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2 years ago

6 If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is

Mathematics

1 answer:

lyudmila [28]2 years ago

4 0

Answer:

1) a right triangle

Step-by-step explanation:

One of the caractheristics of a right triangle, the one in which the sum of the two sides squared is the hypotenuse squared(Pytagorean Theorem), is also the the altitudes of a triangle meet at one of the triangle’s vertices. So 1) is the answer to this question.

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Step-by-step explanation:

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2 years ago

Using Newton's Law of Cooling. You are a medical examiner called to an abandoned house in which a dead body has been discovered.

Artyom0805 [142]

A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
$\frac{dT}{dt} = \alpha(T -52)$

B) Find general solution by separating variables and integrating $\int\frac{dT}{T-52} = \alpha \int dt \\ ln (T-52) = \alpha t + C \\ T = C e^{\alpha t} +52$ :

C) Initial condition is t=0, T = 87
$87 = C +52 \\ C = 35$

D) Total time elapsed is 10 minutes, new temperature is 84
$84 = 35 e^{10\alpha} +52$
solve for alpha
$e^{10\alpha} =\frac{32}{35} \\ \alpha = \frac{ln(32/35)}{10} \\ \alpha = -.00896$

E) Temperature function is:
$T = 35 e^{-.00896 t} +52$
solving for t
$t = \frac{ln (\frac{T-52}{35})}{-.00896}$
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2 years ago

Answer with the explanation step by step

andrey2020 [161]

Answer:

The answer is A. $\frac{3(x-21)}{(x+7)(x-7)}$ .

Step-by-step explanation:

To find the difference of this problem, start by simplifying the denominator, which will look like $\frac{3}{x+7}-\frac{42}{(x+7)(x-7)}$ . Next, multiply $\frac{3}{x+7}$ by $\frac{x-7}{x-7}$ to create a fraction with a common denominator in order to subtract from $\frac{42}{(x+7)(x-7)}$ . The problem will now look like $\frac{3}{x+7}*\frac{x-7}{x-7}-\frac{42}{(x+7)(x-7)}$ .

Then, simplify the terms in the problem by first multiplying $\frac{3}{x+7}$ and $\frac{x-7}{x-7}$ , which will look like $\frac{3(x-7)}{(x+7)(x-7)}-\frac{42}{(x+7)(x-7)}$ . The next step is to combine the numerators over the common denominator, which will look like $\frac{3(x-7)-42}{(x+7)(x-7)}$ .

Next, simplify the numerator, and to simplify the numerator start by factoring 3 out of $3(x-7)-42$ , which will look like $\frac{3(x-7-14)}{(x+7)(x-7)}$ . Then, subtract 14 from -7, which will look like $\frac{3(x-21)}{(x+7)(x-7)}$ . The final answer will be $\frac{3(x-21)}{(x+7)(x-7)}$ .

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2 years ago