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meriva
2 years ago
7

Altitudes AA1 and BB1 are drawn in acute △ABC. Prove that A1C·BC=B1C·AC

Mathematics
1 answer:
Sophie [7]2 years ago
7 0

Answer:

See the attached figure which represents the problem.

As shown, AA₁ and BB₁ are the altitudes in acute △ABC.

△AA₁C is a right triangle at A₁

So, Cos x = adjacent/hypotenuse = A₁C/AC ⇒(1)

△BB₁C is a right triangle at B₁

So, Cos x = adjacent/hypotenuse = B₁C/BC ⇒(2)

From (1) and  (2)

∴  A₁C/AC = B₁C/BC

using scissors method

∴ A₁C · BC = B₁C · AC

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Which out of the 2 choices is correct ?
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Answer:

sinB is correct

Step-by-step explanation:

Calculating each of cos/ sin for ∠B

cosB = \frac{adjacent}{hypotenuse} = \frac{6}{3\sqrt{5} } = \frac{2}{\sqrt{5} } and

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sinB = \frac{opposite}{hypotenuse} = \frac{3}{3\sqrt{5} } = \frac{1}{\sqrt{5} } and

\frac{1}{\sqrt{5} } × \frac{\sqrt{5} }{\sqrt{5} } = \frac{\sqrt{5} }{5}

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Solve p/q=r/s solve for p
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3 years ago
You save 8,500.00 you place 40% in a saving account earning a 4.2 APR compounded annually and the rest in a stock plan. the stoc
babunello [35]

Answer: A.) $509.64

B.) 73.12

Step-by-step explanation:

Saved amount = $8500

Savings account = 0.4 × 8500 = $3400; rate(r)= 4.2%, composed annually.

Stock plan = 8500 - 3400 = $5100

Using compound interest formula for the amount in a savings account :

Period(t) =2

A = P(1 + (r÷n))^nt

A = 3400(1 + (0.042 ÷ 1))^(1×2)

A= 3400( 1 + 0.042)^2

A = 3400(1.042)^2

A = $3691.60

gain on saving = 3691.60 - 3400= $291.60

Stock plan:

First year = 3% decrease

5100(1-0.03) = $4947

Second year = 7.5% increase

4947(1+0.075) = $5318.03

Gain on stock = $5318.03 - $5100 = $218.03

Total profit = $218.03 + $291.60 = $509.63

B.) If 60% had been to savings :

Savings account = 0.4 × 8500 = $5100; rate(r)= 4.2%, composed annually.

Stock plan = 8500 - 5100 = $3400

Using compound interest formula for the amount in a savings account :

Period(t) =2

A = P(1 + (r÷n))^nt

A = 5100(1 + (0.042 ÷ 1))^(1×2)

A= 5100( 1 + 0.042)^2

A = 5100(1.042)^2

A = $5537.386

gain on saving = $5537.386 - 5100= $437.386

Stock plan:

First year = 3% decrease

3400(1-0.03) = $3298

Second year = 7.5% increase

3298(1+0.075) = $3545.35

Gain on stock = $3545.35 - $3400 = $145.35

Total profit = $437.386 + $145.35 = $582.73

PROFIT difference = $582.736 - 509.63 = $73.106

7 0
3 years ago
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