The coordinates of the point on the curve y=x²+3x+4 the tangent at which passes through the origin are - a. (-2,2)(2,14) b. (1, -1) (3,4) c. (2.14)(2,2) d. (1,2) (14,3)
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To find the coordinates of the point on the curve where the tangent passes through the origin, we need to find the equation of the tangent line and then solve for the x-coordinate of the point of tangency.
Let's break it down step by step:
1. Start with the equation of the curve: y = x² + 3x + 4.
2. Find the derivative of the curve to find the slope of the tangent line. The derivative of y = x² + 3x + 4 is dy/dx = 2x + 3.
3. Set the derivative equal to the slope of the line passing through the origin, which is 0 since the line is horizontal. So, 2x + 3 = 0.
4. Solve the equation to find the x-coordinate of the point of tangency. Subtract 3 from both sides: 2x = -3. Divide by 2: x = -3/2.
5. Plug the x-coordinate back into the original equation to find the y-coordinate. y = (-3/2)² + 3(-3/2) + 4 = 9/4 - 9/2 + 4 = 9/4 - 18/4 + 16/4 = 7/4.
6. Therefore, the point on the curve where the tangent passes through the origin is (-3/2, 7/4).
None of the given options match the coordinates (-3/2, 7/4). Therefore, none of the options are correct.
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The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62.The probability that any postcard posted in Portugal on Friday is delivered to the UK within a week is 0.41. Anna is on holiday in Portugal. She posts 15 postcards to the UK on Monday. How many of her postcards can she expect to be delivered within a week? (2 marks)
Solve for x given the lines are parallel.7(x - 710126°
What letter comes next y, b, w,d,u,f,
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Sin x = summit/ trailhead
Cos x = horizontal distance / trailhead
tan x = summit/ horizontal distance
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B. 60
C. 180
D. 90
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Therefore you are simply doing 12 multiplied by 15.
12 × 15
= 180
So your answer is C. 180
Final answer:
To calculate the total number of mortgage payments over a period of 15 years, one should multiply the number of years by 12. Thus, a 15-year mortgage will have 180 payments in total.
Explanation:
The Patels took out a 15-year mortgage. A mortgage is usually paid on a monthly basis. Therefore, to calculate the total number of payments the Patels will make, multiply the number of years by 12 - the number of months in a year. So, 15 years * 12 months/year equals 180 payments. Therefore, the correct answer is C. 180.
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Hope this helps!
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Answer: C
Step-by-step explanation: The surface area of a cube is calculated by , where x is the side length of the cube. So, 6 * (4)^2 = 96 inches squared, or C
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So, 28 x 3 = 84 cookies