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finlep [7]
4 years ago
9

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.

After 6 hours of burning, a candle has a height of 17.4 centimeters. After 23 hours of burning, its height is 7.2 centimeters. What is the height of the candle after 11 hours?
Mathematics
1 answer:
Alborosie4 years ago
7 0
Assume that the rule connecting height of the candle to time is a linear one.  If you do, then we have to find the equation of this line, and then use this equation to predict the height of the candle after 11 hours.

Two points on this line are (6,17.4) and (23, 7.2).  The slope is thus
         7.2-17.4           -6
m = ---------------  =  -----------  or   -3/5.
           23-6                 10

Find the equation of the line.  I'm going to use the slope-intercept formula:

y = mx + b  =>   7.2 = (-3/5)(23) + b.  Solving for b,   b = 21.

Now    we know that y = (-3/5)x + 21

Let x=11 to predict the height of the candle at that time.

y = (-3/5)(11) + 21 = 14.4 inches  (answer)
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A vehicle was travelling at a speed of 72km per hour. What distance did it cover in 2 hours? A. 158km B. 148km C. 168km D. 144km
Andru [333]

Answer:

D. 144km

Step-by-step explanation:

If the vehicle travels 72km every hour, in two hours, it will drive 144km. (72x2=144)

4 0
3 years ago
work out the total area of triangle ABC. calculate the area of AC. sides are:8.2cm and 13.5cm and angle 81 degrees
umka2103 [35]

Answer:

54.67 cm²

Step-by-step explanation:

Given that the two sides of Δ ABC are 8.2 cm and 13.5 cm and the angle included by those sides is 81°.

Let, b = 8.2 cm and c = 13.5 cm and ∠ A = 81°

Hence, area of triangle ABC, Δ = \frac{1}{2} bc \sin A

⇒ Δ = \frac{1}{2} bc \sin 81

⇒ Δ = \frac{8.2 \times 13.5 \times \sin 81}{2}

⇒ Δ = 54.67 cm² (Answer)

7 0
3 years ago
M: 3/2, (4, 6)<br> In point-slope from
omeli [17]

Answer:

y - 4= 3/2 (x-4)

Step-by-step explanation:

4 0
3 years ago
Explain how to find each root, with its multiplicity, for the polynomial y=x^5-27x^2.
Nuetrik [128]

The roots of y = x^{5}-27\cdot x^{2} are 0 (multiplicity 2), -3 (multiplicity 1), -\frac{3}{2}+i\,\frac{3\sqrt{3}}{2} (multiplicity 1) and -\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} (multiplicity 1).

The characteristics of the polynomial can be derived from algebraic techniques. Roots and multiplicity can be found by <em>factoring</em> the polynomial. The multiplicity is represented by a power binomial of the form:

(x-r_{i})^{m},\,m \le n (1)

Where n is the grade of the polynomial.

Now we proceed to factor the formula:

y = x^{5}-27\cdot x^{2}

y = x^{2}\cdot (x^{3}-27)

y = x^{2}\cdot (x^{2}+3\cdot x +9)\cdot (x-3)

Please notice that x^{2}+3\cdot x + 9 have two complex roots.

y = x^{2}\cdot \left(x+\frac{3}{2}-i\,\frac{3\sqrt{3}}{2}  \right)\cdot \left(x+\frac{3}{2}+i\,\frac{3\sqrt{3}}{3}  \right)\cdot (x-3)

The roots of y = x^{5}-27\cdot x^{2} are 0 (multiplicity 2), -3 (multiplicity 1), -\frac{3}{2}+i\,\frac{3\sqrt{3}}{2} (multiplicity 1) and -\frac{3}{2}-i\,\frac{3\sqrt{3}}{2} (multiplicity 1).

We kindly invite to see this question on polynomials: brainly.com/question/1218505

7 0
3 years ago
Solve for x.<br> really beed help before my final!!!!​
S_A_V [24]

Answer:

√19 or 4.36

Step-by-step explanation:

Since one leg is missing, you need to use Pythagorean theorem for this.

The hypotenuse is known so,

c² - a² = b²

c = 10

a = 9

b = ?

10² - 9² = b²

100 - 81 = b²

19 = b²

b = √19

3 0
3 years ago
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