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3 years ago

3(x+1)^(4/3)=48 how do i solve this?

1 answer:

4 0

$3(x+1)^{\frac{4}{3}}=48\\\\\frac{3(x+1)^{\frac{4}{3}}}{3}=\frac{48}{3}\\\\(x+1)^{\frac{4}{3}}=(x+1)^{(\frac{1}{3}*4)}=\sqrt[3]{(x+1)^{4}}=16\\\\(\sqrt[3]{(x+1)^{4}})^{3}=16^{3}\\\\(x+1)^4=4096\\\\\sqrt[4]{(x+1)^4}=\sqrt[4]{4096}=\pm8\\\\\\x+1=\pm8\\\\x+1=8\\x=7\\\\x+1=-8\\x=-9$

Your answers are x = 7 and x = -9.

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Solve the equation. Round to the nearest hundredth. Show work.

denis-greek [22]

Answer:

Final answer is approx x=-0.66.

Step-by-step explanation:

Given equation is $5^{-2x-1}=4^{4x+3}$ .

Now we need to solve equation $5^{-2x-1}=4^{4x+3}$ and round to the nearest hundredth.

$5^{-2x-1}=4^{4x+3}$

$\log(5^{-2x-1})=\log(4^{4x+3})$

$(-2x-1)\log(5)=(4x+3)\log(4)$

$-2x \log(5)- \log(5)=4x \log(4)+3 \log(4)$

$-2x \log(5) -4x \log(4)=3 \log(4) +\log(5)$

$x=\frac{\left(3\log(4)+\log(5)\right)}{\left(-2\log(5)-4\log(4)\right)}$

Now use calculator to calculate log values, we get:

$x=-0.65817959094$

Round to the nearest hundredth.

Hence final answer is approx x=-0.66.

8 0

4 years ago

A bird seed feeder has the approximate shape of a cone with a diameter of 12 centimeters and a height of 25.5 centimeters. What

timurjin [86]

The equation for the volume of a cone is:
$V= \frac{1}{3} \pi r^{2} h$
where V = volume of the cone, r = radius of the circular base, and h = height of the cone.

You are told that the height, h = 25.5 cm. You are also told that the diameter is <span>12 centimeters. Remember that the diameter of a circle is just twice the radius. Divide 12 by 2 to get the radius: r =12/2 = 6 cm.

Since you know </span>h = 25.5 cm and r = 6 cm, plug these values into your equation for volume of a cone and solve for V, volume:
$V= \frac{1}{3} \pi r^{2} h\\
V= \frac{1}{3} \pi (6) ^{2} (25.5)\\
V \approx 961.33$

------

Answer: B) <span>961.33 cm³ </span>

3 0

3 years ago

Read 2 more answers

A floor tile is 20 inches wide. If the perimeter of the tile is 72 inches, what is the length of the tile?

Jobisdone [24]

Answer:

16 inches

Step-by-step explanation:

Given,

Perimeter = 72 inches

Breadth = 20 inches

Perimeter = 2 ( L+B )

72 = 2 ( L+20)

72= 2L + 40

72-40=2L

32/2=L

L=16 inches

therefore , lenght of the tile is 16 inches

7 0

3 years ago

The square root of 42. The answer needs to be simplified. The problem must be solved by using perfect squares. The answer can't

Rasek [7]

From what I can tell, this can't be simplified, because there are no factors of 42 that are perfect squares. I would leave it as the square root of 42.

5 0

3 years ago

True or False: The null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on

olga_2 [115]

Answer:

False

Step-by-step explanation:

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

7 0

3 years ago