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2 years ago

Write the equation 6561 1/4= 9 in logarithmic form.

Mathematics

1 answer:

Vlad1618 [11]2 years ago

8 0

Answer:

b. log6561(9) = 1/4

Step-by-step explanation:

The relationship between the exponential form and the log form is ...

$b^n=x\\\log_b{(x)}=n$

The exponent is the logarithm. The base is the value the exponent is being applied to.

Here, you have ...

$6561^{\frac{1}{4}}=9$

Comparing this to the form above, we see ...

b = 6561, n = 1/4, x = 9

so the log form of the equation is ...

$\boxed{\log_{6561}{(9)}=\frac{1}{4}}$

This matches choice B.

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a ball is thrown with a slingshot at a velocity of 110ft/sec at an angle of 20 degrees above the ground from a height of 4.5 ft.

satela [25.4K]

Answer:

$t=2.47\ s$

Step-by-step explanation:

The equation that models the height of the ball in feet as a function of time is

$h(t) = h_0 + s_0t -16t ^ 2$

Where $h_0$ is the initial height, $s_0$ is the initial velocity and t is the time in seconds.

We know that the initial height is:

$h_0 = 4.5\ ft$

The initial speed is:

$s_0 = 110sin(20\°)\\\\s_0 = 37.62\ ft/s$

So the equation is:

$h (t) = 4.5 + 37.62t -16t ^ 2$

The ball hits the ground when when $h(t) = 0$

$4.5 + 37.62t -16t ^ 2 = 0$

We use the quadratic formula to solve the equation for t

For a quadratic equation of the form

$at^2 +bt + c$

The quadratic formula is:

$t=\frac{-b\±\sqrt{b^2 -4ac}}{2a}$

In this case

$a= -16\\\\b=37.62\\\\c=4.5$

Therefore

$t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}$

$t_1=-0.114\ s\\\\t_2=2.47\ s$

We take the positive solution.

Finally the ball takes 2.47 seconds to touch the ground

4 0

2 years ago

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a

Dahasolnce [82]

Answer: The comparison is mentioned below.

Step-by-step explanation:

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally.

Therefore its slope = length of the equipment vertically / length of equipment horizontally

$m_1$ = 6/4 = 3/2 = 1.5

And, A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally.

Therefore slope, $m_2$ = 10/6 = 5/3=1.67 (approx)

Since, $m_1$ < $m_2$

Thus the slope of equipment first is less than slope of second equipment.

5 0

2 years ago

Read 2 more answers

Divide rs 350 in ratio 2:5

mihalych1998 [28]

Answer:

100 : 250

Step-by-step explanation:

Sum the parts of the ratio, 2 + 5 = 7 parts

Divide the quantity by 7 to find the value of one part of the ratio.

350 ÷ 7 = 50 ← value of 1 part of the ratio, thus

2 parts = 2 × 50 = 100

5 parts = 5 × 50 = 250

350 = 100 : 250 in the ratio 2 : 5

6 0

2 years ago

Mark has three 4 1/2 oz cans and five 8 1/4 oz cans. How many ounces of tomatoes does Mark need?

Mashutka [201]

Answer:

54.74 ounces of tomatoes mark need.

Step-by-step explanation:

Given : Mark has three $4\frac{1}{2}$ oz cans and five $8\frac{1}{4}$ oz cans.

To find : How many ounces of tomatoes does Mark need?

Solution :

Mark has three $4\frac{1}{2}$ oz cans.

i.e. $3\times 4\frac{1}{2}=3\times \frac{9}{2}=\frac{27}{2}$

Mark has five $8\frac{1}{4}$ oz cans.

i.e. $5\times 8\frac{1}{4}=5\times \frac{33}{4}=\frac{165}{4}$

Total ounces of tomatoes does Mark need is

$T=\frac{27}{2}+\frac{165}{4}$

$T=\frac{54+165}{4}$

$T=\frac{219}{4}$

$T=54.75$

Therefore, 54.74 ounces of tomatoes mark need.

7 0

2 years ago

The table below shows the functions to represent the sale f(t), in thousands, of four companies in t years.

Tcecarenko [31]

Hi there

the companies showed an exponential growth in sale are

Company C with
f(t) = 1.26t

Company D with
f(t) = 1.09t

Because
1+r where r is the rate of growth

the rate of growth of Company c is 1+26%

The rate of growth of company D is
1+9%

So it's option d

Good luck!

4 0

2 years ago