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LuckyWell [14K]
3 years ago
11

A triangle has an area of 221.16 in.² the height of the triangle is 29.1 inches what is the length of the base of the triangle

Mathematics
1 answer:
Zigmanuir [339]3 years ago
7 0
The formula you should use is Area = 1/2bh, in other words, area equals half times base times height. Now, substitute everything in, the equation should now be 221.16 = 1/2*b*29.1. This simplifies into 221.16 = 14.55b, now divide 14.55 on both sides, which leaves us to 15.2 = b. However, don't forget the units, which the answer (length of base) should be 15.2 in.^2.
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nikitadnepr [17]
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4 years ago
Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist
yuradex [85]

Answer:

0 < t < 5 is the required interval for the differential equation (t - 5)y' + (ln t)y = 6t to have a solution.

Step-by-step explanation:

Given the differential equation

(t - 5)y' + (ln t)y = 6t

and the condition y(1) = 6

We can rewrite the differential equation by dividing it by (t - 5) as

y' + [(ln t)/(t - 5)]y = 6t/(t - 5)

(ln t)/(t - 5) is continuous on the interval (0, 5) and (5, +infinity).

6t/(t - 5) is continuous on (-infinity, 5) and (5, +infinity)

We see that for these expressions, we have continuity at the intervals (0, 5) and (5, +infinity).

But the initial condition is y = 6, when t = 1.

The solution to differential equation is certain to exist at (0, 5)

Which implies that

0 < t < 5

is the required interval.

3 0
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Step-by-step explanation:

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Vera_Pavlovna [14]

Answer:

\boxed {x = -\frac{1}{7}}

Step-by-step explanation:

Solve for the value of x:

6(4x + 5) = 3(x + 8) + 3

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6(4x + 5) = 3(x + 8) + 3

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-Combine like terms:

24x + 30 = 3x + 24 + 3

24x + 30 = 3x + 27

-Take 3x and subtract it from 24x:

24x + 30 -3x = 3x - 3x + 27

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21x + 30 - 30 = 27 - 30

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-Divide both sides by 21:

\frac{21x}{21} = \frac{-3}{21}

x = \frac{-3}{21}

-Reduce the fraction to the lowest term by extracting and canceling out 3:

x = \frac{-3\div3}{21 \div 3}

\boxed {x = -\frac{1}{7}}

Therefore, the value of x is -\frac{1}{7}.

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