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3 years ago

10 POINTS AND BRAINLIEST FOR CORRECT ANSWER!

Mathematics

2 answers:

Nimfa-mama [501]3 years ago

5 0

Answer:

Step-by-step explanation:

four and eight, use soh cah toa

Zarrin [17]3 years ago

3 0

The sides of the rectangle are 4 and 8 meters long.

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Solve each system of equations X^2+y^2+18x+29=0 X+y=1

tatyana61 [14]

Answer:

two solutions : (-3;4) and (-5;6)

Step-by-step explanation:

hello :

X²+y²+18x+29=0 ..(1)

X+y=1 ...(2)

by (2) : y = 1 - x

put this value in (1) : x² +(1-x)² +18x+29 = 0

x² +1 +x² -2x+18x +29 =0

2x²+16x +30 = 0

x²+8x+15 =0

delta = b²-4ac a=1 b=8 c = 15

delta = (8)²-4(1)(15)=64-60 =4 = 2²

X1=(-8+2)/2 = - 3

X2=(-8-2)/2 = - 5

case 1 : x = -3 y = 1 - (-3) = 4

case 2 : x = -5 y = 1 - (-5) = 6

8 0

3 years ago

2. The volume of both of these trapezoidal prisms is 24 cubic units. Their

Valentin [98]

Answer:

area of a trapezoidal base of each prism with heights 6 and 8 units are 4 square units and 3 square units respectively

Step-by-step explanation:

Let us first be aware of formula of volume for any regular geometrical figure.

Fundamental formula for volume for any regular geometrical figure is.

volume = area of cross section of object* height of object (A)

In the problem stated area of cross section of object will be area of a trapezoidal base.

Given in the question is

Volume of both the trapezoidal prisms = 24 cubic units

*************************************************************************************

For prism with height 6 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 6 * area of a trapezoidal base

=> area of a trapezoidal base = 24/6 = 4 square units

*************************************************************************************

For prism with height 8 unit

Substituting the value of height and volume in formula for trapezoidal prisms

24 = 8 * area of a trapezoidal base

=> area of a trapezoidal base = 24/8 = 3 square units

*************************************************************************************

Therefore area of a trapezoidal base of each prism with heights 6 and 8 units are 4 square units and 3 square units respectively.

4 0

3 years ago

Multiply. 2x(x2 + 2x - 6)

Stels [109]

2x(x2 + 2x - 6)
First add what is in the "(" wich is 2x+2x
2x(4x - 6)
Second multiply the 2x by the 4x & -6
8x-12x
Now subtract the -12x from the 8x
8x-12x = -4x

8 0

3 years ago

Read 2 more answers

What is the exact circumference of a circle with a radius of 15 cm? 10πcm 15πcm 30πcm 60πcm WIIL GIVE BRAINLIEST

ddd [48]

Answer:

Step-by-step explanation:

In order to find circumference you use the formula C (circumference)=2(pi)(r) in which r is the radius. In this case, two and 15 are thirty so to find the circumference all you have is the equation 30 times pi centimeters is equal to the Circumference.

5 0

4 years ago

Read 2 more answers

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

3 years ago