How will the volume of the pyramid change if each side is multiplied by a factor of .5

What is the solution to log (9x)-log 3 = 3?

xeze [42]

Answer:

The solution x = $\frac{e^{3} }{3}$

Step-by-step explanation:

<u>Step 1</u>:-

Given $log(9 x) -log 3 =3$

we have to use formula $log a-log b=log\frac{a}{b}$

$log(9 x)- log 3 = log(\frac{9 x}{3} )$ = $3$

Again by using formula $log a =b$

$a = e^{b}$

so $\frac{9 x}{3} =e^{3}$

<u>step 2:</u>-

$3 x = e^{3}$

$x = \frac{e^{3} }{3}$

The solution of given problem is $x=\frac{e^3}{3}$

5 0

3 years ago

Using the digits 1, 2, 3, 4, 5, 6, 7, and 9, make 4 two-digit prime numbers. What is the sum of those four prime numbers?

mr_godi [17]

Answer:

13, 17, 19, and 23

Step-by-step explanation:

13+17+19+23=72

3 0

3 years ago

Factor 2x2 + 5x − 63

Nimfa-mama [501]

The answer is 5x-59
To get this answer you have to follow pemdas and remember you can’t add variables to non variables, so you just expand the equation
As an example
5x + 6 -2x +7

You would get
13-3x

6 0

1 year ago

A right square pyramid with base edges of length $8\sqrt{2}$ units each and slant edges of length 10 units each is cut by a plan

seropon [69]

Answer:

32 $unit^{3}$

Step-by-step explanation:

Given:

The slant length 10 units
A right square pyramid with base edges of length 8 $\sqrt{2}$

Now we use Pythagoras to get the slant height in the middle of each triangle:

$\sqrt{10^{2 - (4\sqrt{2} ^{2} }) }$ = $\sqrt{100 - 32}$ = $\sqrt{68}$ units

One again, you can use Pythagoras again to get the perpendicular height of the entire pyramid.

$\sqrt{68-(4\sqrt{2} ^{2} )}$ = $\sqrt{68 - 32}$ = 6 units.

Because slant edges of length 10 units each is cut by a plane that is parallel to its base and 3 units above its base. So we have the other dementions of the small right square pyramid:

The height 3 units
A right square pyramid with base edges of length 4 $\sqrt{2}$

So the volume of it is:

V = 1/3 *3* 4 $\sqrt{2}$

= 32 $unit^{3}$

5 0

3 years ago

Can you help me in this plz

Kipish [7]

Answer:

£ 38,110

Step-by-step explanation:

We need to find salary for 1 year (12 months).

Monthly Salary = 1410, so yearly would be:

1410 * 12 = 16,920

26% of total profit. Let's find the profit first:

Profit is Income - Cost

So, that would be (from table):

Profit = 549000 - 473500 = 75,500

26% of that would be:

26/100 = 0.26

0.26 * 75,500 = 19,630

390 bonus for each month she sells atleast 16 cars

Out of 12 months (1 year), she sold at least 16 cars in 4 months, so she gets bonus of 390 for those 4 months, that would make:

390 * 4 = 1560

Total Pay for the year would be summation of all these:

Total Pay = 16,920 + 19,630 + 1560 = £ 38,110

5 0

3 years ago