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2 years ago

What is the gradient of the blue line?? Mathswatch

Mathematics

2 answers:

kirill [66]2 years ago

6 0

 $answer \\ - 5 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps$ 

yaroslaw [1]2 years ago

3 0

Answer:

gradient = -5

Step-by-step explanation:

A line passes (x1, y1) and (x2, y2) has the gradient (slope) which is calculated by:

gradient = (y2-y1)/(x2-x1)

As shown in picture, this blue line passes (-1, 0) and (0, -5)

=> gradient = (-5 - 0)/(0 - -1) = -5/1 = -5

Hope this helps!

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A group of market women sell at least one of yam, plantain and maize.12 of them sell maize,10 sell yam and 14 sell plantain,5 se

mina [271]

Let the three items be M, Y and P.

n{M ∩ Y} only = 4-3 = 1

n{M ∩ P) only = 5-3 = 2

n{ Y ∩ P} only = 2

n{M} only = 12-(1+3+2) = 6

n{Y} only = 10-(1+2+3) = 4

n{P} only = 14-(2+3+2) = 7

n{M∩P∩Y} = 3

Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.

8 0

3 years ago

At the end of a snow storm, Michael saw there was a lot of snow on his front lawn. The temperature increased and the snow began

QveST [7]

Answer:

x-intercept equals 10

interpretation is that, after 10 hours, all of the snow will be melted

Step-by-step explanation:

5 0

2 years ago

Solve the exponential equation for x. 625 = 5 (7x-3)

posledela

Answer:

Step-by-step explanation:

$5^{7x-3}=625\\\\5^{7x-3}=5^4\iff7x-3=4\qquad\text{add 3 to both sides}\\\\7x=7\qquad\text{divide both sides by 7}\\\\x=1$

7 0

3 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago

Solve for aaa: a-\left(-3.75\right)=6.11a−(−3.75)=6.11a, minus, left parenthesis, minus, 3, point, 75, right parenthesis, equals

Ganezh [65]

Answer:

Step-by-step explanation:

To isolate a, we add -3.75 to both sides.

a-(-3.75)=6.11

a-(-3.75)+(-3.75)=6.11+(-3.75)

a=6.11+(-3.75) Simplifying, we get:

a=2.36

(I got this from khan)

4 0

3 years ago