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2 years ago

Solve this GCSE question

Mathematics

2 answers:

mylen [45]2 years ago

7 0

fix in the figures and solve

Alona [7]2 years ago

6 0

Answer:

C 60π cm³

Step-by-step explanation:

1/3 x π x6² x 5

=60π

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

aleksklad [387]

The spider's movement is an illustration of a parabola.

The equation of a parabola is: $\mathbf{y = -\frac{1}{160}(x - 40) + 10}$
The focus of a parabola is: (40,-30)
The axis of symmetry is: $\mathbf{x = 40}$
The directrix is: $\mathbf{y = 50}$

<u>(a) The equation</u>

The spider passes through the origin.

So, we have:

$\mathbf{(x,y) = (0,0)}$

The spider jumps to a maximum height of 10mm, midway 80mm.

So, the vertex is:

$\mathbf{(h,k) = (40,10)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

So, we have:

$\mathbf{0 = a(0 - 40)^2 + 10}$

Subtract 10 from both sides

$\mathbf{a(0 - 40)^2 =- 10}$

$\mathbf{1600a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{160}}$

Substitute $\mathbf{a =- \frac{1}{160}}$ and $\mathbf{(h,k) = (40,10)}$ in $\mathbf{(h,k) = (40,10)}$

$\mathbf{y = -\frac{1}{160}(x - 40) + 10}$

<u>(b) The focus, directrix and the axis of symmetry</u>

The focus of a parabola is:

$\mathbf{Focus= (h, k + p)}$

Where:

$\mathbf{p = \frac{1}{4a}}$

So, we have:

$\mathbf{p = \frac{1}{4 \times -1/160}}$

$\mathbf{p = -\frac{160}{4}}$

$\mathbf{p = -40}$

So, we have:

$\mathbf{Focus = (40,10-40)}$

$\mathbf{Focus = (40,-30)}$

The axis of symmetry is:

$\mathbf{x = h}$

So, we have:

$\mathbf{x = 40}$

The directrix is:

$\mathbf{y = k - p}$

$\mathbf{y = 10 + 40}$

$\mathbf{y = 50}$

Read more about parabolas at:

brainly.com/question/25237745

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3 years ago

37.5 x 10 to the negative 6 in scientific notation?

mestny [16]

The scientific notation is 37.5×10^-6

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4 years ago

·A long distance runner started on a course running at an average speed of 6

bezimeni [28]

Um i didn’t really understand i’m very sorry but i would honestly love to help if i could

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3 years ago

What is three to the third power times two to the fourth power equal?

rewona [7]

The answer is 43 because 3*3*3=27 and 4*4=16

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4 years ago

Write this expression as a complex number in standard form

amm1812

Answer:

$81+144i$

Step-by-step explanation:

$(-3\sqrt{-81})( -5+\sqrt{-9})+ 9i\\\text{Simplify the radicals}\\\sqrt{-81}=\sqrt{-1*81}=\sqrt{81}\cdot\sqrt{-1}=9i\\\sqrt{-9}=\sqrt{-1*9}=\sqrt9\cdot\sqrt{-1}=3i\\=(-3(9i))(-5+3i)+9i\\(-27i)(-5+3i)+9i\\\text{Distribute}\\=135i-81i^2+9i\\i^2=-1\\=135i+9i-81(-1)\\=81+144i$

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3 years ago

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