Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
Answer:
2.5477 feet
Step-by-step explanation:
Refer the image attached to understand my solution.
BC = height of lamppost.
DE = Julia
AD = shadow of Julia
BD = 2 feet. AD = 5 feet
BA = BD + AD
= 2 + 5 = 7 feet
In ΔABC
tan 20° = 
BC = 7 * tan 20°
BC = 2.5477 feet
SO the height of lamppost = 2.5477 feet
Answer:
Women has better study habit than men.
Step-by-step explanation:
For knowing who has better study habits and attitudes toward learning we have to find the mean of both the women and men data.
The first step is that we only take first 18 values of both women(X) and men(Y) data, to make them of same length
Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations.
Calculating all values:
= 141.0556
= 121.25
Thus, women has better study habit than men. Since Mean of X is larger than Mean of Y.
Answer:
no
Step-by-step explanation:
A portion of the Quadratic Formula proof is shown. Fill in the missing statement. Statements Reasons x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared Take the square root of both sides of the equation ? Simplify the right side of the equation x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 2 times a x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 2 times a squared x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over a
