soniabegum0187

Find the volume of the solid whose base is the given region and which has property that each cross section perpendicular to the x-axis is an equilateral triangle. the triangular region with vertices A(1,1); B(3,5); C(3,-2).

You do hot have a thermometer to measure temp you are able to measures the speed of sound through the air. If you measure the sound to be 349m/s. what is the air temp?

Write the following English descriptions of rules using the rule format (e.g., rules like [ +F ] → [ −F ] / #). Use features to describe segments and environments as much as possible. If it’s important for your answer, assume English segments and the corresponding features. (Hint: Suppose the difference between an affricate and a stop is that affricates are post-alveolar and [ +strident ] .)

(1) Laterals delete before a nasal consonant.

(2) Insert a mid front tense vowel between two stops.

(3) Obstruents become voiceless at the end of a word.

(4) At the beginning of words, delete a vowel if there’s another vowel immediately after it.

(5) Nasals become stops if the preceding vowel is nasalized.

(6) Coronal stops become affricates before high front vowels.

(7) All consonants except glides delete if there are two non-glide consonants before them.

(8) A vowel becomes round if there’s another round vowel after it, separated by any number of consonants.

Find the total areas in the shaded regions.

Y=x²

x+y=2

Consider the paraboloid z = x² + 3y² and the plane z = x + y + 4, which intersect the parabolid in a curve C at P(2, 1, 7). Complete parts (a-d) to find the equation of the line tangent to c at P.

a) Find a vector normal to the plane at P.

b) Find a vector normal to the plane tangent to the paraboloid at P.

c) Find a direction vector to the line tangent to C at P. (Hint: Gradient Vector is orthogonal to a tangent plane.)

d) Knowing a point on the tangent line and the director vector, write an equation of the tangent line in parametric form.

1) Find the point on the paraboloid y = x^2 + z^2 where the tangent plane is parallel to the plane 4x + 2y - 12z +3 = 0.

2) Find the equation of the tangent plane to the paraboloid at the point in part 1)

Let (S) be the paraboloid z=10-(x-1)^2-(y-2)^2 and let M be the highest point (relative to the plane Oxy) on (S ). Let (P) be the tangent plane to (S) at M. Which point from the following is on the plane (P) ?