Sequences & Series Questions and Answers

A heavy log is dragged across the ground by two horses pulling on ropes (see the figure below). The magnitudes of the tension forces in the direction of the ropes are 53 pounds and 71 pounds. If the angle between the ropes is 26°, find the magnitude of the resultant force. (Round your answer to the nearest whole number.)

graph g(x) = x^2 - 2x - 8 what are the x and y intercepts?

The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 6 mg. What was the initial mass (in mg) of the sample?__________ What is the mass 5 weeks after the start? ________

Match each formula (a)-(c) with its corresponding table of values (I)-(III). (I) x 2 3 4 5 6 f(x) 11.20 16.13 20.89 25.54 30.09 (II) x 1 2 3 4 5 f(x) 4.40 4.84 5.32 5.86 6.44 (III) x 2 4 6 8 10 f(x) 8.57 18.38 28.71 39.40 50.36 (a) y = 4x^(1.1) (b) y = 6x^0.9 (c) y = 4(1.1)^x

x* is defined as the 3-digit integer formed by reversing the digits of integer x; for instance, 258* is equal to 852. R is a 3-digit integer such that its units digit is 2 greater than its hundreds digit. Quantity A Quantity B R* - R 200 Quantity A is greater. Quantity B is greater. The two quantities are equal. The relationship cannot be determined from the information given.

Algebra By volume, one alloy is 70% copper, 20% zinc, and 10% nickel. A second alloy is 60% copper and 40% nickel. A third alloy is 30% copper, 30% nickel, and 40% zinc. How much of each alloy (in mm^3) must be mixed in order to produce 1000 mm^3 of a final alloy that is 50% copper, 18% zinc, and 32% nickel?

Imagine the point (square root 2/2, negative square root 2/2) on the terminal side of an angle. Find the value for the sine of this angle. A positive B negative

Find the eccentricity of the conic with polar equation r=1/(3-2cosθ)

Find the value of t in the interval [0, 2π) that satisfies the following equation. Sin t = 3/2 a. 0 b. π/2 c. π d. No Solution

S₀ = 1-(t/120) para 0 ≤ t ≤ 120, δ= .05. Percentil 75% de Y40 = ? Y_40 si the whole life annuity

Express p(t)=-3+41+9t² as a linear combination of the vectors in S={1+4,1-t²,t²}.

Two planes take off at the same time from an airport. The first plane is flying at 233 miles per hour on a course of 135.0°. The second plane is flying in the direction 175.0° at 385 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours? (Round your answer to the nearest whole number.)

Two airplanes leave an airport at the same time. The first flies220 km/h in a direction of190⁰. The second flies 140 km/h in a direction of240°. After 4 hr, how far apart are the planes?

Paula is training for a marathon. Her training includes a long run every Sunday which increases in length by 2 km per week. After her Sunday runs total a distance of 252 km she changes her plan to reduce her milage. If her longest Sunday run was 31 km, how long was her run on the first Sunday?

Wirte y as the sum of two vectors, one in Span (u,) and one in Span (u₂,3,4). Assume that (u) is an orthogonal basis for R (Type an integer or simplified fraction for each matrix element)

For a given arithmetic sequence, the 38th term, a₃₈ , is equal to -231, and the 94th term, a₉₄ , is equal to -623. Find the value of the 7th term, a₇.

Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.) f(x, y, z) = x + 2y; x+y+z= 3, y² + z² = 4 maximum= minimum=

Lucky Larry wins $1,000,000 in a state lottery. The standard way in which the state pays such lottery winnings is at a constant rate of $40,000 per year for 25 years. Round your answer to the nearest $10. If Lucky invests each payment from the state at 6% compounded continuously, what is the accumulated future value of the income stream? What is the accumulated present value of the income stream at 6%, compounded continuously? (This amount represents what the state has to invest at the start of its lottery payments, assuming the 6% interest rate holds.)

The population of a certain small town is decreasing according to the function P(t)=22,300(0.982)ᵗ where t represents time in years since the last census. Use the function to determine (to the nearest integer) the population 6 years from the time of the last census.

Use the formula A-P(1+r)ᵗ to find the rate r at which $2000 compounded annually grows to $3380 in 2 years. r = ____% (Round to the nearest percent as needed.)

how do you factor and graph f(x) =2x^7+11x^6+18x^5-24x^3-15x^2+4x+4 Please explain your process of using synthetic division

Find a formula for the nth term of the arithmetic sequence. First term -2 Common difference 8 an = [ ? ]n + [___]

Consider the line y=(7/5)x-4 Find the equation of the line that is perpendicular to this line and passes through the point (5,-2). Find the equation of the line that is parallel to this line and passes through the point (5. -2).

Simplify. 17x⁹y⁴z¹⁷/34x⁶y²z⁷(Assume all variables represent nonzero numbers.)

Find the center and foci of the ellipse: 9x² + 16y² + 126x + 96y + 441 = 0 Center = ([__], [__ ]) Foci = (__ ± √__, __)

Omar has his $4,200 savings in an account earning 43/8% annual interest that is compounded continuously. How much will be in the account at the end of 21/2 years? Round to the nearest cent, and do not include the dollar sign in your answer. Provide your answer below:

Rationalize the denominator 1/(4√3)

For the following set of data, find the percentage of data within 2 population standard deviations of the mean, to the nearest 10th of a percent. Data Frequency 12 2 14 7 16 9 18. 14 34 16 36 10 37 7 41 1

Evaluate the expression (4p-m) +4 where m = -4 and P = 2

Evaluate: Σ 8(1/4)ⁿ‾¹ = [ ? ] Round to the nearest hundredth.

Use the discriminant to determine the number and types of solutions of the quadratic equation. - 5x=-3x² +4 The equation has _____

Determine the amount of the ordinary annuity at the end of the given period. $500 deposited quarterly at 6.7% for 8 years

Complete the table to determine the balance A for $14,000 invested at rater for t years, compounded continuously. (Round your answers to the nearest cent.) r-1.5% t 1 10 20 30 40 50 A $2100 $16247.57 $420000 $630000 $840000 $105000

Find the vertices of the hyperbola. Enter the smallest coordinate first. x²/9 - y²/49 = 1

What does this mean? i=1Σyi₁3 ≥ 9000 , i=1Σyi₂ 3 ≥ 12000

If $92,650 is invested in an account earning 4 2/5% annual interest compounded continuously, then how much interest is accrued in the first 4 years? Round to the nearest cent.

Find the center and foci of the ellipse: 64x² +100y2 + 768x-600y - 3196= 0 Center = Foci =

If R is the parallelogram with vertices (0,0), (4,2), (0,4) and (-4,2) determine the region we would get applying the transformation x=u-v, y = 1/(u + v) to R.

Find the radius of the circle. 3(x - 5)² +3(y+9)² = 48 r=[ ? ]

The following is the actual sales for Manama Company for a particular good: Sales 1 16 2 19 3 25 4 32 5 33 The company wants to determine how accurate their forecasting model, so they asked their modeling expert to build a trend model. He found the model to forecast sales can be expressed by the following model: Ft-5-2.4t Calculate the amount of error occurred by applying the model is:

use the comparison test to determine whether the following series Converge or diverge. (a) Σ1/3K +5 (b) Σ 5 sin ² k/k! (c) Σlnk/k (d) Σk/k 3/2-1/2

If a ball is thrown straight up with a speed of 68 ft/s, its height at time t (in seconds) is given by h(t)=-8t²+68t+5. Use graphing technology to determine the following and round where appropriate. a) What is the maximum height of the ball? b) When does the ball reach its maximum height? c) When does the ball hit the ground?

Determine the vector projection of vector (-4, 0, 7) onto vector (2, -1, 5).

Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. (Zoom in for improved accuracy.) Find the intersection of the line through (0, 1) and (4.1, 2) and the line through (2.3, 3) and (5.4,0).

Evaluate ∭z² dV where E is the region between the spheres x² + y² + z² = 4 and x² + y² + z² =25 and inside z = -√ (1/3)x² + (1/3)y².

Here are the percents of the popular vote won by each successful candidate in 15 presidential elections. 49.6, 55.1, 57.4, 49.7, 61.1, 43.4, 60.7, 50.1, 50.7, 58.8, 53.9, 43.2, 49.2, 47.9, 51.2 What is the minimum?

Graph the line 2x - y = 4 and find the y intercept and the x intercept.

Determine the domain and range of the function f(x) = log₂ (x) - 2. Select the correct answer below: a) Domain: (-∞, 0); Range: (-∞, ∞) b) Domain: (0,∞ ); Range: (-∞, ∞) c) Domain: (-∞, 0); Range: (-∞, 0) d) Domain: (0, ∞); Range: (0, ∞)

Given u=8i+(m)j–22k and v=2i−(3m)j+(m)k, find the value(s) for m such that the said two vectors are perpendicular.

Use the formula A = P(1+r)ᵗ to find the rate r at which $5000 compounded annually grows to $6050 in 2 years. r= (Round to the nearest percent as needed.)