The surface area of a rectangular prism is 115 square inches. What are possible dimensions of the prism?

a graphic designer wants to know the number of regions that are formed when circles overlap in particular. can she find a rule t

kumpel [21]

Answer:

A. 2

Step-by-step explanation:

Its successive multiples and it increases:

+2, +4, +6, +8

it increases by 2 every time which is successive multiples so the answer is A, 2.

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bm%7D%20%20%3D%20n%20" id="TexFormula1" title=" {2}^{m} = n " alt=" {2}^{m} =

sveta [45]

Answer:

$\displaystyle n^3-\frac{1}{n^{2}}$

Step-by-step explanation:

<u>Exponents Properties</u>

We need to recall the following properties of exponents:

$(a^x)^y=(a^y)^x=a^{xy}$

$\displaystyle a^{-x}=\frac{1}{a^x}$

We are given the expression:

$2^m=n$

We need to express the following expression in terms of n.

$8^m-4^{-m}$

It's necessary to modify the expression to use the given equivalence.

Recall $8=2^3 \text{ and }4 = 2^2$ . Thus:

$(2^3)^m-(2^2)^{-m}$

Applying the property:

$(2^m)^3-(2^m)^{-2}$

Substituting the given expression:

$n^3-n^{-2}$

Or, equivalently:

$\mathbf{\displaystyle 8^m-4^{-m}= n^3-\frac{1}{n^{2}}}$

5 0

2 years ago

Use identities to find the values of the sine and cosine functions for the following angle measure.

puteri [66]

Using the cosine double angle formula,

$\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}$

(Note I took the positive case since $\theta$ terminates in the first quadrant)

Using the Pythagorean identity,

$\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}$

(Note I took the positive case since $\theta$ terminates in the first quadrant)

6 0

1 year ago

The National Science Organization is monitoring the continuous exponential decline of an insect species due to deforestation. Th

kakasveta [241]

Answer:

$P\geq 26e^{-0.079t}$

$P\geq 2$

Step-by-step explanation:

We are given that there is an exponential decay.

Also, the decrease is of constant rate 7.9% i.e. 0.079 each year.

Since, the initial amount of the species is atleast 26 million.

Thus, the inequality for the corresponding model will be, $P\geq 26e^{-0.079t}$ ,

where t is the time period for the decay and P is the population.

Moreover, is is given that the population cannot be less than 2 million.

So, we get, $P\geq 2$ .

Hence, the inequalities to determine the possible number of insects over time are given by,

$P\geq 26e^{-0.079t}$

$P\geq 2$ .

4 0

3 years ago

Dakota makes a salad dressing by combining 6 1/3 fluid ounces of oil and 2 3/8 fluid ounces of vinegar in a jar. She then pours

-Dominant- [34]

6 1/3 +2 3/8 = 17/24 so you have to subtract it from the 2 1/4 fluid to know the amount of dressing remaining and your answer should be negative which is -37/24.

6 0

3 years ago