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2 years ago

Subject: Add Maths

Mathematics

1 answer:

riadik2000 [5.3K]2 years ago

6 0

Answer:

ax2+x3+bx−4

Step-by-step explanation:

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Find the exact value of cos(a+b) if cos a=-1/3 and cos b=-1/4 if the terminal side if a lies in quadrant 3 and the terminal side

maria [59]

Answer:

cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

Step-by-step explanation:

cos(a + b) = cos(a).cos(b) - sin(a).sin(b) [Identity]

cos(a) = $-\frac{1}{3}$

cos(b) = $-\frac{1}{4}$

Since, terminal side of angle 'a' lies in quadrant 3, sine of angle 'a' will be negative.

sin(a) = $-\sqrt{1-(-\frac{1}{3})^2}$ [Since, sin(a) = $\sqrt{(1-\text{cos}^2a)}$ ]

= $-\sqrt{\frac{8}{9}}$

= $-\frac{2\sqrt{2}}{3}$

Similarly, terminal side of angle 'b' lies in quadrant 2, sine of angle 'b' will be negative.

sin(b) = $-\sqrt{1-(-\frac{1}{4})^2}$

= $-\sqrt{\frac{15}{16}}$

= $-\frac{\sqrt{15}}{4}$

By substituting these values in the identity,

cos(a + b) = $(-\frac{1}{3})(-\frac{1}{4})-(-\frac{2\sqrt{2}}{3})(-\frac{\sqrt{15}}{4})$

= $\frac{1}{12}-\frac{\sqrt{120}}{12}$

= $\frac{1}{12}(1-\sqrt{120})$

= $\frac{1}{12}(1-2\sqrt{30})$

Therefore, cos(a + b) = $\frac{1}{12}(1-2\sqrt{30})$

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2 years ago

Skyler goes to a school which has 1000 students in it. She asks 40 random students whether they like the new 8.30am start to the

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30/40 say no, so x/1000 would say no. 1000/40=25, 25*30=750. So, about 750 would dislike it.

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2 years ago

Congratulations! You won a free grill in a sweepstakes! You know that you can fit a rectangular grill in your truck that has a w

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Answer: 20 feet perimeter is the largest allowed

Step-by-step explanation: width=2.5 length=no more than 3x2.5

so find longest possible length allowed...

2.5x3=7.5

calculate largest perimeter allowed...

2(7.5+2.5)=20

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2 years ago

Geometry math question no Guessing and Please show work

MAXImum [283]

If the point P(x, y) partitions the segment AB in the ratio 1 : 1, then the point P is midpoint of segment AB.

The formula of a midpoint of segment:

$A(x_A;\ y_A),\ B(x_B,\ y_B)\\\\P_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)$

We have:

$A(13,\ 1)\to x_A=13,\ y_A=1\\B(-5,\ -3)\to x_B=-5,\ y_B-3\\\\P\left(\dfrac{13+(-5)}{2};\ \dfrac{1+(-3)}{2}\right)\to P\left(\dfrac{8}{2};\ \dfrac{-2}{2}\right)\to P(4,\ -1)$

Answer: C. (4, -1)

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3 years ago

The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. a) What is th

amm1812

Answer: Our required probability is 0.39.

Step-by-step explanation:

Since we have given that

X be the exponentially distributed with mean life = 6 years

So, E[x]=6

$\dfrac{1}{\lambda}=6\\\\\lambda=\dfrac{1}{6}$

So, our cumulative distribution function would be

$F(x)=1-e^{-\lambda x}$

We need to find the probability that the CPU fails within 3 years.

$P(X$

Hence, our required probability is 0.39.

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3 years ago