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sweet-ann [11.9K]
3 years ago
12

A textbook store sold a combined total of 294 history and sociology textbooks in a week. The number of history textbooks sold wa

s 86 more than the number
of sociology textbooks sold. How many textbooks of each type were sold?
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
8 0

Answer:

8

Step-by-step explanation:

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\huge{\underline{\boxed{\tt{Answer:}}}}

Let AB be a chord of the given circle with centre and radius 13 cm.

Then, OA = 13 cm and ab = 10 cm

From O, draw OL⊥ AB

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

∴ AL = ½AB = (½ × 10)cm = 5 cm

From the right △OLA, we have

OA² = OL² + AL²

==> OL² = OA² – AL²

==> [(13)² – (5)²] cm² = 144cm²

==> OL = √144cm = 12 cm

Hence, the distance of the chord from the centre is 12 cm.

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3 years ago
HELP i’m having trouble with my homework assignments
Aleksandr-060686 [28]

Answer:

Collin: about $401 thousand

Cameron: about $689 thousand

Step-by-step explanation:

A situation in which doubling time is constant is a situation that can be modeled by an exponential function. Here, you're given an exponential function, though you're not told what the variables mean. That function is ...

P(t)=P_0(2^{t/d})

In this context, P0 is the initial salary, t is years, and d is the doubling time in years. The function gives P(t), the salary after t years. In this problem, the value of t we're concerned with is the difference between age 22 and age 65, that is, 43 years.

In Collin's case, we have ...

P0 = 55,000, t = 43, d = 15

so his salary at retirement is ...

P(43) = $55,000(2^(43/15)) ≈ $401,157.89

In Cameron's case, we have ...

P0 = 35,000, t = 43, d = 10

so his salary at retirement is ...

P(43) = $35,000(2^(43/10)) ≈ $689,440.87

___

Sometimes we like to see these equations in a form with "e" as the base of the exponential. That form is ...

P(t)=P_{0}e^{kt}

If we compare this equation to the one above, we find the growth factors to be ...

2^(t/d) = e^(kt)

Factoring out the exponent of t, we find ...

(2^(1/d))^t = (e^k)^t

That is, ...

2^(1/d) = e^k . . . . . match the bases of the exponential terms

(1/d)ln(2) = k . . . . . take the natural log of both sides

So, in Collin's case, the equation for his salary growth is

k = ln(2)/15 ≈ 0.046210

P(t) = 55,000e^(0.046210t)

and in Cameron's case, ...

k = ln(2)/10 ≈ 0.069315

P(t) = 35,000e^(0.069315t)

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3 years ago
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