Answer:
25.8 ft
Step-by-step explanation:
Draw a right triangle with the right angle at the foot of the tower. The interior angle of the triangle at the top is the complement of the angle of depression. 90 - 74 = 16; it measures 16°. The leg at the bottom has length x. The height of the tower is the vertical leg and is 90 ft. We are looking for x.
For the 16° angle, x is the opposite leg, and 90 ft is the adjacent leg.
tan A = opp/adj
tan 16° = x/(90 ft)
x = 90 ft * tan 16°
x = 25.8 ft
Answer: 25.8 ft
Answer:
3cm/s
Step-by-step explanation:
Area of a square is expressed as:
A = L²
Rate of change of area is expressed as:
dA/dt = dA/dL•dL/dt
Given that
dA/dt = 24cm²/s
L = 4cm
Required
dL/dt
Since dA/dl = 2L
dA/dl = 2(4)
dA/dl = 8cm
Subatitute the given values into the formula
24 = 8 dL/dt
dL/dt = 24/8
dL/dt = 3cm/s
3x + 1 = 1/3x + 9 Multiply through by 3
<span>9x + 3 = x + 27 Subtract x </span>
<span>8x + 3 = 27 Subtract 3 </span>
<span>8x = 24 </span>
<span>x = 3 </span>
<span>AK = 3*3 + 1 = 10 </span>
<span>AB = 2*AK = 20</span>
9. 12 edges
Work: <u>4</u> horizontal edges on top, <u>4</u> horizontal edges on bottom, <u>4</u> vertical edges for sides
10. Ten-thousands place
Work: The 8 is highlighted. The order of places is: <u>ten-thousands</u>, thousands, hundreds, tens, ones
11. 10 4/5
Work: 54 ÷ 5 ——> 50÷5 = <u>10</u> with 4 left over and put into a fraction of <u>4/5</u>
12. 3,000
Work: 2 is in the thousands place so you look to the place behind it and there is an 8. If the number behind is 5 through 9 then you round up. 8 is above 5, therefore, you round the 2 up to a <u>3</u>.
13. 0.45
Work: The pattern is +0.03 so 0.42+0.03=<u>0.45</u>
14. 54 cakes
Work: <u>6 eggs</u> per 1 cake • <u>9 cakes</u> = 6•9=54 eggs used
15. 378 desks in the school
Work: 6 rows • 7 desks per row = 42 desks in 1 classroom. 42 desks • 9 classrooms = 378 desks in the whole school
The nearest thousand would be 25800.
