Answer:
In Tyler scale, 1 inch equals 4 ft.
Step-by-step explanation:
Giving the following information:
Tyler made a scale drawing of a 24 ft longboat. In his drawing, the boat was 6 inches.
<u>We know that 1 ft is 12 inches. Therefore, 24 ft:</u>
24*12= 288 inches
<u>Now, we have to determine the scale that Tyler used.</u>
<u></u>
1 Tyler inch= 288/6= 48 inches
In ft:
1 Tyler inch= 48/12= 4 ft
In Tyler scale, 1 inch equals 4 ft.
Note that the formula for the circumference of a circle is πd, while the formula for the area of a circle is πr².
π≈3.14
A. C=πd
Simply plug in the numbers into the formula.
Diameter=Radius*2
17*2=34
C=34(π)
B. (π)(5²)
Plug in the numbers into the formula. Remember that half of the diameter is the radius.
C. (π)(4.5)
There are two possible formulas that could be used to calculate the circumference of a circle: πd and 2πr.
The expression above is simply multiplying the circle's radius times pi. Therefore, it is not a method that could be used to find the circumference of a circle.
D. (π)(6.5²)
Remember that the formula for calculating the area of a circle is πr².
Half of the diameter is 6.5 (13.5/2=6.5). 6.5 cm. is the radius. Now just plug the numbers into the formula.
(π)(6.5²)
Therefore, the last answer choice is the correct answer.
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Answer:
They are the same.
Step-by-step explanation:
The graphs are same because <em>x</em>² is always positive, so the absolute value part is redundant.
Absolute value of function = - 9 / 3 .
The absolute value or modulus of a real number x, denoted by |x|, is the non-negative value of x without regard to its sign. Namely, |x|=x if x is a positive number, and |x|=-x if x is negative (in which case negating x makes -x positive) , and |0|=0.
For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.
x ≥ 1.52 / 3 x - 1 = 2 / 3 x + 4⇒ -1 = 4 which is not possible .Now for all x ≤ 1.5- 2 /3 x + 1 = 2 / 3 x + 4⇒ 4 / 3 x = -3 x = - 9 /4 Hence absolute value = - 9 / 3 .
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