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3 years ago

Write the expression as a single logarithm Log7X+log7Y-log7Z

1 answer:

6 0

For this, simply use the rules of logs:

- Adding logs of the same base (which is 7 here) is the same as multiplying

-Subtracting logs of the same base is dividing
So the single log would be:

log₇(x*y/z) which is the same as

log₇(xy/z)

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Which question can be answered by finding 2 1/2 divided by 2/3

prohojiy [21]

Answer:

3.75

Step-by-step explanation:

A sample question could be, you have 2 1/2 cups of flour and would like to make cookies that need 2/3 cups of flour per batch. How many batches could you make?

The answer is 3.75.

5 0

3 years ago

Read 2 more answers

Use cylindrical coordinates to evaluate the triple integral ∭ where E is the solid bounded by the circular paraboloid z = 9 - 16

4vir4ik [10]

Answer:

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

Step-by-step explanation:

The Cylindrical coordinates are:

x = rcosθ, y = rsinθ and z = z

From the question, on the xy-plane;

$9 -16 (x^2 + y^2) = 0 \\ \\ 16 (x^2 + y^2) = 9 \\ \\ x^2+y^2 = \dfrac{9}{16}$

$x^2+y^2 = (\dfrac{3}{4})^2$

where:

0 ≤ r ≤ $\dfrac{3}{4}$ and 0 ≤ θ ≤ 2π

∴

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} \int ^{9-16r^2}_{0} \ r \times rdzdrd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 z|^{z= 9-16r^2}_{z=0} \ \ \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 ( 9-16r^2}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} ( 9r^2-16r^4}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( \dfrac{9r^3}{3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3r^3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) d \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) \theta |^{2 \pi}_{0}$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{64}}-\dfrac{243}{320}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{160}})2 \pi$

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

4 0

2 years ago

help me ASAP please

xxMikexx [17]

Answer:

Step-by-step explanation:

I think it is D because exponential graphs usually have a curve to them. And the one you need is exponential decay so D is negative and exponential.

HOPE THIS HELPS! HAVE A GREAT DAY!! :)

5 0

2 years ago

Two identical condominiums were built in a new high-rise building. Condo A’s living room is a rectangle 24 ft. long and 18 ft. w

nadezda [96]

Answer:

The perimeter of a rectangular playground is 46 m. ... 46 – 14 = 32 32 / 2 = 16 ... new carpeting for her family room. Her family room is a 12 ft by 21 ft rectangle. ... Charles has a rectangular flower garden that is 5 yd long and 12 yd wide. ... After installing the carpet, Betty decides to also install floor wood molding for her living.

(i just added names for explanation)

6 0

3 years ago

Write a linear function for the data in each table using function notation.

ASHA 777 [7]

Answer:

A. f(x) = 6.5x
B. f(x) = 3x - 2

Step-by-step explanation:

<h3>Table A</h3>

This is proportional relationship

<u>The function is:</u>

f(x) = 6.5x

<h3>Table B</h3>

<u>The slope is:</u>

(10 - 7)/(4 - 3) = 3

<u>The y-intercept is:</u>

10 - 4*3 = -2

<u>The function is:</u>

f(x) = 3x - 2

5 0

3 years ago

Read 2 more answers