:
-4 = 833(1) + 6(1)^2 + 2(1) + C
Solve for C:
C = -4 - 833 - 6 - 2 = -845
Now we have the function f(x) = 833x + 6x^2 + 2x - 845. To find f(-1), plug in x = -1:
f(-1) = 833(-1) + 6(-1)^2 + 2(-1) - 845
f(-1) = -833 + 6 - 2 - 845
f(-1) = -1674
So, f(-1) equals -1674.
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Evaluate the repeated integral: lolla (-xy + 2 z) dz dy dx a) O 15 b) 60 c) 30 d) 36 e) O72 f) O None of these.
The evaluation of the repeated integral is None of these. (option f)
The repeated integral given is ∫∫∫(-xy + 2z) dz dy dx over the region lolla. This means that you need to integrate the function (-xy + 2z) with respect to z, then with respect to y, and finally with respect to x over the region lolla.
To evaluate this integral, you can use the method of iterated integrals. First, integrate (-xy + 2z) with respect to z, treating x and y as constants:
∫∫(-xy + 2z) dz = -xyz + z² + C
where C is the constant of integration.
Next, integrate the result of the first integral with respect to y, treating x as a constant:
∫[-xyz + z² + C] dy = -xyz + y[-xyz + z² + C] + D
where D is the constant of integration.
Finally, integrate the result of the second integral with respect to x:
∫[-xyz + y(-xyz + z² + C) + D] dx = (-1/2) x² yz + xy(-xyz + z² + C) + Dx + E
where E is the constant of integration.
Now, you need to evaluate this expression over the region lolla. Without further information about the limits of integration for each variable, it is not possible to determine the exact value of this integral.
Therefore, the correct answer is f) None of these.
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