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Molodets [167]
3 years ago
14

Solve the following exponential equations. 10^(x+1) − 10^(x−1) = 1287

Mathematics
1 answer:
Rudiy273 years ago
7 0

Answer:x=2.114

Step-by-step explanation:

Given

10^{x+1}-10^{x-1}=1287

10\times 10^x-\frac{10^x}{10}=1287

Let 10^x=y

10y-\frac{y}{10}=1287

\frac{100y-y}{10}=1287

99y=1287\times 10

y=\frac{12870}{99}=130

10^x=130

Taking \logboth sides

x\log (10)=\log (130)

x=\frac{\log (130)}{1}

x=2.114

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Answer:

∴ ∠BAD = sin^{-1}(0.2044) = 11.8°

Step-by-step explanation:

i) AD = 9 cm

ii) DC = 3 cm

iii) ∠BCD = 35°

iv) Since AB is parallel to DC and ∠ABD = 90°  then we can conclude that ∠BDC = 90°.

v) \frac{BD}{DC}  =  \frac{BD}{3\hspace{0.1cm}cm}  = tan(35) = 0.6128      ∴ BD  = 3 \times 0.6128 = 1.84 cm

vi) ∴ sin(∠ BAD ) = \frac{BD}{AD}      ⇒     sin(∠ BAD ) = \frac{1.84}{9} = 0.2044

     ∴ ∠BAD = sin^{-1}(0.2044) = 11.8°

7 0
4 years ago
Koalas absorb only 25% of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. How many ounces of fiber did he
kolbaska11 [484]
<h3>Answer:</h3>

42 ounces

<h3>Step-by-step explanation:</h3>

In this question, it is asking how many ounces of fiber did the Koala eat that day.

In order to solve this question, we would need to gather some important information from the question.

Important Information:

  • Koalas absorb only 25% of fiber they eat
  • Koala absorbed 10.5 ounces of fiber in 1 day

With the information above, we can solve the question.

We know that koalas only absorb 25% of fiber. We also know that a koala absorbed 10.5 ounces of fiber.

This means that the 10.5 ounces is 25% of fiber. This is 1/4 of the fiber it ate.

Now, we just need to find the other 3/4.

We could just multiply 10.5 by 4 to find how much fiber it ate that day.

10.5*4=42

When you multiply, you should get 42.

This means that the Koala ate 42 ounces of fiber that day.

<h3>I hope this helps you out.</h3><h3>Good luck on your academics.</h3><h3>Have a fantastic day!</h3>
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