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3 years ago

What is the radian measure of the smallest angle formed by the hands of a clock at 7 o'clock?

Mathematics

1 answer:

netineya [11]3 years ago

5 0

See the picture attached to better understand the problem
we know that
a full circle is a 360 degrees
divided in 12 equals parts-------> 360/12-------> 30 degrees each part

<span>the smallest angle formed by the hands of a clock at 7 o'clock has 5 parts
so
5*30</span>°------> 150°

convert to radian
pi radians---------> 180°
x ---------------> 150°
x=150*pi/180--------> x=0.83*pi radians

the answer is
0.83*pi radians or 2.62 radians

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Bill wants to make 10Lcof a 30% saline solution by mixing together a 60% saline solution and a 10% saline solution. How much of

erastovalidia [21]

10 L of 30 % saline solution can be formed by mixing 4 L of 60 % saline solution and 6 L of 10 % saline solution.

Step-by-step explanation:

Let x be the number of liters of 60% saline solution

Now we require 10 L of 30% saline solution.

Liter soln % liters saline %

30 % 10 0.3

60 % x 0.6

10 % 10-x 0.1

Now forming the algebraic equation,

0.6x + 0.1 (10-x) = 10 (0.3)

0.6x + 1 - 0.1 x = 3

0.5 x = 2

x = 4 ( 4 l of 60 % solution is required. So 10 % saline solution required is 10 - 4 = 6 L).

Hence, 10 L of 30 % saline solution can be formed by mixing 4 L of 60 % saline solution and 6 L of 10 % saline solution.

6 0

3 years ago

Read 2 more answers

Will the following two equations have a solution? Explain. y = 3x + 5 y = 3x - 7

r-ruslan [8.4K]

Answer:

There is no solution because the slopes of the two lines are the same.

Step-by-step explanation:

3x + 5 = 3x - 7

-3x - 3x Subtract 3x from both sides

5 ≠ - 7 No solution

If this answer is correct, please make me Brainliest!

7 0

3 years ago

Find the sum of the positive integers less than 200 which are not multiples of 4 and 7

taurus [48]

Answer:

$12942$ is the sum of positive integers between $1$ (inclusive) and $199$ (inclusive) that are not multiples of $4$ and not multiples $7$ .

Step-by-step explanation:

For an arithmetic series with:

$a_1$ as the first term,
$a_n$ as the last term, and
$d$ as the common difference,

there would be $\displaystyle \left(\frac{a_n - a_1}{d} + 1\right)$ terms, where as the sum would be $\displaystyle \frac{1}{2}\, \displaystyle \underbrace{\left(\frac{a_n - a_1}{d} + 1\right)}_\text{number of terms}\, (a_1 + a_n)$ .

Positive integers between $1$ (inclusive) and $199$ (inclusive) include:

$1,\, 2,\, \dots,\, 199$ .

The common difference of this arithmetic series is $1$ . There would be $(199 - 1) + 1 = 199$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times ((199 - 1) + 1) \times (1 + 199) = 19900 \end{aligned}$ .

Similarly, positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $4$ include:

$4,\, 8,\, \dots,\, 196$ .

The common difference of this arithmetic series is $4$ . There would be $(196 - 4) / 4 + 1 = 49$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 49 \times (4 + 196) = 4900 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $7$ include:

$7,\, 14,\, \dots,\, 196$ .

The common difference of this arithmetic series is $7$ . There would be $(196 - 7) / 7 + 1 = 28$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 28 \times (7 + 196) = 2842 \end{aligned}$

Positive integers between $1$ (inclusive) and $199$ (inclusive) that are multiples of $28$ (integers that are both multiples of $4$ and multiples of $7$ ) include:

$28,\, 56,\, \dots,\, 196$ .

The common difference of this arithmetic series is $28$ . There would be $(196 - 28) / 28 + 1 = 7$ terms. The sum of these integers would thus be:

$\begin{aligned}\frac{1}{2}\times 7 \times (28 + 196) = 784 \end{aligned}$ .

The requested sum will be equal to:

the sum of all integers from $1$ to $199$ ,
minus the sum of all integer multiples of $4$ between $1\!$ and $199\!$ , and the sum integer multiples of $7$ between $1$ and $199$ ,
plus the sum of all integer multiples of $28$ between $1$ and $199$ - these numbers were subtracted twice in the previous step and should be added back to the sum once.