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Marina CMI [18]
1 year ago
15

The third term of an A.P is 4m - 2n. If the ninth term of the progression is 2m - 8n. Find the common difference in terms of m a

nd n​
Mathematics
1 answer:
ipn [44]1 year ago
5 0

Let a_n denote the <em>n</em>-th term in the progression. So

a_n=a_{n-1}+d

for some constant difference between terms <em>d</em>.

Solve for a_n explicitly:

a_4=a_3+d

a_5=a_4+d=a_3+2d

a_6=a_5+d=a_3+3d

and so on, up to

a_n=a_3+(n-3)d

We're told that the third term is a_3=4m-2n, and the ninth term is a_9=2m-8n, and according to the recursive rule above, we have

a_9=a_3+6d

Solve for <em>d</em> :

2m-8n=(4m-2n)+6d

-2m-6n=6d

d=-\dfrac{2m+6n}6=\boxed{-\dfrac{m+3n}3}

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An object is moving at a speed of 95 kilometers every 7.5 weeks. Express this speed in
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Answer:

<h2>5,936.76 feet/day</h2>

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Time = 7.5weeks

Since we are to express the answer in feet per day, we will convert the distance to feet and time to days.

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The course length of the Boston Marathon is about 4.2×104 meters. The course length of the Iditarod Trail Invitational ultra-mar
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Answer:

The ultra-marathon Idita Rod Trail is about 38 times longer than the Boston Marathon.

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x -----> the length of the Boston Marathon in meters

y -----> the  length of the Idita rod Trail Invitational ultra-marathon in meters

we have

x=4.2*10^4\ m

y=1.6*10^6\ m

we know that

To find out how many times as long is the course of the Idita rod Trail ultra-marathon as that of the Boston Marathon, divide the length of the Idita rod Trail Invitational ultra-marathon by the length of the  Boston Marathon

so

\frac{y}{x}

\frac{x}{y}=\frac{1.6*10^6}{4.2*10^4}

Remember that

To divide two numbers in scientific notation, divide their coefficients and subtract their exponents

\frac{1.6*10^6}{4.2*10^4}=\frac{1.6}{4.2}*(10^{6-4})=0.381*(10^{2})=38.1

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The ultra-marathon Idita Rod Trail is about 38 times longer than the Boston Marathon.

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