Enter the equation of the circle described below. Center (-1, 4), radius = √3

Lionel needs money quite frequently and doesn't need much interest at all. Which of these options for saving money is best for h

mestny [16]

Answer: Savings account - Apex

4 0

2 years ago

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If cosine theta almost-equals 0.3090, which of the following represents approximate values of sine theta and tangent theta, for

Zepler [3.9K]

Answer:

$\sin \theta = 0.9511$ and $\tan \theta = 3.078$

Step-by-step explanation:

Given that, $\cos \theta = 0.309$ .

Now, we have to calculate the values of $\sin \theta$ and $\tan \theta$ .

We know the identity that, $\sin^{2}\theta + \cos^{2}\theta = 1$

So, $\sin \theta = \sqrt{1 + \cos^{2}\theta} = \sqrt{1 - (0.309)^{2}} = 0.9511$ {Since $0 \leq \theta \leq 90^{\circ}$ }

Now, $\sec \theta = \frac{1}{\cos\theta} = \frac{1}{0.309} = 3.236$

Then, we know the identity, $\sec^{2}\theta - \tan^{2}\theta = 1$

So, $\tan \theta = \sqrt{\sec^{2}\theta - 1} = \sqrt{(3.236)^{2} - 1} = 3.078$ (Answer) {Since $0 \leq \theta \leq 90^{\circ}$ }

6 0

2 years ago

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A sphere of radius 7 in. Is placed inside a rectangular prism with length 15 in., width 18 in., and height 20 in. What is the vo

iragen [17]

Answer:

3964 in³

Step-by-step explanation:

volume of sphere: V = 4/3 πr³

v₁ = 4/3 x 3.14 x 7³ = 1436

volume of prism: v = Bh B = 15 x 18 = 270 h = 20

v₂ = 270 x 20 = 5400

v₂ - v₁ = 5400 - 1436 = 3964 in³

5 0

2 years ago

Which type of data would be best displayed in a histogram?

Vesnalui [34]

Answer:

Option D: the number of fluoride treatments given to students each month for the last 60 months (range 40-620)

Explanation:

The number of fluoride treatments given to students each month may be graphed with the 60 months on the horizontal axis, using a bar for each month.

The height of each bar will represent the number of fluoride treatments for the month and will be read on the vertical axis.

This histogram will permit to compare visually, in a very easy way, how the number of treatments vary month to month. That is why this is an ideal representation for this kind of data. In other form, it would be harder to compare a set of data for so many months and whose range is so broad (40 - 620).

5 0

2 years ago

A geometric sequence has an initial value of 3 and a common ratio of 2. Which function(s) or formula(s) could represent this sit

olasank [31]

Answer:

The functions that represent this situation are A. $f(n)=3\cdot 2^{n-1}$ and C. $a(n)=a(n-1)\cdot 2; a(1)=3$ .

Step-by-step explanation:

A geometric sequence goes from one term to the next by always multiplying or dividing by the same value.

In geometric sequences, the ratio between consecutive terms is always the same. We call that ratio the common ratio.

This is the explicit formula for the geometric sequence whose first term is k and common ratio is r:

$a(n)=k\cdot r^{n-1}$

This is the recursive formula of that sequence:

$a(1)=k\\\\a(n)=a(n-1)\cdot r$

We know that the first term is k = 3 and the common ratio is r = 2. Therefore,

The explicit formula is $f(n)=3\cdot 2^{n-1}$ and the recursive formula is $a(n)=a(n-1)\cdot 2; a(1)=3$ .

6 0

2 years ago