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2 years ago

Compute the magnitude and direction of the sum of the two vectors: 170N of force at 87° and 100N of force at 46°.

Mathematics

1 answer:

krok68 [10]2 years ago

5 0

Answer:

F = 254.08N Θ = 72.03°

Step-by-step explanation:

First of all we find the resolution in both x and y axis

∑Fx = 170cos87 + 100cos46 = 78.36N

∑Fy = 170sin87 + 100sin46 = 241.70N

To find the resultant vector we use pythagorean theorem

F = √(∑Fx)² + ∑(Fy)²

F = √(78.36² + 241.70²)

F = √(64559.1796)

F = 254.08N

the angle between both force can be obtained using

tanθ = ∑Fy / ∑Fx

tanθ = 241.70 / 78.36

tanθ = 3.084

Θ = tan⁻ 3.084

Θ = 72.03°

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Use the triangle below and the given trigonometric ratio to determine which angle in the triangle below is

MrRa [10]

Answer: Angle 2

The 7.5 cm side is opposite angle 2, so opposite = 7.5
The 18 cm side is adjacent to angle 2, so adjacent = 18

Therefore, tan(angle 2) = opposite/adjacent = 7.5/18
Replace "angle 2" with "A" and we have tan(A) = 7.5/18

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3 years ago

Find the distance between the points given. (-3, 2) and (9, -3) A √37 B √61 C 13

Kitty [74]

Answer:

$\huge{ \fbox{ \sf{13 \: units}}}$

Option C is correct.

Step-by-step explanation:

$\star{ \sf{ \: Let \: the \: points \: be \: a \: and \: b}}$

$\star{ \sf{ \: let \: A(-3, 2) \: be \: (x1 \:, y1) \: and \: B(9, -3) \: be \: (x2 \:, y2) }}$

$\underline{ \sf{Finding \: the \: distance \: between \: the \: given \: points}} :$

$\boxed{ \sf{Distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}$

$\mapsto{ \sf{ \sqrt{ {(9 - ( - 3))}^{2} + {( - 3 - 2)}^{2} } }}$

$\mapsto{ \sf{ \sqrt{ {(9 + 3)}^{2} + {( - 3 - 2)}^{2} }}}$

$\mapsto{ \sf{ \sqrt{ {(12)}^{2} + {( - 5)}^{2} } }}$

$\mapsto{ \sf{ \sqrt{144 + 25}}}$

$\mapsto{ \sf{ \sqrt{169} }}$

$\mapsto{ \sf{ \sqrt{ {(13)}^{2} } }}$

$\mapsto{ \sf{ 13 \: units}}$

Hope I helped!

Best regards! :D

~ $\text{TheAnimeGirl}$

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2 years ago

A bicycle has a listed price of $519.95 before tax. If the sales tax rate is 9.75% , find the total cost of the bicycle with sal

jek_recluse [69]

Youre finding 9.75% of 519 you know its going to be near 50 dollars
your answer is 50.695125
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3 years ago

3a=a+36 find the value of a

e-lub [12.9K]

Answer:

a=18

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares,

svp [43]

Answer:

✅The table can be represented by the equation, $y = 4x + 4$

✅The relation is a function.

✅The graph of the function is linear.

Step-by-step explanation:

✍️The first statement: The table can be represented by the equation, $y = 4x + 4$ .

To check if the first statement is correct let's find the equation that can represent the table by finding the slope (m) and y-intercept (b).

Using two pairs, (1, 8) and (2, 12),

Slope = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{2 - 1} = \frac{4}{1} = 4$ .

Substitute, x = 1, y = 8, and m = 4 into y = mx + b to solve for b.

Thus:

8 = (4)(1) + b

8 = 4 + b

Subtract 4 from each side

8 - 4 = b

4 = b

Plug in the values of b and m into y = mx + b.

Thus, the equation that represents the table would be:

$y = 4x + 4$ .

✅Therefore, the first statement is correct.

✍️The second statement: The graph of the function is non-linear.

This is NOT TRUE because the equation of the function, $y = 4x + 4$ , represents the equation of a linear graph in the slope-intercept form. When graphed, it will give us a straight line.

✍️The Third statement: The relation is a function.

This is TRUE because each input value (x-value) has exactly one output value (y-value).

✍️The Fourth statement: The rate of change is NOT constant.

This standby is NOT TRUE.

The rate of change is the slope (m) that we have calculated above to be 4. Between any two pairs, the rate of change remains 4.

Therefore, this statement is not correct.

✍️The Fifth statement: The graph of the function is linear.

This is TRUE. As stated earlier, from the equation generated, it is safe to say that the equation represents graph of a linear function. The graph will be a straight line graph.

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2 years ago