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3 years ago

Find the value ofa.) lim (x²-1)/(x²+1)x−>∞

Mathematics

1 answer:

Fed [463]3 years ago

6 0

Answer:

$\displaystyle\lim_{x \to \infty} \frac{x^2-1}{x^2+1} \\ \text{take $x^2$ common from numerator and denominator} \\ \displaystyle\lim_{x \to \infty} \dfrac{1-\frac{1}{x^2}}{1+\frac{1}{x^2}} \\\text{Now put the limit}\\\displaystyle\lim_{x \to \infty} \frac{1-0}{1+0}= 1$

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Use the formula h(t)=−16t2+v0t+h0 , where v0 is the initial velocity and h0 is the initial height. How long will it take for the

Rama09 [41]

Question:

Britney throws an object straight up into the air with an initial velocity of 27 ft/s from a platform that is 10 ft above the ground. Use the formula h(t)=−16t2+v0t+h0 , where v0 is the initial velocity and h0 is the initial height. How long will it take for the object to hit the ground?

1s 2s 3s 4s

Answer:

It takes 2 seconds for object to hit the ground

Solution:

The given equation is:

$h(t) = -16t^2 + v_0t+h_0$

Initial velocity = 27 feet/sec

$h_0 = 10\ feet$

Therefore,

$h(t) = -16t^2 +27t+10$

At the point the object hits the ground, h(t) = 0

$-16t^2 +27t+10 = 0\\\\16t^2-27t-10=0$

Solve by quadratic formula,

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=16,\:b=-27,\:c=-10:\quad \\\\t=\frac{-\left(-27\right)\pm \sqrt{\left(-27\right)^2-4\cdot \:16\left(-10\right)}}{2\cdot \:16}\\\\t = \frac{27 \pm \sqrt{1369}}{32}\\\\t = \frac{27 \pm 37}{32}\\\\We\ have\ two\ solutions\\\\t = \frac{27+37}{32}\\\\t = \frac{64}{32}\\\\t = 2\\\\And\\\\t = \frac{27-37}{32}\\\\t = -0.3125$

Ignore, negative value

Thus, it takes 2 seconds for object to hit the ground

7 0

3 years ago

Round 81.139 to the nearest tenth

Gnesinka [82]

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up (+1).

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down (no change).

81.139 ≈ 81.1

6 0

3 years ago

Read 2 more answers

Heyy how do I solve this

BARSIC [14]

Answer:

1200 centimeters

Step-by-step explanation:

Hello!

1meter=100centimeters

12meter = ?

$thus \: \frac{12m \times 100cm}{1m} = 1200cm$

7 0

1 year ago

Read 2 more answers

I need help on this and a few more i have been busy lately

BaLLatris [955]

Answer:

ok so we have to make it so we can get rid of one of the varibles by adding or subtracting

so lets multiply the first one by 4

120x+16y=4160

minus the second one so

108x=2160

divide by 108

x=20

then we just plug in

12(20)+16y=2000

240+16y=2000

-240

16y=1760

divide by 16

y=110

(20,110)

Hope This Helps!!!

8 0

2 years ago

Help please will give brainliest thank you

lozanna [386]

Independent, means the first event won't affect the second event.

The independent events would be :

A, B, E, F

3 0

3 years ago

Find the value ofa.) lim (x²-1)/(x²+1)x−>∞​

Find the value ofa.) lim (x²-1)/(x²+1)x−>∞