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2 years ago

Work out the length of x.

Mathematics

1 answer:

julsineya [31]2 years ago

4 0

Answer:

Calculate the value of x. Give your answer ... Hyp. 5.8 m. Opp. 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... the value of x. Give your answer correct to 1 decimal place. ... a. Diagram NOT accumtely drawn. 9,6 cm. 6.4 cm. A. Hyp. To. Aaj. LMN is a right-angled triangle. MN = 9.6 cm. ... x = ton-14.5.

Step-by-step explanation:

please be right

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Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th

saul85 [17]

Answer:

The standard form of the ellipse is $\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$ .

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

$(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)$ (1)

If we know that $V_{1} (x,y) = (4,0)$ and $V_{2}(x,y) = (4, 14)$ , then the coordinates of the center are, respectively:

$(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)$

$(h,k) = (2,0) + (2, 7)$

$(h, k) = (4, 7)$

The length of each semiaxis is, respectively:

$a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}$

$a = 3$

$b = \sqrt{(4-4)^{2}+(0-7)^{2}}$

$b = 7$

The standard equation of the ellipse is described by the following formula:

$\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1$

Where:

$h$ , $k$ - Coordinates of the center of the ellipse.

$a$ , $b$ - Length of the orthogonal semiaxes.

If we know that $h = 4$ , $k = 7$ , $a = 3$ and $b = 7$ , then the standard form of the ellipse is:

$\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$

4 0

3 years ago

A bacterial culture starts with 500 bacteria and doubles in size every half-hour.

tekilochka [14]

Answer:

a). 32000

b). $T_{t}=500\times 4^{t}$

c). 1259

Step-by-step explanation:

Growth of a bacteria is always exponential. Therefore, population of the bacteria is represented by the the geometric sequence.

Sum of the bacterial population after t hours will be represented by

$T_{n}=ar^{n}$

Where a = population at the start

r = ratio with the population is growing

n = time or duration of the growth in one hour

a). Population of 500 bacteria gets doubled after half an hour.

Or gets 4 times after an hour

This sequence will have a common ratio r = 4

and initial population a = 500

Therefore, population of the bacteria after 3 hours will be

$T_{3}=500\times 4^{3}$

$T_{3}=32000$

b). After t hours number of bacteria will be represented by

$T_{t}=500\times 4^{t}$

c). We have to calculate the population after 40 minutes.

That means duration 't' = 40 minutes of $\frac{2}{3}$ hours

By the formula,

$T_{\frac{2}{3}}=500\times 4^{\frac{2}{3}}$

$T_{\frac{2}{3}}=1259.92$ ≈ 1259

Therefore, number of bacteria after 40 minutes will be 1259.

8 0

3 years ago

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Omar went to the football game. He paid $13.50 for admission. He bought a program for $4.75, a bag of popcorn for $3.50, and a l

aalyn [17]

$25.10 is the answer

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2 years ago

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3 years ago

Use the graph of the polynomial function to find the factored form of the related polynomial assume it has no constant factor

tensa zangetsu [6.8K]

Answer:

(D)(x-2)(x+2)

Step-by-step explanation:

As raízes do polinômio são 2 e -2, portanto sua forma fatorada tem que ser (x-x1)(x-x2) se x1=2 e x2=-2. Então:

p(x) = (x-2)(x+2)

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3 years ago

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