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Dmitry [639]
3 years ago
5

Solve for K. log2k=4

Mathematics
1 answer:
alekssr [168]3 years ago
6 0

Answer:

the answer is k=5000

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh
Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

  • The equation of the parabola is \mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}
  • The focus is \mathbf{Focus = (80, -1760)}
  • The directrix is \mathbf{y = \frac{1}{640}}
  • The axis of the symmetry of parabola is: \mathbf{x = 80}

From the question, we have:

\mathbf{Vertex: (h,k) = (80,10)}

\mathbf{Origin: (x,y) = (0,0)}

The equation of a parabola is:

\mathbf{y = a(x - h)^2 + k}

Substitute the values of origin and vertex in \mathbf{y = a(x - h)^2 + k}

\mathbf{0 = a(0 - 80)^2 + 10}

\mathbf{0 = a(- 80)^2 + 10}

\mathbf{0 = 6400a + 10}

Collect like terms

\mathbf{6400a =- 10}

Solve for a

\mathbf{a =- \frac{1}{640}}

Substitute the values of a and the vertex in \mathbf{y = a(x - h)^2 + k}

\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}

The focus of a parabola is:

\mathbf{Focus = (h, \frac{k+1}{4a})}

Substitute the values of a and the vertex in \mathbf{Focus = (h, \frac{k+1}{4a})}

\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}

\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}

\mathbf{Focus = (80, -11\times 160)}

\mathbf{Focus = (80, -1760)}

The equation of the directrix is:

\mathbf{y = -a}

So, we have:

\mathbf{y = \frac{1}{640}} ----- the directrix

The axis of symmetry is:

\mathbf{x = -\frac{b}{2a}}

We have:

\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}

Expand

\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}

Expand

\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}

\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }

A quadratic function is represented as:

\mathbf{y = ax^2 + bx + c}

So, we have:

\mathbf{a = -\frac{1}{640}}

\mathbf{b = \frac{1}{4}}

Recall that:

\mathbf{x = -\frac{b}{2a}}

So, we have:

\mathbf{x = -\frac{1/4}{2 \times -1/640}}

\mathbf{x = \frac{1/4}{1/320}}

This gives

\mathbf{x = \frac{320}{4}}

\mathbf{x = 80}

Hence, the axis of the symmetry of parabola is: \mathbf{x = 80}

Read more about parabola at:

brainly.com/question/21685473

6 0
3 years ago
Write the following in expanded form then in word form . number 355,645​
valkas [14]

Answer:

300000+50000+5000+600+40+5

word form:- three lakh fifty five thousand six hundred forty five.

3 0
3 years ago
A study conducted to determine the relationship between the age, x, in years of a certain brand of motorcycle and its value, y,
kirza4 [7]

Based on the equation, y = -750·x + 8500, the estimated value of a

motorcycle that is 5 years old is <u>$4,750</u>.

<h3>How can the given equation help to estimate the value of the motorcycle?</h3>

The regression equation that models the data is; y = -750·x + 8500

Where;

y = The value of the brand of motorcycle in dollars

x = The age of the motorcycle

When the motorcycle is 5 years old, we have;

x = 5

y = -750 × 5 + 8500 = 4750

Based on the equation, the estimated value of a motorcycle that is 5 years old, y =<u> $4,750</u>

Learn more equations here:

brainly.com/question/20475360

4 0
2 years ago
Juan pulled a red card from the deck of regular playing cards. This probability is 2652 or 12 . He puts the card back into the d
kenny6666 [7]

Answer:

no

Step-by-step explanation:

if he randomly pulls it out it's still the same number of red cards and also the total number of cards as always

can't change

6 0
3 years ago
Read 2 more answers
You are studying for your final exam of the semester. up to this point, you received 3 exam scores of 67%, 68%, and 78℅. to rece
scoray [572]
(67 + 68 + 78 + x) / 4 = 70
(213 + x) / 4 = 70
213 + x = 70 * 4
213 + x = 280
x = 280 - 213
x = 67

(213 + x) / 4 = 79
213 + x = 79 * 4
213 + x = 316
x = 316 - 213
x = 103

lowest u can make is 67, highest u can make is 100
4 0
3 years ago
Read 2 more answers
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