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belka [17]
3 years ago
6

Please Help!!!

Mathematics
1 answer:
mylen [45]3 years ago
6 0
B and C are absurd; if a series converges, it must have a sum, but if a series diverges, it cannot have a sum.

Now, notice that

\dfrac12+\dfrac29+\dfrac4{27}+\dfrac8{81}+\cdots=\dfrac12+\dfrac{2^{2-1}}{3^2}+\dfrac{2^{3-1}}{3^3}+\dfrac{2^{4-1}}{3^4}+\cdots

That is, we can write the sum more compactly as

\dfrac12+\dfrac12\displaystyle\sum_{n=1}^\infty\left(\frac23\right)^n

The series is geometric with common ratio \dfrac23, so the series converges (and thereby has a sum), so the answer is D.
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Length A is 4 ft. after a dilation is performed length B is 7ft. what was the scale factor used?
kogti [31]
1.75

4 x 1.75 = 7 so that is the answer
5 0
3 years ago
The length of each leg of an isosceles right triangle is 4 cm. What is the length of the hypotenuse
miss Akunina [59]

<u>Answer:</u>

5.65 cm

<u>Step-by-step explanation:</u>

We are given that the length of each leg of an isosceles right triangle is 4 cm and we are to find the length of the hypotenuse.

For this, we will use the Pythagoras Theorem:

a ^ 2 = b ^ 2 + c ^ 2

where a is the hypotenuse.

a ^ 2 = 4 ^ 2 + 4 ^ 2

\sqrt { a ^ 2} = \sqrt { 3 2 }

a = 5 . 6 5

Therefore, the length of the hypotenuse is 5.65 cm.

5 0
3 years ago
Read 2 more answers
‼️‼️10 points‼️‼️
My name is Ann [436]

Answer:

The correct answer is B.

Step-by-step explanation:

There is no clear rule regarding the relationship with these numbers. So it is not linear.

Good Luck!

8 0
3 years ago
Read 2 more answers
Simplify n^4 divided by n1/2
agasfer [191]

Given:

Consider the expression is

\dfrac{n^4}{n^{\frac{1}{2}}}

To find:

The simplified form of the given expression.

Solution:

We have,

\dfrac{n^4}{n^{\frac{1}{2}}}

Using the properties of exponents, we get

=n^{4-\frac{1}{2}}               \left[\because \dfrac{a^m}{a^n}=a^{m-n}\right]

=n^{\frac{8-1}{2}}

=n^{\frac{7}{2}}

Therefore, the simplified form of the given expression is n^{\frac{7}{2}}.

5 0
3 years ago
3. A kite is aloft at the end of a 1500 foot string. The string make an angle of 43° with the
sineoko [7]

Answer:

h= 1500\,*\,sin(43^o)

Step-by-step explanation:

Notice that there is a right angle triangle formed with sides as follows:

hypotenuse is the actual 1500 ft string. The acute angle 43 degrees is opposite to the segment that represents the height of the kite from the ground. Therefore, the trigonometric ratio that we can use to find that opposite side to the given angle, is the sine function as shown below:

sin(43^o) = \frac{opposite}{hypotenuse} \\sin(43^o) = \frac{opposite}{1500}\\opposite = 1500\,*\,sin(43^o)\\h= 1500\,*\,sin(43^o)

8 0
3 years ago
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