Answer:
q = 80 degrees
r = 70 degrees
s = 10 degrees
t = 70 degrees
u = 40 degrees
v = 60 degrees
Step-by-step explanation:
starting with the fact that all angles in any triangle always sum up to 180 degrees :
q = 180 - 60 - 40 = 80 degrees
r = 180 - (60+10) - 40 = 180 - 70 - 40 = 70 degrees
the triangle 40-60-q and v-u-blank are similar triangles. your can say the smaller triangle is just a projection of the large triangle through the focal point at angle q.
that means the angles must be equal.
v = 60 degrees
u = 40 degrees
similar for 10-r-blank and t-s-blank.
s = 10 degrees
t = 70 degrees
To solve for x,
4.7x = 2.5x + 8.8
minus 2.5x from both sides:
2.2x = 8.8
divide both sides by 2.2:
2.2x/2.2 = 8.8/2.2
simplify:
x = 4
Answer:
the answer is 6/11
hope this helped! have a great day :D
I would invest $500 to be compounded as Compound Interest is $1,540,250 while Simple Interest is $50.
<u>Step-by-step explanation:</u>
Step 1:
Calculate simple interest in the first case. Given details are Principal (P) = $500, Rate (R) = 5% and Time (T) = 2 years
⇒ Simple Interest (SI) = PRT/100 = 500 × 5 × 2/100 = $50
Step 2:
Calculate compounded interest for the second case. Given details are Principal (P) = $500, Interest rate (r) = 3%, Number of times it is compounded (n) = 12, time (t) = 2 years
⇒ Compound Interest (CI) = [P (1 + r/n)^n × t] - P
⇒ CI = [500 (1 + 3/12)^12 × 3] - 500
⇒ CI = [500 (1 + 1/4)^36] - 500
⇒ CI = [500 (5/4)^36] - 500
⇒ CI = [500 × 3081.5] - 500 = 1540750 - 500
⇒ CI = $1,540,250
Answer:
1) -15/4
2) -15/2
Step-by-step explanation:
1) Let u=4t. Then the limits become u=4(0)=0 and u=4(4)=16. Also du=4 dt upon differentiating the equation.
So the integral can be written as
Integral( 1/4 f(u) , u=0 to u=16)
We are given Integral( f(u) , u=0 to u=16) is -15. So a fourth of that is our answer for the first question.
2) Let u=t^2. Then the limits become u=(0)^2=0 and u=(4)^2=16. Also upon differentiating we obtain equation du =2 t dt.
So the integral becomes
Integral( 1/2 f(u) , u=0 to u=16).
We are given Integral( f(u) , u=0 to u=16) is -15. So a half of that is our answer for the second question.
