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3 years ago

What is the slope intercept equation of the line shown? X=2 Y=2 Y=2r X=2y

Mathematics

2 answers:

bagirrra123 [75]3 years ago

5 0

Answer:

Y=2

Step-by-step explanation:

svetoff [14.1K]3 years ago

3 0

Y = 2r hope this helped gg go next uwu baka

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Evaluate the double integral.

Fynjy0 [20]

Answer:

$\iint_D 8y^2 \ dA = \dfrac{88}{3}$

Step-by-step explanation:

The equation of the line through the point $(x_o,y_o)$ & $(x_1,y_1)$ can be represented by:

$y-y_o = m(x - x_o)$

Making m the subject;

$m = \dfrac{y_1 - y_0}{x_1-x_0}$

∴

we need to carry out the equation of the line through (0,1) and (1,2)

i.e

y - 1 = m(x - 0)

y - 1 = mx

where;

$m= \dfrac{2-1}{1-0}$

m = 1

Thus;

y - 1 = (1)x

y - 1 = x ---- (1)

The equation of the line through (1,2) & (4,1) is:

y -2 = m (x - 1)

where;

$m = \dfrac{1-2}{4-1}$

$m = \dfrac{-1}{3}$

∴

$y-2 = -\dfrac{1}{3}(x-1)$

-3(y-2) = x - 1

-3y + 6 = x - 1

x = -3y + 7

Thus: for equation of two lines

x = y - 1

x = -3y + 7

i.e.

y - 1 = -3y + 7

y + 3y = 1 + 7

4y = 8

y = 2

Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7

∴

$\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy$

$\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy$

$\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg) dy$

$\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy$

$\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy$

$\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ([y^2(-4y+8)] \bigg ) \ dy$

$\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( -4y^3+8y^2 \bigg ) \ dy$

$\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1$

$\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1$

$\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg]$

$\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg]$

$\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg]$

$\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg]$

$\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{-45+56}{3}\bigg]$

$\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{11}{3}\bigg]$

$\iint_D 8y^2 \ dA = \dfrac{88}{3}$

4 0

3 years ago

A patrolman spends 25% every day completing paperwork. The patrolman’s shift each day is 8 hours. How much of his time does he s

Mrrafil [7]

$8 \times 25\% \\ = 8 \times \dfrac{25}{100} \\ = 2$

Answer : He spends 2 hours doing paperwork each day.

Hope this helps. - M

4 0

4 years ago

How many minutes are in 2/4 if an hour

Katyanochek1 [597]

2/4 of an hour is half an hour so 2/4 of an hour is 30 minutes. Hope it helps

5 0

3 years ago

Read 2 more answers

A(n) = -5 + 6(n - 1)a(n)=−5+6(n−1)a, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 6, left parenthesis, n, min

DENIUS [597]

Answer:

The 12th term is 61

Step-by-step explanation:

I will assume that your a(n) = -5 + 6(n - 1) is correct; the rest is redundant (duplicative, unneeded).

To find the 12th term, substitute 12 for n in the above formula:

a(12) = -5 + 6(12 - 1) = -5 + 6(11) = 66 - 5, or 61

The 12th term is 61

6 0

3 years ago

What is the approximate area of a circle with a radius of 4 feet? Use 3.14

Eva8 [605]

Answer:

≈ 50 ft²

Step-by-step explanation:

Area of circle:

A = πr²

Given:

r = 4 ft, π = 3.14

Then:

A= 3.14 * 4² = 50.24 ≈ 50 ft²

8 0

3 years ago