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2 years ago

Factorise 4b^2 + 16b

1 answer:

5 0

Factorise 4b² + 16b ⇒ 4b(b+4)

expand (a-1)(a-2) ⇒ a(a-2) - 1(a-2) ⇒ a² - 2a - 1a + 2 ⇒a² - 3a + 2

factorise x² + 8x + 7 ⇒(x + 1) (x + 7)

evaluate y⁶ / y² ⇒ y * y * y * y * y * y / y * y = y⁴

if x = -1 and y = 5, find z when z = x² + 2y² ;
z = -1² + 2(5²) ⇒ 1 + 2(25) ⇒1 + 50 = 51

Make x the subject: y = 4x - 3
y = 4x - 3
<u>+3 +3</u>
3 + y = 4x
<u>÷4 ÷4 </u>
(3+y)/4 = x

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Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an

Natasha_Volkova [10]

Answer:

The volume of the solid is 243 $\sqrt{2} \ \pi$

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0 ≤ ρ² ≤ 81

0 ≤ ρ ≤ 9

The intersection that takes place in the sphere and the cone is:

$x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81$

$2(x^2 + y^2) =81$

$x^2 +y^2 = \dfrac{81}{2}$

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

$z = \sqrt{x^2+y^2}$

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; $\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}$

Thus, volume: $V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi$

$V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho$

$V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}$

$V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]$

V = 243 $\sqrt{2} \ \pi$

4 0

3 years ago

The regular price of a child's entry ticket to a water park is $6 less than that for an adult's. The park offers half off all en

hjlf

Distribute +1
78=1/2x+x-6
combine like terms
1=(2/2)
(1/2)+(2/2)= 3/2
78=3/2x-6
Add 6 to both sides
84=3/2x
Divide by (3/2)
x=$56=adult ticket
Child ticket = x-6=56-6=$50
$50

7 0

3 years ago

What’s the slope of C=50t+100

balandron [24]

Answer:

Explanation:

This equation is in y = mx+b form.

The m is the slope and the b is the y intercept. So, 50 is the slope and 100 is the y-intercept.

6 0

3 years ago

Read 2 more answers

Use the distributive property to find (y+6)(y+4)

____ [38]

Answer:

Look down below for the answer :))

Step-by-step explanation:

y + 6 = 6y

y + 4 = 4y

4y x 6y = 24y

3 0

3 years ago

Plsss answer this!!!

egoroff_w [7]

Answer:

(-2,-2)

Step-by-step explanation:

The domain is -2 -2 because that's all the x values that are possible on this graph

5 0

3 years ago