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2 years ago

AB = 6cm , AC = 12cm Calculate the length of CD Give your answer to 3 significant figures

Mathematics

1 answer:

Len [333]2 years ago

6 0

Answer:

144-36=108

Square root 108 = 10.4cm (cb)

Soh Cah toa

Sin(55) =o/h

=10.4/h

H x sin55 =10.4

÷sin55

H= 10.4/sin55

H=12.7cm

CD is 12.7cm to 3 s.f.

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Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.

Alexus [3.1K]

(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k

nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix

I will only convert the 1st one fully, you should be able to do the rest

1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
(-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)

k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5

basically completee the square with x and find P by force factoring a 4 out

2. directix: y=-1.75

3. directix: y=1.5

4. directix: y=17.25

5. d: -37.5

6. d: 9.25

7. d=2.625

order them yourself

7 0

3 years ago

Please help me with this one!!

Tema [17]

Answer:

$21 in^{2}$

Step-by-step explanation:

The square in the middle has a length and width of 3, so multiply. 9.

All of the triangles have a base of 3 and a height of 2. The area equation for triangles is

$A=bh\frac{1}{2}$

So base*height is 6. Divide that by 2 or multiply by 1/2.

You get 3. There are 4 triangles, so multiply that by 4. 12.

Add 12 and 9 together, and you get:

$21 in^{2}$

I hope this helps!

6 0

3 years ago

Leta has $45 in her account in May. How much money does she have in her account in August

wariber [46]

45-15= 30-28= 2+18=20
Is that what the question was asking??

5 0

3 years ago

3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d

pychu [463]

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
$\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}$

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

To obtain $4000 after two years, let A = 4000 and t = 2.

Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.

Substitute and solve for P:

$\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}$

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

$\displaystyle A = Pe^{rt}$

Where e is Euler's number.

Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:

$\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}$

In conclusion, about $3692.47 should be deposited.

8 0

2 years ago

A number is 6 times another number and their difference is 30. What are the numbers?

Alenkasestr [34]

Answer:

x=36

y=6

Step-by-step explanation:

Let the numbers be x and y

Condition 1

x=6y ----------(1)

Condition 2

x-y=30 ------------(2)

Putting 1 in 2

6y-y=30

5y=30

Dividing both sides by 5

y=6

Now

Putting y=6 in 1

We get

x=6(6)

x=36

8 0

4 years ago