A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is given by the function f(t) = - 16t + 404t + 8. Find its maximum height. Its maximum height is feet. If necessary, round to two decimal places. Do not include units.

Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: A company manufactures rope, and the total cost of producing r feet of rope is Cr dollars.To…

Q: Assume lim f(x) = 14, lim g(x) = 6, and lim h(x) = 5. Compute the following limit and state the…

A: We can answer and explain the answer as below.

Q: ans 늘 sin ()+c 19 -4x² teinx dx I+ x2 dx ans: į sini'Ln'xte 3. sečxdx ensesin 3tanx 15-9tañx dx

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

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Q: Match the vector field with its graph. F(x, y) = yi -6+ 世 -5+

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Q: s(2) dr=3 and s (4)d. f (x)dx: =-2. what is (x)dx? Make sure to justify your answer -2 or the…

A: We can find the answer as below using property of integration.

Q: What is the equation of the tangent plane normal to x2 + y2 + z = 9 at the point (1, 2, 4)? O 2x -…

A: Given; f(x,y,z)=x^2+y^2+z-9  Point (1,2,4)

Q: Inn 1 1 1 1 + 25 1 1 a) Σ-(-1)" (- b) 1+ 4 1 + 64 n-Inn. 9. 16 36 49

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Q: Determine the rate of change at (0, 2) of the function 1 h (x, y) V1+x² + 2y² in the direction of…

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Question

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Q: Find the volume of the solid that is bounded by the surfaces z = = 92 - x2 - y2 in the first octant.…

A: 0≤ z ≤ 81-x2-y2z=0x2+y2=920≤y≤81-x20≤x≤9

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: This question can be solved using the concept of domain.

Q: Matching Type. Match the functions in Column A with their corresponding derivatives in Column B.…

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Q: Clairaut's Theorem Give one example of a function where the Clairaut Theorem fails, and justify your…

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: This is a problem related to derivative of the function. For calculating the unit if derivative…

Q: Use substitution to find the Taylor series at x 0 of the function 4 sin (-x). Choose the correct…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 4 1 lim t→+∞ \ 3t2 +4' 2t (?, ?)

A: The given limit ; limt→+∞t2+43t2+4,12t

Q: The point P(p, 1), where p > 0, lies on the curve x² + 2xy³ – 3y* = 0. a) Calculate the value of p.…

A: Since point , P(p,1) lies on the given curve, therefore this point will satisfy the curve .Using…

Q: ASAP

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Q: Find the dimensions of a rectangle with a maximum perimeter that can be inscribed in the ellipse 4x…

A: Given ellipse 4x2+9y2=36                ->Equation(1)Let (x,y) be the upper right corner of the…

Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y2

A: Given: I=∫03∫0∞ x21+y2dydx As we know that; ∫11+x2dx=tan-1x+C And ∫a·fxdx=a·∫fxdx, where a is…

Q: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: From 1990 to 2000 the student tuition at a University grew from $12,000 to $18,000. (a) Using the…

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Q: -z“, where T is The temperature at a point (x, y, z) is given by T(x,y, z) = 200e measured in…

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Q: 8* – 2* 10. lim, »0 4x

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Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: Which of the following is NOT a correct way to express the vector v = (2,-4) a) 2î - 4 where î =…

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Q: 7) FIND EQUATION Of THE TANGENT AN LINE TO THE PARAMZTRIL X=t-+もt こe AT t =0. CURVE

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Q: Evaluate the definite integral. Using Fundamental Theorems Calculus. sin x 4 – x² dx V1 + x2

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Q: Find the symmetric equations of the line that passes through the points (-2, 1, 0) and (1, 3, 5).

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Q: Water is being poured at the rate of 2z m' /min into an inverted conical tank that is 12-meter deep…

A: We need to find rate of water leaking.

Q: Part A) approximate the area under h(x)=x^2 from x=0 to x=2 using four rectangles and a left…

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Q: Answer the questions for the following polar equation. 3 r 3= 3+10cos0 (a) Identify the conic as a…

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Q: es conve n=1

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Q: 3 - (3x + 3ry')dx - (3y - 2y - 3xy)dy = 0

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Q: Evaluate the iterated integral. /3 6. y cos(x) dy dx

A: I=∫0π3∫09y cos x dy dx =∫0π3cos(x) ∫09y dy dx  =∫0π3 cos(x) y2209 dx  =∫0π3 cos(x)812 dx

Q: Evaluate the triple iterated integral. xyz³ dx dy dz

A: ∫02∫02∫-14xyz3dxdydz=∫02∫02x2yz32x=-1x=4dydz…

Q: 5) FIND THE MACLAURIN MALLAL fOR SERIES fa)=x cos (2x) %3D

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Q: ||r(t) × r"(t)|| ||M(t)|| Use the formula k(t) to find k(t). r(t) = t²i + t'"j 242 t7 K(t) = (4+ 121…

A: Cross product

Q: Use only the fact that 3x(2 - x)dx = 4 and the properties of integrals to evaluate the integrals in…

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Q: et +e-* find the length of the curve h(x) = from x = 0 to x = In 2. 2

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: 3) Fiad fue area of the reigon bounded by the goaphs of algebraic functioans. tue the +6, g(d) =0,…

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Q: Describe the domain and range of the function. (x, y) = 9x2 - y Domain: y): x is any real number, y…

A: We need to find domain and range.

Q: | (2x - y) dx + (x + 7y) dy. Evaluate C: x-axis from (0, 0) to (0, -7) and (0, -7) to (4, -7)

A: x-axis from 0,0 to 0,-7 indicates that interval of y is from 0 to -7 y-axis from 0,-7 to 4,-7…

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (9t + 4)i + tj, 0 sts 1

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Q: Evaluate the iterated integral / / хуdydxdz. Do not round. Give the answer in the form of the common…

A: Given: I=∫02∫04-z2∫0xxydydxdz   As we know that; The Power rule: ∫xndx=xn+1n+1+C