17. What is the vertex of a quadratic function y = x2 -3x - 10? 49 a) (-) b) () e) (--) 49 3

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A: Consider the given information and the figure:

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Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

A:

Q: 3. Find two positive numbers whose product is 100 and whose sum is a minimum.

A: Let the numbers be x,y According to question = x*y =100                     y = 100/x  Sum of…

Q: Assume that the total revenue received from the sale of x items is given by, R(x) = 29 In (3x + 1),…

A: Given data :  R(x) = 29 ln(3x+1) C(x) = x/2

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by 3 L(x,y) = x²…

A: We will use partial derivative to find x and y.

Q: 15, Find a) fxedx b). dx using the substitution of x- cost.

A: We have to evaluate the integrals

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A: The average cost per duclimer  can be estimated by the following function…

Q: If k = 3, for approximately what values of x in the interval [0, 1] will the error in the quadratic…

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Q: Suppose you have a 2.5 grade point average in 3 courses. What is the minimum average you can have in…

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Q: Provide two positive numbers with a product of 169 and a sum which is a minimum.

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Q: Next There is a line through the origin that divides the region bounded by the parabola y = 4x –…

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Q: How to find the minimum value of y for the  equation:  5.79702sin(0.009055x) +8.499779

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Q: 8. What is t line x = 5

A: We have given a region bounded by the curve y=3-6x , x=5and x-axisthe region is show in the graph

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: 1. Find two positive numbers whose product is 100 and whose sum is a minimum.

A: Let the numbers are x and y.   It is known that to minimize a function we have to equate the first…

Q: 6. Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

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Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

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Q: The slope of the tangent line to the parabola y=4x2+2x+6y=4x2+2x+6 at the point (-3,36) is: ?

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Q: What is the difference between the maximum and minimum of the quantity (x2y2)/25 where x and y are…

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Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

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Q: The life expectancy for females born during 1980-1985 was approximately 80.6 years. This grew to 81…

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Q: Suppose you have a 2.5 grade point average in 3 courses. What is the minimum average you can have in…

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Q: 3. Find the exact area of the piece of land in San Francisco, Surigao del Norte which is bounded by…

A: Topic:- application of integration

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

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Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

Q: 1. The sum of two positive number is 42. What are these numbers if their product is a maximum?

A: As per our guidelines we can help you in solving only first question. Rest of the problems, you have…

Q: Evaluate S(z² + 3z)dz along the straight line from (2,0) to (2, 2) and then from (2, 2) to (0, 2).

A:

Q: What is the particular solution for y′=−6x+3 that passes through the point (−4,−8)? Do not include…

A: The given differential equations is y′=−6x+3.

Q: 4. A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the…

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Q: the area of the largest rectangle that can be drawn with one side along the x-axis and the two…

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Q: 13. A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then…

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Q: Find the point P on the line y=3x that is closest to the point (40,0). What is the least distance…

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Q: find the length of the curve y = 2x6+1/8x2 from x is greater than or equal to 1 and less than or…

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Q: csec?x +secX -2=0

A: Given equation sec2x+secx−2=0

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: The mean of 5 positive integers is 16. What is th maximum value that one of this numbers may have?

A: Given problem is :

Q: 8. Suppose that 2+ V4 - x2 -2 2 If F(0) = 2, find the maximum value of F(x).

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Q: Find the length of the curve on the interval 3/2 Y= (10x+ 15) 15

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Q: 2 5. Write the equation of the line tangent to y=4-x when x=-1.

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Q: The minimum v value of this quadratic function is 0 v At the point ( ), the x-axis intercepts with…

A: We use the data from the graph to complete the sentences. The minimum value of this quadratic…

Q: A line that is normal to the curve x^2+3xy-4y^2=0 at (6,6) intersects the curve at what other point?

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Q: What are the coordinates of the point on the graph of Ax) = (x+ 1)(x+ 2) at which the tangent is…

A: solution:-f(x)=x+1x+2      =x2+3x+2slope of tangent=ddxf(x)                             =ddxx2+3x+2…

Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

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Q: 2. Suppose Kim can run at 8 miles per hour and swim at 2 miles per hour. As shown in the figure…

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Q: 11. Determine three positive numbers whose sum is 21, so that your product is the maximum possible…

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Q: 1. What is the maximum product of two positive numbers which are solutions to 4x+y = 16?

A: 4x+y=16

Q: Suppose the labor cost​ (in dollars) for manufacturing a camera can be approximated by…

A: Let us take a continuous function f(x,y) such that double derivative of function is also continuous.…

Q: 1 Find the length of the curve ソ= 9 from x =1 to x=2. 28x7,

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Q: What is the average distancebetween the parabola y = 30x(20 - x) and the x-axis on theinterval [0,…

A: The equation of parabola is given by y=30x20-x on [0, 20] The expression to evaluate the average of…