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2 years ago

The diagram shows the cross-section of a wall of a cinema.

Mathematics

1 answer:

Anna71 [15]2 years ago

7 0

Answer:

280 m²
£133

Step-by-step explanation:

The area of the wall is the sum of the areas of the different sections of the wall. The cost to paint it will be the product of the cost of a tin of paint and the number of tins required.

Here, the shape of the wall can be divided into two trapezoids and a rectangle. Each shape has a corresponding area formula. Left-to-right, their areas are ...

Left Trapezoid

A = 1/2(b1 +b2)h

A = 1/2(10 m +11 m)(4 m) = 42 m²

Middle Rectangle

A = LW

A = (13 m)(11 m) = 143 m²

Right Trapezoid

A = 1/2(b1 +b2)h

A = 1/2(11 m +8 m)(10 m) = 95 m²

Wall Area

The total area to be painted is the sum of the above areas:

total area = 42 m² +143 m² +95 m² = 280 m²

The area that needs to be painted is 280 m².

A tin of paint covers 15 m², so the number of tins needed is ...

(15 m²)t = 280 m²

t = 280/15 = 18 2/3 . . . . . . divide by the coefficient of t

We can only buy whole tins, so we need to buy 19 tins. Their cost will be ...

(£7 /tin)(19 tins) = £133

It will cost £133 to paint the wall.

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HELP ASAP 100 POINTS!!!

nikklg [1K]

<h3>Answer: choice 4. f(x) and g(x) have a common x-intercept</h3>

===========================================================

Explanation:

For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.

The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.

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Side notes:

Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
Choice 2 is not true. Point B is not on the parabola.
Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.

7 0

3 years ago

Read 2 more answers

What is 3/8 x 16/7? i don't know. it is for my math homework?

liberstina [14]

Multiply the top and bottom.

3/8 * 16/7 = 48/56

Simplified: 5/7

6 0

3 years ago

Find sinϴ and cosϴ if tanϴ=1/4 and sinϴ>0

eduard

If you're using the app, try seeing this answer through your browser: brainly.com/question/2787701

_______________

$\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\
\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\
\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}$

Square both sides:

$\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\
\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\
\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}$

$\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\
\mathsf{17\,sin^2\,\theta=1}\\\\
\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}$

Since $\mathsf{sin\,\theta}$ is positive, you can discard the negative sign. So,

$\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}$

Substitute this value back into $\mathsf{(i)}$ to find $\mathsf{cos\,\theta:}$

$\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}$

I hope this helps. =)

Tags: trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus

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