<h3>Number of minutes in 3/4 of an hour is :
</h3>
<h3>n = 3/4 × 60 = 45 minutes.
</h3>
<h3>Now, If it continues to rain at that rate for 15 more minutes :
</h3><h3>
</h3><h3>So, time taken = 45 + 15 min = 1 hour.
</h3><h3>
</h3><h3>Let, rain gauge is filled x fraction in 1 hour.
</h3>
<h3>So,
</h3>
<h3>Hence, this is the required solution.</h3>
Answer:
See below.
Step-by-step explanation:
I will assume that 3n is the last term.
First let n = k, then:
Sum ( k terms) = 7k^2 + 3k
Now, the sum of k+1 terms = 7k^2 + 3k + (k+1) th term
= 7k^2 + 3k + 14(k + 1) - 4
= 7k^2 + 17k + 10
Now 7(k + 1)^2 = 7k^2 +14 k + 7 so
7k^2 + 17k + 10
= 7(k + 1)^2 + 3k + 3
= 7(k + 1)^2 + 3(k + 1)
Which is the formula for the Sum of k terms with the k replaced by k + 1.
Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.
But the formula is true for 1 term because 7(1)^2 + 3(1) = 10 .
So it must also be true for all subsequent( 2,3 etc) terms.
This completes the proof.
The answer would be 3d and 4d
Complementary angles equal 90 degrees so
The measures of the two angles = 90
(4y +5) + (4y +8) = 90
4y + 4y = 8y and 5 + 8 = 13
90 - 13 = 77
8y = 77
77/8 = 9 5/8
y = 9 5/8
Now we can plug this into each measyre to find the answer
9 5/8 x 4 = 38.50
38.50 + 5 = 43.50
38.50 + 8 = 46.50
46.5 + 43.5 = 90
The first angle measures 43.5
The second angle measures 46.5
I hope this helps!
