Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3) a) quadratic function; quadratic term: 6x^2; linear term: 24x; constant term: −6 b) linear function; linear term: −21x; constant term: −6 c) quadratic function; quadratic term: −18x^2; linear term: −21x; constant term: −6 d) linear function; linear term: −18x^2; constant term: −6

The correct Option is C).  quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6

Step-by-step explanation:

Given : f(x) = (3x + 2)(-6x - 3)

Now, f(x) = -18x² -9x -12x - 6

⇒ f(x) = -18x² - 21x - 6

Now, since the highest degree of the given function f(x) is 2 so the function f(x) is quadratic.

Now, quadratic term is one which has highest power x = 2 So, quadratic term = -18x²

Linear term is one which has  power x = 1 So, linear term = -21x

Constant term is one which has power of x = 0. So, constant term = -6

Hence, The correct Option is C).  quadratic function; quadratic term: −18x²; linear term: −21x ; constant term: −6

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.