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4 years ago

Suppose a varies directly as b, and a=7 when b=2 find b when a =21

1 answer:

6 0

Because α varies directley to β
$\alpha = k \beta$
(k = constant)

α=7 when β=2
7= 2k
k= $\frac{7}{2}$

so when α=21
21= $\frac{7}{2}$ b
b= 6

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Find the limit, if it exists. (If an answer does not exist, enter DNE.)

lys-0071 [83]

let's change some the 0.1 to say 1/10, just the fraction version of it.

$\bf \lim\limits_{x\to \left( \frac{1}{10} \right)^-}~\cfrac{10x-1}{|10x^3-x^2|}\implies \lim\limits_{x\to \left( \frac{1}{10} \right)^-}~\cfrac{10(-x)-1}{10(-x)^3-(-x)^2}$

$\bf \cfrac{-10x-1}{-10x^3-x^2}\implies \cfrac{-10\left( \frac{1}{10} \right)-1}{-10\left( \frac{1}{10} \right)^3-\left( \frac{1}{10} \right)^2}\implies \cfrac{-1-1}{-\frac{1}{100}-\frac{1}{100}}\implies \cfrac{-2}{\frac{-2}{100}} \\\\\\ \cfrac{~~\begin{matrix} -2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\cdot \cfrac{100}{~~\begin{matrix} -2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 100$

when checking an absolute value expression, we do the one-sided limits, since an absolute value expression is in effect a piecewise function with ± versions, so for the limit from the left we check the negative version.

8 0

3 years ago

Jorge used to pay $26 to park his car for 6.5 hours in a parking garage,

den301095 [7]

Answer:

The parking garage went from charging 4$ an hour to 6$ an hour.

there is a 50% increase

Step-by-step explanation:

3 0

3 years ago

Solve PLZ The width of a rectangle is 33 inches and the area is at least 165 inches. Which inequality could be used to find the

garri49 [273]

Answer:

Step-by-step explanation:

at least are key words for $\geq$ symbol

Area is L x W and since you have W its basically:

$33x\geq 165$

6 0

4 years ago

John has a sink that is shaped like a half-sphere. The sink has a volume of 1072 in?. One

hodyreva [135]

Answer:

Anthony must scoop out of the sink 85 cups of water to empty it

Step-by-step explanation:

The formula of the volume of a sphere is  $V=\frac{4}{3}\pi r^{3}$  , where r is its radius

The formula of the volume of a cylinder is V = πr²h, where r is the radius of its base and h is its height

∵ The sink is shaped like a half-sphere

∵ The sink has a volume of 1072 in³

∵ One cup has a diameter of 2 in

- The radius is half the diameter

∴ The radius of the cup = $\frac{1}{2}$ × 2 = 1 in.

∵ The height of the cup is 4 in

- Find the volume of the cup using the 2nd formula above

∴ V = π(1)²(4) = 4π in³

To find the number of cups that Anthony use to scoop out of the sink to empty it divide the volume of the sink by the volume of the cup

∵ The volume of the sink = 1072 in³

∵ The volume of the cup = 4π in³

∴ The number of the cups = 1072 ÷ 4π

∴ The number of the cups = 85.3070495

- Round it to the nearest whole number

∴ The number of cups is 85

Anthony must scoop out of the sink 85 cups of water to empty it

8 0

4 years ago

What is 5 to the power of 1 in expanded form

fomenos

Answer:

5^1 in expended from is 5

hope it helps.

3 0

3 years ago