Use the graph to write a linear function that relates y to x . y=___

Cody was 165cm tall on the first day of school this year, which was 10% taller than he was on the first day of school last year.

klemol [59]

Answer: 148.5

Step-by-step explanation:

well there is no real question here but cody is 165 which means you have to multiply that by 10% or 0.10 which gives you 16.5 and subtract that from the total

4 0

3 years ago

Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 &lt

Paladinen [302]

Answer:

$y(x)=4a\sqrt{3}* sin(x)-3a$

Step-by-step explanation:

We have a separable equation, first let's rewrite the equation as:

$\frac{dy(x)}{dx} =\frac{3a+y}{tan(x)}$

But:

$\frac{1}{tan(x)} =cot(x)$

So:

$\frac{dy(x)}{dx} =cot(x)*(3a+y)$

Multiplying both sides by dx and dividing both sides by 3a+y:

$\frac{dy}{3a+y} =cot(x)dx$

Integrating both sides:

$\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx$

Evaluating the integrals:

$log(3a+y)=log(sin(x))+C_1$

Where C1 is an arbitrary constant.

Solving for y:

$y(x)=-3a+e^{C_1} sin(x)$

$e^{C_1} =constant$

So:

$y(x)=C_1*sin(x)-3a$

Finally, let's evaluate the initial condition in order to find C1:

$y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a$

Solving for C1:

$C_1=4a\sqrt{3}$

Therefore:

$y(x)=4a\sqrt{3}* sin(x)-3a$

3 0

4 years ago

Find the PERIMETER and the AREA of the following figure, 16 ft 8 ft 10 ft

Fed [463]

9514 1404 393

Answer:

perimeter: 36 +16√5 ft ≈ 71.777 ft
area: 288 ft²

Step-by-step explanation:

Perimeter

The perimeter is the total length of all the sides. The length of the horizontal sides is 8 ft + 10 ft = 18 ft. The length of the slant sides can be found using the Pythagorean theorem. For side length s, we have ...

s^2 = 8^2 + 16^2

s^2 = 64 +256 = 320

s = √320 = 8√5

Then the perimeter is ...

P = 2(8√5 + 18) = 36 +16√5 ≈ 71.777 . . . feet

__

Area

The area is given by the formula ...

A = bh

where b is the base and h is the height.

A = (18 ft)(16 ft) = 288 ft²

4 0

3 years ago

Consider the relationship between the place values of the 4s in this number. 444.44 . Choose all answers that are correct. A. Th

Effectus [21]

A and B PLEASE check though I am still human and I make mistakes

3 0

3 years ago

A circle is centered at (5, −9) and has a radius of 12. Which of the following is the equation for this circle? (x − 5)2 + (y +

Nady [450]

Answer:

(x-5)^2 + (y+9)^2 = 144

Step-by-step explanation:

The equation of a circle can be written as

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-5)^2 + (y- -9)^2 = 12^2

(x-5)^2 + (y+9)^2 = 12^2

(x-5)^2 + (y+9)^2 = 144

7 0

3 years ago

Use the graph to write a linear function that relates y to x . y=____