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2 years ago

Kenneth ran a marathon (26.2) miles) in 5.5 hours. What was Kenneth’s average speed? (Round your answer to the nearest tenth.)

Mathematics

1 answer:

Serga [27]2 years ago

3 0

Answer:

4.8 miles per hour.

Step-by-step explanation:

Average speed=Total distance/Time taken

=26.2miles/5.5hour

=4.8 miles per hour

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Need help with this question

Amiraneli [1.4K]

Answer:

1 and 3, 2 and 4

Step-by-step explanation:

Supplementary angles total to 180° or should form a straight line. 1 and 3, 2 and 4 are vertical angles which equal one another and are not supplementary.

6 0

2 years ago

In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. Acc

Troyanec [42]

Answer:

Step-by-step explanation:

(a)

Consider the following:

$A=\frac{\pi}{4}=45°\\\\B=\frac{\pi}{3}=60°$

Use sine rule,

$\frac{b}{a}=\frac{\sinB}{\sin A}
\\\\=\frac{\sin{\frac{\pi}{3}}
}{\sin{\frac{\pi}{4}}}\\\\=\frac{[\frac{\sqrt{3}}{2}]}{\frac{1}{\sqrt{2}}}\\\\=\frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{1}=\sqrt{\frac{3}{2}}$

Again consider,

$\frac{b}{a}=\frac{\sin{B}}{\sin{A}}
\\\\\sin{B}=\frac{b}{a}\times \sin{A}\\\\\sin{B}=\sqrt{\frac{3}{2}}\sin {A}\\\\B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Thus, the angle B is function of A is, $B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

Now find $\frac{dB}{dA}$

Differentiate implicitly the function $\sin{B}=\sqrt{\frac{3}{2}}\sin{A}$ with respect to A to get,

$\cos {B}.\frac{dB}{dA}=\sqrt{\frac{3}{2}}\cos A\\\\\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos A}{\cos B}$

When $A=\frac{\pi}{4},B=\frac{\pi}{3}$ , the value of $\frac{dB}{dA}$ is,

$\frac{dB}{dA}=\sqrt{\frac{3}{2}}.\frac{\cos {\frac{\pi}{4}}}{\cos {\frac{\pi}{3}}}\\\\=\sqrt{\frac{3}{2}}.\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}\\\\=\sqrt{3}$

In general, the linear approximation at x= a is,

$f(x)=f'(x).(x-a)+f(a)$

Here the function $f(A)=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{A}]$

At $A=\frac{\pi}{4}$

$f(\frac{\pi}{4})=B=\sin^{-1}[\sqrt{\frac{3}{2}}\sin{\frac{\pi}{4}}]\\\\=\sin^{-1}[\sqrt{\frac{3}{2}}.\frac{1}{\sqrt{2}}]\\\\\=\sin^{-1}(\frac{\sqrt{2}}{2})\\\\=\frac{\pi}{3}$

And,

$f'(A)=\frac{dB}{dA}=\sqrt{3}$ from part b

Therefore, the linear approximation at $A=\frac{\pi}{4}$ is,

$f(x)=f'(A).(x-A)+f(A)\\\\=f'(\frac{\pi}{4}).(x-\frac{\pi}{4})+f(\frac{\pi}{4})\\\\=\sqrt{3}.[x-\frac{\pi}{4}]+\frac{\pi}{3}$

Use part (c), when $A=46°$ , B is approximately,

$B=f(46°)=\sqrt{3}[46°-\frac{\pi}{4}]+\frac{\pi}{3}\\\\=\sqrt{3}(1°)+\frac{\pi}{3}\\\\=61.732°$

8 0

2 years ago

The equation of a circle is given below. (x-0.5)^{2}+(y-3.5)^{2} = 16(x−0.5) 2 +(y−3.5) 2 =16left parenthesis, x, minus, 0, poin

Mashutka [201]

Answer:

<h2>The radius is 4 units long.</h2>

Step-by-step explanation:

The given equation is

$(x-0.5)^{2} +(y-3.5)^{2} =16$

This equation belongs to a circle, which center is at (0.5, 3.5) and its radius is 4.

You can deduct its elements, becase this equation of the circle is explicit, which means the constant term represents the square power of the radius. Solving that, we have

$r^{2} = 16\\r=\sqrt{16}\\ r=4$

Therefore, the radius is 4 units long.

3 0

2 years ago

A rectangular kitchen is 4 meters longer than it is wide. If the area of the kitchen is 192 square feet meters, how many meters

Lunna [17]

Lets x = width
length = x + 4 (4 meters longer than wide)

A = L * W
192 = x ( x +4)
192 = x^2 + 4x
x^2 + 4x - 192 = 0
(x +16)(x-12) = 0
x - 12 = 0, x = 12
x + 16 = 0, x = -16
so width x = 12
length = 12 + 4 = 16 (4 meters longer than wide)

answer. J
16

3 0

2 years ago

Factor the trinomial x^2-2x-35

Oliga [24]

Answer:

(x-7)(x+5)

Step-by-step explanation:

3 0

2 years ago

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