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3 years ago

Tan^4x-sec^4x=1-2 sec^2(x) verify

1 answer:

6 0

Tan⁴x - sec⁴x = 1 - 2sec²x

tan²x = sec²x - 1

tan⁴x - sec⁴x = 1 - 2sec²x
(tan²x)² - sec⁴x = 1 - 2sec²x
(sec²x - 1)² - sec⁴x = 1 - 2sec²x

(sec²x)² - 2 * sec²x + 1 - sec⁴x = 1 - 2sec²x
sec⁴x - 2 sec²x + 1 - sec⁴x = 1 - 2sec²x

sec⁴x can be cancelled:
- 2 sec²x + 1 = 1 - 2sec²x

1 - 2sec²x = 1 - 2sec²x

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6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to t

Vesna [10]

At the end of 28 years, there will be 22,083.2 dollars in the account.

Step-by-step explanation:

Step 1; First we must calculate how much interest there is in total over 28 years. The annual interest rate is 8.25% i.e. 8.25% of 6,700 dollars which equals 552.75 dollars. As the years' pass, more and more will be put into the account due to interest. After 28 years, there will be an interest of 229.6% (8.25% per year * 28 years)of the initial amount.

Step 2; We must find the money due to interest and add it with the money that was put in initially. The interest amount is 2.296 times the 6,700 dollars which was put in. The interest equals 15,383.2 dollars. With this, the initial 6,700 dollars is added which comes to a total of 22,083.2 dollars

3 0

4 years ago

Read 2 more answers

A tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obta

Andru [333]

Answer:

Step-by-step explanation:

According to the given question, a tire company has developed a new type of steel-belted radial tire. Extensive testing indicates the population of mileages obtained by all tires of this new type is normally distributed with a mean of 37,000 miles and a standard deviation of 3,887 miles.

Let us define X be the random variable shows that the mileages tires normally distributed with

mean

μ = 37000

standard deviation

σ =3, 887

Therefore

X ~ (μ = 37000, σ =3,887)

The company wishes to offer a guarantee providing a discount on a new set of tires if the original tires purchased do not exceed the mileage stated in the guarantee. Therefore the guaranteed mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage is determined as:

P(X < k) = 0.02

$\Rightarrow P\left ( \frac{X-\mu }{\sigma }\leq \frac{k-\mu }{\sigma } \right )=0.02
\\\\P\left ( Z \leq \frac{k-37,000 }{3,887 } \right )=0.02$

From the standard normal curve 2% area is determined as -2.0537 and hence

$\frac{k-37,000}{3,887}=-2.0537\\\\k=37000-7982.7319\\\\k=29017.2681\\\\\Rightarrow k=29018$

If we consider z value at two decimal places then

$\frac{k-37,000}{3,887} =-2.05\\\\\Rightarrow k=29032
$

Therefore the guaranteed 29032 mileage be if the tire company desires that no more than 2 percent of the tires will fail to meet the guaranteed mileage.

The area under the standard normal curve is determined as:

6 0

4 years ago

If anyone can give me the answer that will be greatly appreciated :)

vfiekz [6]

42-x=58

or, -x=58-42

with change in side sign also chamges we change sides to make like terms in one side and unlike in amother side.

or, -x= 16

or,x=-16.

therefore x=-16...

Hope this helps you.

3 0

3 years ago

Paula knits hats. The number of hats h she can knit varies directly with the amount of yarn (y) in yards she has. The constant o

maria [59]

Answer:

Part 1) The equation is $h=42y$

Part 2) The number of hats Paula can knit is 42 per yard of yarn

Part 3) see the procedure

Part 4) For 378 yards of yarn Paula can knit 9 hats

Step-by-step explanation:

Let

h -----> the number of hats

y ----> the amount of yarn in yards

k ---> constant of proportionality

Part 1) Write an equation to represent the relationship between the numbers of yards of yarn Paula has and the number of hats she can knit

we know that

A relationship between two variables, h, and y, represent a proportional variation if it can be expressed in the form $h/y=k$ or $h=ky$

we have

$k=42$

substitute

$h=42y$

Part 2) What does the constant if proportionality 42, represent in this problem?

The constant of proportionality represent the slope of the linear equation

The value of the slope is $42\ \frac{hats}{yd}$

That means that the number of hats Paula can knit is 42 per yard of yarn

Part 3) Complete the table showing the yards of yarn and the number of hats Paula can knit

we have

$h=42y$

Part a) For y=0 yd Find the value of h

substitute in the linear equation the value of y and solve for h

$h=42(0)=0\ hats$

Part b) For h=3 hats Find the value of y

substitute in the linear equation the value of h and solve for y

$3=42y$

$y=3/42\ yd$ ----> $y=1/14\ yd$

Part c) For y=210 yd Find the value of h

substitute in the linear equation the value of y and solve for h

$h=42(210)=8,820\ hats$

Part d) For y=378 yd Find the value of h

substitute in the linear equation the value of y and solve for h

$h=42(378)=15,876\ hats$

Part 3) For h=11 hats Find the value of y

substitute in the linear equation the value of h and solve for y

$11=42y$

$y=11/42\ yd$

Part 4) Interpret the meaning of the point (378,9)

we have that

y=378 yd

h=9 hats

That means -----> For 378 yards of yarn Paula can knit 9 hats

7 0

3 years ago

WHOEVER ANSWERS IT WILL GET BRAINIST ASAP DUE IN 5 MINUTES

Elodia [21]

Answer:

Step-by-step explanation:

4 0

3 years ago