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3 years ago

(__) = (sec x-1)(sec x+1)

Mathematics

1 answer:

podryga [215]3 years ago

8 0

This would be tan^2 x.

This can be solved simply with some identities of trigonometric functions.

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The sum of three consecutive even numbers is 84. What is the smallest of the three numbers?

kari74 [83]

Answer: 26

Step-by-step explanation: In this problem we have 3 consecutive even numbers whose sum is 84 and it asks us to find the smallest number.

Consecutive even numbers can be represented as x, x + 2, and x + 4.

Since the sum of these is 84, our equation reads

x + (x + 2) + (x + 4) = 84.

Simplifying on the left we get 3x + 6 = 84.

Subtract 6 from both sides and we have 3x = 78.

Divide both sides by 3 and x = 26.

So our smallest number is 26.

6 0

4 years ago

What is 6x^3+4x^2+2x divided by 2x

Alex Ar [27]

Answer:

3x^2 + 2x

Step-by-step explanation:

8 0

3 years ago

A survey found that 64% of the people prefer action over comedy movies

Verdich [7]

They like action not comedy

4 0

4 years ago

Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen

Jobisdone [24]

Parameterize $S$ by the vector function

$\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k$

so that the normal vector to $S$ is given by

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k$

with magnitude

$\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}$

In this case, the normal vector is

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k$

with magnitude $\sqrt{1^2+2^2+1^2}=\sqrt6$ . The integral of $f(x,y,z)=e^z$ over $S$ is then

$\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx$

where $T$ is the region in the $x,y$ plane over which $S$ is defined. In this case, it's the triangle in the plane $z=0$ which we can capture with $0\le x\le8$ and $0\le y\le\frac{8-x}2$ , so that we have

$\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}$

5 0

3 years ago

Determine if the expression 9y5 – 10y3 is a polynomial or not. If it is a polynomial,

Stolb23 [73]

I am going to assume that the equation was supposed to be $9y^{5}$ $-10y^{3}$

Answer:

It is a polynomial. It is a binomial and it has a degree of 5.

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables so $9y^{5}$ $-10y^{3}$ will be considered a polynomial.

A binomial is a polynomial with 2 terms.

The degree of a polynomial is the highest exponent in it which in this equation is 5.

8 0

3 years ago