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3 years ago

Csc α - sin α =cos α cot α Show how this is an identity?

1 answer:

8 0

Csc a - sin a = cos a cot a
1/sin a - sin a = cos a (cos a / sin a)
(1 - sin^2 a)/sin a = cos^2 a/sin a
cos^2 a/sin a = cos^2 a/sin a

Therefore, the given equation is an identity.

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Help plzzz thank you !

VashaNatasha [74]

Answer:

a. Ameribank-$15,157.50

b. Capital Two-$4,646.25

Step-by-step explanation:

a. Tad's savings is $15,000, we calculate his total amount at the end of the year for each bank:

#Ameribank

$A=P+I=P+PRT\\\\=15000+15000\times 0.0105\times 1\\\\=\$15,157.50$

#Huffington( we use the effective rate to calculate the compound amount):

$i_m=(1+i/m)^m-1\\\\=(1+0.0095/12)^[12}-1=0.009541\\\\A=P(1+i_m)^n\\\\=15000(1.009541)^1\\\\=\$15,143.12$

#Sixth-Third, Take 1 yrs=52 weeks:

$i_m=(1+i/m)^m-1\\\\=(1+0.01/52)^{52}-1=0.01005\\\\A=15000(1.01005)^1\\\\=\$15,150.74$

#Hence, Ameribank is the best option as his money grows to $15,157.50 which is greater than all the remaining two options.

b. We use the compound interest formula $A=P(1+r/n)^{nt}$ to determine which bank gives the best option:

#Capital Two. r=3.75%, n=12,t=4

$A=P(1+r/n)^{nt}\\\\=4000(1+0.0375/12)^{12\times4}\\\\=\$4,646.25$

#J.C Morgan, t=2, r=3.55% n=12

$A=P(1+r/n)^{nt}\\\\=4000(1+0.0355/12)^{12\times 2}\\\\=\$4,293.87$

#Silverman Slacks, n=12,t=3, r=3.65%

$A=P(1+r/n)^{nt}\\\\=4000(1+0.0365/12)^{12\times3}\\\\=\$4,462.14$

We compare the investment amounts after t years:

$Capital>Silver>Morgan=4646.25>4462.14>4293.87$

Hence, Capital two is the best option with an investment amount of $4,646.25

8 0

3 years ago

Read 2 more answers

a rectangle is made by joining two squares adjacent to each other as shown below. if one squared has an area of 144 squared cent

liberstina [14]

Answer:

Hello! After reading your question I have deduced that the correct answer is 288² cm.

Step-by-step explanation:

The way I came to this conclusion was as follows:

Firstly:

If said rectangle is two squares put side by side (adjacent), then a valid assumption is that both squares are the same size.

This is because all four sides of a square have to be equal.

Thus if the two squares are joined together on one side, then all the other sides of both the squares will be the same length.

Thus both of the squares are going to be the same size, so they will have the same area.

Secondly:

If the area of one square is 144² cm then the area of the other square should also be 144² cm.

Thus if you combine the areas of both the squares, that make up the rectangle, you are left with the area of the rectangle being 288² cm.

I hope this helped!

3 0

2 years ago

Sam evaluated the expression x2y for x = 7 and y = 9. He got a value of 49. which of the follwing statements is correct

Marrrta [24]

B. sam forgot to multiply.
The correct answer is
 x^2*y=(7^2)*(9)=49*9=441

7 0

3 years ago

Order the fractions from least to greatest. 1 -1.25, 0.125, 1 4

liberstina [14]

Answer:

-1.25, -1/4, -1/8, 0.125

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Dwayne walks a total of 960 feet around 3 sides of a square city block. Which

Ugo [173]

Answer:

The perimeter is 1280ft

Step-by-step explanation:

Let the side length of the square be s.

Then the distance around three sides is 3s.

According to the question the distance around 3 sides of a square city block is 960 feet.

This implies that:

$3s = 960$

$s = \frac{960}{3}$

$s = 320$

The perimeter of a square is

$p = 4s$

Substitute s=320 to get:

$p = 4(320)$

$p = 1280$

The perimeter is 1280 ft

5 0

3 years ago

Read 2 more answers