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2 years ago

Gianna is substituting t = 2 and t = 7 to determine if the two expressions are equivalent.

Mathematics

2 answers:

MatroZZZ [7]2 years ago

4 0

The answer is A, I took the test.

lara [203]2 years ago

3 0

Answer: A. Both expressions are equivalent to 35 when t=2.

Step-by-step explanation:

Given: Gianna is substituting t = 2 and t = 7 to determine if the two expressions are equivalent.

At t=2

$5(2t+3)=5(2(2)+3)=5(4+3)=5(7)=35$

$5t+25=5(2)+25=10+25=35$

Therefore, both expressions are equivalent to 35 when t=2.

At t=7

$5(2t+3)=5(2(7)+3)=5(14+3)=5(17)=85$

$5t+25=5(7)+25=35+25=60$

Hence, A is the write option.

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What is the domain of validity for csctheta =start fraction 1 over sine theta end fraction? (1 point) all real numbers all real

dem82 [27]

We know the following relationship:

$csc(\theta)=\frac{1}{sin(\theta)}$

The domain of a function are the inputs of the function, that is, a function $f$ is a relation that assigns to each element $x$ in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function $csc(\theta)$ we can write its domain as follows:

1. Domain of validity for $csc(\theta)$ :

$D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0$

When:

$sin(\theta)=0$ ?

when:

$\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi$

where k is an integer either positive or negative. That is:

$sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...$

To match this with the choices above, the answer is:

"All real numbers except multiples of $\pi$ "


2. which identity is not used in the proof of the identity $1+cot^{2}(\theta)=csc^{2}(\theta)$ :

This identity can proved as follows:

$sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)$

The identity that is not used is as established in the statement above:

"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

 $\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)$

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2 years ago

Read 2 more answers

You just discovered that you have 100 feet of fencing and you have decided to make a rectangular garden. Assume the lengths of t

Tju [1.3M]

Answer:

10*10=100

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Step-by-step explanation:

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2 years ago

Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De

Gala2k [10]

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable X represent the time a child spends waiting at for the bus as a school bus stop.

The random variable X is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is, $\lambda=\frac{1}{\mu}=\frac{1}{7}$ .

The probability density function of X is:

$f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0$

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

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Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

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Answer:

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