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3 years ago

14

Marianne is completing a 4 mile route for charity.Every 1/10 mile is marked along the route. For each mile,she runs 7/10 mile an

d walks 3/10.How many miles does marianne run??

1 answer:

Dmitriy789 [7]3 years ago

5 0

Seven tenths of every mile she goes she runs. So we would multiply 4 by seven tenths and get 2.8 miles. And to find out how many miles she walks, we would multiply 4 by three tenth and get 1.2

hope this helped!!

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express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]

Lemur [1.5K]

The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$ .

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

To learn more about definite integral refer to:

brainly.com/question/24353968

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1 year ago

Evaluate the integral e^xy w region d xy=1, xy=4, x/y=1, x/y=2

LUCKY_DIMON [66]

Make a change of coordinates:

$u(x,y)=xy$
$v(x,y)=\dfrac xy$

The Jacobian for this transformation is

$\mathbf J=\begin{bmatrix}\dfrac{\partial u}{\partial x}&\dfrac{\partial v}{\partial x}\\\\\dfrac{\partial u}{\partial y}&\dfrac{\partial v}{\partial y}\end{bmatrix}=\begin{bmatrix}y&x\\\\\dfrac1y&-\dfrac x{y^2}\end{bmatrix}$

and has a determinant of

$\det\mathbf J=-\dfrac{2x}y$

Note that we need to use the Jacobian in the other direction; that is, we've computed

$\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}$

but we need the Jacobian determinant for the reverse transformation (from $(x,y)$ to $(u,v)$ . To do this, notice that

$\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}$

we need to take the reciprocal of the Jacobian above.

The integral then changes to

$\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv$
$=\displaystyle\frac12\int_{v=}^{v=}\int_{u=}^{u=}\frac{e^u}v\,\mathrm du\,\mathrm dv=\frac{(e^4-e)\ln2}2$

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3 years ago

William has a lemonade stand today he made $17.55 and lemonade sales and one-third that amount in cookie sales how much money di

IgorC [24]

Answer:

Well to find 1/3 of something you have to multiply it by 1/3.

1/3 in decimal form is .33 repeating.

17.55 * .33 = 5.79

17.55 + 5.79 = $23.34

$23.34 is the total profit.

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3 years ago

For what value of x is line a parallel to line b?<br><br> (Yo, please help me so I can go to sleep.)

iogann1982 [59]

X=20

If they're parallel the other number in the same spot as 5x+15 equals that, so 5x+15=115 because if they are parallel they're the same if same spot and same line going through them.

115-15 = 100
5x=100
Divide by 5 both sides
X=20

If x=20 then these lines would be parallel

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3 years ago

What is the y-value of the vertex of the function f(x) = –(x + 8)(x – 14)?

maxonik [38]

we have

$f(x)=-(x+8)(x-14)$

Convert to vertex form

$f(x)=-(x+8)(x-14)\\f(x)=-( x^{2}-14x+8x-112) \\f(x)=-( x^{2}-6x-112)\\f(x)=-x^{2}+6x+112$

we know that

the equation of a vertical parabola in vertex form is equal to

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

where

(h,k) is the vertex

$f(x)=-x^{2}+6x+112$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-112=-(x^{2}-6x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-112-9=-(x^{2}-6x+9)$

$f(x)-121=-(x^{2}-6x+9)$

Rewrite as perfect squares

$f(x)-121=-(x-3)^{2}$

$f(x)=-(x-3)^{2}+121$

the vertex is the point $(3,121)$

therefore

<u>the answer is </u>

The y-value of the vertex is $121$

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3 years ago