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3 years ago

The sum of the first 5 terms of a geometric sequence is 496, and the common ratio is 1/2. what is the first term

Mathematics

1 answer:

CaHeK987 [17]3 years ago

8 0

the answer is 6

have a nice day

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What is the inverse of y=pi/2+sin x

Alekssandra [29.7K]

Answer:

$f^{-1}(x)=\sin ^{-1}(x-\frac{\pi}{2})$

Step-by-step explanation:

The given function is

$y=\frac{\pi}{2}+\sin x$

To find the inverse of this function, we interchange x and y.

$x=\frac{\pi}{2}+\sin y$

we now solve for y.

$x-\frac{\pi}{2}=\sin y$

Take the sine inverse of both sides to obtain;

$\sin ^{-1}(x-\frac{\pi}{2})=y$

Hence the inverse of the given function is;

$f^{-1}(x)=\sin ^{-1}(x-\frac{\pi}{2})$

where $\frac{\pi}{2}-1\le x\le \frac{\pi}{2}+1$

6 0

3 years ago

Read 2 more answers

Help really fast round 93.0129 to the nearest thousandth

maksim [4K]

The thousandth place is the 3rd digit after the decimal.

So your answer is 93.013

3 0

3 years ago

Read 2 more answers

Which sequences of transformations will map circle M onto circle N?

sergiy2304 [10]

Answer:

1: Reflect M across the x-axis

2: Dilate about the center by 3/2

Step-by-step explanation:

Given

See attachment for M and N

Required

Which maps M to N

The coordinates of the radius of the circles are:

$M = (5,5)$

$N = (5,-5)$

And the radius of circles are:

$r_M=2$

$r_N=3$

The first transformation from M to M' is:

- Reflect across the x-axis

The rule is:

$(x,y) \to (x,-y)$

$M(5,5) \to M'(5,-5)$

At this point, M' and N now have the same center but different radius.

The second transformation from M' to N is:

- Dilate about the center by dividing the radius of N by the radius of M

i.e.

$k =\frac{r_N}{r_M}$

$k =\frac{3}{2}$

At this point, M has been completely mapped to N.

4 0

3 years ago

if the cost price of 10 tables is equal to the selling price of 16 tables , find out the gain or loss percentage

Dovator [93]

Hi,

To solve this problem, Let us take the LCM of 10 and 16 which will come 80.

Now suppose the cost price of 10 tables =₹n CP of 80 tables will be ₹ 8n

According to the question, CP of 10 tables is equal to the SP of 16 tables, then

the SP of 16 tables will also be ₹ n.

So, SP of 80 tables will be ₹ 5n

So, Loss = CP-SP

→ 8n - 5n = ₹ 3n

Loss%= (3n×100)/8n

Loss%= 37.5%.

Hence the correct answer will be a loss of 37.5%.

4 0

3 years ago

the price of a pair of shoes increases from $50 to $64. What is the percent increase. Please Help, god bless

Vera_Pavlovna [14]

Answer:

Step 1: Calculate the change by subtracting old cost ($50) from the new cost ($64)

Step 2: Divide that change by the old cost ($50). You will get a decimal number

Step 3: Convert the decimal number to a percentage by multiplying by 100%

Step-by-step explanation:

Try this first

3 0

3 years ago