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3 years ago

Consider the functions f(x)=(ax^2-b)/(x^2-4) and g(x)=(x^2-cx+d). if the limit as x approaches 3 equals 6, what is the relations

hip between a and b?

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

6 0

$6=\dfrac{a\cdot3^2-b}{3^2-4}\\\\
6=\dfrac{9a-b}{5}\\\\\
9a-b=30\\\\
\boxed{b=9a-30}$

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Solve completely (all missing sides and all missing angles) using trig ratios or laws. Round to the nearest tenth.

hodyreva [135]

Answer:

Step-by-step explanation:

3. Use Cosine law to find the length of the unknown side (PR)

q² = p² + r² - 2prCos Q

q is the opposite side of ∠Q;

p is the opposite side of ∠P; p = 33

r is the opposite sides of ∠R ; r = 67

q² = 33² + 67² - 2* 33*67 Cos 19°

= 1089 + 4489 - 4422 * 0.95

= 1089 + 4489 - 4200.9

= 1377.1

q = √1377.1

q = 37.1

PR = 37.1

To find the angle use law of sin

$\sf \dfrac{q}{Sin \ Q} =\dfrac{p}{Sin \ P}\\\\\\\dfrac{37.1}{Sin \ 19}=\dfrac{33}{Sin \ P} \\\\\\\dfrac{37.1}{0.33}=\dfrac{33}{Sin \ P}\\\\\\37.1* Sin \ P = 33 *0.33\\\\Sin \ P =\dfrac{33*0.33}{37.1}$

Sin P = 0.3

$P = Sin^{-1} 0.3\\$

P = 17.5°

∠R = 180 - (19 + 17.5)

= 143.5°

6 0

2 years ago

Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking

marusya05 [52]

Answer:3 minute

Step-by-step explanation:

Sakura speaks hungarian =150 words per minute

Sakura speaks polish =190 words per minute

and it is given she speaks 270 more words in polish than in hungarian

She speaks for a total of 5 minutes

let she speaks hungarian for t mins

therefore $150\times t+270=190\left ( 5-t\right )$

t=2 mins

therefore sakura speaks hungarian for 2 mins and polish for 3 mins

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3 years ago

Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$ .

Thus Kendra dives out of the water surface at 6 feet from the board.

3 0

2 years ago

Divide the fractions and simplify the answer 60 / 2 2/3

balu736 [363]

2 2/3 as a decimal is 2.66666667. 60 divided by 2.66666667 is 22.5.
As a fraction, the answer will be 22 5/10

Please mark my answer as the brainliest answer, I'd really appreciate it, thanks!

6 0

3 years ago

Read 2 more answers

Hurry 3(x+4)-5(x-1)<5

Oxana [17]

Answer:

x>6

Step-by-step explanation:

3x+12-5x+5<5

-2x+17<5

-2x<-12

x>6

7 0

2 years ago