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4 years ago

Verify the identity. sin quantity x plus pi divided by two = cos x

1 answer:

5 0

$\bf sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
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\textit{also recall that }cos\left( \frac{\pi }{2} \right)=0\qquad \qquad sin\left( \frac{\pi }{2} \right)=1\\\\
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sin\left( x+\frac{\pi }{2} \right)\implies sin(x)cos\left( \frac{\pi }{2} \right)+cos(x)sin\left( \frac{\pi }{2} \right)
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sin(x)\cdot 0+cos(x)\cdot 1\implies \boxed{cos(x)}$

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To visit her grandmother, Melek takes a motorcycle 3.8 kilometers and a horse 3.32 kilometers. In total, the journey takes 50.54

lbvjy [14]

Answer:

Therefore, total number of Kilometers Melek covered =3.3 + 3.32 = 6.62 kilometers.

Step-by-step explanation:

Distance covered by motorcycle = 3.8 kilometers.

Distance covered by horse = 3.32 kilometers.

Total time taken to complete the journey = 50.54 minutes.

We need to find the total number of kilometers Melek took the journey.

We are given time. But we need not to do anything with given time.

We just need to add the journey took by motorcycle and journey took by horse.

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8 0

3 years ago

In a recent survey of college professors, it was found that the average amount of money spent on entertainment each week was nor

Alenkinab [10]

Answer:

0.0918

Step-by-step explanation:

We know that the average amount of money spent on entertainment is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.

The mean and standard deviation of average spending of sample size 25 are

μxbar=μ=95.25

σxbar=σ/√n=27.32/√25=27.32/5=5.464.

So, the average spending of a sample of 25 randomly-selected professors is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.

The z-score associated with average spending $102.5

Z=[Xbar-μxbar]/σxbar

Z=[102.5-95.25]/5.464

Z=7.25/5.464

Z=1.3269=1.33

We have to find P(Xbar>102.5).

P(Xbar>102.5)=P(Z>1.33)

P(Xbar>102.5)=P(0<Z<∞)-P(0<Z<1.33)

P(Xbar>102.5)=0.5-0.4082

P(Xbar>102.5)=0.0918.

Thus, the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.5 is 0.0918.

5 0

4 years ago

If m<mkl=83. m<jkl=127. and m<jkm=(9x-10). find the value of x

kirza4 [7]

MKL = 83, JKL = 127, JKM = 9x - 10 given

JKL + MKL = JKM angle addition postulate

127 + 83 = 9x - 10 substitution

210 = 9x - 10 simplify (add like terms)

220 = 9x addition property of equality

$\frac{220}{9}$ = x

3 0

4 years ago

Solve the following problems. Reduce your answers to their simplest form. a. 13⁄41 + 27⁄82 b. 3 5⁄24 + 6 7⁄24 + 4 9⁄24 c. 5 2⁄3

KATRIN_1 [288]

13⁄41 + 27⁄82 = 26/82 + 27/82 = 53/82

3 5/24 + 6 7/24 + 4 9/24 = 13 20/24 = 13 5/6

5 2⁄3 + 29⁄69 + 6 21⁄23 = 5 46/69 + 29/69 + 6 63/69 = 11 138/69 = 13

3 9⁄10 + 4⁄9 + 7⁄45 + 4 = 3 81/90 + 40/90 + 14/90 + 4 = 7 135/90 = 8 1/2

6 – 7⁄15 = 5 15/15 - 7/15 = 5 6/15

11 3⁄8 – 7⁄8 = 10 11/8 - 7/8 = 10 4/8 = 10 1/2

 7 1⁄6 – 3 4⁄9 = 7 9/54 - 3 18/54 = 6 63/54 - 3 18/54 = 3 45/54 = 3 5/6

5 3⁄8 – 3 2⁄5 = 5 15/40 - 3 16/40 = 4 55/40 - 3 16/40 = 1 39/40

4 0

3 years ago

Read 2 more answers

Simplify: sin^2xcos^2x-cos^2x

shtirl [24]

Answer:

-cos^4(x)

Step-by-step explanation:

Step 1: Use the Pythagorean identity : 1=cos^2(x) + sin^2(x)

1-sin^2(x) = cos^2(x)

-1+sin^2(x) = -cos^2(x)

cos^2(x) (-cos^2(x))

Step 2: Factor out common terms cos^2(x)

cos^2(x) (sin^2(x)-1)

Ans: -cos^4(x)

8 0

2 years ago