Express the area of the entire rectangle.

What is 3a+2c=26 solve for a and c

blondinia [14]

Simplifying

3a + 2b + c = 26

Solving

3a + 2b + c = 26

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2b' to each side of the equation.

3a + 2b + -2b + c = 26 + -2b

Combine like terms: 2b + -2b = 0

3a + 0 + c = 26 + -2b

3a + c = 26 + -2b

Add '-1c' to each side of the equation.

3a + c + -1c = 26 + -2b + -1c

Combine like terms: c + -1c = 0

3a + 0 = 26 + -2b + -1c

3a = 26 + -2b + -1c

Divide each side by '3'.

a = 8.666666667 + -0.6666666667b + -0.3333333333c

Simplifying

a = 8.666666667 + -0.6666666667b + -0.3333333333c

3 0

2 years ago

Read 2 more answers

An observer on a cliff 1000 yards above sea level sights two ships due east. The angles of depression from the observers perspec

Anika [276]

Answer:

480.53 yards

Step-by-step explanation:

cos(35) = 1000/hypotenuse1 - multiply by h (hypotenuse)

(h1)cos(35) = 1000 - divide by cos(35)

h1 = 1000 / cos(35)

h1 = 1220.7746

Same thing with the angle of depression of 54 degrees.

h2 = 1000 / cos(54)

h2 = 1701.3016

h2 - h1 = 480.53

3 0

2 years ago

If for every 12 blue streamers there is 9 gold streamers, how many blue streamers will I have if I have 36 gold streamers?

neonofarm [45]

Answer:

You will have 48 blue streamers.

Step-by-step explanation:

This question can be solved by proportions, using rule of three.

We have that:

For 12 blue streamers, there are have 9 gold streamers. How many blue streamers are there when there are 36 gold streamers?

12 blue - 9 gold

x blue - 36 gold

Applying cross multiplication

$9x = 36*12$

Simplifying by 9

$x = 4*12 = 48$

You will have 48 blue streamers.

4 0

2 years ago

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and betw

vfiekz [6]

First, complete the square in the equation for the second circle to determine its center and radius:

x ² - 10x + y ² = 0

x ² - 10x + 25 + y ² = 25

(x - 5)² + y ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

x = r cos(θ)

y = r sin(θ)

Then

x ² + y ² = 100 → r ² = 100 → r = 10

x ² - 10x + y ² = 0 → r ² - 10 r cos(θ) = 0 → r = 10 cos(θ)

y = 5 → r sin(θ) = 5 → r = 5 csc(θ)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to y = 5 at the point (0, 5).

Split up the region at 3 angles θ₁, θ₂, and θ₃, which denote the angles θ at which the curves intersect. They are

θ₁ = 0 … … … by solving 10 = 10 cos(θ)

θ₂ = π/6 … … by solving 10 = 5 csc(θ)

θ₃ = 5π/6 … the second solution to 10 = 5 csc(θ)

Then the area of the region is given by a sum of integrals:

$\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)$

$=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta$

To compute the integrals, use the following identities:

sin²(θ) = (1 - cos(2θ)) / 2

cos²(θ) = (1 + cos(2θ)) / 2

and recall that

d(cot(θ))/dθ = -csc²(θ)

You should end up with an area of

$=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta$

$=\boxed{25\sqrt3+\dfrac{125\pi}3}$

We can verify this geometrically:

• the area of the larger circle is 100π

• the area of the smaller circle is 25π

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line y = 5, has area 100π/3 - 25√3

Hence the area of the region of interest is

100π - 25π - (100π/3 - 25√3) = 125π/3 + 25√3

as expected.

3 0

2 years ago

Please help I’m really need the help (NO LINKS ) (NO LYING ) PART 2 again

ohaa [14]

Answer:

A. 15

B. 25.6

C. 41.6

Step-by-step explanation:

You need to divide

6 0

2 years ago