All categories

2 years ago

P1 = (1,5). P2 = (x,2) .p1p2=5

Mathematics

1 answer:

Alex787 [66]2 years ago

6 0

$\qquad\qquad\huge\underline{{\sf Answer}}♨$

Let's use distance formula :

$\qquad \sf \dashrightarrow \: \sqrt{(x - 1) {}^{2} + (2 - 5) {}^{2} } = 5$

$\qquad \sf \dashrightarrow \: {(x - 1) {}^{2} + ( - 3) {}^{2} } = 5 {}^{2}$

$\qquad \sf \dashrightarrow \:(x - 1) {}^{2} + 9 = 25$

$\qquad \sf \dashrightarrow \:(x - 1) {}^{2} = 16$

$\qquad \sf \dashrightarrow \:(x - 1) = 16$

$\qquad \sf \dashrightarrow \:(x - 1) = \pm4$

$\qquad \sf \dashrightarrow \:x = 5 \: \: or \: \: - 3$

You might be interested in

Convert the mixed number to an improper fraction. enter your answer below using the slash mark ( / ) as the fraction bar

eduard

The Answer Fam Is 99/10

5 0

4 years ago

As a bowl of soup cools, the temperature of the soup is given by the twice-differentiable function H for 0<img src="https://tex.

Aleks04 [339]

The rate of change of temperature with time at a point in time is given by

the derivative of the function for the temperature of the soup.

The correct responses are;

a) H'(5) is approximately -2.6 degrees Celsius per minute.

b) Yes

c) The equation for the line tangent is y = -3.6·t + 90.8
The approximate value of C(5) is 72.8 °C

d) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.

Reasons:

a) From the data in the table, we have;

The approximate value of H'(5) is given by the average value of the rate of

change of the temperature with time between points, t = 3, and t = 8

Therefore;

$\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}$

Which gives;

$\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}$

Therefore, H'(5) = -2.6°C per minute

b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12

At t = 0, H(0) = 90 °C

At t = 12, H(12) = 58 °C

58 °C < 60 < 90 °C

Therefore, there exist a temperature, of 60 °C between 90° C and 58 °C

c) The given derivative of C is, $C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}$

At t = 3, we have;

$The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1$

Therefore, we have;

y - 80 ≈ -3.1 × (x - 3)

The equation for the tangent is; y = -3.6 × (x - 3) + 80

y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8

The equation for the tangent is; y = -3.6·x + 90.8

The value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8

C(5) ≈ 72.8°

d) Based on the the model above, the rate at which the temperature of the

soup is changing at t = 3 minutes is -3.6 degrees per minute.

Learn more about calculus and concepts here:

brainly.com/question/20336420

8 0

3 years ago

What is 4 2/3 + 2 1/5 + 3 1/2

Elena L [17]

Answer:

$10\frac{11}{30}$

Step-by-step explanation:

Convert the mixed fractions into improper fractions.

$14/3+11/5+7/2$

Add the values.

$311/30$

$10\frac{11}{30}$

$=10.36666666667$

6 0

4 years ago

The actual distance between two cities is 1250 mi. the shortest distance between the two cities on a map is 10 in. what is the s

Varvara68 [4.7K]

So the scale is usually ine inch of the map to actual distance right?we
So we need to calculate how much one inch is.
So we are told 10 inches is 1250 miles right?
So for one inch we need to divide the number of inches for the equivalent distance.
In this case it is 10 and 1250 miles.
So dividing 1250 by 10 gives you 125 right?
That means for every one inch on the map it is 125 miles right.
This can be written like 1:125.
This is how they write scales in the map.
It means for one unit in the map it is 125 units in real life

6 0

3 years ago

A camera has a listed price of $888.99 before tax. If the sales tax rate is 7.75% , find the total cost of the camera with sales

Aleksandr [31]

take 888.99, multiple it by 1.0775 (tax plus original price) to get the answer (957.886725 or 957.889)

4 0

4 years ago

Read 2 more answers

P1 = (1,5). P2 = (x,2) .p1p2=5 ​

P1 = (1,5). P2 = (x,2) .p1p2=5