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3 years ago

Simplify ,without using a calculator(2 1/2)2 + (0.5)2

Mathematics

2 answers:

Sindrei [870]3 years ago

6 0

Step-by-step explanation:

2 1/2 × 2

=5/2 × 2

(0.5)2

=0.5×2

5+1

vazorg [7]3 years ago

3 0

Answer:

Step-by-step explanation:

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This is due at 8:00PM please someone help

krek1111 [17]

10. A 11. D 12. A (wasn’t too sure about question 12)

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3 years ago

The equation y=-7x-5 and the solution of (-2,9)

Black_prince [1.1K]

Y=-7x-5
9=-7(-2)-5
9=14-5
9=9
Please mark the brainliest, if you think i helped!

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4 years ago

Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

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3 years ago

If you place a cup of 210 degree Fahrenheit coffee on a table in a room that is 68 degrees fareinheit, and ten minutes later, it

Lana71 [14]

Newton's Law of Cooling

Tf=Ts+(Ti-Ts)e^(-kt) where Tf is temp at time t, Ts is temp of surroundings, Ti is temp of object/fluid. So we need to find k first.

200=68+(210-68)e^(-10k)

132=142e^(-10k)

132/142=e^(-10k)

ln(132/142)=-10k

k=-ln(132/142)/10

k≈0.0073 so

T(t)=68+142e^(-0.0073t) so how long until it reaches 180°?

180=68+142e^(-0.0073t)

112=142e^(-0.0073t)

112/142=e^(-0.0073t)

ln(112/142)=-0.0073t

t= -ln(112/142)/(0.0073)

t≈32.51 minutes

8 0

3 years ago

What is the range in interval notation of the function graphed below?

attashe74 [19]

Answer:

Range tells you how high and low the graph of this parabola goes in the “y” (vertical) directions.

1. We can see that the parabola peaks on the y-axis at y = 4. That’s as HIGH as it goes.

2. We also see that both sides of the parabola descend to the level of y = -7. That’s as LOW as it is shown to go.

So putting these together, we say the Range is given by:

-7 <= y <= 3

AMBIGUITY WARNING:

Because the two branches of the parabola go fall right down to the edge of the picture boundary, it’s UNCLEAR whether the parabola truly stops at y = -7 or CONTINUES on (to negative infinity).

In THAT case, the RANGE simplifies to:

Y <= 4

Done.

Step-by-step explanation:

5 0

2 years ago

Simplify ,without using a calculator(2 1/2)2 + (0.5)2 ​

Simplify ,without using a calculator(2 1/2)2 + (0.5)2