Plssss help. High school mathematics

The hour hand on a clock is 4 cm long, and the minute hand is 10 cm long. What is the exact distance between the tips of the han

Allushta [10]

Answer:

2 sqrt(19)

Step-by-step explanation:

We know that the angle between the two hands

360 /12 *2 = 60 degrees

We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12

This is a triangle where we know 2 sides and the angle between them.

We can use the law of cosines to determine the third side

c^2 = a^2 + b^2 -2abcosC

Where C is the angle between sides a and b

a =4 and b = 10 C = 60 and we are looking for side c

c^2 = 4^2 + 10^2 -2*4*10 cos60

c^2 =16+100 - 80cos 60

c^2 = 76

Take the square root of each side

sqrt(c^2) = sqrt(76)

c = sqrt(76)

c =sqrt(4) sqrt(19)

c =2 sqrt(19)

4 0

2 years ago

The upper-left coordinates on a rectangle are (-6,0)(−6,0)left parenthesis, minus, 6, comma, 0, right parenthesis, and the upper

nikklg [1K]

Answer:

See attachment for rectangle

Step-by-step explanation:

Given

$A = (-6,0)$

$B = (-4,0)$

$Area = 12$

Required

Draw the rectangle

First, we calculate the distance between A and B using distance formula;

$AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

So, we have:

$AB = \sqrt{(-6 - -4)^2 + (0- 0)^2}$

$AB = \sqrt{(-2)^2 + (0)^2}$

$AB = \sqrt{4 + 0}$

$AB = \sqrt{4}$

$AB = 2$

The above represents the length of the triangle.

Next, calculate the width using:

$Length * Width = Area$

$2* Width = 12$

Divide both sides by 2

$Width = 6$

This implies that, the width of the rectangle is 6 units.

We have:

$A = (-6,0)$

$B = (-4,0)$

Since A and B are at the upper left and right, then the ther two points are below.

6 units below each of the above point are:

$C = (-6,0-6)\\$ => $C = (-6,-6)$

$D = (-4,0-6)$ => $D = (-4,-6)$

Hence, the points of the rectangle are:

$A = (-6,0)$

$B = (-4,0)$

$C = (-6,-6)$

$D = (-4,-6)$

<em>See attachment for rectangle</em>

6 0

3 years ago

stion 1 OT 5A researcher recorded the number of swans and the number of ducks in a lake every month. Function s represents the n

Anon25 [30]

Given functions are

$s(n)=2(1.1)^n+5_{}$ $d(n)=4(1.08)^n+3$

The total number of ducks and swans in the lake after n months can be determined by adding the functions s(n) and d(n).

$t(n)=s(n)+d(n)$

$t(n)=(2(1.1)^n^{}+5)+(4(1.08)^n+3)$

$t(n)=2(1.1)^n+5+4(1.08)^n+3$

$t(n)=2(1.1)^n+4(1.08)^n+5+3$

$t(n)=2(1.1)^n+4(1.08)^n+8$

Taking 2 as common, we get

$t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack$

Hence The total number of ducks and swans in the lake after n months is

$t(n)=2\lbrack(1.1)^n+2(1.08)^n+4\rbrack$

8 0

1 year ago

WILL GIVE BRAINLIEST<br><br>solve for x : -4 = (2/3)x <br><br>show steps please

cupoosta [38]

<h2>Answer: x = -6</h2>

<h3>Step-by-step explanation:</h3>

To solve for x, we have to find a way to make x the subject of the equation (get x on one side and everything else on the other side)

since -4 = (2/3)x [mutiply both sides by 3]

⇒ -4 × 3 = 2x [divide both sides by 2]

⇒ (-12/2) = x [simplify by dividing -12 by 2]

∴ x = -6

3 0

2 years ago

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Which point is on the circle centered at the origin with a radius of 5 units?

Aleonysh [2.5K]

Answer:

(2,√21)

Step-by-step explanation:

The circle centered at the origin has equation:

${x}^{2} + {y}^{2} = 25$

Any point that satisfies this equation lie on this circle.

When x=2, we substitute and solve for y.

${2}^{2} + {y}^{2} = 25 \\ 4 + {y}^{2} = 25 \\ {y}^{2} = 25 - 4 \\ {y}^{2} = 21$

Take square root to get:

$y = \pm \sqrt{21}$

Therefore (2,-√21) and (2,√21) are on this circle.

From the options, (2,√21) is the correct answer

3 0

3 years ago

Read 2 more answers