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Nat2105 [25]
3 years ago
8

Dave builds a wheelchair ramp with 1 metre of wood. He wants the vertical height of the ramp to be 50 centimetres. What does the

angle of elevation need to be?
Mathematics
1 answer:
Yakvenalex [24]3 years ago
7 0

Answer:

\theta=30^{o}

Step-by-step explanation:

1 m is 100 cm

The hypotenuse is 100 cm and the opposite side is 50 cm

sin \theta=\frac {50}{100}

\theta=30^{o}

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The value of r so the line that passes through (-5,2) and (3,r) has a slope of -1/2 is -2

<u>Solution:</u>

Given that line is passing through point (-5, 2) and (3, r)

Slope of the line is \frac{-1}{2}

Need to determine value of r.

Slope of a line passing through point \left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)  is given by following formula:

\text { Slope } m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}  --- eqn 1

\text { In our case } x_{1}=-5, y_{1}=2, x_{2}=3, y_{2}=\mathrm{r} \text { and } m=-\frac{1}{2}

On substituting the given value in (1) we get

\begin{array}{l}{-\frac{1}{2}=\frac{r-2}{3-(-5)}} \\\\ {\text { Solving the above expression to get value of } r} \\\\ {=>-\frac{1}{2}=\frac{r-2}{3+5}} \\\\ {=>-8=\frac{r-2}{3+5}} \\\\ {=>-8=2(r-2)} \\\\ {=>-8=2 r-4} \\\\ {=>2 r=-8+4} \\\\ {=>2 r=-4} \\\\ {=>r=\frac{-4}{2}=-2}\end{array}

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8 0
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Calcular la edades actuales de una madre y sus dos hijos sabiendo que hace 14 años la dad de la madre era 5
rodikova [14]

The present age of mother and her daughter respectively are; 40 and 10 years respectively.

<h3>How to Solve Algebra Word Problems?</h3>

Let x and y be the present age of mother and her daughter respectively.

Therefore;

x + y = 50

x = 50 − y     .....(1)

After 20 years, mother's age will be twice her daughter's age at the time. Thus;

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Plugging eq 1 into eq 2 gives us;

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y = 10

Thus;

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x = 40

Thus, the present age of mother and her daughter is 40 and 10 years respectively.

Translation of the question into English is;

The sum of the present ages of mother and her daughter is 50 years. After 20 years, mother's age will be twice her daughter's age at the time. Find their present ages.

Read more about Algebra Word Problems at; brainly.com/question/21405634

#SPJ1

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