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3 years ago

Evaluate the expression. (16 divided by 8) plus (24 divided by 6)

Mathematics

1 answer:

just olya [345]3 years ago

8 0

Answer:

Step-by-step explanation:

(16/8)+(24/6)

(2)+(4)

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SOMEONE HELP BECAUSE I DONT GET THIS

Leno4ka [110]

Answer:

x = 18

m<A = 166°

Step-by-step explanation:

The parallel lines are cut by a transversal, so corresponding angles A and B are congruent.

7x + 40 = 3x + 112

4x = 72

x = 18

m<A = 7x + 40 = 7(18) + 40 = 126 + 40 = 166

6 0

2 years ago

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4.b) A strawberry order costs $241.50. How many pounds did the grocer order?

hram777 [196]

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3 years ago

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The midpoint of RS is M(1, 2). One endpoint is R(-6, 6). Find the coordinates of endpoint S.

AysviL [449]

Answer:

The coordinates of point S are (8,-2)

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

Let

Point S(x2,y2)

substitute the given values

$(1,2)=(\frac{-6+x2}{2},\frac{6+y2}{2})$

<em>Solve for x2</em>

$1=(-6+x2)/2\\2=-6+x2\\x2=2+6=8$

<em>Solve for y2</em>

$2=(6+y2)/2\\4=6+y2\\y2=4-6=-2$

therefore

The coordinates of point S are (8,-2)

5 0

3 years ago

Use spherical coordinates to find the volume of the region that lies outside the cone z = p x 2 + y 2 but inside the sphere x 2

Harman [31]

I assume the cone has equation $z=\sqrt{x^2+y^2}$ (i.e. the upper half of the infinite cone given by $z^2=x^2+y^2$ ). Take

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

The volume of the described region (call it $R$ ) is

$\displaystyle\iiint_R\mathrm dx\,\mathrm dy\,\mathrm dz=\int_0^{2\pi}\int_0^{\sqrt2}\int_{\pi/4}^\pi\rho^2\sin\varphi\,\mathrm d\varphi\,\mathrm d\rho\,\mathrm d\theta$

The limits on $\theta$ and $\rho$ should be obvious. The lower limit on $\varphi$ is obtained by first determining the intersection of the cone and sphere lies in the cylinder $x^2+y^2=1$ . The distance between the central axis of the cone and this intersection is 1. The sphere has radius $\sqrt2$ . Then $\varphi$ satisfies

$\sin\varphi=\dfrac1{\sqrt2}\implies\varphi=\dfrac\pi4$

(I've added a picture to better demonstrate this)

Computing the integral is trivial. We have

$\displaystyle2\pi\left(\int_0^{\sqrt2}\rho^2\,\mathrm d\rho\right)\left(\int_{\pi/4}^\pi\sin\varphi\,\mathrm d\varphi\right)=\boxed{\frac43(1+\sqrt2)\pi}$

4 0

2 years ago

The average of six tests is 82. What is the total of the six tests?

ira [324]

Since the average of 6 tests is 6, and we know that the average is found by dividing the total score by the number of tests, we can just multiply the average by the number of tests to find the total score. Doing this, we get 82 * 6 which simplifies to 492.

8 0

2 years ago