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3 years ago

The fastest human has ever run is 27 mph how many miles per minute did the human run

Mathematics

1 answer:

Phoenix [80]3 years ago

7 0

$\sf \frac{27~ miles}{1 ~hour} \times \frac{1~ hour}{60~ minutes} = \boxed{\frac{9}{20}~miles~per~minute}$

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Prove: If a chord of a circle makes an angle of 30° with a diameter, prove that the distance from the center to the chord is one

Svet_ta [14]

Answer:

See explanation.

Step-by-step explanation:

Let BC be the diameter of the circle with center at point O, AB be the chord and ∠ABC=30°. OD is the distance from the center to the chord.

Consider triangle BDO. This triangle is special 30°-60°-90° right triangle. The leg OD is opposite to the angle of 30° and is half of the hypotenuse. The hypotenuse of the triangle BDO is BO. BO is the radius of the circle and is equal to half of the diameter AB. Thus,

$OD=\dfrac{1}{2}BO=\dfrac{1}{2}\cdot \dfrac{1}{2}AB=\dfrac{1}{4}AB.$

5 0

3 years ago

Please help soon!

Jlenok [28]

Answer:

a) Translate the graph of f(x) down 3 units.

b) (8,-1) is a point on the graph of g(x)

Step-by-step explanation:

The transformations that subtract a constant number of units from the functional expression f(x) are transformations that lower the graph of the function in those many units,

Therefore they correspond to a translation of the original graph down the number of units involved.

In this case, the number of units involved is "3" (due to the "-3" added to the expression for f(x). So he correct answer for the first part is: Translate the graph of f(x) down 3 units.

For the second part, one has to try each of the coordinate pairs given in the new function g(x) to see which one results in a true statement:

1) Testing (-8,-1) by checking if replacing x with the value "-8" renders "-1" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(-8)=\sqrt[3]{-8} -3\\g(-8)=-2-3\\g(-8)=-5$

so this is NOT a point on the graph of g(x).

2) Testing (-1,-2) by checking if replacing x with the value "-1" renders "-2" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(-1)=\sqrt[3]{-1} -3\\g(-1)=-1-3\\g(-1)=-4$

so this is NOT a point on the graph of g(x).

3) Testing (2,-1) by checking if replacing x with the value "2" renders "-1" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(2)=\sqrt[3]{2} -3\\$

the cubic root of 2 is not a rational number, because 2 is not a perfect cube, so the expression cannot be reduced, so this is NOT a point on the graph of g(x).

4) Testing (8,-1) by checking if replacing x with the value "8" renders "-1" for the y-value: $g(x)=\sqrt[3]{x} -3\\g(8)=\sqrt[3]{8} -3\\g(8)=2-3\\g(8)=-1$

Therefore this pair (8,-1) IS a point on the graph of g(x).

5 0

3 years ago

Read 2 more answers

One-sixth + StartRoot 6 =

Nataliya [291]

Answer: 2.62

Step-by-step explanation: 1/6+√6= 2.62

change 1/6 into a decimal by dividing 1 by 6 you get 0.16 with 6 repeating then find the square root of 6 which is 2.44948974... that's rounded to 2.45 then 2.45+0.16 repeating the 6, then simplify to get 2.62.

hope i helped!

4 0

3 years ago

Which of the following are exterior angles? Check all that apply.

Norma-Jean [14]

Answer:

f d a c

Step-by-step explanation:

i took this quix before i think

6 0

2 years ago

If A is an n× n matrix, then det A = det AT . Verify this theorem for 2 × 2 matrices.

Bond [772]

Answer:

Verified

Step-by-step explanation:

Let A matrix be in the form of

$\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

Then det(A) = ad - bc

Matrix A transposed would be in the form of:

$\left[\begin{array}{cc}a&c\\b&d\end{array}\right]$

Where we can also calculate its determinant:

det(AT) = ad - bc = det(A)

So the determinant of the nxn matrix is the same as its transposed version for 2x2 matrices

4 0

3 years ago