Answer:
= 150 square units
Step-by-step explanation:
Area of a right triangle is given by the formula;
1/2 bh ; where b is base and h is the height of the triangle
using Pythagoras theorem, we can find the height;
h² = 20² - 16²
h = √144
= 12 units
The base of the small triangle can also be found using Pythagoras theorem;
b² = 15² - 12²
b = √ 81
= 9
Therefore;
Area = 1/2 bh
= 1/2 × 12 × (16+9)
= 1/2 × 12 × 25
= 6 × 25
= 150 square units or 150 u²
Answer:
36 yd³
Step-by-step explanation:
The above solid shape given is a triangular prism.
The volume of triangular prism is given as ½ × base length of the triangle (b) × height of the triangle (h) × the length of the prism (l)
Base length of triangle (b) = 9 yd
Height of the triangle (h) = 2 yd
Length of the prism (l) = 4 yd
Volume = ½bhl
Volume = ½*9*2*4
Volume = 9*4
Volume of prism = 36 yd³
Very complicated problem, but thank goodness I have too much time and am a nerd.
Basically model 1st account as so.
Fv=pv(1+I)^N
Fv future value
Pv present value
I interest
N number years
So first equation is interest earned after 3 years
Y=5000(1+0.023)^3
Y=5353 (rounded up)
So we know that the interest earned is 5353-5000 which is 353.
Now Ronisha (clearly the name of a future investment genius) invests these 353$ in a new account.
Now remember we’re not solving for FV we’re cause we’re given that: 55.2$
However this is the interest earned not the future value. So if interest earned is fv - pv and we know pv
Fv - 353 = 55.2
Fv = 408.2$
So now we reuse the formula
408.2 = 353(1+0.032)^x
Now just solve for x:
First divide both sides by 353
1.156 = 1.032^x
Remember the log rule that states x=b^y is same as y=logb(x)
So using the same logic:
X= log1.032(1.156)
Use some kind of calculator for that where you can adjust log base. But you basically get:
X= 4.602
So Ronisha has to basically invest 5 years or 4.6 years which is 4 years and 7 months.
Omg nevermind, wait it’s simple interest….
Sorry here’s the simple solution. My bad, but I worked so hard on the top part I don’t want to delete it.
I=prt
Interest = principal * rate * time
I= 5000(0.023)(3)=345
Then just do the same but plug 55.2 for I
55.2 = 345(0.032)t
Now solve for t
55.2 = 11.04t
t= 5
As you can see, similar logic where ultimately it takes 5 years. But this “genius” Ronisha should’ve just done compounding interest (my first calculation) and gotten it done in 4.6 years. Almost 5 months faster.
<span>length of the side = 1.2 / 4 = 0.3 m
area = 0.3</span>² = 0.09 m²
