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3 years ago

X and y interpects of f(x)=x^2-49

1 answer:

5 0

Y intercept is when x = 0
X intercept is when y = 0

Y intercept is 0^2 - 49 = ?
-49

X intercept you would have to factor. You’d get (x-7)(x+7) meaning the graph touches o at the x values 7 and -7

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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:

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

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3 years ago

What is 6cm in fraction form

julia-pushkina [17]

The answer is 2 3/8 in.

7 0

3 years ago

What’s 5.03 in simplest form

kondaur [170]

Answer:

5 3/10

Step-by-step explanation:

To simplify this decimal you need to convert it to a fraction

You get 503/100 since the decimal is in the hundredths place so its over 100

You can leave it as an improper fraction or convert it to a mixed number by dividing 503/100 which will get you 5 3/10.

8 0

3 years ago

Read and solve please thank you!

MariettaO [177]

Answer: 3inch cubed

Step-by-step explanation:

.5•.5•.5= .125

.125•24=3

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3 years ago

Read 2 more answers

What is the approximate value of X round to the nearest 10th

Alik [6]

Answer:

The correct answer is C) 4.6

Step-by-step explanation:

To find this, use the trigonometry functions. In this case, since we have the hypotenuse and are looking for the opposite, we use Sin.

Sin(α) = OPP/HYP

Sin(50) = x/6

6Sin(50) = x

4.6 = x

6 0

3 years ago