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3 years ago

If dave runs 1.8 kilometers in 15 minutes , what is his average rate

Mathematics

1 answer:

lana66690 [7]3 years ago

4 0

His average rate is 120 meters per minute.

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Use a half-angle identity to find the exact value

Tatiana [17]

Given:

$\cos 15^{\circ}$

To find:

The exact value of cos 15°.

Solution:

$$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}$

Using half-angle identity:

$$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}$

$$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}$

Using the trigonometric identity: $\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}$

$$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$

Let us first solve the fraction in the numerator.

$$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$

Using fraction rule: $\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}$

$$=\sqrt{\frac {2+\sqrt{3}}{4}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$

Using $\sqrt{4} =2$ :

$$=\frac{\sqrt{2+\sqrt{3}}}{2}$

$$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}$

5 0

3 years ago

A plane can fly 11 miles per minute. The plane will fly 6 trips, and each trip is 500 miles. How many hours will the plane fly?

BabaBlast [244]

Answer:

4 hours 33 minutes

Step-by-step explanation:

multiply the distance of each trip by the amount of trips taken to find the total distance traveled:

500x6=3000 miles

time=distance/speed:

3000/11= apro 273 mins

= 4 hours 33 minutes

5 0

3 years ago

CAN SOMEONE PLEASE HELP ME!!!!

love history [14]

Answer:

The balance after the payment is $1263.84.

Step-by-step explanation:

The formula for amount after compound interest is

$A=P(1+\frac{r}{n})^{t}$

Where, P is principal, r is rate of interest, n is number of time interest compounded in a period, number of periods.

According to the given information,

P=1455.69

r=0.128

n=365

t=45

Put these values in the above formula,

$A=1455.69(1+\frac{0.128}{365})^{45}$

$A\approx 1478.84$

The amount after compound interest is $1478.84. Add late fee chages $35 in this amount and subtract the payment of $250. So, the balance amount after payment is

$Balance=1478.84+35-250=1263.84$

Therefore the balance after the payment is $1263.84.

8 0

3 years ago

How do you create a model of 15% of 60

Misha Larkins [42]

The answer is 9 by the way. Draw a circle with sixty slices, shade in 15% or 9 slices.

6 0

3 years ago

Towns X, Y, and Z are on the same straight road. Town Y is between Town X and Town Z. Town X is 57 miles from Town Z, and Town Y

Ber [7]

29 miles
because town y is between town x and town z so you can take the distance between town x and town z and subtract the distance from town y to town z

3 0

3 years ago