Answer:
Nerys pays 3.1/3.84,5=84,5£per year
Eleri pays 3.84,5=253,5£per year
253,5-84,5=169£ more pay Eleri
The domain of the function is the range of values of x that can be used to be replaced in the equation for it to become true. We are given that the value of f(x) should range only from -1 to 3. We evaluate each of the choices and see if the values of f(x) will fall within the range.
(a) -12; f(x) = 2^(-12) - 10 = -9.9999 (NOT AN ANSWER)
(b) -10; f(x) = 2^(-10) - 10 = -9.999 (NOT AN ANSWER)
(c) -9; f(x) = 2^(-9) - 10 = -9.999 (NOT AN ANSWER)
(d) -6; f(x) = 2^(-6) - 10 = -9.98 (NOT AN ANSWER)
(e) -2; f(x) = 2^(-2) - 10 = -9.75 (NOT AN ANSWER)
Hence, none of the choices will allow the value of f(x) to fall between -1 and 3.
Answer:

Step-by-step explanation:
Perform the multiplication and addition:

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<em>Comment on the squaring</em>
There are several ways you can find the square (x+4)².
- Use your knowledge that (x+a)² = x²+2ax+a².
- Use FOIL* to compute (x+4)(x+4) = x² +4x +4x +4² = x²+8x+16
- Use the distributive property: (x+4)(x+4) = x(x+4) +4(x+4) = x² +4x +4x +4² (same as FOIL for two binomials)
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* FOIL is mnemonic for {First, Outer, Inner, Last} referring to pairs of terms in the factors (x +a)(x +b). The x terms are the First terms. The Outer terms are the first x and b. The Inner terms are "a" and the second x. The Last terms are "a" and "b". You are to form the sum of those pairs of terms to find the product of the binomials.
Answer:
Step-by-step explanation:
Looking at the right angle triangle that contains x and y, we would apply trigonometric ratio to determine x an y. Taking 60 degrees as the reference angle,
Hypotenuse = y
Adjacent side = x
Opposite side = 36
Therefore,
Sin # = opposite side / hypotenuse
Sin 60 = 36/y
y = 36/Sin60 = 36/0.8660 = 41.57
Cos # = adjacent side/hypotenuse
Cos 60 = x/41.57
x = 41.57Cos 60 = 41.57 × 0.5 = 20.785
Sin45 = z/36
z = 36Sin45 = 36 × 0.7071 = 25.4556
The balloon has a volume
dependent on its radius
:

Differentiating with respect to time
gives

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

The surface area of the balloon is

and differentiating gives

so that at the moment the radius is 3 m, its area is increasing at a rate of
