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3 years ago

Item 20The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?

Mathematics

1 answer:

AnnZ [28]3 years ago

4 0

60% of 10 is 6, so 10x6 is the area which is 60ft^2

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Drag each length to match it to an equivalent length. 2 yards 5 inches returned to choices list. 2 feet 8 inches4 yards9 feet2 y

Grace [21]

Answer:

2 yards 5 inches will be equivalent to 77 inches

Step-by-step explanation:

Given length -

2 yards 5 inches

One yard has 36 inches

Two yards will have 2*36 = 72 inches

Thus, 2 yards 5 inches will sum up to 72 inches + 5 inches = 77 inches

Hence, 2 yards 5 inches will be equivalent to 77 inches

6 0

3 years ago

Calculate the volume of the solid. Round answer to the nearest hundredth.

alex41 [277]

Answer:

191.1 cm^3

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

3(2x+1)=7-2(x+5) Can you please show me how to solve this step by step please

Talja [164]

3(2x+1) = 7-2(x+5)
6x+3 = 7-2x-10
-3 -3
6x = 7-2x-10-3
+2x +2x
8x = -6
---- -----
8 8
x = -3/4

8 0

3 years ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that y is a function of x :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ x ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$

We can simplify this further to

$\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}$

7 0

3 years ago

Which facts are true for the graph of the function below? Check all that apply.

AlekseyPX

B. the x-intercept is (1,0).

5 0

3 years ago