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2 years ago

In the diagram shown, AE 1/3AC and ED ll CB. Explain why df must be one-fourth length of CD

Mathematics

1 answer:

Blizzard [7]2 years ago

8 0

The value of the length DF is 1/4 of that of CD because of the Angle Bisector Theorem for triangles.

<h3>What is the Angle Bisector Theorem?</h3>

The Angel Bisector Theorem states that if a ray bisects an angle of a triangle, it dissects the side of the triangle that is opposite to the dissected angle into parts that are proportionate to the adjacent sides.

Note that the angle that has been dissected here is ∠CBD. Thus,

$\frac{DF}{CF}$ = $\frac{BD}{BC}$

See the link below for more about Angle Bisector Theorem of the Triangle:

brainly.com/question/21475560

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I’m having a lot of trouble, can someone guide me, step by step?

shutvik [7]

Answer:

Hi hopefully this helps you!

Step-by-step explanation:

To find the area of a circle you can use the formula A = πr^2

The radius of a circle is just the diameter divided by 2. In this case we know the diameter is 3, so the radius is 1.5

A = π(1.5)^2

= 7.07

Because this is a semicircle, divide this area by 2

= 3.53429 in^2

Add up the area of this semi circle with the area of the rectangle

A = (3.53429) + (3x4)

= 15.53429 in^2

To find the circumference/ perimeter of a circle use this formula C = 2πR

C = 2π(1.5)

= 9.42478 inches

Again because this is a semicircle, divide by 2

= 9.42478 / 2

= 4.71239 inches

To find the perimeter of this entire shape add up the circumference of the semicircle and the rectangle's sides and bottom

P = 4.71239 + 4 + 4 + 3

= 15.71239 inches

So the final answer would be

A = 15.53 squared inches

P = 15.71 inches

Hope this helps! Best of luck in your studies <3

6 0

2 years ago

Two-thirds of a number is equal to 20. What is the number?

IRISSAK [1]

Answer:

The number is 30

Step-by-step explanation:

Let x be the number

2/3 x = 20

Multiply each side by 3/2 to isolate x

3/2 *2/3x = 20*3/2

x = 30

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.

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

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

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

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

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

2 years ago

Caitlin earns $17 per hour tutoring students after school. If Caitlin tutored for 12 hours this month, how much money did she ea

pishuonlain [190]

Answer:

204

Step-by-step explanation:

7 0

3 years ago

What does the point (1, 25) mean in the situation

d1i1m1o1n [39]

X-axis and y-axis
x=1 and y=25
(x,y)

Can you mark as Brainiest? Hope it helps!

3 0

3 years ago