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3 years ago

Solve the value of sin²45°+cos²45°

Mathematics

1 answer:

Ulleksa [173]3 years ago

8 0

Answer:

Step-by-step explanation:

sin²x = (sinx)²

cos²x = (cosx)²

Step 1: Define

sin²45° + cos²45°

Step 2: Rewrite

(sin45°)² + (cos45°)²

Step 3: Evaluate

sin45° = √2/2

cos45° = √2/2

(√2/2)² + (√2/2)²

1/2 + 1/2

You might be interested in

Given f(x)=4x+5 and g(x)= x^2+x; find (f∘g)(-5)<br> Please show all steps thank you

Greeley [361]

Answer:

$(f\circ g)(-5)=85$

Step-by-step explanation:

We are given:

$\displaystyle f(x)=4x+5\text{ and } g(x)=x^2+x$

And we want to find:

$(f\circ g)(-5)$

This is equivalent to:

$\displaystyle =f(g(-5))$

So, we will evaluate g(-5) first, which yields:

$\displaystyle g(-5)=(-5)^2+(-5)=25-5=20$

So:

$=f(g(-5))=f(20)$

Then:

$\displaystyle f(20)=4(20)+5=80+5=85$

Therefore:

$(f\circ g)(-5)=85$

6 0

3 years ago

The time taken to assemble a laptop computer in a certain plant is a random variable having a normal distribution of 20 hours an

ludmilkaskok [199]

Answer:

a) 40.13% probability that a laptop computer can be assembled at this plant in a period of time of less than 19.5 hours.

b) 34.13% probability that a laptop computer can be assembled at this plant in a period of time between 20 hours and 22 hours.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

$\mu = 20, \sigma = 2$