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2 years ago

Simplify: sin^2xcos^2x-cos^2x

Mathematics

1 answer:

shtirl [24]2 years ago

8 0

Answer:

-cos^4(x)

Step-by-step explanation:

Step 1: Use the Pythagorean identity : 1=cos^2(x) + sin^2(x)

1-sin^2(x) = cos^2(x)

-1+sin^2(x) = -cos^2(x)

cos^2(x) (-cos^2(x))

Step 2: Factor out common terms cos^2(x)

cos^2(x) (sin^2(x)-1)

Ans: -cos^4(x)

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A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (ha

Neko [114]

Answer:

Volume: $\frac{2}{3}\pi r^3$

Ratio: $\frac{2}{9}r$

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

$V'=\frac{V}{2}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3$

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

$A=4 \pi r^2$

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so $2\pi r^2$ . Moreover, we have to add the surface of the base, which is $\pi r^2$ . So the total surface area of the hemispherical tank is

$A'=2\pi r^2 + \pi r^2 = 3 \pi r^2$

Therefore, the ratio betwen the volume and the surface area of the hemisphere is

$\frac{V'}{A'}=\frac{\frac{2}{3}\pi r^3}{3\pi r^2}=\frac{2}{9}r$

6 0

3 years ago

Given a+b=7 and a–b=3, find: 2a·2b

nekit [7.7K]

I believe the answer is 40

5 0

3 years ago

Select all of the equations that are equivalent to<br>2-5y=-7

insens350 [35]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

8 is the difference of d and 3.75

maria [59]

Answer:

11.75

Step-by-step explanation:

From the question above 8 is the difference of d and 3.75

We are required to find the value of d

d-3.75= 8

d= 8 + 3.75

d= 11.75

Hence the value of d is 11.75

7 0

2 years ago

At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with

MatroZZZ [7]

Answer:

a)Slope: $\hat \beta_1 =\frac{7625.9}{1248.9}=6.106$

Intercept: $\hat \beta_o = 157.955 -6.106 (69.686)=-267.548$

b) $r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657$

And the determination coeffecient is $r^2 = 0.657^2 =0.432$

Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.

n=110, $\sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8$