positive

Q: Find the measure of the side of the right triangle whose length is designated by a lowercase letter....

A: we know that in right angle triangle  tanθ=altitudebase                                  ..1 here, a...

Q: Find and simplify the difference quotient [f(x + h) - f(x)]/h, h ≠ 0 for the given function : f(x) =...

A: we have to simplify and find the difference quotient  f(x+h)-f(x)h    , h≠0and given that f(x)=-x2+2...

Q: Evaluate the definite integral.

A: ∫15x2x-1 dx Consider, ∫x2x-1 dx Put, 2x-1=t⇒21-0=dtdx⇒2 dx=dt⇒dx=dt2 Therefore, ∫x2x-1 dx=∫t+12tdt2 ...

Q: Constant Function Rule Prove that if u is the vector function with the constant value C, then du/dt ...

A: It is given that the function ut is a vector function whose value is always equal to constant C.The ...

Q: You have 600 feet of fencing to enclose a rectangular field. However, one side of the field lies alo...

A: Let the length of field be x feet Let the width of field be y feet Perimeter of field having one sid...

Q: you will use a CAS to help find the absoluteextrema of the given function over the specified closed ...

A: The function f(x)=-x4+4x3-4x+1, -34,3. We have to answer the following...

Q: Express the following as a sum, difference, or multiple of logarithms. log 2 a

A:

Q: Evaluate the integral.

A: Given: ∫01 tan-1x1+x2 dx To find: Value of the integral.

Q: A straight wire 50cm long is bent into the shape of an L.  What is the shortest possible distance be...

A: Suppose the wire bent into the shape of  L  be the right triangle ∆PQR with QR=x cm,  PQ=50-x cm By...

Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the ...

A: GIVEN DATA : Function y=f(x)=4+3-x       TO FIND : Equation of the tangent line at (x,y)=(-1,6) to t...

Q: Use the circle shown in the rectangular coordinate system to draw the angle 405° in standard positio...

A: To draw the angle 405o 405o=360o+45o Therefore 405o is in the first quadrant since 360o completes on...

Q: Find the area of the surface obtained by revolving the given curve about the x-axis. on (0, In(3)

A:

Q: Solve the formula for the specified variable. Do you recognize the formula? If so, what does it desc...

A: Given :           P=C+MC

Q: R(t) - 60t - 212; t = 3 Find the average rate of change of R(t) over the time intervals [t, t + h], ...

A: Consider the given function, Rt=60t-2t2R3+h=603+h-23+h2=-2h2+48h+162R3=603-232=162   The average rat...

Q: Use integration to find a general solution of the differential equation

A: Given: dydx = xex2  To find: General solution of the given differential equation.

Q: A wheelchair ramp is to be built with a slope 3/28. What angle will the ramp make with the horizonta...

A: We have given that wheelchair ramp is built with slope 3/28. We have to construct a diagram for it. ...

Q: Find the exact value of the expression.Do not use a calculator.

A: Given: Trigonometric identities:  

Q: Suppose it has been determined that the probability is 0.8 that a rat injected with cancerous cells ...

A:

Q: Coordinate unit vectors Compute the following cross products. Then make a sketch showing the two vec...

A:  Compute the following cross products. Then make a sketch showing the two vectors and their cross pr...

Q: Sketch the graph of a function that has a local maximumat 2 and is differentiable at 2.

A: We have to sketch graph of function that has local maximum at 2 and is differentiable at 2. We know ...

Q: Find equations of all tangent lines to the graph of y = 4x + 40x² + 125x + 118 which pass through th...

A: We have given equation of graph y=4x3+40x2+125x+118. We have to find equations of all tangents which...

Q: Divide using long division. State the quotient, q(x), and the remainder, r(x) : (x2 + 8x + 15) ÷ (x ...

A: To divide: x2+8x+15÷x+5 using long division. Solution: x+5x+3x2+8x+15x2+5x                          ...

Q: Find the indicated series by the given operation. Show that by integrating term by term the expansio...

A: Expansion of 11-x=1+x+x2+x3+... Therefore, Expansion of 11-x2=1+x2+x4+x6+... ⇒-2x1-x2=-2x-2x3-2x5-2x...

Q: Use the method of your choice to find the solution of the following initial value problem. y '(t) = ...

A:

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y + 9e...

A: Use Green Theorem to evaluate  ∫C5y+9exdx+10x+7cosy2dy where, C is the boundary of the region enclos...

Q: QUESTION 1 Find the domain of the composite function f g. f(x) 8(x) =x + 6 %3D x + 9' O (x|x -9) {x ...

A: we have to find the domain of the composite function fog. the given functions are: f(x)=5x+9 g(x)=x+...

Q: A telephone pole is 55 feet tall. A guy wire 80 feet long is attached from the ground to the top of ...

A: Let BC be the pole.And AB is the guy wire.Length of the pole given = a = 55 feetLength of the wire =...

Q: *indefinite integral* ((sin^−1 (t))^2) dt

A:

Q: a. Identify the function’s local extreme values in the given domain,and say where they occur.b. Grap...

A: Given function is gx=x-2x2-1. a. Given domain is 0 ≤ x < 1. Local maximum and local minimum does ...

Q: It's multiple choice but I don't know how to get the answer

A:

Q: QUESTION 8 Let s= f(t) be the position of a rock t seconds after it is thrown vertically upward. To ...

A:

Q: Evaluate each limit and justify your x - 2x² - 8x lim xS4 V x - 4

A: limx→4x3-2x2-8xx-4, We have to find the limit of this expression.

Q: In Exercises 1–8, find the eccentricity of the ellipse. Then find and graph the ellipse’s foci and d...

A: Consider the given ellipse 16x2+25y2=400

Q: If In a = 2, In b = 3, and In c = 5, evaluate the following: %3| %3| a (a) In (b) In Va*b°cª 413 4 |...

A: GIVEN DATA : The value of ln a=2, ln b=3 and ln c=5        TO FIND : Evaluate  (a). lna4b3c2 (b). ln...

Q: The imaginary unit i is defined as i = __________, where i2 = ___________

A: Imaginary unit is represented by i.

Q: Consider the circle x2 + y2 − 6x − 8y = 0 as shown. (a) Find the center and radius of the circle. (b...

A: Given that, x2+y2-6x-8y=0

Q: Find k so that 4x + 3 is a factor of 20x3 + 23x2 - 10x + k.

A: If 4x+3 is a factor, then on plugging -34 for x in the given expression, the result is 0.

Q: Equal vectors For the points A(3, 4), B(6, 10), C(a + 2, b + 5), and D(b + 4, a – 2), find the value...

A: Given points are A(3,4),B(6,10),C(a+2,b+5), and D(b+4,a-2) Also given that AB→=CD→

Q: Find the Jacobian J of the transformation

A:

Q: Scientists can determine the age of ancient objects by themethod of radiocarbon dating. The bombardm...

A: Here, we will use the known half-life of C to find the radioactivity after time t. We know that radi...

Q: Assume ƒ is a continuous on [2, 4],, and ƒ(2)= 4. Evaluate ƒ(4).

A: we have been given that f is continuous on [2,4] and f(2)=4. we have to evaluate f(4). the given exp...

Q: An island is 2 miles due north of its closest point along a straight shoreline. A visitor is staying...

A: Draw a diagram representing the situation.

Q: For the value of b will y=x^3 + bx^2 + cx + d have a point of inflection at x=1

A:

Q: Solve the problem on the applications of differential equations.

A: Let M(t) be the mass of the organic material in the tank at time t and Mt=CtVt, where C(t) and V(t) ...

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.