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2 years ago

A chord 20 inches long is 4 inches from the center

Mathematics

1 answer:

Lilit [14]2 years ago

5 0

Answer:

The radius of the circle is 10.8 inches

Step-by-step explanation:

Given:

Length of the chord = 20 inches

Distance of the chord from the center of the circle = 4 inches

To find:

radius of the circle=?

Solution:

As shown in the figure below, the radius, r, is the hypotenuse of a right triangle. One leg of the triangle is 4 and the other is half o f20 , or 10. Using the Pythagorean theorem to calculate the length of R, as follows:

$(4)^2 +(10)^2= (R)^2$

$16 +100= (R)^2$

$116= (R)^2$

$R =\sqrt{116}$

R= 10.77

R = 10.8 inches

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The force of gravity on Mars is different than on Earth. The function of the same situation on Mars would be represented by the

sweet-ann [11.9K]

Answer:

If thrown up with the same speed, the ball will go highest in Mars, and also it would take the ball longest to reach the maximum and as well to return to the ground.

Step-by-step explanation:

Keep in mind that the gravity on Mars; surface is less (about just 38%) of the acceleration of gravity on Earth's surface. Then when we use the kinematic formulas:

$v=v_0+a\,*\,t\\y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2$

the acceleration (which by the way is a negative number since acts opposite the initial velocity and displacement when we throw an object up on either planet.

Therefore, throwing the ball straight up makes the time for when the object stops going up and starts coming down (at the maximum height the object gets) the following:

$v=v_0+a\,*\,t\\0=v_0-g\,*\,t\\t=\frac{v_0}{t}$

When we use this to replace the 't" in the displacement formula, we et:

$y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2\\y-y_0=v_0\,(\frac{v_0}{g} )-\frac{g}{2} \,(\frac{v_0}{g} )^2\\y-y_0=\frac{1}{2} \frac{v_0^2}{g}$

This tells us that the smaller the value of "g", the highest the ball will go (g is in the denominator so a small value makes the quotient larger)

And we can also answer the question about time, since given the same initial velocity $v_0$ , the smaller the value of "g", the larger the value for the time to reach the maximum, and similarly to reach the ground when coming back down, since the acceleration is smaller (will take longer in Mars to cover the same distance)

3 0

2 years ago

What is the smallest solution to this equation?

Lapatulllka [165]

Answer:

x = - 6

Step-by-step explanation:

Given

$\frac{2}{3}$ x² = 24 ( multiply both sides by 3 )

2x² = 72 ( divide both sides by 2 )

x² = 36 ( take the square root of both sides )

x = ± $\sqrt{36}$ ← note plus or minus

x = ± 6

solutions are x = - 6, x = + 6

The smallest solution is x = - 6

8 0

2 years ago

Help please if you can will give branliest

Yuliya22 [10]

Answer:

i’m thinking it might be 10?

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions

salantis [7]

Dimensions are length 20 meter and width 14 meter

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

A rectangle has width that is 6 meters less than the length

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

The area of the rectangle is given by formula:

$Area = length \times width$

Substituting the values we get,

$Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0$

Solve the above equation by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}$

$a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14$

Since, length cannot be negative, ignore a = -14

Thus solution of length is a = 20

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

6 0

2 years ago

Find the value of x

riadik2000 [5.3K]

Answer:

4√5

Step-by-step explanation:

Use Pythagorean theorem

a^2=21^2-19^2

a^2=441-19^2

a^2=441-361

a^2=80

a= √80

simplify

6 0

2 years ago