formula for triangular prism

Given:

The equation is:

[tex]4x+2xy^2+44=y^3[/tex]

To find:

The equation of the tangent on the given equation at point (-3,2).

Solution:

We have,

[tex]4x+2xy^2+44=y^3[/tex]

Differentiate with respect to x.

[tex]4(1)+2[x(2yy')+y^2(1)]+0=3y^2y'[/tex]

[tex]4+4xyy'+2y^2=3y^2y'[/tex]

[tex]4+2y^2=3y^2y'-4xyy'[/tex]

[tex]4+2y^2=(3y^2-4xy)y'[/tex]

Isolate y'.

[tex]\dfrac{4+2y^2}{3y^2-4xy}=y'[/tex]

Now, we need to find the value of the derivative at point (-3,2).

[tex]y'_{(-3,2)}=\dfrac{4+2(2)^2}{3(2)^2-4(-3)(2)}[/tex]

[tex]y'_{(-3,2)}=\dfrac{4+8}{12+24}[/tex]

[tex]y'_{(-3,2)}=\dfrac{12}{36}[/tex]

[tex]y'_{(-3,2)}=\dfrac{1}{3}[/tex]

It means the slope of the tangent line is [tex]\dfrac{1}{3}[/tex].

The equation of tangent line that passes through the point (-3,2) with slope [tex]\dfrac{1}{3}[/tex] is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-2=\dfrac{1}{3}(x-(-3))[/tex]

[tex]y-2=\dfrac{1}{3}x+1[/tex]

[tex]y=\dfrac{1}{3}x+1+2[/tex]

[tex]y=\dfrac{1}{3}x+3[/tex]

Therefore, the equation of tangent line is [tex]y=\dfrac{1}{3}x+3[/tex].

Answer:

B

Step-by-step explanation:

Y=MX+C , where y=slope intercept, m=gradient and C=y-intercept

-5=6(-6)+c

-5=-36+c

-5+36=c

C=31

Hence,

y=MX+c

y=6x+31

Answer:

9:18

Step-by-step explanation:

1:2 means that you have to multiply the first number by 2 to get the second number. Therefore, you have to multiply 9 by 2, which is equal to 18. Therefore, it would be 9:18.

If this has helped please mark as brainliest

note: I don’t really like giving people answers. I like them to learn:

To find a(n) area of a triangle, all you need to do is use the triangle shape to make a rectangle and then calculate the area of the rectangle and divide it by the number of triangles you used to make the triangle.

for your triangle I can imagine it needs four triangles to make a rectangle.

unless you want to multiply 1/2x6x11 to get your answer.

hope this helped !

Answer:

Step-by-step explanation:

2×πr² + 2πr×h =

= 2×π×4² + 2π×4×10.5 =

= 32π + 84π =

= 116π ≈

≈ 364.42 cm²

The total metal needed to make the can is 364.42 square centimeters if the soup can will have a radius of 4 cm and a height of 10.5 cm.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We have:

The radius of the soup can r = 4 cm

The height of the soup can h = 10.5 cm

We know the surface area of the cylinder:

[tex]\rm S = 2\pi r(r+h)[/tex]

[tex]\rm S = 2\pi \times 4(4+10.5)[/tex]

S = 364.42 square cm

Thus, the total metal needed to make the can is 364.42 square centimeters if the soup can will have a radius of 4 cm and a height of 10.5 cm.

Learn more about the cylinder here:

brainly.com/question/3216899

#SPJ2

Answer:

I think it is 5 units left and 7 units down, then rotate 270°.

Step-by-step explanation:

                  HOPE THIS HELPS YOU!!! :) :) :) :) :)

                    SORRY IF IT'S WRONG. :) :) :) :) :)

Answer: Use the app photo math, you just take a picture and it gives you the answer and shows you the steps:)

1) x> 5

2) x< 2

3) x<-6

4) x< 2

5) x> 2

6) x> - 7/2

Step-by-step explanation:

See the images below for the work:)  The images will be in order with the number the first problem will be the answer to the first.

Answer:

[tex]\sf 1)\:4x - 2 > 2x + 8[/tex]

Add 2 from both sides:

[tex]\sf 4x-2+2>2x+8+2[/tex]

[tex]\sf 4x>2x+10[/tex]

Subtract 2x from both sides:

[tex]\sf 4x-2x>2x+10-2x[/tex]

[tex]\sf 2x>10[/tex]

Divide both sides by 2:

[tex]\sf \cfrac{2x}{2}>\cfrac{10}{2}[/tex]

[tex]\boxed{\sf x>5}[/tex]

_______________________________

[tex]\sf 2)\: -3x - 6 > 4x - 20[/tex]

Add 6 from both sides:

[tex]\sf -3x-6+6>4x-20+6[/tex]

[tex]\sf -3x>4x-14[/tex]

Subtract 4x from both sides:

[tex]\sf -3x-4x>4x-14-4x[/tex]

[tex]\sf -7x>-14[/tex]

Multiply both sides by -1:

[tex]\sf\left(-7x\right)\left(-1\right)<\left(-14\right)\left(-1\right)[/tex]

[tex]\sf 7x<14[/tex]

Divide both sides by 7:

[tex]\sf \cfrac{7x}{7}<\cfrac{14}{7}[/tex]

[tex]\boxed{\sf x<2}[/tex]

_______________________________

[tex]\sf 3)\: 4(x + 1) < 3x - 2[/tex]

Apply distributive property:

[tex]\sf 4x+4<3x-2[/tex]

Subtract 4 from both sides:

[tex]\sf 4x+4-4<3x-2-4[/tex]

[tex]\sf 4x<3x-6[/tex]

Subtract 3x from both sides:

[tex]\sf 4x-3x<3x-6-3x[/tex]

[tex]\boxed{\sf x<-6}[/tex]

_______________________________

[tex]\sf 4)\: 2x + 3 + x < -2x + 1 + 12[/tex]

Combine like terms:

[tex]\sf (2x+x)= 3x[/tex]

[tex]\sf( 1+12)=13[/tex]

[tex]\sf 3x+3<-2x+13[/tex]

Subtract 3 from both sides:

[tex]\sf 3x+3-3<-2x+13-3[/tex]

[tex]\sf 3x<-2x+10[/tex]

Add 2x from both sides:

[tex]\sf 3x+2x<-2x+10+2x[/tex]

[tex]\sf 5x<10[/tex]

Divide both sides by 5:

[tex]\sf \cfrac{5x}{5}<\cfrac{10}{5}[/tex]

[tex]\boxed{\sf x<2}[/tex]

________________________________

[tex]\sf 5)\: 2(x - 1) > 4x + 4 - 5x[/tex]

Combine like terms:

[tex]\sf (4x-5x)=-x[/tex]

[tex]\sf 2\left(x-1\right)>-x+4[/tex]

Apply distributive property:

[tex]\sf 2x-2>-x+4[/tex]

Add 2 from both sides:

[tex]\sf 2x-2+2>-x+4+2[/tex]

[tex]\sf 2x>-x+6[/tex]

Add x from both sides:

[tex]\sf 2x+x>-x+6+x[/tex]

[tex]\sf 3x>6[/tex]

Divide both sides by 3:

[tex]\sf \cfrac{3x}{3}>\cfrac{6}{3}[/tex]

[tex]\boxed{\sf x>2}[/tex]

_______________________________

[tex]\sf 6)\: 2 + 4x -7 < 8x + 2 - 2x[/tex]

Subtract 2 from both sides:

[tex]\sf 2+4x-7-2<8x+2-2x-2[/tex]

[tex]\sf 4x-7<8x-2x[/tex]

Combine like terms:

[tex]\sf (8x-2x)=6x[/tex]

[tex]\sf 4x-7<6x[/tex]

Add 7 from both sides:

[tex]\sf 4x-7+7<6x+7[/tex]

[tex]\sf 4x<6x+7[/tex]

Subtract 6x from both sides:

[tex]\sf 4x-6x<6x+7-6x[/tex]

[tex]\sf -2x<7[/tex]

Multiply both sides by -1:

[tex]\sf \left(-2x\right)\left(-1\right)>7\left(-1\right)[/tex]

[tex]\sf 2x>-7[/tex]

Divide both sides by 2:

[tex]\sf \cfrac{2x}{2}>\cfrac{-7}{2}[/tex]

[tex]\boxed{\sf x>-\frac{7}{2}}[/tex]

_______________________________________

Answer:

16°

Step-by-step explanation:

2x° + 6° = 38°

x° = (38°- 6°)÷2=16°

Answer:

5

Step-by-step explanation:

(1/5)/(1/25) = 25/5 =5

negative exponents means the numbers flip

Answer:

4/3 I think hope it works

Answer:

√(V / π × h), where V is the volume of the cylinder, h is the height, and π(Pi) is a mathematical constant with an approximate value of 3.14

Answer:

√(V / π × h)

Step-by-step explanation:

Radius of the cylinder ---> √(V / π × h)

V = volume of the cylinder

h = height of the cylinder

π = Pi ( approximate value of pi is 3.14)

9514 1404 393

Answer:

Step-by-step explanation:

The graph of this square root function extends upward and to the right of the point (-5, -1). The domain is the horizontal extent of the graph, so is ...

  x ≥ -5

The range is the vertical extent of the graph, so is ...

  y ≥ -1

Answer:

11

Step-by-step explanation:

[tex]\left(6x+4\right)+10x=180[/tex]

[tex]16x+4-4=180-4[/tex]

[tex]16x=176[/tex]

[tex]\frac{16x}{16}=\frac{176}{16}[/tex]

[tex]x=11[/tex]

Answer:

B

Step-by-step explanation:

graph A does not appear to pass the 'vertical line test'

Answer:

Ahimsa, it means 'non-injury' and 'non-killing'

Answer:

24

Step-by-step explanation:

if you add all of them together u get 108 divide it by 44 and u get 24

Answer:

70

Step-by-step explanation:

∠J and ∠K are supplementary angles

Supplementary angles have a sum of 180°

Thus, ∠J + ∠K = 180

110 + ∠K = 180

subtract 110 from each side

180 - 110 = 70

110 - 110 cancels out

we're left with ∠K = 70°

Answer:

8*3=24

24 yd^2

3*8

Step-by-step explanation:

Answer:

95.2

Step-by-step explanation:

because u multiply 8.5 by 11.2 and get 95.2

Answer:

[tex] - {x}^{2} + 7x - 5[/tex]

Step-by-step explanation:

Hope it is helpful....

Answer:

Base length of plane from control tower = 73,880 feet (Approx.)

Step-by-step explanation:

Given:

Height of plane from ground = 20,000 feet

Height of control tower = 200 feet

Angle of elevation from control tower = 15°

Find:

Base length of plane from control tower

Computation:

Height of plane from control tower = 20,000 - 200

Height of plane from control tower = 19,800 feet

Tan θ = Perpendicular / Base

Tan15 = 19,800 / Base length of plane from control tower

0.268 = 19,800 / Base length of plane from control tower

Base length of plane from control tower = 73,880 feet (Approx.)

Answer:

17

Step-by-step explanation:

Range is the biggest number minus the smallest number. So 20-3=17

Answer:

1.4 · 10³

Step-by-step explanation:

6.58 · [tex]10^{6}[/tex] ÷ 4.7 · 10³

6.58 ÷ 4.7 = 1.4

[tex]10^{6}[/tex] - 10³ = 10³

1.4 · 10³

Answer:

3.0926 x 10^10

Step-by-step explanation:

Answer:

Around 33.33% increase

Step-by-step explanation

Answer:

-1

Step-by-step explanation:

Answer:

option E

Step-by-step explanation:

have a great day

Answer:

50 gram

Step-by-step explanation:

The actual percentage recipe = 100%

Percentage Increase in recipe = 60%

Recipe used as a result of increment = 80 gram

Hence,

100% + 60% = 80

160% = 80g

If :

160% = 80

100% = x

Cross multiply

1.6x = 80 * 1

1.6x = 80

x = 80 / 1.6

x = 50

Recipe required 50 gram

Answer:

[tex]G = (-1.5,1.5)[/tex]

Step-by-step explanation:

Given

[tex]M = (-7,5)[/tex]

[tex]A = (6,5)[/tex]

[tex]T = (4,-2)[/tex]

[tex]H = (-9,-2)[/tex]

Required

Determine the coordinate of G

From the complete question, G is at the intersection of MT and AH.

So, G is calculated using midpoint formula

[tex]G = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]

For MT:

[tex]M = (-7,5)[/tex]      [tex]T = (4,-2)[/tex]

[tex]G = \frac{1}{2}(-7 + 4, 5 -2)[/tex]

[tex]G = \frac{1}{2}(-3, 3)[/tex]

Open bracket

[tex]G = (-1.5,1.5)[/tex]

To show that [tex]G = (-1.5,1.5)[/tex]

We have:

[tex]A = (6,5)[/tex]       [tex]H = (-9,-2)[/tex]

[tex]G = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]

[tex]G =\frac{1}{2}(6-9,5-2)[/tex]

[tex]G = \frac{1}{2}(-3, 3)[/tex]

Open bracket

[tex]G = (-1.5,1.5)[/tex]

Hence, the coordinates of G is:

[tex]G = (-1.5,1.5)[/tex]