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2 years ago

Which of the following represents the measures of all angles coterminal with a 418° angle?

Mathematics

2 answers:

Anit [1.1K]2 years ago

8 0

The correct answer is B

zhannawk [14.2K]2 years ago

5 0

Answer:

The correct option is 2.

Step-by-step explanation:

The given angle is

$418^{\circ}$

If we have an angle θ, where θ lies between 0 to 360°, then the co-terminal angles are defined as

$\theta+360n$

Where, n is any integer.

$418^{\circ}=58^{\circ}+360^{\circ}$

So, 58° is a co-terminal angle of 418°. All the co-terminal angle of 418° are

$58+360n$

Where n is an integer.

Therefore option 2 is correct.

You might be interested in

-6/5 divided by 12/25

Tema [17]

Answer:

-1 17/25

Solution with Steps

−65−1225=?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(-6/5, 12/25) = 25

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(−65×55)−(1225×11)=?

Complete the multiplication and the equation becomes

−3025−1225=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

−30−1225=−4225

This fraction cannot be reduced.

The fraction

−4225

is the same as

−42÷25

Convert to a mixed number using

long division for -42 ÷ 25 = -1R17, so

−4225=−11725

Therefore:

−65−1225=−11725

4 0

2 years ago

The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 88/(2 + x2 + y2), where T is measured in °C and x,

-Dominant- [34]

Answer:

$D_uT(3,1)=-\frac{44}{9}*\frac{1}{\sqrt{2} } \approx-3.46$

Step-by-step explanation:

To find the rate of change of temperature with respect to distance at the point (3, 1) in the x-direction and the y-direction we need to find the Directional Derivative of T(x,y). The definition of the directional derivative is given by:

$D_uT(x,y)=T_x(x,y)i+T_y(x,y)j$

Where i and j are the rectangular components of a unit vector. In this case, the problem don't give us additional information, so let's asume:

$i=\frac{1}{\sqrt{2} }$

$j=\frac{1}{\sqrt{2} }$

So, we need to find the partial derivative with respect to x and y:

In order to do the things easier let's make the next substitution:

$u=2+x^2+y^2$

and express T(x,y) as:

$T(x,y)=88*u^{-1}$

The partial derivative with respect to x is:

Using the chain rule:

$\frac{\partial u}{\partial x}=2x$

Hence:

$T_x(x,y)=88*(u^{-2})*\frac{\partial u}{\partial x}$

Symplying the expression and replacing the value of u:

$T_x(x,y)=\frac{-176x}{(2+x^2+y^2)^2}$

The partial derivative with respect to y is:

Using the chain rule:

$\frac{\partial u}{\partial y}=2y$

Hence:

$T_y(x,y)=88*(u^{-2})*\frac{\partial u}{\partial y}$

Symplying the expression and replacing the value of u:

$T_y(x,y)=\frac{-176y}{(2+x^2+y^2)^2}$

Therefore:

$D_uT(x,y)=(\frac{1}{\sqrt{2} } )*(\frac{-176x}{(2+x^2+y^2)^2} -\frac{176y}{(2+x^2+y^2)^2})$

Evaluating the point (3,1)

$D_uT(3,1)=(\frac{1}{\sqrt{2} } )*(\frac{-176(3)-176(1)}{(2+3^2+1^2)^2})=(\frac{1}{\sqrt{2} })* (-\frac{704}{144})=(\frac{1}{\sqrt{2} }) ( - \frac{44}{9})\approx -3.46$