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3 years ago

If sine of x equals square root of 2 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.

1 answer:

7 0

Sin x = square root (2) / 2

In order for us to get for cos x and tan x, first we need to know what
Hypotenuse, Adjacent, and Opposite sides.

sin x = opposite / hypotenuse.

adjacent = square root (hypotenuse^2 - opposite^2)
adjacent = square root (2^2 - square root(2)^2)
adjacent = square root (4 - 2)
adjacent = square root (2)

cos x = adjacent / hypotenuse
tan x = opposite / adjacent..

cos x = square root (2) / 2
tan x = square root (2) / <span>square root (2) = 1

So, </span>cos x = square root (2) / 2 and tan x<span> = 1</span>

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darren has 3/4 of a gallon of soil.he needs to plant 5 small plants.if he splits the soil evenly between the plants.how much soi

nika2105 [10]

Number of plants = 5

Amount of soil present for 5 plants = 3/4 gallons

Now here we have to find how much soil will each plant get.

So we have to apply unitary method here to find how much would each plant get the share of soil.

Soil required by 5 plants = 3/4 gallons

Soil required by 1 plant = 3/4 divided by 5 = 3/20 gallons

Answer: Each plant will get 3/20 gallons of soil.

7 0

2 years ago

Read 2 more answers

A rectangular area is to be fenced in with 300 feet of chicken wire. find the maximum area that can be enclosed.

GarryVolchara [31]

Let the lengths of the sides of the rectangle be x and y. Then A(Area) = xy and 2(x+y)=300. You can use substitution to make one equation that gives A in terms of either x or y instead of both.

2(x+y) = 300
x+y = 150
y = 150-x

A=x(150-x) <--(substitution)

The resulting equation is a quadratic equation that is concave down, so it has an absolute maximum. The x value of this maximum is going to be halfway between the zeroes of the function. The zeroes of the function can be found by setting A equal to 0:
0=x(150-x)
x=0, 150

So halfway between the zeroes is 75. Plug this into the quadratic equation to find the maximum area.

A=75(150-75)
A=75*75
A=5625

So the maximum area that can be enclosed is 5625 square feet.

6 0

2 years ago

Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 an

Leya [2.2K]

Parameterize the lateral face $T_1$ of the cylinder by

$\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v$

where $0\le u\le2\pi$ and $0\le v\le3$ , and parameterize the disks $T_2,T_3$ as

$\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)$
$\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)$

where $0\le r\le2$ and $0\le\theta\le2\pi$ .

The integral along the surface of the cylinder (with outward/positive orientation) is then

$\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}((2\cos u)^2+(2\sin u)^2+v^2)\left\|{{\mathbf r}_1}_u\times{{\mathbf r}_2}_v\right\|\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+0^2)\left\|{{\mathbf r}_2}_r\times{{\mathbf r}_2}_\theta\right\|\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+3^2)\left\|{{\mathbf r}_3}_r\times{{\mathbf r}_3}_\theta\right\|\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r^3\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r(r^2+9)\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr$
$=136\pi$

7 0

3 years ago

If the sum of three consecutive numbers is 852, what is the middle one?

denis-greek [22]

Divide the total by the quantity of numbers:

852/3 = 284

Because there are an odd quantity of numbers (3) the answer is the middle number.

The answer is 284

5 0

2 years ago

What is the y-intercept of the graph of y = 2.5x? a. 2.5 c. 0 b. 1 d. -1

Alla [95]

Answer:

answer is C

Step-by-step explanation:

General equation of a line is expressed as shown:

y = mx+c where;

m is the slope or gradient of the line

c is the intercept of the line

Given the equation of the line graph as y =2.5x

Comparing the given equation with the general equation, it is seen that m = 2.5 and c = 0 (since there is no value for the intercept)

Based on the explanation, the y-intercept of the graph is therefore 0

5 0

2 years ago