Wbich of the following statements describes the set of integers gieater than --3 but less than 6?

Lady bird [3.3K]

$\dfrac{x}{2.5}=\dfrac{x+2.4}{2.5+2}\\
\dfrac{x}{2.5}=\dfrac{x+2.4}{4.5}\\
4.5x=2.5(x+2.4)\\
4.5x=2.5x+6\\
2x=6\\
x=3$

4 0

3 years ago

Scott wants to cover his patio with concrete pavers. If the patio is shaped like a trapezoid whose bases are 11 feet and 13 feet

GenaCL600 [577]

Answer:

Scott will need 168 ft² of pavers to cover his patio

Explanation:

Scott wants to cover a trapezoid-shaped patio

This means that:

To get the number of square feet of pavers he'll need, we need to get the area of his patio

Area of trapezium id calculated as follows:

$Area = \frac{base_{1}+base_{2}}{2} * height$

We are given that:

base₁ = 11 ft

base₂ = 13 ft

height = 14 ft

We now substitute with the givens to get the area as follows:

$Area = \frac{11+13}{2} * 14 = 168ft^2$

This means that:

Scott will need 168 ft² of pavers to cover his patio

Hope this helps :)

5 0

3 years ago

last month Dory biked 11 times as many miles as Carly. Together they biked a total of 156 miles.How many miles did Dory bike las

matrenka [14]

Dory = 11 x Carly

Together => d + c = 156

11c + c = 156

12c = 156
C = 156 : 12
C = 13
Carly biked 13 miles

Dory = 11 x c = 11 x 13 = 143 miles

Prove
143 + 13 = 156 miles together

8 0

4 years ago

Please help w this! Its a calculus question! look at the picture for the problem,

neonofarm [45]

Since you mentioned calculus, perhaps you're supposed to find the area by integration.

The square is circumscribed by a circle of radius 6, so its diagonal (equal to the diameter) has length 12. The lengths of a square's side and its diagonal occur in a ratio of 1 to sqrt(2), so the square has side length 6sqrt(2). This means its sides occur on the lines $x=\pm3\sqrt2$ and $y=\pm3\sqrt2$ .

Let $R$ be the region bounded by the line $x=3\sqrt2$ and the circle $x^2+y^2=36$ (the rightmost blue region). The right side of the circle can be expressed in terms of $x$ as a function of $y$ :

$x^2+y^2=36\implies x=\sqrt{36-y^2}$

Then the area of this circular segment is

$\displaystyle\iint_R\mathrm dA=\int_{-3\sqrt2}^{3\sqrt2}\int_{3\sqrt2}^{\sqrt{36-y^2}}\,\mathrm dx\,\mathrm dy$

$=\displaystyle\int_{-3\sqrt2}^{3\sqrt2}(\sqrt{36-y^2}-3\sqrt2)\,\mathrm dy$

Substitute $y=6\sin t$ , so that $\mathrm dy=6\cos t\,\mathrm dt$

$=\displaystyle\int_{-\pi/4}^{\pi/4}6\cos t(\sqrt{36-(6\sin t)^2}-3\sqrt2)\,\mathrm dt$

$=\displaystyle\int_{-\pi/4}^{\pi/4}(36\cos^2t-18\sqrt2\cos t)\,\mathrm dt=9\pi-18$

Then the area of the entire blue region is 4 times this, a total of $\boxed{36\pi-72}$ .

Alternatively, you can compute the area of $R$ in polar coordinates. The line $x=3\sqrt2$ becomes $r=3\sqrt2\sec\theta$ , while the circle is given by $r=6$ . The two curves intersect at $\theta=\pm\dfrac\pi4$ , so that

$\displaystyle\iint_R\mathrm dA=\int_{-\pi/4}^{\pi/4}\int_{3\sqrt2\sec\theta}^6r\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle\frac12\int_{-\pi/4}^{\pi/4}(36-18\sec^2\theta)\,\mathrm d\theta=9\pi-18$

so again the total area would be $36\pi-72$ .

Or you can omit using calculus altogether and rely on some basic geometric facts. The region $R$ is a circular segment subtended by a central angle of $\dfrac\pi2$ radians. Then its area is

$\dfrac{6^2\left(\frac\pi2-\sin\frac\pi2\right)}2=9\pi-18$

so the total area is, once again, $36\pi-72$ .

An even simpler way is to subtract the area of the square from the area of the circle.

$\pi6^2-(6\sqrt2)^2=36\pi-72$

6 0

3 years ago

William runs 5 meters in 20 steps. How many kilometers will he run if he takes 1,000 steps ?

kap26 [50]

This means 5 meters/20 steps = x/1,000 steps. 20 times 50 is 1,000, so 5 times 50 is 250 meters. 5/20 can be also reduced to 1/4 = x/1000. Use cross products rule to get 4x = 1,000. Divided both sides by 4 to get x = 250 meters.

3 0

4 years ago

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Wbich of the following statements describes the set of integers gieater than --3 but less than 6?​

Wbich of the following statements describes the set of integers gieater than --3 but less than 6?