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kolbaska11 [484]
3 years ago
6

The equation d = 2t^ gives the distance from the start point of a toy boat that starts at rest and accelerates at 4 cm/s2. The e

quation d = 10t - 8 gives the distance from the start point of a second boat that starts at rest 8 cm behind the first boat and travels at a constant rate of 10 cm/s.
a) By setting the equations equal to each other, you can determine when the cars are the same distance from the start point: 2t2 = 10t - 8. Rewrite the equation so it is equal to 0 on the right hand side of the equation.

b) Factor the expression on the left side of the equation.

c) boats are the same distance from the start point at t = 1 and t = 4. Explain how the factors you found in part b were used to find these two times.
Mathematics
1 answer:
WITCHER [35]3 years ago
8 0

Answer:

Step-by-step explanation:

Given that:

d = 2t^2 and d = 10t - 8

If we equate both since they are distances, we have:

2t^2 = 10t - 8  

Algebraically, moving the equation to the right side, we get:

2t^ 2 = 10t -8 \\ \\ 2t^2 -10t +8 =0

To factor the equation on the left side:

2t^2 - 10t + 8 = 0

Factor out 2 on the left-hand side:

2 (t^2 -5t + 4) =0

=2 (t^2 -t-4t + 4)

= 2[t(t-1)-4(t-1)]

=2(t-1) (t-4)

To determine the time when the two boats have to cover an equal distance:

2(t -1)(t-4) =0 \\ \\(t-1)(t-4) =0

Thus:

t - 1 = 0 \  or \  t - 4 = 0 \\ \\ t = 1  \   or   \  t = 4

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Stella [2.4K]

Answer:

Tan C = 3/4

Step-by-step explanation:

Given-

∠ A = 90°, sin C = 3 / 5

<u>METHOD - I</u>

<u><em>Sin² C + Cos² C = 1</em></u>

Cos² C = 1 - Sin² C

Cos² C = 1 - \frac{9}{25}

Cos² C = \frac{25 - 9}{25}

Cos² C = \frac{16}{25}

Cos C = \sqrt{\frac{16}{25} }

Cos C = \frac{4}{5}

As we know that

Tan C = \frac{Sin C}{Cos C }

<em>Tan C = \frac{\frac{3}{5} }{\frac{4}{5} }</em>

<em>Tan C = \frac{3}{4}</em>

<u>METHOD - II</u>

Given Sin C = \frac{3}{5} = \frac{Height}{Hypotenuse}

therefore,  

AB ( Height ) = 3; BC ( Hypotenuse) = 5

<em>∵ ΔABC is Right triangle.</em>

<em>∴ By Pythagorean Theorem-</em>

<em>AB² + AC² = BC²</em>

<em>AC² </em><em>= </em><em>BC² </em><em>- </em><em> AB</em><em>² </em>

<em>AC² = 5² - 3²</em>

<em>AC² = 25 - 9</em>

<em>AC² = 16</em>

<em>AC  ( Base) = 4</em>

<em>Since, </em>

<em>Tan C = \frac{Height}{Base}</em>

<em>Tan C = \frac{AB}{AC}</em>

<em>Hence Tan C = \frac{3}{4}</em>

<em />

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3 years ago
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Step-by-step explanation:

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Find the values of s_1 and r for a geometric sequence with s_4= 18 and s_6= 72<br>​
dmitriy555 [2]
<h3>Answer: Choice A</h3>

s_1 = 2.25, \ r = 2

============================================

Work Shown:

s_4 = 18\text{ is the fourth term}\\\\s_5 = r*s_4 = 18r\\\\s_6 = r*s_5 = r*(18r) = 18r^2 = 72\\\\\text{So,}\\\\18r^2 = 72\\\\r^2 = \frac{72}{18}\\\\r^2 = 4\\\\r = \sqrt{4}\\\\r = 2

Use that r value and s_4 = 18 to find the first term

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You could use s_6 = 72 in place of s_4 = 18 (just make sure to use n = 6 instead of n = 4).

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