Answer:
k = 4
Step-by-step explanation:
16k = 16(4) = 64 and
64 = 4 × 4 × 4
![\sqrt[3]{64}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B64%7D)
= ![\sqrt[3]{4^{3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B4%5E%7B3%7D%20%7D)
= 4
Yes, I think part A is asking you to find the unit rate :)
Answer:
a) 8cm
b) 19.8cm
Step-by-step explanation:
The key to these types of questions is to keep proportions in mind.
To solve the first question, you want to find the proportion of the smaller triangle to the bigger triangle. The length of AE is 6cm, but the length of AD is (6+4) = 10cm. So the proportion of the bigger triangle to the smaller triangle is 10/6. So to find the lengths of the sides of the bigger triangle, we want to keep this number in mind.
The BE side is parallel to CD, so we have to use length of BE multiplied by the proportion in order to get the length of CD.
CD = 4.8 * (10/6) = 8
CD = 8cm
For the second question, you use the same concept to find all the other side lengths. The only one you need left for the shape EBCD is side BC. Do the same thing you did before, take the length of the side of the smaller triangle that corresponds with side AC on the bigger triangle. In this case, it's AB, which is 4.5cm. Multiply this by 10/6 to get AC.
AC = 4.5 * (10/6) = 7.5
AC = 7.5
But we're not done. We just found the length of AC, but we need the length of BC to calculate the perimeter. To do this, we want to take the length of AC - the length of AB.
7.5 - 4.5 = 3
So the length of BC is 3cm. Now, to find the perimeter, just add all the sides of EBCD together.
4.8 + 4 + 8 + 3 = 19.8cm.
Hope this helps.
Answer:
Option D. 10,779 feet
Step-by-step explanation:
Given from the figure attached,
PT = OB = 7000 ft
PB = OT = x feet
and angle of elevation (∠POT) = 30°
By applying Tan rule in the triangle POT,
tan33° =
= 
tan33° = 
x = 
x = 10779 feet
Therefore, distance between the bird (B) and plane (P) is 10,779 feet.
Option D. will be the answer.
Answer:
The ideal size will be a 45cmx45cm square, giving you a perimeter of 180cm.
Step-by-step explanation:
The shortcut answer here is that the square will always be the most efficient rectangle for border to area, so the sides should be the square root of 2025 cm, or 45 cm each, giving you a total of 180 minimum perimeter.
The full solution is to express the perimeter as a function of the length and width, define either length or width as a function of the other, take the entire expression's derivative and solve for zero. Let's do it:
So first the area:
2025 = wl
l = 2025 / w
Now the sides:

Then we can take its derivative with respect to w

Now we can set the derivative to zero, and solve for w:

So the width being 45, we can get the length by dividing the area by that amount, which of course is also 45.