Answer:
![\frac{64}{q^{4}}](https://tex.z-dn.net/?f=%5Cfrac%7B64%7D%7Bq%5E%7B4%7D%7D)
or
![64q^{-4}](https://tex.z-dn.net/?f=64q%5E%7B-4%7D)
Step-by-step explanation:
Remember the properties
Product rules
![a^{n} a^{m}=a^{n+m}](https://tex.z-dn.net/?f=a%5E%7Bn%7D%20a%5E%7Bm%7D%3Da%5E%7Bn%2Bm%7D)
Power rules
![(a^{n})^{m}=a^{n*m}](https://tex.z-dn.net/?f=%28a%5E%7Bn%7D%29%5E%7Bm%7D%3Da%5E%7Bn%2Am%7D)
we have
![(-2p^{-5}q4p^{5}q^{-3})^{2}](https://tex.z-dn.net/?f=%28-2p%5E%7B-5%7Dq4p%5E%7B5%7Dq%5E%7B-3%7D%29%5E%7B2%7D)
Applying the product rules
![(-2(4)p^{-5+5}q^{-3+1})^{2}](https://tex.z-dn.net/?f=%28-2%284%29p%5E%7B-5%2B5%7Dq%5E%7B-3%2B1%7D%29%5E%7B2%7D)
![(-8p^{0}q^{-2})^{2}](https://tex.z-dn.net/?f=%28-8p%5E%7B0%7Dq%5E%7B-2%7D%29%5E%7B2%7D)
![(-8q^{-2})^{2}](https://tex.z-dn.net/?f=%28-8q%5E%7B-2%7D%29%5E%7B2%7D)
Applying the power rules
![64q^{-4}](https://tex.z-dn.net/?f=64q%5E%7B-4%7D)
![\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5C%3Aa%5E%7B-b%7D%3D%5Cfrac%7B1%7D%7Ba%5Eb%7D)
![64q^{-4}=\frac{64}{q^{4}}](https://tex.z-dn.net/?f=64q%5E%7B-4%7D%3D%5Cfrac%7B64%7D%7Bq%5E%7B4%7D%7D)
Q1.the given scale factor is 1:16
the area is 7 square feet
when calculating the area the scale factor is squared as well.
since the scale factor is 16, to find out area the scale should be squared that is,
16*16 = 256
then the new area is 7 square feet * 256
actual area = 256 * 7 = 1792 square feet
Q2. the rectangle with length 6 inches and width 3 inches.
the perimeter of the rectangle before changing dimensions are;
=(6*2) + (3*2)
= 12 + 6 = 18 inches
after multiplying the dimensions by 8,
new length = 6*8 = 48 inches
new width = 3*8 = 24 inches
new perimeter = (48*2) + (24*2)
= 96 + 48
= 144 inches
the perimeter ratio from new to old = 144:18
the perimeter has increased by (144/18) times
= 144/18 = 8
answer is perimeter increased by a factor of 8
q3)
area of the triangle
= 1/2 * height * base
= 1/2 * (5-2) *(4-(-3))
= 1/2 * 3 * 7
= 10.5 units²
area of semicircle
=pi*r2
r = 2-(-1.5)
= 3.5
area = 3.14 * (3.5)²
= 38.465 units²
total area = area of triangle + area of semicircle
= 10.5 + 38.465
= 48.965
round it off to the closest tenth
area = 49 units²
Answer:
Step-by-step explanation:
i think 1/4 of the circle has been taken by red.
and for the second answer it's 30%
Answer:
545.119
Step-by-step explanation:
75 * (1 + .2/12)^10 * 12
75 * (1.016667)^10*12
Now things get a little tricky. What does 10*12 mean? I'm taking it to mean 120
75 * (1.016667)^120
75 * 7.268
545.119
Answer:
22 46 15
Step-by-step explanation:
i looked it up because i was even confused. but i think this is right. hope this helps.