Notice that
13 - 9 = 4
17 - 13 = 4
so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :
149 = 9 + 4k
140 = 4k
k = 140/4
k = 35
This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.
Put another way, we have
but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.
ANSWER
x=27
EXPLANATION
The two triangles are similar so the corresponding sides are equal.
Cross multiply to get;
Expand:
65x=39x+702
Group similar terms:
65x-39x=702
Simplify
26x=102
Divide both sides by 26,
x=702/26
x=27
Answer:
c) three
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Step-by-step:
The tetrahedron is a triangular pyramid with equilateral triangles on each face.
Answer:
Step-by-step explanation:
Rewrite the differential equation as:
Integrate both sides with respect to x:
Integrate one more time both sides with respect to x:
Now that we find the solution, let's find its derivate:
Evaluating the initial conditions:
Replacing the value of the constants that we found in the differential equation solution:
