# calc

Popular questions-
## Calc

Find the linear approximation of the function g(x) = fifth root(1 + x) at a = 0. g(x)≈ 1+(x/5) Correct: Your answer is correct. Use it to approximate the numbers fifth root (0.95) and fifth root (1.1) (Round your answers to three decimal places.)

*asked by Anonymous on May 11, 2018* -
## Calc

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. a) Find the initial population. b) Write an exponential growth model for the

*asked by Erica on January 6, 2011* -
## Calc

If a rock is thrown upward on the planet Mars with a velocity of 17 m/s, its height (in meters) after t seconds is given by H = 17t − 1.86t^2. (a) Find the velocity of the rock after one second. (b) Find the velocity of the rock when t = a. (c) When will

*asked by Katrina on October 17, 2011* -
## calc

Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2].

*asked by bill on February 28, 2011* -
## Calc

The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function below, where I is the light intensity (measured in thousands of foot-candles). P = (120 I) / (I^2 + I + 1) For what light intensity

*asked by Aaron on November 30, 2009* -
## Calc

A rectangular page is to contain 30 sqaure inches of print. The margins on each side are 1 inch. Find the dimensions of the page sucha that the least amount of paper is used. A farmer plans to fence a rectangular pasture adjacent to a river. The pasture

*asked by Amber on July 7, 2017* -
## CALC

Use Newton's method to approximate a root of the equation x3+x+3=0 as follows. Let x1=–1 be the initial approximation. The second approximation x2 is _____? and the third approximation x3 is _____?

*asked by Adam on May 29, 2010* -
## calc

integral: sqrt (16 + 6x − x^2) dx

*asked by sam on June 27, 2014* -
## Calc

A sample of a radioactive substance decayed to 93.5% of its original amount after a year. a) What is the half-life of the substance? ? years (b) How long would it take the sample to decay to 10% of its original amount? ? years

*asked by Lee on November 8, 2009* -
## Calc

A baseball is thrown upwards from a height of 2 meters with an initial velocity of 10 meters per second. Use the fact that -9.8 meters per second squared is constant acceleration due to gravity to answer the following: The maximum height of the ball The

*asked by Emily on November 1, 2016* -
## Calc

If y=tanu, u=v-(1/v), and v=lnx. What is the value of dy/dx at x=e?

*asked by Sarah on December 6, 2016* -
## Calc

A paper cup is to be designed in the shape of a right circular cone. It must have a capacity of 12 fluid ounces (1 fluid ounce = 1.80469 cubic inches) of soft drink but it must use a minimum amount of material in its construction. What should the

*asked by jo on July 30, 2012* -
## calc

When the height of a cylinder is 12 cm and the radius is 4 cm, the circumference of the cylinder is increasing at a rate of pie/4 cm/m in, and the height of the cylinder is increasing four times faster than the radius. How fast is the volume of the

*asked by marrisa smith on November 30, 2016* -
## Calc

Consider the following. cos(x) + sqrt(y)= 1 (a) Find y' by implicit differentiation. y' = 2y^(1/2) sin(x) Correct: Your answer is correct. (b) Solve the equation explicitly for y and differentiate to get y' in terms of x. y' = ? (c) Check that your

*asked by Anonymous on May 11, 2018* -
## Calc

Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm. (in cm^3) Thank you so much!!

*asked by Erica on April 25, 2011* -
## Calc

A model for the food-price index (the price of a representative "basket" of foods) between 1984 and 1994 is given by the function I(t)=0.00009045t5+0.001438t4−0.06561t3+0.4598t2−.6270t+99.33 Where t is measured in years since midyear 1984, so

*asked by Anonymous on March 26, 2015* -
## Calc

A buoy oscillates in simple harmonic motion as waves go by. The buoy moves a total of 3.5 feet from its low point to its high point and it returns to its high point every 10 seconds. What is the equation that describes this motion if it reaches its high

*asked by Emily on July 30, 2008* -
## calc

A particle moves along the x-axis with velocity v(t) = t^2 − 1, with t measured in seconds and v(t) measured in feet per second. Find the total distance travelled by the particle from t = 0 to t = 2 seconds.

*asked by Anonymous on August 13, 2015* -
## calc

Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4

*asked by ANONYMOUS on November 25, 2015* -
## calc

Use a linear approximation (or differentials) to estimate the given number. sqrt(99.6) so i think i start with f(x)=sqrt(100-x) so f'(x)= 1/2(100-x)^-1/2 (-1) using a=0 f(x)= 10 and f'(x)= -0.05 when using L(x)=f(a)+f'(a)(x-a) where x=a I get 10 + -0.05(x)

*asked by kirsten on March 22, 2015* -
## calc

The velocity of a particle moving along the x-axis is v(t) = t2 – 2t, with t measured in minutes and v(t) measured in feet per minute. To the nearest foot find the total distance travelled by the particle from t = 0 to t = 3 minutes..

*asked by Anonymous on August 22, 2015* -
## Calc

A body of an unknown temperature was placed in a room that was held at 30°F. After 10 minutes, the body's temperature was 0°F, and 20 minutes after the body was placed in the room the body's temperature was 15°F. Estimate the body's initial temperature.

*asked by Erica on January 6, 2011* -
## calc

If a point moves on the hyperbola x^2-4y^2=36 in such a way that x-coordinate increases at constant rate of 20 units per second. How fast is the y coordinated changing at point (10,4)? please help!!! Differentiating implicitly with respect to t, 2 x dx/dt

*asked by keneth on November 9, 2006* -
## calc

Let F of x equals the integral from 1 to 3 times x of the natural logarithm of t squared. Use your calculator to find F″(1).

*asked by Anonymous on July 29, 2015* -
## calc

Determine if the following functions grow faster, slower, or at the same rate as the function 2e^(2x) as x → ∞. a. 3.2^(2x) b. e^(x/6) c. 1/8 e^(2x)

*asked by tony on December 16, 2013* -
## Calc

When pi/2

*asked by Leanna on July 15, 2011* -
## Calc

If f(x) = e^(sin x), how many zeros does f '(x) have on the closed interval [0, 2π]?

*asked by Erica on January 2, 2011* -
## calc

Give 2 positive and 2 negative angles that are coterminal with each angle? 1. 30 degrees 2. 135 degreed 3. -93 degrees

*asked by peter on March 31, 2009* -
## Calc

A spherical tank of radius 100ft is full of gasoline weighing 40 pounds per cubic feet how much work is done in pumping the gasoline to the top of the tank?

*asked by Lyn on May 9, 2019* -
## Calc

Find y'' by implicit differentiation. 5x2 + y2 = 3 y'' =?

*asked by Anonymous on May 11, 2018* -
## Calc

The maker of an automobile advertises that it takes 13 seconds to accelerate from 25 kilometers per hour to 90 kilometers per hour. Assuming constant acceleration, compute the following. The acceleration in m/s^2 The distance the car travels during the 13

*asked by Kelly on November 18, 2016* -
## calc

The differential equation dy dx equals the quotient of x and y squared. will have a slope field with negative slopes in quadrant I will have a slope field with positive slopes in all quadrants will produce a slope field with columns of parallel tangents

*asked by Anonymous on July 3, 2015* -
## calc

Find the area of the region bounded by the curves y equals the inverse sine of x divided by 4, y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.

*asked by Anonymous on June 29, 2015* -
## Calc

Three students have ordered a 14 inch diameter pizza. They slice it with 2 parallel cuts, giving them 3 pieces with equal area. The two cuts are equidistant from the center of the pizza. Find the horizontal distance between one cut and the center of the

*asked by Danielle on November 23, 2014* -
## Calc

Let f be the function given by f(x) = tan x and let g be the function given by g(x) = x^2. At what value of x in the interval 0≤x≤π do the graphs of f and g have parallel tangent lines?

*asked by Erica on January 2, 2011* -
## Calc

lim x->0 X*e^(cos 1/x)

*asked by Anonymous on January 25, 2015* -
## Calc

A cup of coffee at 90 degrees celsius is put into a 30 degree celsius room when t =0 . The coffee's temperature, f (t ) , is changing at a rate given by f '(t )=-8(0 .8) t degrees celsius per minute, where t is in minutes. Estimate the coffee's temperature

*asked by Natalie on July 21, 2014* -
## CALC

An open box is to be constructed so that the length of the base is 4 times larger than the width of the base. If the cost to construct the base is 5 dollars per square foot and the cost to construct the four sides is 3 dollars per square foot, determine

*asked by Jessica on April 8, 2011* -
## Calc

A rotating beacon is located 1 kilometer off a straight shoreline. If the beacon rotates at a rate of 3 revolutions per minute, how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer down the

*asked by Jon on November 11, 2007* -
## Calc

A toy manufacturer's cost for producing q units of a game is given by C(q) = 1480 + 3.8q + 0.0006q2. If the demand for the game is given by p = 8.6 − 1/440q how many games should be produced to maximize profit? (Round your answer to the nearest integer.)

*asked by Anonymous on April 20, 2020* -
## calc

a man 6 feet tall is walking away from a lamp post at the rate of 60 feet per minute. when the person is 6 feet from the lamp post, his shadow is 12 feet long. find the rate at which the length of his shadow is increasing when he is 145 feet from the lamp

*asked by homestead high on November 3, 2016* -
## calc

The area A = πr2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 3ft?

*asked by Anonymous on June 9, 2015* -
## calc

Nutrition Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 224 grams of protein and at

*asked by liz on September 16, 2011* -
## Calc

A 100 inch piece of wire is divided into 2 pieces and each piece is bent into a square. How should this be done in order of minimize the sum of the areas of the 2 squares? a) express the sum of the areas of the squares in terms of the lengths of x and y of

*asked by katie on November 16, 2010* -
## Calc

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.3 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is,

*asked by Ash on September 30, 2018* -
## Calc

Find the area of the region bounded by the curves y = sin^-1(x/6), y = 0, and x = 6 obtained by integrating with respect to y. Please include the definite integral and anti-derivative.

*asked by LilPeep on January 3, 2018* -
## Calc

Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y = 5/x

*asked by Kelly on October 29, 2016* -
## Calc

Find the particular solution that satisfies the differential equation and the initial condition. f '(s) = 10s − 4s3, f(3) = 7 & f ''(x) = 6, f '(2) = 14, f(2) = 19

*asked by Emily on October 26, 2016* -
## calc

Suppose that an accelerating car goes from 0 mph to 58.6 mph in five seconds. Its velocity is given in the following table, converted from miles per hour to feet per second, so that all time measurements are in seconds. (Note: 1 mph is 22/15 feet per sec =

*asked by Anonymous on April 17, 2015* -
## Calc

An Olympic-sized swimming pool is a rectangular prism that is 50m long, 25m wide, lled with water to a depth of 1.5m. We are going to pump the water out of the pool with a pump that is 0.5 meters above the surface of the water. Compare the costs of

*asked by Jen on May 18, 2014* -
## Calc

A video games shop is analyzing its sales performance using matrices. Matrix A contains the unit sales data for each product category (horizontally) per week (vertically). Matrix B contains the unit sales data for weekends for each category (horizontally)

*asked by Chris on April 25, 2013* -
## Calc

A lighthouse is fixed 130 feet from a straight shoreline. A spotlight revolves at a rate of 11 revolutions per minute, (22 rad/min ), shining a spot along the shoreline as it spins. At what rate is the spot moving when it is along the shoreline 12 feet

*asked by Bubba on February 14, 2011* -
## Calc

Find the area of the largest rectangle that can be inscribed under the curve y = e^(-x^2) in the first and second quadrants.

*asked by Erica on December 7, 2010* -
## calc

A pitcher throws a baseball straight into the air with a velocity of 72 feet/sec. If acceleration due to gravity is -32 ft/sec2, how many seconds after it leaves the pitcher's hand will it take the ball to reach its highest point? Assume the position at

*asked by ANONYMOUS on November 25, 2015* -
## Calc

A Norman window is constructed by adjoining a semicircle to the top of a rectangular window as shown in the figure below. If the perimeter of the Norman window is 24 ft, find the dimensions that will allow the window to admit the most light.

*asked by Coc on November 4, 2015* -
## Calc

A a conical container of radius 5ft and height 20ft is filled to a height of 18ft of a liquid weighing 50.6lb/ft^3. How much work will it take to pump the contents to the rim? How much work will it take to pump the liquid of a level of 2ft above the rim?

*asked by Anonymous on February 10, 2013* -
## calc

A kite 80 feet above the ground moves horizontally at a speed of 8 ft/sec. At what rate is the angle between the string and the horizontal decreasing when 100 ft of string have been let out?

*asked by need help on December 16, 2011* -
## Calc

Find the value of (f o g)' at the given value of x. f(u)= u/u^2-1 u=g(x)=3x^2+x+3 x=0 is it a. 5/32 b. 13/32 c. 1/8 d. 5/32

*asked by Gretchen on November 29, 2011* -
## calc

A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What dimensions for the pen

*asked by Andres on October 12, 2011* -
## Calc

Find the points on the graph of y = 1/x where the graph is parallel to the line 4x + 9y = 3.

*asked by Michael on December 3, 2010* -
## Calc

Use implicit differentiation to find dy/dx. ln xy + 5x = 30

*asked by Erica on December 2, 2010* -
## Calc

Find the cartesian coordinates of the following points given in polar coordinates. b. (2 rt2, 3pi/4) I cant figure this one out

*asked by Jessica on March 26, 2008* -
## Calc

A bacteria culture is growing at a rate of r(t) = 3e^0.4t thousand bacteria per hour after t hours. How much did the bacteria population increase during the first two hours? (Round your answer to three decimal places.)

*asked by James on April 28, 2020* -
## Calc

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i − x j + z2 k S is the helicoid

*asked by Anon on November 23, 2016* -
## Calc

Use the limit process to find the area of the region between the graph of the function and the x-axis over the given interval. y = −4x + 6, [0, 1]

*asked by Jenna on October 29, 2016* -
## CALC

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by y =sqrt(x), y = 0, and x = 1; ρ(x, y) = 27x m=? (x,y)=?

*asked by Anon. on October 18, 2016* -
## calc

A poster is to contain 50 square inches of printed matter with margins of 4 inches at the top and bottom and 2 inches at each side. Find the OUTER dimensions if the total area of the poster is the smallest possible.

*asked by o on March 14, 2016* -
## calc

Find the interval on which the curve y= integral x to 0 of 6/(1+2t+t^2) dt is concave upward

*asked by Anonymous on June 7, 2015* -
## calc

lim x → ∞ tan−1(x7 − x9)

*asked by kirsten on February 15, 2015* -
## Calc

Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at the foci of the

*asked by Tyler on May 1, 2013* -
## calc

What function should be used to maximize the volume of an open box that has a surface area of 24 and has a square bottom. x is the bottom and h is the height.

*asked by daryl on December 19, 2012* -
## Calc

At the time of the birth of a child, a parent wants to begin a college fund that will grow to $50000 by the child's 18th birthday. Interest is compounded continuously at 8.5%. What should the initial investment (P0) be?

*asked by Anonymous on April 18, 2011* -
## Calc

How do you integrate sin²x?

*asked by Erica on February 2, 2011* -
## Calc

Gravel is being dumped from a conveyor belt at a rate of 10 ft^3/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 23 feet high?

*asked by Pierre on October 28, 2010* -
## calc

a) A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 40 ft/s^2. What is the distance covered before the car comes to a stop? b) A car braked with a constant deceleration of 40 ft/s^2 and produced skid

*asked by Jill on November 22, 2009* -
## Calc

A plane flying horizontally at an altitude of 1 mi and a speed of 510 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 6 mi away from the station. (Round to the nearest

*asked by Peter on November 8, 2009* -
## Calc

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 1-x^2. What are the dimensions of such a rectangle with the greatest possible area?

*asked by Manny on April 5, 2009* -
## calc

Find x. Supplementary angles with measures 10x+7 and 7x+3. Complementary angles with measures 3x-5 and 6x-40.

*asked by bob on March 31, 2009* -
## calc

If 4x2+3x+xy=2 and y(2)=–10 , find y'(2) by implicit differentiation. i keep getting the wrong answer for this problem evn when plugging 2 in for y.

*asked by sara on May 9, 2008* -
## calc

The half-life of polonium is 139 days, but your sample will not be useful to you after 95 % of the radioactive nuclei present on the day the sample arrives has disintegrated. For about how many days after the sample arrives will you be able to use the

*asked by barb on April 10, 2007* -
## Calc

Compute Δy and dy for the given values of x and dx = Δx. y = x^2 − 7x, x = 6, Δx = 0.5

*asked by Andy on February 26, 2017* -
## calc

find the tangent line equation at x=cost+sin2t, y=sint+cos2t, t=0

*asked by Lielle on December 16, 2016* -
## Calc

This problem is really weird. I have to explain why MVT applies for f(x)=2sinx-sin2x on the closed interval 7pi,8pi and then determine all values of c in the interval (7pi,8pi) that satisfies the conclusion of the theorem. However, the condition of MVT is

*asked by Anoop on December 5, 2016* -
## Calc

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + z4 k S is the part of the

*asked by Anon on November 23, 2016* -
## Calc

Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.) (a) (3, −3, 2) (b) (−2, −2sqrt3, 5)

*asked by ANON on October 25, 2016* -
## Calc

Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the plane 8x + y + z = 4

*asked by Anon on October 18, 2016* -
## Calc

If R = [−2, 2] × [−2, 0], use a Riemann sum with m = 4, n = 2 to estimate the value of (y2 − 2x2) dA. Take the sample points to be the upper left corners of the squares.

*asked by Anon. on October 11, 2016* -
## Calc

Evaluate the integral by reversing the order of integration.(2 integrals) 0 to 4 5ex2 dx dy 3y to 12

*asked by Anon on October 11, 2016* -
## calc

Given the position function, s of t equals negative t cubed divided by 3 plus 13 times t squared divided by 2 minus 30 times t, between t = 0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle

*asked by Mel on January 8, 2016* -
## Calc

An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume. Dimensions of the bottom of

*asked by David on November 16, 2015* -
## calc

Which of the following is the general solution of the differential equation dy dx equals the quotient of 8 times x and y?

*asked by Anonymous on July 1, 2015* -
## Calc

The marginal cost of manufacturing x yards of a certain fabric is C′(x)=3−0.01x+0.000006x2 (in dollars per yard). Find the increase in cost if the production level is raised from 3500 to 8500 yards. Increase in cost =

*asked by Danielle on April 28, 2015* -
## calc

A company runs food service concessions for sporting events throughout the country. Their marketing research department chose a particular football stadium to test market a new jumbo hot dog. It was found that the demand for the new hot dog is given

*asked by Dan on April 6, 2015* -
## calc

Give the starting value a, the growth rate r, and the continuous growth rate k. Round the answer for r to two decimal places Q = 0.414(e^0.885)^t a = ? r = ?% k = ?% I found a to be 0.414 but when finding the percentage for r and k I got stuck.

*asked by lenny on October 3, 2014* -
## calc

When 30 orange trees are planted per acre each tree yields 150 oranges For each additional tree per acre, the yield decreases by 3 oranges per tree. Express the total yield of oranges per acre, Y , as a function of the number of trees planted per acre, x,

*asked by sara on December 2, 2013* -
## calc

Find the perimeter of region R which is bounded by y = 1/(x^2+1) and y = -cos(x).

*asked by taylor on December 19, 2012* -
## calc

1. Let R be the region bounded by the x-axis, the graph of y=sqr(x) , and the line x=4 . a. Find the area of the region R. b. Find the value of h such that the vertical line x = h divides the region R into two regions of equal area. c. Find the volume of

*asked by naseba on March 29, 2012* -
## Calc

The temperature at any point in the plane is given by the function T(x,y)= 100/(x^2+y^2+1). Find the direction at the point (3,2) in which the temperature does not increase or decrease. Help, please? Thanks!

*asked by Brittany on February 28, 2011* -
## Calc

The temperature at any point in the plane is given by function f(x,y) = 100/(x^(2)+y^(2)+1). Find a direction at the point (3,2) in which the temperature does not increase or decrease. Help, please? Thank you.

*asked by Dani on February 27, 2011* -
## Calc

Use a graph to estimate the limit: lim θ->0 (sin(5θ)/θ) Note: θ is measured in radians. All angles will be in radians in this class unless otherwise specified. I tried graphing it on my calculator but the limit I got is incorrect.

*asked by Josie on January 25, 2011*