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4 years ago

Write parametric equations of the line with the equation 2x+3y=5

1 answer:

7 0

We have
2x+3y=5

Step 1
find two points of the line
for x=0--------------> y=5/3 point (0,1.67)
for y=0 --------------> x=5/2 point (2.5,0)

The vector between two points is v =(2.5-0,0-1.67)=(2.5.-1.67)

Vector form: r=ro+tv----------> (2.5,0)+(2.5,-1.67)t

Parametric form
x=2.5+2.5t
y=-1.67t

the answer is
x=2.5+2.5t
y=-1.67t

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Suppose that we don't have a formula for g(x) but we know that g(3) = −5 and g'(x) = x2 + 7 for all x. (

True [87]

So it tells us that g(3) = -5 and g'(x) = x^2 + 7.

So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))

now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16

Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84

So we have our linear approximation for the two.

If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35

So just to check our linear approximations use that to find g(2.99) and g(3.01)

g(2.99) = -5.1597
g(3.01) = -4.8397

So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.

5 0

4 years ago

4. Look at the polyhedron that you chose at the beginning. Which two solids do you need to create your polyhedron? How many of e

andrey2020 [161]

Answer:

I am currently doing that one as well right know and I think that you need two octahedrons, and 8 tetrahedrons

Step-by-step explanation:

6 0

4 years ago

Write an equation in point-slope form of the line that passes through the given points. Then write the equation in slope-interce

Nonamiya [84]

First we need to find the slope
y2-y1/x2-x1
-6-4/-3-2
-10/-5 <---this can be simplified
Slope=2
Point slope:
y-y1=m(x-x1)
Now take the first pair of coordinates and plug them in their proper spots it helps to label them then plug in
y1=4
x1=2
m=slope=2
Now plug them in our final answer would be :
y-4=2(x-2)
Slope intercept:
<span>y = mx + b
</span><span>where:
m is the slope of the line
b is the y-intercept of the line
Slope is known
y=2x+b
To find the b you pick one of the given coordinates let's do (2,4)
Plug them into what we have
y=2x+b
4=2(2)+b
solve for b
4=4+b
subtract 4 from both sides
b=0 therefore the equation would simply be
y=2x</span>

7 0

4 years ago

Point T has coordinates (10,20). To calculate the coordinates of point T′ in the image,

Hatshy [7]

Answer: $T'(18,36)$

Step-by-step explanation:

For this exercise it is important to know the definition of "Dilation".

A Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape but have different sizes.

If the Dilation is centered at the origin, and knowing the scale factor of $\frac{9}{5}$ , you need to multiply each coordinate of the point T by the scale factor in order to find the coordinates of the Image T'.

Knowing that the point T has the following coordinates:

$T(10,20)$

You get that the coordinates of the Image T' are the shown below:

$T'=(\frac{9}{5}*10,\frac{9}{5}*20)\\\\T'=(18,36)$

6 0

4 years ago

The net of a rectangular prism is shown below.

Mamont248 [21]

Answer:

Step-by-step explanation:

Using a net to find the surface area of a rectangular prism

Finding the areas of each of the rectangles and squares of the net of a rectangular prism and adding up those areas gives the surface area or total surface area of the prism.

For example, if the length of one side of the cube 4 units then the area of one its face is 4 × 4 = 16 square units. From the net, we can see that there are six equal faces and so we get the total surface area is 6 × 16 = 96 square units.

Surface Area of a Rectangular Prism using Nets

A rectangular prism or cuboid is formed by folding a net as shown −

Cuboid

We can see from the net that there are two rectangles with dimensions 3 cm by 6 cm, two rectangles with dimensions 2 cm by 6 cm and two rectangles with dimensions 2 cm by 3 cm. The total surface area is then

2 × 3 × 6 + 2 × 2 × 6 + 2 × 2 × 3 = 72 cm2

Example 1:

Find the surface area of the given rectangular prism in square cm.

Rectangular Prism in Square cm

Solution

Step 1:

Using net, the surface area of a rectangular prism

= 2lw+wh+lh; l = 6 ; w = 5; h = 3

Step 2:

Surface area of given prism = 26×5+6×3+3×5

= 230+18+15

= 126 square cm

Example 2:

Find the surface area of the given rectangular prism in square cm.

Rectangular Prism Square cm

Solution

Step 1:

Using net, the surface area of a rectangular prism

= 2lw+wh+lh; l = 5; w = 6; h = 4

Step 2:

Surface area of given prism = 25×6+5×4+6×4

= 230+20+24

= 148 square cm

6 0

3 years ago

Read 2 more answers