Prove that if x, y, z is a Pythagorean triple, then at least one of x and y is divisible by 3, and at least one of x, y, z is divisible by 5

Q: It is known that 3 3 S³ S² emax {x,y} dydx = ae³ + b, where a, b are integers. Determine the value…

A:

Q: A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 6.…

A: A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 6.…

Q: 1 Jo (1 + 4xy) dx dy

A:

Q: Find the future value (in $) of an ordinary annuity of $700 paid at the end of every 6-month period…

A:

Q: Combine the given expression into a single logarithm with coefficient one: ½lnx + ln(x + 1) (x − 1)…

A:

Q: a. How much pollution is in the lake after 11 hours? The amount of pollution that remains in the…

A:

Q: I the curl of the vector field F = ■ F = j+ k

A:

Q: Use the Laws of logarithms to rewrite the expression in a form with no logarithm of a product,…

A:

Q: Let be one of the acute angles of a right triangle. The trigonometric functions of the angle are…

A:

Q: The volume of a cube is increasing at 24 cubic inches per minute. What is the rate of change of its…

A: Let the volume of the cube be:  VdVdt=24

Q: derivative for this question. I gave the easy function. a) Domain of f(x) is b) Find the…

A:

Q: Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will…

A:

Q: Test the series below for convergence using the Ratio Test 2" n! M8 The limit of the ratio test…

A: ∑n=1∞2nn!

Q: Depreciation of Equipment For assets such as machines, whose market values drop rapidly in the early…

A:

Q: Find the derivative of the function. f'(s) = f(s) = (s³ + 1)e−s³

A:

Q: A bookstore sells 96 calculus textbooks per month at $120 each. The owners estimate that for each…

A: let number of $10 price increase is x

Q: A manufacturer has determined that the marginal profit from the production and sale of x ice cream…

A:

Q: Express the lengths a, b, c, and d in the figure only in terms of the trigonometric ratios of 0. The…

A:

Q: An open-top cylindrical tank with a volume of 2000 cubic meters is to be constructed using steel.…

A:

Q: |||| Solving a triangle with the law of sines: Problem type 1 Consider a triangle ABC like the one…

A:

Q: A function f (x) passes through the points (15,24), (18,37), and (22,25). Use Newton's Divided…

A: Points (15,24), (18,37) and (22,25)

Q: Find the point on the line 2x+2y−2=0 which is closest to the point (3,−5).

A: We can solve this question using calculus or coordinate geometry  Easier will be using coordinate…

Q: Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated…

A: If -4+i is a zero of the function, then -4-i must also be a zero (since the coefficients of the…

Q: Consider the following function. Function f(x) = 3x3 + 2x2 − 61x + 20 Factor (x + 5) (a) Verify…

A:

Q: Sketch a right triangle corresponding to the trigonometric function of the acute angle ?. Use the…

A: cotθ=4 As we know ⇒cotθ=BasePerpendicular=BP=41⇒B=4,P=1

Q: =-xi-jaroun j around and across the closed semicircular path that consists of the semicircular arch…

A: Given the field is:  F= -x2i-y2j We need to find the circulation and flux of the field F.

Q: Use algebra to rewrite the integrand; then integrate and simplify. (Remember the constant of…

A: The given integration is:∫7x2-42x3 dx

Q: f(x) = x5 - 5x a) Find the critical numbers of f. b) Determine the intervals on which f is…

A: The given function is: f(x)=x5-5x

Q: Given that the graph of f(x) passes through the point (5,7) and that the slope of its tangent line…

A: The graph of fx passes through the point 5, 7 and the slope of its tangent line at x, fx is 3x+5. To…

Q: For the given cost function C(x) = 32400+300x + x², First, find the average cost function. Use it to…

A: The given cost function : Cx=32400+300x+x2.We have to first the average cost function.Then we have…

Q: + SSD ²² Find (x + 4y)dA where D = {(x,y) | x² + y² ≤ 25, x ≥ 0}

A:

Q: Perform the indicated operation and write the answer in the form of a +bi. (6+5)-10i O -5+6i O 6+5/…

A: let  K=(6+5i)-10i

Q: (a) Iff has a local minimum value at c, show that the function g(x) = -f(x) has a local maximum…

A: It is given that the function is gx=-fx and f has local minimum value at c. a) It is required to…

Q: Consider the function f(x) = 12x5 + 15x4 - 240x³ + 1. f(x) has inflection points at (reading from…

A:

Q: Find the equation of the line that is tangent to the curve y= 2x cos x at the point (pi,-2pi) The…

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find the directional derivative of the function at P in the direction  of the unit vector u=cos…

Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

A:

Q: please do e

A:

Q: An open-top cylindrical tank with a volume of 2000 cubic meters is to be constructed using steel.…

A: Let radius of cylindrical tank =r m and height of cylindrical tank =h m

Q: Learning Target IA2: I can compute the volume of a solid of revolution using the method of…

A: To solve the following

Q: Given f(x) = 3x² + 7x, find f'(x) using the limit definition of the derivative.

A:

Q: (7.3890 )

A:

Q: Use the Fundamental Theorem to show that the following is true. b b Sf(x)dx= f(x)dx + f(x)dx C с b a…

A: By Fundamental Theorem of Calculus, ∫abfxdx=Fb-Fa where F'x=fx

Q: using cofactors. HONT 14 2 10 0 00 1 2 0 0 -2 1

A:

Q: Given that f'(x) = cos(x), ƒ'(π/2) = 7 and f(7/2) f'(x) = f(x) = ← ▲ = 4 find:

A: f"x=cosx Integrating both sides ∫f" xdx=∫cosxdx f'x=sinx+c Put x=π2 f'π2=sinπ2+c 7=1+c c=7-1 c=6…

Q: Solve the right triangle. 460 √15100 Find the length of the side opposite to the given angle. (Round…

A:

Q: Find the radius r of a circle with an arc length

A:

Q: Question 4 Approximate the zero of ƒ(x) = x³ − x + 1 in [-2, -1] to within 0.00001. Edit View Insert…

A: To find out the zero of the function in the given range.

Q: If A is the area of the intersection of the regions enclosed by the graphs of r= 1 + cos and = 2 cos…

A: To find the area of the region enclosed by the two polar curves, we need to find the points of…

Q: Using the substitution u = (A) (B) C D 1+1 du [₁ -1/2 du [(u ¹/2 - u-1/2) d du (u - 1) / u-²1) x + 1…

A: