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2 years ago

Write the equation of the parabola given: Focus: (2,-9) Directrix: y=1

Mathematics

1 answer:

stellarik [79]2 years ago

8 0

So the vertex, exactly between the focus and directrix, must be at (h, k) = (1,
–2).

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Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

zloy xaker [14]

Answer:

$k=0$

$\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}$

$\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}$

Step-by-step explanation:

We are given the function:

$\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}$

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

$\displaystyle (20) = 20e^{k(1)}$

Simplify:

$1= e^k$

Anything raised to zero (except for zero) is one. Therefore:

$k=0$

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

$\displaystyle (40) = 20e^{k(1)}$

Simplify:

$\displaystyle 2 = e^{k}$

We can take the natural log of both sides:

$\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}$

By definition, ln(e) = 1. Hence:

$\displaystyle k = \ln 2$

Therefore:

$2k+1 = 2\ln 2+ 1 \approx 2.3863$

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

$\displaystyle (10) = 20e^{k(1)}$

Simplfy:

$\displaystyle \frac{1}{2} = e^k$

Take the natural log of both sides:

$\displaystyle \ln \frac{1}{2} = k\ln e$

Therefore:

$\displaystyle k = \ln \frac{1}{2}$

Therefore:

$\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931$

3 0

2 years ago

(05.02 MC)

Elanso [62]

His work should have looked like this.

2x + y = 5
x − 2y = 10

y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10 When he added in both sides, he subtracted 10 from 10,
5x = 20 instead of adding 10 from 10 to make 20.
x = 4
2(4) + y = 5
8 + y = 5

y = -3

4 0

2 years ago

4x+17=23. Find the solution to this equation

Elden [556K]

Answer:

1.5

Step-by-step explanation:

4x + 17 = 23

- 17 -17

4x=6

then divide 4 from both sides and you get

x=1.5

7 0

2 years ago

Read 2 more answers

What is the answer to 25% of 50

a_sh-v [17]

Answer:

12.5

Step-by-step explanation:

.25 x 50= 12.5

8 0

2 years ago

80% din 2.3 km este egal cu...... m

ycow [4]

Can you ummm finish the question

3 0

2 years ago