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3 years ago

What is the equation of a line passing through (-3,7) and having a slope of -1/5?

Mathematics

1 answer:

german3 years ago

8 0

Answer:

x+5y = 32

Step-by-step explanation:

Equation of a line with slope m and passes through (x1,y1) is y-y1 = m(x-x1)

Equation is,

y-7 = (-1/5) (x-(-3))

y-7 = (-1/5)(x+3)

Multiply by 5,

5(y-7) = -(x+3)

5y-35 = -x-3

x+5y = -3+35

x+5y = 32

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3 years ago

How to solve<br> 3/5e-6=-2/5(e-10)-7

kaheart [24]

$\frac{3}{5} e-6=- \frac{2}{5}(e-10)-7$
$\frac{3}{5} e-6=- \frac{2}{5} e- \frac{2}{5}*(-10) -7 \\ \frac{3}{5} e-6=- \frac{2}{5} e+ \frac{20}{5} -7= \frac{3}{5} e-6=- \frac{2}{5} e+4 -7= \\$
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6 0

3 years ago

In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows:

BabaBlast [244]

Answer

$a=0$ , $b=2$

$g_1(x)=\frac{5x}{2}$ , $g_2(x)=7-x$

Step-by-step explanation:

Given that

$\int \int Df(x,y)dA=\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy+\int_5^7\int_0^{7-y} f(x,y)dxdy\; \cdots (i)$

For the term $\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy$ .

Limits for $x$ is from $x=0$ to $x=\frac {2y}{5}$ and for $y$ is from $y=0$ to $y=5$ and the region $D$ , for this double integration is the shaded region as shown in graph 1.

Now, reverse the order of integration, first integrate with respect to $y$ then with respect to $x$ . So, the limits of $y$ become from $y=\frac{5x}{2}$ to $y=5$ and limits of $x$ become from $x=0$ to $x=2$ as shown in graph 2.

So, on reversing the order of integration, this double integration can be written as

$\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx\; \cdots (ii)$

Similarly, for the other term $\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy$ .

Limits for $x$ is from $x=0$ to $x=7-y$ and limits for $y$ is from $y=5$ to $y=7$ and the region $D$ , for this double integration is the shaded region as shown in graph 3.

Now, reverse the order of integration, first integrate with respect to $y$ then with respect to $x$ . So, the limits of $y$ become from $y=5$ to $y=7-x$ and limits of $x$ become from $x=0$ to $x=2$ as shown in graph 4.

So, on reversing the order of integration, this double integration can be written as

$\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy=\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx\;\cdots (iii)$

Hence, from equations $(i)$ , $(ii)$ and $(iii)$ , on reversing the order of integration, the required expression is

$\int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx+\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx$

$\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\left(\int _ {\frac {5x}{2}}^5 f(x,y)+\int _5 ^ {7-x} f(x,y)\right)dydx$

$\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^{7-x} f(x,y)dydx\; \cdots (iv)$

Now, compare the RHS of the equation $(iv)$ with

$\int_a^b\int_{g_1(x)}^{g_2(x)} f(x,y)dydx$

We have,

$a=0, b=2, g_1(x)=\frac{5x}{2}$ and $g_2(x)=7-x$ .

3 0

3 years ago

Jacob has six times as many baseball cards as his sister Rebecca. Together they have a total of 861 cards. Write an equation and

Vesna [10]

Let Rebecca equal x and Jacob equal 6x.
6x + x = 861
7x = 861
Multiply both sides by the reciprocal of 7 which is 1/7.
(1/7)7x = 861(1/7)
x = 123
Since Rebecca equals x we know that she has 123 cards. If we multiply this answer by 6 we get the number of cards Jacob has.
6(123) = 738
Therefore the final answer is:
Jacob = 738
Rebecca = 123
I hope this helps:)
Please comment if there are any problems.

6 0

3 years ago

Read 2 more answers

What is the equation of a line passing through (-3,7) and having a slope of -1/5?​

What is the equation of a line passing through (-3,7) and having a slope of -1/5?