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2 years ago

8

Hurry I'm almost out of time !!!!

2 answers:

stich3 [128]2 years ago

8 0

Answer:

v= 7*6/2 *8 (The last one)

Step-by-step explanation:

To find the volume you have to multiply the base and the height which is 7 and 6 and divide it by 2. Then you multiply the 8.

djverab [1.8K]2 years ago

5 0

It is the last one because it is

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Someone help me please! will give brainliest.

Monica [59]

Answer: Graph B and Graph D

4 0

3 years ago

Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the pa

konstantin123 [22]

Answer:

$y=2x-8$

Step-by-step explanation:

The given parametric equation is;

$x=6+ln(t),y=t^2+3$

<h3><u>BY ELIMINATING THE PARAMETER</u></h3>

To eliminate the parameter we make $t$ the subject in one equation and put it inside the other.

We make $t$ the subject in $x=6+ln(t)$ because it is easier.

$\Rightarrow x-6=ln(t)$

$\Rightarrow {e}^{x-6}=e^{ln(t)}$

$\Rightarrow {e}^{x-6}=t$

Or

$t={e}^{x-6}$

We now substitute this into $y=t^2+3$ .

This gives us;

$y=(e^{x-6})^2+3$ .

$\Rightarrow y=e^{2(x-6)}+3$ .

We have now eliminated the parameter.

The equation of the tangent at (6,4) is given by;

$y-y_1=m(x-x_1)$

where the gradient function is given by;

$\frac{dy}{dx}=2e^{2(x-6)}$

We substitute $x=6$ into the gradient function to obtain the gradient.

$\Rightarrow m=2e^{2(6-6)}$

$\Rightarrow m=2e^0$

$\Rightarrow m=2$

The equation of the tangent becomes

$y-4=2(x-6)$

We simplify to obtain

$y=2x-12+4$

$y=2x-8$

<h3><u>WITHOUT ELIMINATING THE PARAMETER</u></h3>

The given parametric equation is;

$x=6+ln(t),y=t^2+3$

For $x=6+ln(t)$

$\frac{dx}{dt}=\frac{1}{t}$

For $y=t^2+3$

$\frac{dy}{dt}=2t$

The slope is given by;

$\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$\frac{dy}{dx}=\frac{2t }{\frac{1}{t} }$

$\frac{dy}{dx}=2t^2$

At the point, (6,4), we plug in any of the values into the parametric equation and find the corresponding value for $t$ .

Notice that

When $x=6$ , $6=6+\ln(t)$

$6-6=\ln(t)$

$0=\ln(t)$

$e^0=e^\ln(t)$

$1=t$

when $y=4$ , $4=t^2+3$

$4-3=t^2$

$1=t^2$

$t=\pm1$

But the slope is the same when we plug in any of these values for t.

$\frac{dy}{dx}=2(\pm1)^2=2$

The equation of the tangent becomes

$y-4=2(x-6)$

We simplify to obtain

$y=2x-12+4$

$y=2x-8$

7 0

3 years ago

The area of the base (B) of a triangular pyramid is 28 cm. The perimeter (p) is 20 cm, and the slant height (S) is 5 cm. Determi

kenny6666 [7]

Answer:

The pyramid's surface area is 78 square centimeters

Step-by-step explanation:

The formula of the surface area of a pyramid is S.A = A + $\frac{1}{2}$ p s, where

A is the area of its base
p is the perimeter of its base
s is the slant height of it

∵ The area of the base of a triangular pyramid is 28 cm²

∴ A = 28 cm²

∵ The perimeter of the base is 20 cm

∴ p = 20 cm

∵ The he slant height is 5 cm

∴ s = 5 cm

- Substitute these values in the formula of the surface area

above to find it

∵ S.A = 28 + $\frac{1}{2}$ (20)(5)

∴ S.A = 28 + 50

∴ S.A = 78 cm²

The pyramid's surface area is 78 square centimeters

5 0

3 years ago

HELP ME ASAP I WILL GIVE BRAINIEST TO THE FIRST THAT IS CORRECT

Rudiy27

Answer:

13.7 miles

Step-by-step explanation:

If you make 6 1/3 into 6.3 and subtract that from 20, you will get 13.7 miles.

4 0

3 years ago

Angle abc and dcb make a linear pair. of abc=2x+9 and dbc=10x+15,find x

Anuta_ua [19.1K]

Answer:

x = 13

Step-by-step explanation:

A linear pair of angles sum to 180° , then

2x + 9 + 10x + 15 = 180 , that is

12x + 24 = 180 ( subtract 24 from both sides )

12x = 156 ( divide both sides by 12 )

x = 13

8 0

3 years ago