All categories

2 years ago

A rain gutter is made from aluminum sheets that

Mathematics

1 answer:

netineya [11]2 years ago

4 0

Answer:

Step-by-step explanation:

For any quadratic function f(x)=ax²+bx+c given in form f(x)=a(x-h)²+k, where:

h=-b/2a and k=f(h) the point (h, k) is vertex of the function graph.

It means that k is maximum (if a<0) or minimum (if a>0) value of function and x=h is the x which will maximize function.

A(x) = x(28-2x) = 28x - 2x² = - 2x² + 28x ⇒ a = -2 , b = 28

h = -28/[2•(-2)] = 7

You might be interested in

Picture explains<br> asdasdasd

tamaranim1 [39]

Answer:

Yes, AB is tangent

Step-by-step explanation:

The tangent is perpendicular to the radius. The given triangle is right if AB is tangent.

Use Pythagorean to verify

20² = 16² + 12²
400 = 256 + 144
400 = 400

Confirmed

7 0

1 year ago

Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

2 years ago

Colin buys a car for £42800.

guapka [62]

Answer:

Principal=₹42800

Rate of interest=5% but 2 years so multiply by 2 =5×2=10%

Time=2 years

Simple interest=42800×10×2/100= ₹8560

Amount=42800+8560=Rs51360

The answer is ₹ 51360

Please make me as brainliest

Step-by-step explanation:

8 0

2 years ago

Jacka and Jill are 28 miles apart on the same path. If Jack skateboards 4 miles per hour, and Jill bikes 6 miles per hour, How l

Alexeev081 [22]

Idk really know I just trying the get points

6 0

2 years ago

Read 2 more answers

A drawing has a scale of 3 in. : 2 ft. What is the scale factor of the drawing?

icang [17]

The scale factor of the drawing as described is; 1.5in/ft

<h3>Scale factor of drawings</h3>

According to the question;

The given scale factor of the drawing is; 3 in: 2 ft.

In essence, 3 inches on the drawing board represents 2 ft of the object.

Hence, by finding the quotient of the units, we have;

3in/2ft = 1.5 in/ft