We are told that the principle is the same for both investments so we can say:
315=P(r+4)/100 and 175=Pr/100 solving both for P you have:
P=31500/(r+4) and P=17500/r since P=P:
17500/r=31500/(r+4)
175(r+4)=315r
175r+700=315r
-140r+700=0
-140r=-700
r=5
So the rates are 5% and (5+4)=9%
check...
P(9/100)=315 and P(5/100)=175
P=31500/9 and P=17500/5
P=157500/45 and P=157500/45
So P=P
note: P=$3500
3500(9/100)=$315
3500(5/100)=$175
9514 1404 393
Answer:
yes
Step-by-step explanation:
The width of the rectangle is given by ...
W = A/L
W = (20 cm²)/(8 cm) = 2.5 cm
__
The modified rectangle has a length of (8 cm +2 cm) = 10 cm, and an area of (20 cm² +4 cm²) = 24 cm². Its width will be ...
W = (24 cm²)/(10 cm) = 2.4 cm
The percentage change in size is ...
((2.4 cm)/(2.5 cm) -1) × 100% = -4%
The width of the rectangle decreased less than 5%. Noah is correct.
No, it’s doesn’t pass the vertical line test.
Answer:
31 centimeters long for each edge
Step-by-step explanation:
Answer:
Cos(15) = Cos(45-30)
Sin(15) = Sin(45-30)
Cos(45-30) - Sin(45-30)
Simplifying both brackets
Recall
Cos(A+B) = CosACosB - SinASinB (For cosine... The sign is always the opposite during expansion. If you look... Cos(A+B) became negative during its expansion;So if It was Cos(A–B)... Its expansion is CosACosB + SinASinB)]
Sin(A+B) = SinACosB + CosASinB
Now let's go!
Cos(45-30) = Cos45Cos30 + Sin45Sin30
From Trig
Cos45 = 1/√2
Cos30 = √3/2
Sin45 = 1/√2
Sin30 = 1/2
Substituting
Cos(45-30) = (1/√2).(√3/2) + (1/√2).(1/2)
= √3/(2√2) + 1/(2√2)
= 1 + √3/(2√2).
For
Sin(45 - 30)
= Sin45cos30 – Cos45Sin30
= (1/√2).(√3/2) – (1/√2).(1/2)
= √3/(2√2) – 1/2√2
= √3 – 1/(2√2)
So the question was
Cos15 - Sin15
Substituting...
1 + √3 / 2√2 – (√3 - 1)/ 2√2
When the Minus interacts with the parenthesis
We have
1 + √3 - √3 + 1 / (2√2)
= 2/2√2
= 1/√2.
THE ANSWER IS 1/√2 AND NOT 1/2.
YOU CAN VERIFY THIS WITH YOUR CALCULATOR ALSO.
YOU'LL HAVE 0.7071 WHICH IS SAME AS 1/√2.
HAVE A GREAT DAY!
