Answer:
(13/2) cm
Step-by-step explanation:
The hypotenuse here is of length 13 cm. The shorter leg lies opposite to the 30° angle. Recall that the sine function is defined as
opposite side
sin Ф = -----------------------
hypotenuse
which, in this case, works out to:
opposite side
sin 30° = -----------------------
13 cm
and so the length of the opposite side (which is also the "shorter leg") is
shorter leg length = (13 cm)(sin 30°) = (13 cm)(1/2) = (13/2) cm
Volume: 2112.5π
Surface Area: 663π
First, let's find the height of the cylinder. Using the formula for lateral surface area, 2*π*r*h:
2*π*13*h = 325π
(divide π by both sides)
26h = 325
h = 12.5 in.
Next, let's solve the surface area of the cylinder using the formula π*r²*h.
π * 13² * 12.5 = π * 169 * 12.5 = 2112.5π.
Next, let's solve the surface area using the formula 2πrh + 2πr².
(2 * π * 13 * 12.5) + (2 * π * 13²) = 325π + 338π = 663π.
<h3>
Answer: A. 18*sqrt(3)</h3>
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Explanation:
We'll need the tangent rule
tan(angle) = opposite/adjacent
tan(R) = TH/HR
tan(30) = TH/54
sqrt(3)/3 = TH/54 ... use the unit circle
54*sqrt(3)/3 = TH .... multiply both sides by 54
(54/3)*sqrt(3) = TH
18*sqrt(3) = TH
TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer
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An alternative method:
Triangle THR is a 30-60-90 triangle.
Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.
The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.
Now use the pythagorean theorem
a^2 + b^2 = c^2
(TH)^2 + (HR)^2 = (TR)^2
(x)^2 + (54)^2 = (2x)^2
x^2 + 2916 = 4x^2
2916 = 4x^2 - x^2
3x^2 = 2916
x^2 = 2916/3
x^2 = 972
x = sqrt(972)
x = sqrt(324*3)
x = sqrt(324)*sqrt(3)
x = 18*sqrt(3) which is the length of TH.
A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.
4d + 12 = 4(d + 3)
Basically, you just need to determine what 4d and 12 have in common. In this case, they both divide evenly by 4. Therefore 4 (d + 3) = 4d + 12 according to the distributive property.
Answer:
(A)increasing
Step-by-step explanation:
Given the time and total distance ran by Myra in the table below.
We observe that as time increases, Myra's distance also increases. It is the speed(0.2 miles per minute) which is constant.
Therefore Option A is the correct option.
