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3 years ago

Please help!!!!!!!!!!!!!!

Mathematics

1 answer:

Montano1993 [528]3 years ago

6 0

<h3>Answer: 7.1</h3>

=========================================================

Explanation:

The two points are (x1,y1) = (1,3) and (x2,y2) = (8,4)

Use the distance formula to get,

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (3-4)^2}\\\\d = \sqrt{(-7)^2 + (-1)^2}\\\\d = \sqrt{49 + 1}\\\\d = \sqrt{50}\\\\d = \sqrt{25*2}\\\\d = \sqrt{25}*\sqrt{2}\\\\d = 5\sqrt{2}\\\\d \approx 7.0710678\\\\d \approx 7.1$

Alternatively, you can plot the two points A(1,3) and B(8,4) on the same xy grid. Then plot point C(8,3). Note that C has the same x coordinate as B, and the same y coordinate as A. Triangle ABC is a right triangle, where the 90 degree angle is at point C. The distance from A to B is the same as finding the length of AB, which is the hypotenuse.

This means we can apply the pythagorean theorem to find the hypotenuse AB. The distance formula is a modified version of the pythagorean theorem. Refer to the diagram below.

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Find an explicit solution of the given initial-value problem.dy/dx = ye^x^2, y(3) = 1.

tamaranim1 [39]

Answer:

$y=exp(\int\limits^x_4 {e^{-t^{2} } } \, dt)$

Step-by-step explanation:

This is a separable equation with an initial value i.e. y(3)=1.

Take y from right hand side and divide to left hand side ;Take dx from left hand side and multiply to right hand side:

$\frac{dy}{y} =e^{-x^{2} }dx$

Take t as a dummy variable, integrate both sides with respect to "t" and substituting x=t (e.g. dx=dt):

$\int\limits^x_3 {\frac{1}{y} } \, \frac{dy}{dt} dt=\int\limits^x_3 {e^{-t^{2} } } dt$

Integrate on both sides:

$ln(y(t))\left \{ {{t=x} \atop {t=3}} \right. =\int\limits^x_3 {e^{-t^{2} } } \, dt$

Use initial condition i.e. y(3) = 1:

$ln(y(x))-(ln1)=\int\limits^x_3 {e^{-t^{2} } } \, dt\\ln(y(x))=\int\limits^x_3 {e^{-t^{2} } } \, dt\\$

Taking exponents on both sides to remove "ln":

$y=exp (\int\limits^x_3 {e^{-t^{2} } } \, dt)$

7 0

3 years ago

Burka [1]

Answer:

$2x^2+13$

Step-by-step explanation:

Given

$(-5x^2-2x+4)+(8x^2-x-1)-(x+2)(x-5)$

Required

Simplify

Expand brackets

$(-5x^2-2x+4)+(8x^2-x-1)-(x^2-5x+2x-10)$

$(-5x^2-2x+4)+(8x^2-x-1)-(x^2-3x-10)$

Open all brackets

$-5x^2-2x+4+8x^2-x-1-x^2+3x+10$

Collect Like Terms

$-5x^2+8x^2-x^2-2x-x+3x+4-1+10$

$2x^2+13$

<em>Hence, the polynomial simplifies to </em> $2x^2+13$ <em> and it has a degree of 2</em>

5 0

3 years ago

PLEASE HELP!<br>I'm confused..<br><br>Solve each equation for y.<br>please show work

8090 [49]

Answer:

b. y = 2/3x +5
c. y = -3 or -1/2

Step-by-step explanation:

b. The particualar steps for solving a linear equation such as this may vary from one equation to another. In general, you want to put all the y-terms on one side of the equal sign and everything else on the other side. Here's how we'll do that in this case.

Use the distributive property to eliminate parentheses.

... 6x -3y +12 = 4x -3

Find the unwanted terms on the side of the equation where y is, then add their opposite. In this case, we're adding -(6x+12)

... -3y = (4x -3) -(6x +12) = -2x -15

Divide by the coefficient of y.

... y = -2x/(-3) -15/(-3)

... y = 2/3x +5

____

c. This is a 2nd-degree (quadratic) equation with y as its only variable. The factor (2y+1) appears in both terms so we can use the distributive property to factor it out. Then the equation becomes ...

... (y +3)(2y +1) = 0

The zero product rule tells us this product will be zero only when one or the other of the factors is zero. This fact helps us find the values of y that are the solution to the equation.

For y+3 = 0:

... y + 3 = 0

... y = -3 . . . . . . add -3 to both sides of the equation

For 2y +1 = 0:

... 2y +1 = 0

... y +1/2 = 0 . . . . divide by 2

... y = -1/2 . . . . . . add -1/2

The solutions are y = -3 or y = -1/2.

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3 years ago

Find the surface area of a cylinder with a base diameter of 6 m and a height of 4 m

Lorico [155]

Answer:

SA=131.94689

Step-by-step explanation:

SA=2πrh+2πr^2

SA=2*3.14*3*4+2*3.14*3^2

SA=131.94689

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3 years ago

A bike to do tricks with has 20-inch-diameter wheels. Find the area of each wheel. Round to the nearest whole number. (Hint: Use

Kamila [148]

Area = $\pi r^2$

Area = 22/7 x 10 x 10

Area = 314 in^2

(the answer is option A, its rounded)

Hope this helps

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4 years ago