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3 years ago

5. Which image in the collage to the right is an

Mathematics

1 answer:

OleMash [197]3 years ago

3 0

Answer:

B. A water wheel in a dry river

Step-by-step explanation:

Work is said to be done when a force moves a body or an object through a certain distance in the direction of the force. Thus for work to be done, force and distance are required.

i.e Work done = Force x distance

It is measured in Joules.

Also, the work done by an object could be a measured of potential energy.

So that,

Work done = potential energy = mass x gravitational force x height

Considering the collage in the question, since the water wheel is in a dry river no work is done. Water wheel is a device that functions through the flow of water body, thus causing its rotation.

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3 years ago

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Suppose that fanf g are continuous functions,

shtirl [24]

The required result based on given continuous functions is: 207. See the explanation for same below.

<h3>What are continuous functions?</h3>

A continuous function in mathematics is one in which a continuous variation (that is, a change without a jump) of the argument causes a continuous variation of the function's value.

<h3>What is the calculation for the above solution?</h3>

Since G and F are continuous functions,

$\int_{12}^{28}) \, f(x) dx$ = 19

$\int_{12}^{28}) \, f(x) dx$ = 35

Therefore,

$\int_{12}^{28}) \, [K g(x) - 2 f(x)] dx$

= K $\int_{12}^{28}) \, g(x) dx -2 \int_{12}^{28}) \, f(x) dx$

So, given that K = 7, we have

7 x 35 - 2 x 19
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1 year ago

4. Gloria the grasshopper is working on her hops.

aivan3 [116]

The path that Gloria follows when she jumped is a path of parabola.

The equation of the parabola that describes the path of her jump is $\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

The given parameters are:

$\mathbf{Height = 20}$

$\mathbf{Length = 28}$

<em>Assume she starts from the origin (0,0)</em>

The midpoint would be:

$\mathbf{Mid = \frac 12 \times Length}$

$\mathbf{Mid = \frac 12 \times 28}$

$\mathbf{Mid = 14}$

So, the vertex of the parabola is:

$\mathbf{Vertex = (Mid,Height)}$

Express properly as:

$\mathbf{(h,k) = (14,20)}$

A point on the graph would be:

$\mathbf{(x,y) = (28,0)}$

The equation of a parabola is calculated using:

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

Substitute $\mathbf{(h,k) = (14,20)}$ in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = a(x - 14)^2 + 20}$

Substitute $\mathbf{(x,y) = (28,0)}$ in $\mathbf{y = a(x - 14)^2 + 20}$

$\mathbf{0 = a(28 - 14)^2 + 20}$

$\mathbf{0 = a(14)^2 + 20}$

Collect like terms

$\mathbf{a(14)^2 =- 20}$

Solve for a

$\mathbf{a =- \frac{20}{14^2}}$

$\mathbf{a =- \frac{20}{196}}$

Simplify

$\mathbf{a =- \frac{5}{49}}$

Substitute $\mathbf{a =- \frac{5}{49}}$ in $\mathbf{y = a(x - 14)^2 + 20}$

$\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

Hence, the equation of the parabola that describes the path of her jump is $\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

See attachment for the graph

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3 years ago

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