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3 years ago

Can someone answer this question please?

Mathematics

1 answer:

Mekhanik [1.2K]3 years ago

8 0

Steps:
1. calculate the values of y at x=0,1,2. using y=5-x^2
2. calculate the areas of trapezoids (Bottom+Top)/2*height
3. add the areas.

1.
x=0, y=5-0^2=5
x=1, y=5-1^2=4
x=2, y=5-2^2=1
2.
Area of trapezoid 1 = (5+4)/2*1=4.5
Area of trapezoid 2 = (4+1)/2*1=2.5

Total area of both trapezoids = (4.5+2.5) = 7

Exact area by integration:
integral of (5-x^2)dx from 0 to 2
=[5x-x^3/3] from 0 to 2
=[5(2-0)-(2^3-0^3)/3]
=10-8/3
=22/3
=7 1/3, slight greater than the estimation by trapezoids.

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3 years ago

Determine if

Gnesinka [82]

The values of a and b are 1/4 and 1/5 respectively

<h3>How to determine the true statement?</h3>

The function is given as:

16x^2 - 25y^2 = 1

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A horizontal hyperbola that passes through the origin is represented as:

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Rewrite 16x^2 - 25y^2 = 1 as

$\frac{x^2}{1/16} - \frac{y^2}{1/25} = 1$

By comparison, we have:

$a^2 = \frac{1}{16}$

$b^2 = \frac{1}{25}$

Solve for a and b

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

$b = \frac{1}{5}$

Hence, the values of a and b are 1/4 and 1/5 respectively

Read more about hyperbola at:

brainly.com/question/27799190

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1 year ago

Write each fraction as an expression with negative exponents.

Artemon [7]

The answer is w⁻²/v⁻².

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Since 1/xᵃ = x⁻ᵃ, then 1/v⁻²w² = w⁻²/v⁻²

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2 years ago

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Using the definition of the Vertical shifts of graphs of the function :

"Suppose c>0,

To graph y=f(x)+c, shift the graph of y=f(x) upward c units.

To graph y=f(x)-c, shift the graph of y=f(x) downward c units"

Again we recall the definition of Horizontal shifts of graphs:

" suppose c>0,

the graph y=f(x-c), shift the graph of y=f(x) to the right by c units

the graph y=f(x+c), shift the graph of y=f(x) to the left by c units. "

consider $f(x)=x^3$ is the parent function.

$h(x)=x^3+8$ shifts the graph $f(x)=x^3$ upward by 8 units

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7 0

3 years ago

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x^2+1/2x+1/16=4/9 Factor the perfect-square trinomial on the left side of the equation. (x + )² = 4/9

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Answer: x= 1/4

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3 years ago

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